Published online 1 May 2002

Gaia as a complex adaptive system

Timothy M Lenton and Marcel van OijenCentre for Ecology and Hydrology Edinburgh Research Station Bush Estate Penicuik Midlothian EH26 0QB UK

We de ne the Gaia system of life and its environment on Earth review the status of the Gaia theoryintroduce potentially relevant concepts from complexity theory then try to apply them to Gaia We con-sider whether Gaia is a complex adaptive system (CAS) in terms of its behaviour and suggest that thesystem is self-organizing but does not reside in a critical state Gaia has supported abundant life for mostof the last 38 Gyr Large perturbations have occasionally suppressed life but the system has always recov-ered without losing the capacity for large-scale free energy capture and recycling of essential elementsTo illustrate how complexity theory can help us understand the emergence of planetary-scale order wepresent a simple cellular automata (CA) model of the imaginary planet Daisyworld This exhibits emergentself-regulation as a consequence of feedback coupling between life and its environment Local spatialinteraction which was absent from the original model can destabilize the system by generating bifurcationregimes Variation and natural selection tend to remove this instability With mutation in the modelsystem it exhibits self-organizing adaptive behaviour in its response to forcing We close by suggestinghow arti cial life (lsquoAlifersquo) techniques may enable more comprehensive feasibility tests of Gaia

Keywords Gaia theory complexity theory Earth system Daisyworld feedbacks adaptive change

1 INTRODUCTION

This article focuses on the complex coupled system of lifeand its environment on Earth named lsquoGaiarsquo (Lovelock1972) and de ned more rigorously below There alreadyexists a Gaia theory that attempts to explain the develop-ment and functioning of the speci c system (Lovelock1988 Lenton 1998) Aspects of the Gaia theory may alsobe applicable to other planets with abundant life (Lenton2002) Our perspective is what can a general theory ofcomplex systems lsquocomplexity theoryrsquo contribute to Gaiatheory We highlight gaps in our current understanding ofGaia address whether Gaia is a CAS and consider howcomplexity theory can help improve our understandingof Gaia

The Gaia theory replaced the original Gaia hypothesisof atmospheric homeostasis by and for the biota (Lovelockand Margulis 1974) in the mid-1980s The Gaia theorytakes a larger whole system perspective viewing self-regu-lation as a key emergent property of the system withmodels to demonstrate how such behaviour can ariseautomatically (Watson amp Lovelock 1983 Lovelock 1988)A challenge for Gaia theory is to nd principles thatexplain how regulation can emerge at the global scale fromnatural selection of environment-altering traits at the indi-vidual level (Hamilton amp Lenton 1998 Lenton 1998) Towhat degree the ontogeny (pathway of development) ofGaia is unique or deterministic is a major question(Schwartzman 1999) There is a need to improve ourability to predict what may happen after speci c pertur-

Author for correspondence (tlentcehacuk)

One contribution of 11 to a special Theme Issue lsquoThe biosphere as acomplex adaptive systemrsquo

Phil Trans R Soc Lond B (2002) 357 683ndash695 683 Oacute 2002 The Royal SocietyDOI 101098rstb20011014

bations of the system including human activities Further-more hypotheses for the effect of life on Earth need tobe more rigorously framed and their testability improved(Kleidon 2002 Lenton 2002) Currently most progressis being made in understanding speci c feedback mech-anisms using models of xed structure To advance Gaiatheory we need to consider the behaviour of manycoupled interactions and feedbacks and the evolution ofliving components and resulting change at the systemlevel We also need to test the feasibility of general hypoth-eses for the emergence of planetary-scale order Theserequirements in turn demand new theory and new model-ling approaches Complexity theory may offer both

It has previously been suggested that both the biosphere(the region in which life exists) and Gaia (the coupled sys-tem of life and its environment on Earth) are CASs (Lewin1993 Levin 1998) in which case Gaia may be the largestin a hierarchy of CASs including cells organisms and eco-systems (C G Langton and S A Kauffman quoted inLewin (1993)) This view has received relatively littleattention from Gaia theorists we know of only oneattempt to test whether Gaia is a complex system (L FKlinger personal communication) If it is what does thisteach us about the system

We consider which results from complexity theory arerelevant to Gaia and how the methods of complexitytheory can be applied to advance our understanding ofGaia First we de ne the system of interest (sect 2) andreview the status of Gaia theory (sect 3) before summarizingrelevant concepts from complexity theory (sect 4) Weaddress whether Gaia is a CAS (sect 5) and consider howplanetary-scale self-organization can emerge (sect 6) Theuse of Daisyworld models to explore such emergence issummarized (sect 7) and a simple CA version of Daisyworldis presented which gives new insights (sect 8) The use of

684 T M Lenton and M van Oijen Gaia as a complex adaptive system

lsquoAlifersquo techniques for assessing the probability of planetaryself-organization is discussed (sect 9) and we close by sum-marizing how complexity theory has already altered ourunderstanding of Gaia (sect 10)

2 GAIA

We de ne Gaia as the thermodynamically open systemat the Earthrsquos surface comprising life (the biota) atmo-sphere hydrosphere (ocean ice freshwater) dead organicmatter soils sediments and that part of the lithosphere(crust) that interacts with surface processes (includingsedimentary rocks and rocks subject to weathering) Theupper boundary of the system is at the top of the atmo-sphere with outer space The inner boundary is harder tode ne and can be taken to depend on the time-scale ofprocesses under consideration For time-scales longerthan the recycling of the crust (ca 108 years) the line maybe drawn between the crust and the mantle For processesthat can approach steady state rapidly (in less than 103

years) the outer surface of the crust may be consideredthe boundary of the system A rigid de nition thatexcludes any component of the crust from Gaia has beensuggested (Volk 1998) but we think this is too exclusiveInclusion of the entire Earthrsquos interior has also beenimplied (Lovelock 1991) but we think that this is tooinclusive Processes such as volcanism and plate tectonicsare ultimately driven by a heat energy source in the Earthrsquosinterior which (like the Sun) is not signi cantly in uencedby surface processes and hence is best considered to belsquooutsidersquo the system

Abundant energy is exchanged across the upper bound-ary of Gaia (ca 175 acute 101 7 W) but relatively little matterOnly hydrogen atoms can readily escape Earthrsquos gravity(currently ca 27 acute 108 H atoms cm2 2 s 2 1) Incomingmeteoroids supply a small ux of matter to the Earthrsquossurface (more than 101 1 g yr 2 1) and atmosphere (as andwhen they are vaporized) (Isaacs et al 1996) Occasionalasteroid (large meteorite) impacts add matter and can alsoprovide suf cient energy to eject meteoroids into spaceMatter is exchanged across the lower boundary of Gaiabut relatively little energy Available geothermal energy(ca 3 acute 101 3 W) is tiny in comparison to solar energyExchange uxes of matter across the lower boundary aresigni cant but for many elements are orders of magnitudesmaller than the internal cycling uxes (eg ca 5 acute 101 3

mol C yr2 1 input and output ca 15 acute 101 7 mol C yr 2 1

cycled within the system)The energy input to Gaia has been gradually increasing

(ca 1 every 108 years) as the Sun becomes more lumi-nous with time Variations in the Earthrsquos orbital para-meters also alter the total energy input and its distributionacross the Earthrsquos surface on time-scales of 103ndash105 yearsDecay of angular momentum of the Earthndashmoon systemcauses the Earth to spin more slowly with time Occasionalasteroid impacts provide massive perturbations of theEarthrsquos surface releasing large amounts of energy forexample ca 102 4 J in the Chicxulub impact at the Cre-taceousndashTertiary boundary 65 Myr ago Thermal decay ofthe Earthrsquos interior heat source causes a gradual decline involcanic and tectonic activity including sea- oor spreadingrates (volcanic and metamorphic matter input was prob-ably three times greater ca 3 Gyr ago) Occasional catas-

Phil Trans R Soc Lond B (2002)

trophic out ow of lava ( ood basalt volcanism) occursSuch events may be triggered by asteroid impact(Rampino 1987) thus providing a possible link betweenperturbation from above and below Gaia

We distinguish Gaia from the lsquoEarth systemrsquo (anincreasingly popular term) in that the Earth systemincludes states before the origin of life whereas Gaia refersto the system with abundant life and because the Earthsystem is sometimes taken to include the entire interior ofthe Earth We also distinguish Gaia from the lsquobiospherersquo(the region inhabited by living organisms) These aresometimes treated synonymously but the boundaries ofGaia are almost certainly wider because the in uence ofliving organisms extends beyond the region they inhabitThe upper boundary of the biosphere is more than 50 kmabove the Earthrsquos surface in the mesosphere where viablemicroscopic fungi and bacteria have been collected byRussian rockets (Imshenetsky et al 1978) whereas theexosphere extends above 500 km The lower boundary ofthe biosphere is unknown but organisms have been foundto be thriving at depths of a few kilometres in the Earthrsquoscrust It has been suggested that a lsquodeep hot biospherersquocould survive independently of surface life but if it couldpersist at all this would be a much simpler system runningoff a relatively tiny amount of free energy

Gaia has many remarkable physical and chemicalproperties especially when contrasted with our neigh-bouring planets Mars and Venus The Earthrsquos atmo-sphere is in extreme thermodynamic disequilibrium withreactive gases at concentrations many orders of magnitudefrom those predicted at geochemical and photochemicalsteady state (Lovelock 1975) Oxygen is extraordinarilyabundant at 021 atm instead of less than 102 1 2 atm(Kasting 1991) Other reactive gases are at anomalouslyhigh concentrations given abundant oxygen Forexample methane concentration is more than 103 0 timesequilibrium (Lovelock 1975 Sagan et al 1993) Themajority of nitrogen should be as NO 2

3 dissolved in theocean rather than N2 in the atmosphere (Lewis amp Randall1923 Sillen 1967) By contrast carbon dioxide makes upa remarkably small fraction of the atmosphere when com-pared with Mars and Venus The composition of theEarthrsquos atmosphere shows dynamic stability over periodsmuch longer than the residence time of speci c gases(Lovelock amp Margulis 1974) For example the O2 reser-voir with a geologic residence time of ca 32 Myr hasvaried by less than a factor of two over the past 350 Myr(Lenton 2001) Other master variables of Gaia also showevidence of regulation The Earthrsquos average surface tem-perature has tended to decline or remain relatively con-stant over the past ca 4 Gyr despite a ca 30 increasein solar luminosity Liquid water has been retained at theEarthrsquos surface (in contrast to Mars and Venus) Hydro-gen escape to space and consequent water loss has beenminimized by the oxidizing state of the atmosphere for thepast ca 20 Gyr and the existence of a cold trap at thetropopause Ocean salinity has never reached toxic con-centration pH has remained close to neutral The chemi-cal composition of Gaia as a whole is such that abundantfree energy is available from chemical reaction mostnotably from the reaction of O2 with organic compounds

Perhaps the most remarkable property of Gaia is theongoing presence and profusion of life The Earthrsquos sur-

Gaia as a complex adaptive system T M Lenton and M van Oijen 685

face has remained habitable for more than 385 Gyr(Mojzsis et al 1996) The relatively stable organic carboncontent and isotopic composition of the crust indicate thatlife has been abundant for most of the past 38 Gyr(Schidlowski 1988) Life has been invoked to explainmany of the Earthrsquos remarkable physical and chemicalproperties The abundance of oxygen in the presentatmosphere is almost entirely a biological product Atmo-spheric oxygen has increased in a stepwise fashion frompO2 0002 atm more than 22 Gyr ago and has beensuf cient to support eukaryotes (pO2 001 atm) for atleast the last 2 Gyr (Han amp Runnegar 1992) The stabilityof O2 over the past 350 Myr has enabled the continuouspersistence of large metazoa (requiring O2 ca 015 atm)and slowly regenerating trees (requiring O2 ca 03 atm)(Lenton amp Watson 2000b) The scarcity of carbon dioxidein the atmosphere and consequent cooling of the planetis due to biologically ampli ed silicate rock weatheringwhich drives the dominant sink in the long-term carboncycle (Lovelock amp Watson 1982 Schwartzman 1999)Within Gaia there is greatly enhanced cycling of matterespecially of the elements essential to life For examplephosphorus is cycled an average of 46 times through aterrestrial ecosystem before being lost to the ocean whereit is cycled an average of 280 times before being nallyburied in new rocks (Volk 1998) Return of water to theatmosphere is increased approximately three times by thepresence of vascular plants on the land surface (Betts1999 Kleidon 2002) These recycling effects greatlyincrease global gross primary productivity (Volk 1998Kleidon 2002)

3 GAIA THEORY

The Gaia theory seeks to explain the remarkable proper-ties of the system just described especially its far-from-equilibrium ordered state dynamic stability habitability ourishing of life and pattern of change over time(Lovelock 1988 Lenton 1998) From the outset Gaia hasbeen viewed as a cybernetic (feedback control) system(Lovelock amp Margulis 1974) The essential elements ofthe theory are (i) life affects its environment all organ-isms alter their environment by taking in free energy andexcreting high-entropy waste products in order to main-tain a low internal entropy (Schrodinger 1944) (ii) growth(including reproduction) organisms grow and multiplypotentially exponentially (iii) environment constrains lifefor each environmental variable there is a level or rangeat which growth of a particular organism is maximizedand (iv) natural selection once a planet contains differenttypes of life (phenotypes) with faithfully replicated heri-table variation (genotypes) growing in an environment of nite resources natural selection determines that the typesof life that leave the most descendants come to dominatetheir environment

The overall behaviour of Gaia is governed by a combi-nation of positive and negative feedback Positive feedbacktends to add to change while negative feedback tends tocounteract change Growth is intrinsically a positive feed-back process (the more life there is the more life it canbeget) The growth of life drives lifersquos effects on itsenvironment to become global in scale The extreme ther-modynamic disequilibrium of the Earthrsquos atmosphere

Phil Trans R Soc Lond B (2002)

biotic

abiotic

environmental

feedback

selection

growth

Figure 1 A subdivision of types of environmental feedback

indicates that this has occurred The fact that life altersits environment and is also constrained by it means thatenvironmental feedback is inevitable Environmental feed-back arises at the local level (eg due to the evolution ofenvironment-altering traits) With growth environmentalfeedback has the potential to become global in scale Thetypes of environmental feedback can be classi ed in a hier-archy (Lenton 1998)

The rst distinction is between abiotic and biotic feed-back to the environment ( gure 1) The response of lifeto a particular environmental variable includes habitabilitybounds for the organisms in question whereas abioticresponses have no automatic correlation with what is hab-itable for life Abiotic responses to a particular environ-mental variable are typically simple increasing ordecreasing functions ( gure 2ab) If they also affect thevariable in question then either negative feedback or posi-tive feedback will result Negative abiotic feedback ( gure2a) can stabilize the environment in either a habitable oran uninhabitable state Positive abiotic feedback ( gure2b) can drive the environment into an uninhabitable statealthough in many cases it is not suf ciently strong to doso By contrast organisms tend to have a peaked growthresponse to many environmental variables ( gure 2cd) Ifthey also affect a particular environmental variable thenthe resulting system will have both negative and positivefeedback regimes either side of the optimum for growthand for a range of forcing it will by de nition tend to sta-bilize in a habitable state For a weak biotic effect on theenvironment ( gure 2c) the stable state can be in eitherthe negative or the positive feedback regime For a strongbiotic effect on the environment ( gure 2d) the systemwill tend to transit the positive feedback regime and stabil-ize in the negative feedback regime For some forcing (eg gure 2d) multiple solutions can occur such that life main-tains the environment in a habitable state when otherwiseit would be uninhabitable If the system is forced beyondthe unstable solution in the positive feedback regime thenlife will collapse catastrophically

Biotic environmental feedback can be subdivided( gure 1) into feedback on growth and feedback on selec-tion (Lenton 1998) Non-selective feedback on growthoccurs when the effect of a trait on the environment altersthe growth rate of the organisms carrying it but theenvironmental alteration is a side-effect of the trait thatdoes not hamper its selective advantage Feedback onselection occurs when the effect of a trait on the environ-ment alters the forces of selection determining its value

An important example of negative feedback on growth( gure 2d) is that resulting from plant-induced ampli -cation of rock weathering This inadvertently tends to

686 T M Lenton and M van Oijen Gaia as a complex adaptive system

environment variable (E) environment variable (E)

environment variable (E)environment variable (E)

abio

tic

var

iable

(A

)ab

ioti

c v

aria

ble

(A

)

life

var

iable

(L

)li

fe v

aria

ble

(L

)

E = f (A) A = f (E)

E = f (L)

L= f (E)

L= f (E)

E = f (L)

A = f (E)

E = f (A)

(a)

(b)

(c)

(d )

Figure 2 General representations of types of environmental feedback for xed forcing (a) abiotic negative feedback (b)abiotic positive feedback (c) weak biotic feedback and (d) strong biotic feedback Large open circles indicate stable statesSmall lled circles indicate unstable states The arrows indicate the general direction of change for starting states withineach regime The schematic diagrams are loosely based on the following global cases described in more detail in the text(a) abiotic silicate weathering rate and temperature (b) ice cover and temperature (c) boreal forest cover and temperature(d) growth rate of rock weathering organisms and temperature

decrease atmospheric CO2 and cool the planet DecliningCO2 and cooling below optimum growth temperaturetend to suppress plant growth closing the feedback loopRock weathering traits are probably selected for as ameans of acquiring rock-bound nutrients (especiallyphosphorus) and changes in CO2 and temperature do notaffect this requirement or the resulting selection (It ismore likely that local build-up of phosphorus in soil woulddo that) The feedback from changing CO2 and tempera-ture is very slow and requires a global spread of the traitover many generations before it affects growth Howeverit is key to the long-term regulation of atmospheric CO2

and temperature and can thus be bene cial to plantgrowth in the long term In particular it counteractsincreasing solar luminosity that could otherwise drive theEarthrsquos surface temperature above optimal levels Someabiotic negative feedback ( gure 2a) would exist in aworld without life but with tectonics and a hydrologicalcycle (Walker et al 1981) However rock-weatheringorganisms greatly strengthen the feedback (Lovelock ampWatson 1982 Schwartzman amp Volk 1989) They maythus extend their own future persistence on Earth(Lenton amp Von Bloh 2001)

An example of positive feedback on growth ( gure 2c)is that resulting from the dark snow-shedding foliage oftrees in the boreal forest By absorbing solar radiation thetrees are warmed (especially relative to snow cover) andtheir growth is enhanced This warms their surroundingsthus further enhancing growth (Bonan et al 1992) Thepositive feedback is constrained in that temperatures inthe boreal regions remain below the optimum for growthfor much of the year but they are increased such that

Phil Trans R Soc Lond B (2002)

forest is able to persist over large regions that would other-wise be too cold for growth (Betts 1999)

An example of negative feedback on selection is thatresulting from nitrogen xation in the worldrsquos oceansmany terrestrial ecosystems and some freshwater lakesNitrogen xation is an energetically demanding processwhich will only be selected for when there is a lack ofavailable nitrogen relative to other potentially growth-lim-iting nutrients By xing nitrogen the responsible organ-isms ultimately increase the amount of nitrogen availablein their environment for non-nitrogen- xers Thisremoves the selective advantage of being a nitrogen xerand hence the proliferation of nitrogen xation is self-lim-ited This mechanism regulates the nitrate content of theworldrsquos oceans relative to the phosphate content in a pro-portion close to organismsrsquo requirements (Red eld 1958Lenton amp Watson 2000a)

An example of positive feedback on selection is thatresulting from the ability of sphagnum moss to acidify soilThis environmental change gives the moss a selectiveadvantage relative to other potential invading plants andencourages succession to a peat bog (Klinger 1991Hamilton 1996) There are probably other self-limiting(negative) feedbacks on bog growth given that we do notlive in a world dominated by peat bogs (although theauthors live in a country dominated by them) Interest-ingly examples of positive feedback on selection tend tobe more localized than examples of negative feedbackon selection

One of the possible fates for Gaia is for abiotic positivefeedback ( gure 2b) to take the planet into an uninhabit-able or barely habitable state In the ice-albedo positive

Gaia as a complex adaptive system T M Lenton and M van Oijen 687

feedback effect snow and ice form surfaces that are highlyre ective (high albedo) to solar radiation thus coolingtheir surroundings and encouraging the spread of snowicecover In simple models a modest reduction in solar inputis ampli ed by this feedback to cause complete ice coverof the Earth (Budyko 1968 Sellers 1969) the so-calledlsquosnowball Earthrsquo (Hoffman et al 1998) Recent simula-tions suggest that a lsquoslushball Earthrsquo state with open waterin equatorial oceans may be more realistic and less fatalto life (Hyde et al 2000) If a snowball Earth attractorexists it should be unstable because CO2 input from vol-canoes can gradually accumulate in the atmosphere untilradiative forcing is suf cient to melt continental ice cover

A key challenge to Gaia theory from evolutionary biol-ogists is to explain how order especially self-regulationcan arise at the global scale without invoking teleology orselection at the level of the planet (Doolittle 1981 Daw-kins 1983) Such criticisms inspired the formulation of theDaisyworld model (Lovelock 1983 Watson amp Lovelock1983) which demonstrates that self-regulation canemerge automatically from competing populations alter-ing their local environments in different ways (see sect 7 andsect 8) The idea that evolution within Gaia could have pro-duced organisms that contribute to regulating the planetis still variously criticised as untenable altruism vulnerableto cheats or demanding large-scale group selection(Hamilton 1995) It is sometimes argued that randomvariation and natural selection are necessary and suf cientto explain the self-regulation of organisms and candidatesuper-organisms (eg temperature regulated social insectcolonies Ehrlich 1991) in which case self-regulation ofGaia could not occur However regulation can emergeautomatically (Saunders 1994 Watson 1999) and hencethe mechanisms by which regulation emerges in physi-ology may have parallels at the planetary scale (Koeslaget al 1997 Saunders et al 1998) even though planetaryregulation cannot be re ned by selection We think thatwith an appreciation of feedback principles the theoriesof Gaia and natural selection can be reconciled (Lenton1998)

Equally there is a need to extend the original cyberneticview of Gaia to encompass evolution The continuousgeneration and selection of different environment-alteringtraits ensures that the feedback structure of Gaia remainsdynamic Evolution within the biota drives changes in thestate parameters and structure of the system (eg the riseof atmospheric oxygen) This in turn facilitates the evolu-tion of new forms of life It can also alter the set pointsof regulation when they are not xed by thermodynamicchemical or geophysical constraints (Lenton amp Lovelock2000) Complexity theory may provide a framework fordeveloping Gaia theory by synthesizing principles fromcybernetics and evolutionary biology

4 COMPLEXITY THEORY

Complexity theory is a general theory of complexdynamic systems The Latin complexus comes from theGreek pleko meaning to plait or twine Thus a complexsystem is literally one consisting of interwoven partsComplex can also mean dif cult to understand or analyseA broad de nition of a complex system is one whoseproperties are not fully explained by an understanding of

Phil Trans R Soc Lond B (2002)

dynamical

systems

complex

ordered

critical

chaotic

simple

Figure 3 A subdivision of dynamical systems in terms ofbehaviour

its component parts (Gallagher amp Appenzeller 1999) Bycontrast simple systems are ones whose properties arefully explained by the properties of their component parts(eg a pendulum) Emergence describes the collectivebehaviour of complex systems It can be local or globalLocal emergent properties are well studied in physicswhere they are often termed lsquointensive propertiesrsquo (egpressure and temperature of an ideal gas) Global emer-gent properties are the more original focus of complexitytheory

Complexity theory aims to understand the origin oforganization In doing so it adopts different modellingmethodologies to those commonly used to study speci csystems For example rather than predicting the dynamicsof a given organization rules of interaction between allpossible objects are speci ed and it is left open whichobjects appear in a given simulation An example of thisapproach is the use of CA Attempts to simulate lsquoAlifersquocommunities and ecosystems are also particularly relevantto Gaia

The relationship between complexity theory and otherdisciplines can be viewed in terms of a behavioural classi- cation of systems ( gure 3) In this case complex sys-tems are a subset of dynamical systems and complexitytheory is part of dynamic systems theory which also con-siders simple systems Complex systems can be subdividedinto ordered systems critical systems and chaotic systemsChaos describes unpredictable behaviour emerging fromnonlinear equations giving high sensitivity to initial con-ditions Order describes a tendency to reside in one stateor limit cycle between a limited number of states Betweenfrozen order and unpredictable chaos much interest hasbeen focused on a critical regime dubbed lsquothe edge ofchaosrsquo Complexity theory can be seen as an extension ofcybernetics (control theory) which focuses on feedbackand feed-forward systems with predictable behaviour Italso encompasses AI and lsquoAlifersquo research By contrastchaos theory focuses on systems with unpredictablebehaviour

This special issue focuses on the subset of CAS A lsquobot-tom-uprsquo de nition of a CAS has been given (Levin 1998)based on three essential elements (i) sustained diversityand individuality of components (ii) localized interactionamong those components and (iii) an autonomous pro-cess that selects from among these components based onthe results of local interactions a subset for replication orenhancement From these essential elements it is argued(Levin 1998) that the following properties (Holland 1995)emerge (1) continual adaptation (2) absence of a globalcontroller (3) hierarchical organization (4) generation of

688 T M Lenton and M van Oijen Gaia as a complex adaptive system

Table 1 Orders of control in complex systems (after Joslashrgensen amp Straskraba 2000)

order scope for adaptation example system discussed in text

rst xed parameters and structure original Daisyworld modelsecond variable parameters xed structure CA Daisyworldthird variable structure and parameters lsquoAlifersquo Guild modelfourth change of goal functions Gaia ()

perpetual novelty and (5) far-from-equilibrium dynamicsCommonly given examples of CASs are cells individualorganisms and ecosystems

What is the typical behaviour of a CAS First they dis-play lsquoself-organizationrsquo in the sense of emergence ofordered behaviour and structure from many parts withsuf cient connections independent of natural selection(Kauffman 1993) The concept was inspired by the resultsof mathematical models which starting from arbitraryinitial conditions and obeying only simple local rules pro-duced large-scale order The second law of thermody-namics forbids true self-organization increasing order isonly possible in thermodynamically open systems Thusself-organization is dissipative requiring free energy inputand producing high-entropy output CASs may also showlsquoself-organized criticalityrsquo (Bak et al 1987) meaning atendency to reside in the edge of chaos regime allowingchange without getting locked into frozen order A power-law distribution of responses is thought to be characteristicof self-organized critical systems but may occur morewidely in nature

Complex systems can be described in terms of theirorder of dynamics and control (Joslashrgensen amp Straskraba2000 table 1) First-order dynamical systems have xedparameters and structure and hence can only achievefeedback control Second-order dynamical systems havevariable parameters as well as states but xed structureThird-order systems have variable structure as well asparameters and states The distinction in fourth-order sys-tems is that changes in states parameters and structurelead to a change in the goal functions that determine thelong-term behaviour of a system (Wilhelm amp Bruggemann2000) How do CASs t into this classi cation Theelement of replication or enhancement indicates that theirstructure is variable allowing third-order control Thegeneration of continual adaptation suggests that CASs arefourth order with internally generated changes in goalfunctions

In what sense are such behaviours adaptive Adaptationhas two common meanings in biology (i) in evolution itis a change in the structure or functioning of organismsthat makes them better suited to their environment and(ii) in physiology it is an alteration in an organismrsquosresponse to its environment Evolutionary adaptation (i) isusually thought of as the consequence of natural selectionacting on heritable variation The capacity for physiologi-cal adaptation (ii) can be the product of evolutionaryadaptation (i) lsquoAdaptiversquo is used in complexity theory todescribe system development as well as response and isoften applied to systems that are not subject to naturalselection as a whole (although their parts may be) Hencelsquoadaptiversquo behaviours described by complexity theoristsare not necessarily lsquoadaptationsrsquo in the sense used by evo-

Phil Trans R Soc Lond B (2002)

lutionary biologists (i) or physiologists (ii) One way outof this semantic mine eld is to consider natural selectionas just one (rather than the only) form of selection Otherforms of selection can emerge at levels above that of natu-ral selection acting on heritable variation eg in the pro-cess of foraging by social insect colonies utilizingpheromone signals (stigmurgy) or in models of the evo-lution of altruism as a consequence of emergent spatialpatterns (Paolo 2000) If selection can be broader thanjust natural selection then there can be lsquoadaptiversquo behav-iours that are not necessarily the product of natural selec-tion

5 IS GAIA A COMPLEX ADAPTIVE SYSTEM

Gaia is a complex system in that it has many interwovenparts and properties that are not fully explained by anunderstanding of the parts for example the stability ofcomponents of the atmosphere Gaia also ful ls the CAScriteria given previously (Levin 1998) as it contains sus-tained diversity and individuality of components (egorganisms) localized interaction among these compo-nents and at least one autonomous selection process(natural selection) Gaia also possesses non-local interac-tion of components because there is global mixing of theatmosphere and oceans This gives rise to globally mixedvariables atmospheric gases with lifetimes longer thanatmospheric mixing (ca 1 yr) and dissolved chemicalspecies in the ocean with lifetimes longer than ocean mix-ing (ca 1000 yr) There are also non-local interactions inthe climate system described as lsquoteleconnectionsrsquo

If Gaia is a CAS we can expect it to display character-istic properties and behaviour Gaia does indeed sharegeneric CAS properties (Holland 1995) far-from equilib-rium dynamics (of life the atmosphere and aspects ofocean chemistry) generation of perpetual novelty(through evolution) hierarchical organization (eg organ-isms ecosystems Gaia) and absence of a global control-ler However non-local interaction simpli es the systemand offers the possibility that from its many complexcomponents Gaia could display emergent simplicity in itsbehaviour In what sense might Gaia be adaptive Gaiahas not evolved by natural selection at the whole systemlevel but various types of selection operate within the sys-tem The system can be viewed physiologically as cap-tured in the term lsquogeophysiologyrsquo (Lovelock 1986) andmay respond to forcing in a manner resembling physio-logical adaptation There is change at the system level andthere may also be developmental trends that enhance lifeas a whole eg an increase global gross primary pro-ductivity with time

Is Gaia self-organizing It is often said that Gaia is self-regulating but what order of control (table 1) is actually

Gaia as a complex adaptive system T M Lenton and M van Oijen 689

achieved There are many examples of rst-order feed-back control (examples in sect 3) Gaia also contains evo-lution which continually reshapes the system and thusallows higher levels of system control The evolution ofresponses to prevailing environmental conditions and theevolution of environment-altering traits represent changesin the parameters and structure of the system allowing forsecond- and third-order control For example the coloniz-ation of the land surface by vascular plants altered the cli-mate in a self-bene cial manner (Betts 1999) and led toa reorganization of biogeochemical cycles including adrop in carbon dioxide (Berner 1998) global cooling anda rise in oxygen (Lenton 2001) Changes in the Earthrsquoshistory such as the switch from anaerobic to aerobic con-ditions as oxygen rose ca 2 Gyr ago and the resultingincrease in free-energy availability to the biota could beviewed as fourth-order control a change in goal functionfrom an anaerobic lsquoupside-downrsquo biosphere (Walker1987) to an aerobic attractor state that allowed the pro-liferation of new types of life Thus Gaia may be viewedas self-organizing and more in terms of the levels of con-trol achieved

Is Gaia in a self-organized critical state If one contraststhe current state of Gaia with that of Mars or Venus orthe suggested lsquosnowball Earthrsquo state Gaia is more com-plex and less lsquofrozenrsquo into order (of course Mars is literallyfrozen as would be the snowball Earth) It has been sug-gested that the Earthrsquos biota is in a self-organized criticalstate on the basis that extinction events have a distributionclosely approximated by a power law (Kauffman 1993)Proponents of complexity theory propose that the majorityof all extinction events are internally generated by thedynamics of coevolution of species If so this would indi-cate criticality of the biota but not necessarily criticalityof Gaia An alternative hypothesis is that the majority ofextinction events are caused by external perturbation Inthe case of mass extinctions there is good evidence for acausative asteroid impact at the CretaceousndashTertiaryboundary 65 Myr ago (Alvarez et al 1980) Simple mod-els of coevolution (Bak amp Sneppen 1993) or of environ-mental stress (Newman 1997) (without speciesinteraction) as the cause of extinction both exhibit apower law Of the two the environmental stress modelhas an exponent much closer to actual data We concludethat although some extinction may result from coevo-lution there is not yet a convincing case that the biota isin a critical state To test whether Gaia is in a critical statea frequency response analysis of environmental recordsmight be more appropriate For example the carbondioxide and methane records in the Vostok ice core(Petit et al 1999)

6 EMERGENCE OF GAIA

Complexity theory stimulates us to search for a com-plexity threshold for a planet with life beyond which theemergence of self-organization (including self-regulation)and adaptive behaviour becomes likely in other wordsa planetary analogue for the emergence of auto-catalyticnetworks (Kauffman 1993) In coupled open systems oflife and environment does self-organization become vastlymore probable beyond a critical lsquosizersquo (eg number of

Phil Trans R Soc Lond B (2002)

organisms) Also can we pinpoint a particular time in theEarthrsquos history when Gaia emerged

Once life arose it must soon have depleted its surround-ings of substrates thus posing a pressing need for recy-cling Key biogeochemical transformations of essentialelements are present deep in the tree of life among theancient kingdoms of archaea and bacteria supporting aview that nutrient recycling evolved early One furtherrequirement is important for the emergence of planetaryscale self-organization in order to achieve global signi -cance life must have an abundant source of free energyThe earliest types of photosynthesis used relatively scarcesubstrates such as H2S Once oxygenic photosynthesisemerged using the abundant H2O as a substrate then the ux of free energy captured by the biota increased mas-sively (DesMarais 2000) Thus we suggest the genesis ofGaia came with the origin of widespread oxygenic photo-synthesis This occurred at least 28 Gyr ago (DesMarais2000) and possibly as early as 38 Gyr ago (Schidlowski1988)

A remarkable property of Gaia that demands an expla-nation is that its abiotic state variables have stayed at lev-els that support abundant life for most of the last 38 GyrEarly strong versions of the Gaia hypothesis suggestedthat all life-forbidding state variable levels are unreachablebecause there is selection against the processes that wouldlead there Selection at the level of the system as a wholeseems untenable (Doolittle 1981 Dawkins 1983) How-ever it may still be the case that life-forbidding state-vari-able levels are dif cult to reach for at least two reasons(i) if an organism is driving an environmental variabletowards an uninhabitable state its growth and spread willbe suppressed (by negative feedback) such that the systemwill stabilize within the habitable regime and (ii) when-ever organisms become so abundant that the side-effectsof their metabolism become life-threatening on a globalscale different organisms will evolve for which the abun-dant pollutants and the polluters themselves becomeresources If natural selection has enough substrate(genotypic variation) on which to operate such checksand balances are always likely to evolve and make extremeconditions unreachable This old idea (originating fromSmith 1776) could explain the likelihood of regulation atliveable levels as a side-effect of evolution in suf cientlydiverse biota

Uninhabitable or barely habitable states (with life inrefugia) can be reached because of global scale environ-mental perturbation eg massive asteroid impact (Watson1999) or extreme external forcing eg future increases insolar luminosity (Lovelock amp Whit eld 1982 Lenton ampVon Bloh 2001) It is also possible that the evolution ofparticularly strong biotic effects could lsquoovershootrsquo anddrive the environment into a barely habitable stateespecially if there is a time-delay in self-limiting negativefeedback (this is a counter argument to (i) above) Fur-thermore variables that cannot function as a resource toany organism may be able to build up to toxic levels (acounter argument to (ii) above) However useless anddangerous waste products may generally kill off their pro-ducers before disrupting the functioning of Gaia as awhole

Gaia has suffered massive perturbations (asteroidimpacts) and lsquosnowball Earthrsquo states may have occurred

690 T M Lenton and M van Oijen Gaia as a complex adaptive system

in which life only hung on in refugia However abundantlife has always reappeared sometimes remarkably quickly(DrsquoHondt et al 1998) New types of life appear in thewake of mass extinction but there is also a system lsquomem-oryrsquo carried in the gene pool This suggests an interestingpossibility if in response to perturbation a new traitevolves that contributes to recovery then if it remains inthe gene pool and a similar perturbation occurs again thesystem may recover faster the second time In this senseGaia may gain from experience

7 SIMULATING PLANETARY SCALE EMERGENCEWITH DAISYWORLDS

The persistence of life and recovery of Gaia from per-turbation suggest that self-regulation occurs We wouldlike to know how it can emerge and whether it is a chanceor a highly probable outcome of lifendashenvironment coup-ling The feasibility and probability of the emergence ofplanetary scale lsquoself-organizationrsquo andor lsquoadaptive behav-iourrsquo can be evaluated using a synthetic approach of math-ematical modelling

The rst such attempt to simulate the emergence ofplanetary scale self-regulation was the Daisyworld model(Watson amp Lovelock 1983) In Daisyworld global tem-perature regulation emerges automatically from feedbackcoupling between life and its environment with selectionat the component (individual organism) but not the sys-tem (whole planet) level In Daisyworld the environmentis reduced to one variable temperature and life is reducedto two types black and white daisies inhabiting bareground The daisies share the same optimum temperaturefor growth of 225 degC and outer limits to growth of 5 degCand 40 degC The daisy types affect their environment inopposite ways by virtue of their different re ectivity(albedo) The white daisies re ect more solar radiationthan bare ground whilst the black daisies absorb moreHence the local temperature of the daisies differs blackdaisies are always warmer and white daisies are alwayscooler than bare ground The system is forced by a gradualincrease in solar luminosity as has occurred on the Earth

With only one type of daisy present there is a range offorcing for which negative feedback occurs and a point atwhich positive feedback occurs In the case of black daisiesonly when they can establish their spread is ampli ed bypositive environmental feedback (similar to gure 2c butthe effect of life on the environment is stronger) As lumi-nosity increases the population of black daisies declinesthus providing negative feedback on temperature In thecase of white daisies only when they can germinate theirspread is immediately suppressed by their cooling effectAs luminosity increases their population increases pro-viding negative feedback on temperature A regime isentered where white daisies maintain the planet in a habit-able state when otherwise it would be uninhabitable( gure 2d) Eventually they collapse catastrophically withpositive feedback With both types of daisy present thereis a range of forcing for which global temperature actuallydecreases as forcing increases This is an example oflsquosuper-negativersquo feedback (the sign of response is oppositeto that of the forcing (Sardeshmukh 2000))

The Daisyworld model has been portrayed as a CAS(Lewin 1993) but this deserves closer examination It

Phil Trans R Soc Lond B (2002)

possesses rst-order feedback control (table 1) and theregime of super-negative feedback was unexpected fromits parts However the original model does not explicitlyinclude interacting local components The system isdescribed by coupled equations and its behaviour can beunderstood analytically (Saunders 1994 Weber 2001)

If time-delays are introduced into the population andtemperature equations of Daisyworld then apparentlychaotic behaviour can be generated (Zeng et al 1990)Varying the time-delay reveals a series of period doublingscharacteristic of the transition from order to deterministicchaos (De Gregorio et al 1992ab) There is no real-worldjusti cation for the time-delays and it has been shownthat the average of the lsquochaoticrsquo solutions is close to thetemperature regulation in the original model (Jascourt ampRaymond 1992) Introducing an unrealistically large heatcapacity to Daisyworld generates limit cycle oscillations ofthe two daisy populations and temperature (Nevison et al1999) (ie generates the rst period doubling) Thesestudies show that the original Daisyworld model resideswell into the ordered regime and is not in a critical state

Subsequent versions of Daisyworld arguably show theemergence of higher-order control (although the nal prop-erty of temperature regulation is similar in each case)Variants of the model with adaptation of the optimumgrowth temperature of the daisies (Robertson amp Robinson1998 Lenton amp Lovelock 2000) include alteration ofparameters but this is enforced through further para-meters A more fully second-order control system is a Dai-syworld with random mutation of daisy albedo (some ofthe parameters) and subsequent selection (Lenton 1998Lenton amp Lovelock 2001) The structure of this modelcould be said to change in that new daisy lsquospeciesrsquo appearThis suggests there may be some third- and fourth-ordercontrol

8 CA DAISYWORLDS

To ful l the CAS criteria models must include localinteraction of components CA provide a tool for thisHence we have followed the lead of others (Von Bloh etal 1997) and constructed a CA version of Daisyworld toexplore the effects of local interaction and the capacity foradaptive system behaviour The original equations(Watson amp Lovelock 1983) are retained where possibleThe CA grid and rules are simply used to replace thepopulation equations We consider a square grid witheight neighbours to each cell rather than four nearestneighbours (Von Bloh et al 1997) There is no diffusivetemperature eld just the original equations for local tem-peratures of daisies (determined by albedo global tem-perature and insulation parameter q) and globaltemperature (determined by average albedo of the systemand luminosity forcing) Seeding is used to enable popu-lations to establish (but once they are established it haslittle impact) First we consider the original case of popu-lations of lsquoblackrsquo (albedo aB = 025) and lsquowhitersquo (albedoaW = 075) daisies covering bare ground (albedo aG = 05)For an empty cell with nB black neighbours each withgrowth rate b B and nW white neighbours each with growthrate b W the following colonization rules apply

The probability that black will colonize when only theyare present is

Gaia as a complex adaptive system T M Lenton and M van Oijen 691

P(B|nW = 0) = 1 2 (1 2 b B)nB (81)

The probability that white will colonize when only theyare present is

P(W|nB = 0) = 1 2 (1 2 b W )nW (82)

The probability that the cell remains empty is

P(E) = (1 2 P(B|nW = 0))(1 2 P(W|nB = 0)) (83)

The probability that black will colonize when both arepresent is

P(B) = (1 2 P(E))P(B|nW = 0)

P(B|nW = 0) 1 P(W|nB = 0) (84)

The probability that white will colonize when both arepresent is

P(W) = (1 2 P(E))P(W|nB = 0)

P(B|nW = 0) 1 P(W|nB = 0) (85)

The probability of seeding an empty cell is xed

P(S) = h ( h = 0001 in the results shown) (86)

The probability of death at an occupied cell is also xed

P(D) = g ( g = 03 as in the original model) (87)

The 2D CA model has less smooth dynamics than theoriginal zero-dimensional model in that it can exhibitbifurcations and limit cycling ( gure 4) The growth equa-tions are such that for one type alone ( gure 4ac) it canreach carrying capacity on the grid even when its localtemperature and growth rate are sub-optimal This isbecause the presence of many identical neighbours canmake colonization of an empty cell highly probable evenwhen growth rate is suppressed by temperature (equations(81) or (82)) For black daisies alone ( gure 4ab) asforcing is increased a bifurcation point is reached wherethe global temperature is such that the local temperatureof black daisies becomes uninhabitable (b B = 0 when thetemperature of black daisies TB = 40 degC) This generatespartial collapse (ca 30 die-back of the daisies) immedi-ate recovery and resulting oscillations of temperature andpopulation As forcing is increased further a second bifur-cation point is reached Then the trajectories combinebefore the black daisies disappear For white daisies alone( gure 4cd) there are two period doublings and thebeginnings of a third (inset in gure 4d) before a returnto a single trajectory

The one daisy-type model illustrates an lsquoovershootrsquoproblem for Gaia life may develop the capacity to drivean environmental variable into an uninhabitable or barelyhabitable state if the environmental effect is strong andlocal interactions that encourage growth outweigh nega-tive feedback on growth from the environment The modeldoes not include natural selection in that all the daisiesare identical and are always equally t in terms of growthrate (although in the initial growth phase clusters formand cells at the edge of clusters are better able to spreadthan those within clusters) The model does include a sys-tem selection process between bare ground and one daisytype under a certain range of forcing daisies are selectedover bare ground outside that range bare ground willsuccessfully take over from daisies

Phil Trans R Soc Lond B (2002)

When black and white types can both arise the limitcycle regimes are removed and the solution resembles theoriginal zero-dimensional model ( gure 4ef ) The twodifferent daisy types have different growth rates and hence tness thus adding a crude form of natural selection tothe model (although there is no evolution) With thisadditional selective process the model stays more rmlyin the ordered regime The system is stabilized by at leastthree effects (i) if one daisy type reaches an uninhabitabletemperature the other may still be able to spread (becausetheir local temperatures differ) (ii) in the mid-range offorcing a combination of black and white generates a glo-bal temperature closer to optimal and (iii) the presenceof one daisy type reduces the area available to the otherto expand into

We have introduced random mutation of albedo to themodel generalizing the colonization equations (81)ndash(85)to deal with any albedo type Mutation is assumed alwaysto occur in the process of colonization of an empty cell(asexual reproduction that always generates mutatedoffspring) Albedo can mutate within a parameterizedwidth of the parent albedo (plusmn D a) Within this rangeeither side of the parent albedo an offspring albedo is ran-domly chosen Limits to mutation are set at am in = 0 andam ax = 1

With mutation and natural selection within the modelsystem ( gure 5) its behaviour could be said to be lsquoadap-tiversquo in that it lsquoevolvesrsquo to counteract forcing When themodel is seeded with the original lsquoblackrsquo daisies(aB = 025) and these are allowed to mutate as forcingincreases progressively paler daisies evolve cooling theplanet and then maintaining the temperature close to con-stant Increasing D a brings the average planetary tempera-ture more rapidly towards the optimum for daisy growthThe tendency for bifurcation ( gure 4a) is removed byincreasing D a ( gure 5) because this tends to generate anearly increase in average albedo In a sensitivity analysisof the stabilizing effect of albedo diversity am ax ndash am in wasprogressively increased around a central value ofaB = 025 without any mutation and this was also foundto remove the bifurcations Albedo mutation extends therange of temperature regulation beyond that in the originalmodel because paler types than the original lsquowhitersquo onescan arise The latter result has been found in other vari-ants of Daisyworld (Stocker 1995 Von Bloh et al 1997Lenton amp Lovelock 2001)

A more complex 2D CA version of Daisyworld has pre-viously been formulated with albedo mutation and a con-tinuous temperature eld (Von Bloh et al 1997) Thissystem exhibits the remarkable property that underenforced habitat fragmentation using a percolating fractalthe system is able to regulate temperature unimpaired upto a lsquocriticalrsquo threshold at which daisy areas become iso-lated and regulation starts to break down Once uninhabi-ted land forms a spanning cluster regulation is completelyremoved By contrast trivial reductions in habitat (eg agrowing square of lsquoconcretersquo) impair temperature regu-lation in a linear fashion In the former case adjacent dai-sies can affect the temperature of small uninhabited areasbut overall temperature regulation depends on compe-tition among daisies across an entire connected space Inother words the emergent property of global temperatureregulation relies on uninhibited local interaction tting

692 T M Lenton and M van Oijen Gaia as a complex adaptive system

100

50

0

80

60

40

20

0

plusmn20

100

50

0

100

50

0

80

60

40

20

0

plusmn20

80

60

40

20

0

plusmn20

05 10 15 20

05 10 15 20

05 10 15 20 05 10 15 20

05 10 15 20

05 10 15 20

solar luminosity (_) solar luminosity (_)

solar luminosity (_) solar luminosity (_)

solar luminosity (_) solar luminosity (_)

gri

d c

over

(

)g

rid

cov

er (

)

gri

d c

ov

er (

)

glo

bal

tem

per

ature

(degC

)g

lob

al t

emp

erat

ure

(degC

)g

lob

al t

emper

atu

re (

degC)

15

plusmn508 11

(a) (b)

(c) (d)

(e) ( f )

Figure 4 Simulations of xed albedo populations in a simple CA Daisyworld (64 acute 64 grid) Parameters are as in the originalmodel (Watson amp Lovelock 1983) and the CA rules are described in sect 8 Solar luminosity (in normalized units) is increased insteps of 0004 at each of which the model is updated The left-hand graphs show percentage grid cover by the daisies versusluminosity and the right-hand graphs show global average temperature (degC) versus luminosity Temperature is a function ofluminosity and the albedo a and grid cover of daises and empty cells (ab) Seeding with lsquoblackrsquo daisies (aB = 025) denotedby lled circles (cd) Seeding with lsquowhitersquo daisies (aW= 075) denoted by open circles (ef ) Seeding with both black and whitedaisies (albedo of each seed chosen at random) The inset in (d ) shows the period doubling in the temperature trajectory withonly white daisies

in nicely with the criteria for a CAS The system is self-organizing and may arguably be in a critical state near thelimit at which daisy areas become disconnected

9 FEASIBILITY TESTS OF GAIA USING lsquoALIFErsquo

A key criticism of Daisyworld is that it is limited in onlyconsidering one predetermined type of interactionbetween the local and the global and it is one that will

Phil Trans R Soc Lond B (2002)

tend to generate regulation The daisies affect theirenvironment in the same way at the local and the globalscale Hence what is selected for at the individual leveltends to be bene cial at the global level With two or moredaisy types present there is negative selective feedbackmaking regulation likely (Lenton 1998)

lsquoAlifersquo techniques offer a promising way of makingunbiased tests of the potential for emergence of planetaryscale self-organization The model environment lsquoTierrarsquo

Gaia as a complex adaptive system T M Lenton and M van Oijen 693

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

0

20151005

solar luminosity (ndash)

grid

cov

er (

)

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

(a) (b)

(c)(d)

( f )(e)

Figure 5 CA Daisyworld simulations with albedo mutation (64 acute 64 grid) In each simulation there is seeding with theoriginal lsquoblackrsquo daisies (aB = 025) which fall in the range coloured in blue The model is updated with each increase in solarluminosity of 0004 normalized units and at each update empty cells can be colonized with offspring cells that differ at mostby plusmn D a from the albedo of their parent cell Left- and right-hand graphs show grid cover by daisy populations () and globalaverage temperature (degC) respectively The albedo colour scheme in the left-hand graphs is 0ndash02 black 02ndash04 blue 04ndash06 green 06ndash08 orange 08ndash10 red The graphs show the effect of increasing mutation range (ab) D a = 001 (cd) D a =002 (ef ) D a = 01

(Ray 1991) evolved a community of arti cial life-formsthat reproduce in different ways including parasiticallyThe model lsquolife-formsrsquo compete for resource (processortime) but they do not produce waste products Hencetheir interaction with their environment is not thermody-namically complete in the way that it is for real life-formswhich can only maintain an ordered (low entropy) stateby transforming matter as well as energy

The evolution of matter recycling is addressed usinglsquoAlifersquo techniques in the Guild model (Downing amp Zvirin-sky 1999) From one ancestral lsquospeciesrsquo a communityevolves which is able to recycle a given set of lsquochemicalsrsquo(which can be thought of as different molecular forms ofthe same key nutrient element) Such recycling enablesgreatly enhanced productivity in real ecosystems and Gaia

Phil Trans R Soc Lond B (2002)

(Volk 1998) The mechanism of emergence of recyclingis quite different from the spontaneous emergence of auto-catalytic cycles in systems of very large numbers of chemi-cal reactions (Kauffman 1993) In the Guild model lsquoAlifersquochances upon closed recycling of a small set of chemicalsand this is reinforced by selection This illustrates part ofthe mechanism (ii) that we highlighted in sect 6

The main criticisms of the original Guild model are thatthere is no treatment of energy in the system and that adeviation of the local environment from the global isassumed that may not be justi ed for some real world ana-logues A lsquoGuild IIrsquo model is being developed (K Down-ing personal communication) that includes free energyand entropy in the abstract chemistry (eg it takes freeenergy to build larger molecules) and makes the local

694 T M Lenton and M van Oijen Gaia as a complex adaptive system

environment the interior of proto-cells In this modeldespite a relatively small input of free energy in chemicalform recycling and regulation can emerge

An ideal model world for testing Gaia would containarti cial life-forms that transform lsquomatterrsquo and lsquoenergyrsquoare lsquothermodynamicallyrsquo constrained grow and replicatewith a heritable genome subject to random mutationinteract with one another and evolve new ways of alteringtheir environment related to their internal functioningThe environment would contain many lsquophysicalrsquo andlsquochemicalrsquo variables some homogeneous (well mixed) andothers heterogeneous The resulting system behaviourwould be observable and testable by perturbation

10 CONCLUSIONS

Many scientists now accept that planetary regulationinvolving the biota occurs (Longhurst 1998) However westill have to determine whether Gaiarsquos coming into exis-tence and survival was coincidental or probable and howfragile or robust the system is at present We have arguedthat Gaia is a complex system with self-organizing andadaptive behaviour but that it does not reside in a criticalstate Complexity theory modelling approaches havehelped us simulate and understand the emergence of plan-etary order lsquoAlifersquo techniques can take this further andhelp in assessing the probability of emergence of planetaryregulatory properties Our attempts to apply complexitytheory to Gaia have yielded a broader view of selectionthan previously encompassed in the Gaia theory (Lenton1998) Gene-based natural selection is just one type andlevel of selection operating within Gaia and it is not anecessary condition for regulation The existence of differ-ent types of selection operating at different levels makes iteasier to understand how planetary-scale self-regulationcan arise It also makes it easier to accept that a Gaia-likesystem may be a probable outcome once there is abundantlife on a planet with the capacity for large-scale freeenergy capture

We thank Ricard Sole and Simon Levin for the invitation towrite this article

REFERENCES

Alvarez L W Alvarez W Asaro F amp Michel H V 1980Extraterrestrial cause for the CretaceousndashTertiary extinctionScience 208 1095ndash1108

Bak P amp Sneppen K 1993 Punctuated equilibrium and criti-cality in a simple model of evolution Phys Rev Lett 714083ndash4086

Bak P Tang C amp Wiesenfeld K 1987 Self-organized criti-calitymdashan explanation of 1f noise Phys Rev Lett 59381ndash384

Berner R A 1998 The carbon cycle and CO2 over Phanero-zoic time the role of land plants Phil Trans R SocLond B 353 75ndash82 (DOI 101098rstb19980192)

Betts R A 1999 Self-bene cial effects of vegetation on cli-mate in an oceanndashatmosphere general circulation modelGeophys Res Lett 26 1457ndash1460

Bonan G B Pollard D amp Thompson S L 1992 Effects ofboreal forest vegetation on global climate Nature 359716ndash718

Budyko M I 1968 The effect of solar radiation variations onthe climate of the Earth Tellus 21 611ndash619

Phil Trans R Soc Lond B (2002)

Dawkins R 1983 The extended phenotype Oxford UniversityPress

De Gregorio S Pielke R A amp Dalu G A 1992a Feedbackbetween a simple biosystem and the temperature of theEarth J Nonlinear Sci 2 263ndash292

De Gregorio S Pielke R A amp Dalu G A 1992b A delayedbiophysical system for the Earthrsquos climate J Nonlinear Sci2 293ndash318

DesMarais D J 2000 When did photosynthesis emerge onEarth Science 289 1703ndash1705

DrsquoHondt S Donaghay P Zachos J C Luttenberg D ampLindinger M 1998 Organic carbon uxes and ecologicalrecovery from the CretaceousndashTertiary mass extinctionScience 282 276ndash279

Doolittle W F 1981 Is nature really motherly The CoEvol-ution Q Spring 58ndash63

Downing K amp Zvirinsky P 1999 The simulated evolutionof biochemical guilds reconciling Gaia theory and naturalselection Artif Life 5 291ndash318

Ehrlich P 1991 Coevolution and its applicability to the Gaiahypothesis In Scientists on Gaia (ed S H Schneider amp PJ Boston) pp 118ndash120 London MIT Press

Gallagher R amp Appenzeller T 1999 Beyond reductionismScience 284 79

Hamilton W D 1995 Ecology in the large Gaia and GenghisKhan J Appl Ecol 32 451ndash453

Hamilton W D 1996 Gaiarsquos bene ts New Scientist 15162ndash63

Hamilton W D amp Lenton T M 1998 Spora and Gaia howmicrobes y with their clouds Ethol Ecol Evol 10 1ndash16

Han T-M amp Runnegar B 1992 Megascopic eukaryotic algaefrom the 21 billion-year-old Negaunee iron-formationMichigan Science 257 232ndash235

Hoffman P F Kaufman A J Halverson G P amp SchragD P 1998 A Neoproterozoic snowball earth Science 2811342ndash1346

Holland J 1995 Hidden order how adaptation builds complexityReading MA Addison-Wesley

Hyde W T Crowley T J Baum S K amp Peltier W R2000 Neoproterozoic lsquosnowball Earthrsquo simulations with acoupled climateice-sheet model Nature 405 425ndash429

Imshenetsky A A Lysenko S V amp Kazakov G A 1978Upper boundary of the biosphere Appl Environ Microbiol35 1ndash5

Isaacs A Daintith J amp Martin E (eds) 1996 Concise sciencedictionary Oxford University Press

Jascourt S D amp Raymond W H 1992 Comments on lsquoChaosin daisyworldrsquo by X Zeng et al Tellus 44B 243ndash246

Joslashrgensen S E amp Straskraba M 2000 Ecosystems as cyber-netic systems In Handbook of ecosystem theories and manage-ment (ed S E Joslashrgensen amp F Muller) pp 249ndash264London Lewis Publishers

Kasting J F 1991 Box models for the evolution of atmo-spheric oxygen an update Global and Planetary Change 97125ndash131

Kauffman S A 1993 The origins of order self-organization andselection in evolution Oxford University Press

Kleidon A 2002 Testing the effect of life on Earthrsquos func-tioning how Gaian is the Earth system Climatic Change 52383ndash389

Klinger L F 1991 Peatland formation and ice ages a possibleGaian mechanism related to community succession InScientists on Gaia (ed S H Schneider amp P J Boston) pp247ndash255 London MIT Press

Koeslag J H Saunders P T amp Wessels J A 1997 Glucosehomeostasis with in nite gain further lessons from theDaisyworld parable J Endocrinol 154 187ndash192

Lenton T M 1998 Gaia and natural selection Nature 394439ndash447

684 T M Lenton and M van Oijen Gaia as a complex adaptive system

lsquoAlifersquo techniques for assessing the probability of planetaryself-organization is discussed (sect 9) and we close by sum-marizing how complexity theory has already altered ourunderstanding of Gaia (sect 10)

2 GAIA

We de ne Gaia as the thermodynamically open systemat the Earthrsquos surface comprising life (the biota) atmo-sphere hydrosphere (ocean ice freshwater) dead organicmatter soils sediments and that part of the lithosphere(crust) that interacts with surface processes (includingsedimentary rocks and rocks subject to weathering) Theupper boundary of the system is at the top of the atmo-sphere with outer space The inner boundary is harder tode ne and can be taken to depend on the time-scale ofprocesses under consideration For time-scales longerthan the recycling of the crust (ca 108 years) the line maybe drawn between the crust and the mantle For processesthat can approach steady state rapidly (in less than 103

years) the outer surface of the crust may be consideredthe boundary of the system A rigid de nition thatexcludes any component of the crust from Gaia has beensuggested (Volk 1998) but we think this is too exclusiveInclusion of the entire Earthrsquos interior has also beenimplied (Lovelock 1991) but we think that this is tooinclusive Processes such as volcanism and plate tectonicsare ultimately driven by a heat energy source in the Earthrsquosinterior which (like the Sun) is not signi cantly in uencedby surface processes and hence is best considered to belsquooutsidersquo the system

Abundant energy is exchanged across the upper bound-ary of Gaia (ca 175 acute 101 7 W) but relatively little matterOnly hydrogen atoms can readily escape Earthrsquos gravity(currently ca 27 acute 108 H atoms cm2 2 s 2 1) Incomingmeteoroids supply a small ux of matter to the Earthrsquossurface (more than 101 1 g yr 2 1) and atmosphere (as andwhen they are vaporized) (Isaacs et al 1996) Occasionalasteroid (large meteorite) impacts add matter and can alsoprovide suf cient energy to eject meteoroids into spaceMatter is exchanged across the lower boundary of Gaiabut relatively little energy Available geothermal energy(ca 3 acute 101 3 W) is tiny in comparison to solar energyExchange uxes of matter across the lower boundary aresigni cant but for many elements are orders of magnitudesmaller than the internal cycling uxes (eg ca 5 acute 101 3

mol C yr2 1 input and output ca 15 acute 101 7 mol C yr 2 1

cycled within the system)The energy input to Gaia has been gradually increasing

(ca 1 every 108 years) as the Sun becomes more lumi-nous with time Variations in the Earthrsquos orbital para-meters also alter the total energy input and its distributionacross the Earthrsquos surface on time-scales of 103ndash105 yearsDecay of angular momentum of the Earthndashmoon systemcauses the Earth to spin more slowly with time Occasionalasteroid impacts provide massive perturbations of theEarthrsquos surface releasing large amounts of energy forexample ca 102 4 J in the Chicxulub impact at the Cre-taceousndashTertiary boundary 65 Myr ago Thermal decay ofthe Earthrsquos interior heat source causes a gradual decline involcanic and tectonic activity including sea- oor spreadingrates (volcanic and metamorphic matter input was prob-ably three times greater ca 3 Gyr ago) Occasional catas-

Phil Trans R Soc Lond B (2002)

trophic out ow of lava ( ood basalt volcanism) occursSuch events may be triggered by asteroid impact(Rampino 1987) thus providing a possible link betweenperturbation from above and below Gaia

We distinguish Gaia from the lsquoEarth systemrsquo (anincreasingly popular term) in that the Earth systemincludes states before the origin of life whereas Gaia refersto the system with abundant life and because the Earthsystem is sometimes taken to include the entire interior ofthe Earth We also distinguish Gaia from the lsquobiospherersquo(the region inhabited by living organisms) These aresometimes treated synonymously but the boundaries ofGaia are almost certainly wider because the in uence ofliving organisms extends beyond the region they inhabitThe upper boundary of the biosphere is more than 50 kmabove the Earthrsquos surface in the mesosphere where viablemicroscopic fungi and bacteria have been collected byRussian rockets (Imshenetsky et al 1978) whereas theexosphere extends above 500 km The lower boundary ofthe biosphere is unknown but organisms have been foundto be thriving at depths of a few kilometres in the Earthrsquoscrust It has been suggested that a lsquodeep hot biospherersquocould survive independently of surface life but if it couldpersist at all this would be a much simpler system runningoff a relatively tiny amount of free energy

Gaia has many remarkable physical and chemicalproperties especially when contrasted with our neigh-bouring planets Mars and Venus The Earthrsquos atmo-sphere is in extreme thermodynamic disequilibrium withreactive gases at concentrations many orders of magnitudefrom those predicted at geochemical and photochemicalsteady state (Lovelock 1975) Oxygen is extraordinarilyabundant at 021 atm instead of less than 102 1 2 atm(Kasting 1991) Other reactive gases are at anomalouslyhigh concentrations given abundant oxygen Forexample methane concentration is more than 103 0 timesequilibrium (Lovelock 1975 Sagan et al 1993) Themajority of nitrogen should be as NO 2

3 dissolved in theocean rather than N2 in the atmosphere (Lewis amp Randall1923 Sillen 1967) By contrast carbon dioxide makes upa remarkably small fraction of the atmosphere when com-pared with Mars and Venus The composition of theEarthrsquos atmosphere shows dynamic stability over periodsmuch longer than the residence time of speci c gases(Lovelock amp Margulis 1974) For example the O2 reser-voir with a geologic residence time of ca 32 Myr hasvaried by less than a factor of two over the past 350 Myr(Lenton 2001) Other master variables of Gaia also showevidence of regulation The Earthrsquos average surface tem-perature has tended to decline or remain relatively con-stant over the past ca 4 Gyr despite a ca 30 increasein solar luminosity Liquid water has been retained at theEarthrsquos surface (in contrast to Mars and Venus) Hydro-gen escape to space and consequent water loss has beenminimized by the oxidizing state of the atmosphere for thepast ca 20 Gyr and the existence of a cold trap at thetropopause Ocean salinity has never reached toxic con-centration pH has remained close to neutral The chemi-cal composition of Gaia as a whole is such that abundantfree energy is available from chemical reaction mostnotably from the reaction of O2 with organic compounds

Perhaps the most remarkable property of Gaia is theongoing presence and profusion of life The Earthrsquos sur-

Gaia as a complex adaptive system T M Lenton and M van Oijen 685

face has remained habitable for more than 385 Gyr(Mojzsis et al 1996) The relatively stable organic carboncontent and isotopic composition of the crust indicate thatlife has been abundant for most of the past 38 Gyr(Schidlowski 1988) Life has been invoked to explainmany of the Earthrsquos remarkable physical and chemicalproperties The abundance of oxygen in the presentatmosphere is almost entirely a biological product Atmo-spheric oxygen has increased in a stepwise fashion frompO2 0002 atm more than 22 Gyr ago and has beensuf cient to support eukaryotes (pO2 001 atm) for atleast the last 2 Gyr (Han amp Runnegar 1992) The stabilityof O2 over the past 350 Myr has enabled the continuouspersistence of large metazoa (requiring O2 ca 015 atm)and slowly regenerating trees (requiring O2 ca 03 atm)(Lenton amp Watson 2000b) The scarcity of carbon dioxidein the atmosphere and consequent cooling of the planetis due to biologically ampli ed silicate rock weatheringwhich drives the dominant sink in the long-term carboncycle (Lovelock amp Watson 1982 Schwartzman 1999)Within Gaia there is greatly enhanced cycling of matterespecially of the elements essential to life For examplephosphorus is cycled an average of 46 times through aterrestrial ecosystem before being lost to the ocean whereit is cycled an average of 280 times before being nallyburied in new rocks (Volk 1998) Return of water to theatmosphere is increased approximately three times by thepresence of vascular plants on the land surface (Betts1999 Kleidon 2002) These recycling effects greatlyincrease global gross primary productivity (Volk 1998Kleidon 2002)

3 GAIA THEORY

The Gaia theory seeks to explain the remarkable proper-ties of the system just described especially its far-from-equilibrium ordered state dynamic stability habitability ourishing of life and pattern of change over time(Lovelock 1988 Lenton 1998) From the outset Gaia hasbeen viewed as a cybernetic (feedback control) system(Lovelock amp Margulis 1974) The essential elements ofthe theory are (i) life affects its environment all organ-isms alter their environment by taking in free energy andexcreting high-entropy waste products in order to main-tain a low internal entropy (Schrodinger 1944) (ii) growth(including reproduction) organisms grow and multiplypotentially exponentially (iii) environment constrains lifefor each environmental variable there is a level or rangeat which growth of a particular organism is maximizedand (iv) natural selection once a planet contains differenttypes of life (phenotypes) with faithfully replicated heri-table variation (genotypes) growing in an environment of nite resources natural selection determines that the typesof life that leave the most descendants come to dominatetheir environment

The overall behaviour of Gaia is governed by a combi-nation of positive and negative feedback Positive feedbacktends to add to change while negative feedback tends tocounteract change Growth is intrinsically a positive feed-back process (the more life there is the more life it canbeget) The growth of life drives lifersquos effects on itsenvironment to become global in scale The extreme ther-modynamic disequilibrium of the Earthrsquos atmosphere

Phil Trans R Soc Lond B (2002)

biotic

abiotic

environmental

feedback

selection

growth

Figure 1 A subdivision of types of environmental feedback

indicates that this has occurred The fact that life altersits environment and is also constrained by it means thatenvironmental feedback is inevitable Environmental feed-back arises at the local level (eg due to the evolution ofenvironment-altering traits) With growth environmentalfeedback has the potential to become global in scale Thetypes of environmental feedback can be classi ed in a hier-archy (Lenton 1998)

The rst distinction is between abiotic and biotic feed-back to the environment ( gure 1) The response of lifeto a particular environmental variable includes habitabilitybounds for the organisms in question whereas abioticresponses have no automatic correlation with what is hab-itable for life Abiotic responses to a particular environ-mental variable are typically simple increasing ordecreasing functions ( gure 2ab) If they also affect thevariable in question then either negative feedback or posi-tive feedback will result Negative abiotic feedback ( gure2a) can stabilize the environment in either a habitable oran uninhabitable state Positive abiotic feedback ( gure2b) can drive the environment into an uninhabitable statealthough in many cases it is not suf ciently strong to doso By contrast organisms tend to have a peaked growthresponse to many environmental variables ( gure 2cd) Ifthey also affect a particular environmental variable thenthe resulting system will have both negative and positivefeedback regimes either side of the optimum for growthand for a range of forcing it will by de nition tend to sta-bilize in a habitable state For a weak biotic effect on theenvironment ( gure 2c) the stable state can be in eitherthe negative or the positive feedback regime For a strongbiotic effect on the environment ( gure 2d) the systemwill tend to transit the positive feedback regime and stabil-ize in the negative feedback regime For some forcing (eg gure 2d) multiple solutions can occur such that life main-tains the environment in a habitable state when otherwiseit would be uninhabitable If the system is forced beyondthe unstable solution in the positive feedback regime thenlife will collapse catastrophically

Biotic environmental feedback can be subdivided( gure 1) into feedback on growth and feedback on selec-tion (Lenton 1998) Non-selective feedback on growthoccurs when the effect of a trait on the environment altersthe growth rate of the organisms carrying it but theenvironmental alteration is a side-effect of the trait thatdoes not hamper its selective advantage Feedback onselection occurs when the effect of a trait on the environ-ment alters the forces of selection determining its value

An important example of negative feedback on growth( gure 2d) is that resulting from plant-induced ampli -cation of rock weathering This inadvertently tends to

686 T M Lenton and M van Oijen Gaia as a complex adaptive system

environment variable (E) environment variable (E)

environment variable (E)environment variable (E)

abio

tic

var

iable

(A

)ab

ioti

c v

aria

ble

(A

)

life

var

iable

(L

)li

fe v

aria

ble

(L

)

E = f (A) A = f (E)

E = f (L)

L= f (E)

L= f (E)

E = f (L)

A = f (E)

E = f (A)

(a)

(b)

(c)

(d )

Figure 2 General representations of types of environmental feedback for xed forcing (a) abiotic negative feedback (b)abiotic positive feedback (c) weak biotic feedback and (d) strong biotic feedback Large open circles indicate stable statesSmall lled circles indicate unstable states The arrows indicate the general direction of change for starting states withineach regime The schematic diagrams are loosely based on the following global cases described in more detail in the text(a) abiotic silicate weathering rate and temperature (b) ice cover and temperature (c) boreal forest cover and temperature(d) growth rate of rock weathering organisms and temperature

decrease atmospheric CO2 and cool the planet DecliningCO2 and cooling below optimum growth temperaturetend to suppress plant growth closing the feedback loopRock weathering traits are probably selected for as ameans of acquiring rock-bound nutrients (especiallyphosphorus) and changes in CO2 and temperature do notaffect this requirement or the resulting selection (It ismore likely that local build-up of phosphorus in soil woulddo that) The feedback from changing CO2 and tempera-ture is very slow and requires a global spread of the traitover many generations before it affects growth Howeverit is key to the long-term regulation of atmospheric CO2

and temperature and can thus be bene cial to plantgrowth in the long term In particular it counteractsincreasing solar luminosity that could otherwise drive theEarthrsquos surface temperature above optimal levels Someabiotic negative feedback ( gure 2a) would exist in aworld without life but with tectonics and a hydrologicalcycle (Walker et al 1981) However rock-weatheringorganisms greatly strengthen the feedback (Lovelock ampWatson 1982 Schwartzman amp Volk 1989) They maythus extend their own future persistence on Earth(Lenton amp Von Bloh 2001)

An example of positive feedback on growth ( gure 2c)is that resulting from the dark snow-shedding foliage oftrees in the boreal forest By absorbing solar radiation thetrees are warmed (especially relative to snow cover) andtheir growth is enhanced This warms their surroundingsthus further enhancing growth (Bonan et al 1992) Thepositive feedback is constrained in that temperatures inthe boreal regions remain below the optimum for growthfor much of the year but they are increased such that

Phil Trans R Soc Lond B (2002)

forest is able to persist over large regions that would other-wise be too cold for growth (Betts 1999)

An example of negative feedback on selection is thatresulting from nitrogen xation in the worldrsquos oceansmany terrestrial ecosystems and some freshwater lakesNitrogen xation is an energetically demanding processwhich will only be selected for when there is a lack ofavailable nitrogen relative to other potentially growth-lim-iting nutrients By xing nitrogen the responsible organ-isms ultimately increase the amount of nitrogen availablein their environment for non-nitrogen- xers Thisremoves the selective advantage of being a nitrogen xerand hence the proliferation of nitrogen xation is self-lim-ited This mechanism regulates the nitrate content of theworldrsquos oceans relative to the phosphate content in a pro-portion close to organismsrsquo requirements (Red eld 1958Lenton amp Watson 2000a)

An example of positive feedback on selection is thatresulting from the ability of sphagnum moss to acidify soilThis environmental change gives the moss a selectiveadvantage relative to other potential invading plants andencourages succession to a peat bog (Klinger 1991Hamilton 1996) There are probably other self-limiting(negative) feedbacks on bog growth given that we do notlive in a world dominated by peat bogs (although theauthors live in a country dominated by them) Interest-ingly examples of positive feedback on selection tend tobe more localized than examples of negative feedbackon selection

One of the possible fates for Gaia is for abiotic positivefeedback ( gure 2b) to take the planet into an uninhabit-able or barely habitable state In the ice-albedo positive

Gaia as a complex adaptive system T M Lenton and M van Oijen 687

feedback effect snow and ice form surfaces that are highlyre ective (high albedo) to solar radiation thus coolingtheir surroundings and encouraging the spread of snowicecover In simple models a modest reduction in solar inputis ampli ed by this feedback to cause complete ice coverof the Earth (Budyko 1968 Sellers 1969) the so-calledlsquosnowball Earthrsquo (Hoffman et al 1998) Recent simula-tions suggest that a lsquoslushball Earthrsquo state with open waterin equatorial oceans may be more realistic and less fatalto life (Hyde et al 2000) If a snowball Earth attractorexists it should be unstable because CO2 input from vol-canoes can gradually accumulate in the atmosphere untilradiative forcing is suf cient to melt continental ice cover

A key challenge to Gaia theory from evolutionary biol-ogists is to explain how order especially self-regulationcan arise at the global scale without invoking teleology orselection at the level of the planet (Doolittle 1981 Daw-kins 1983) Such criticisms inspired the formulation of theDaisyworld model (Lovelock 1983 Watson amp Lovelock1983) which demonstrates that self-regulation canemerge automatically from competing populations alter-ing their local environments in different ways (see sect 7 andsect 8) The idea that evolution within Gaia could have pro-duced organisms that contribute to regulating the planetis still variously criticised as untenable altruism vulnerableto cheats or demanding large-scale group selection(Hamilton 1995) It is sometimes argued that randomvariation and natural selection are necessary and suf cientto explain the self-regulation of organisms and candidatesuper-organisms (eg temperature regulated social insectcolonies Ehrlich 1991) in which case self-regulation ofGaia could not occur However regulation can emergeautomatically (Saunders 1994 Watson 1999) and hencethe mechanisms by which regulation emerges in physi-ology may have parallels at the planetary scale (Koeslaget al 1997 Saunders et al 1998) even though planetaryregulation cannot be re ned by selection We think thatwith an appreciation of feedback principles the theoriesof Gaia and natural selection can be reconciled (Lenton1998)

Equally there is a need to extend the original cyberneticview of Gaia to encompass evolution The continuousgeneration and selection of different environment-alteringtraits ensures that the feedback structure of Gaia remainsdynamic Evolution within the biota drives changes in thestate parameters and structure of the system (eg the riseof atmospheric oxygen) This in turn facilitates the evolu-tion of new forms of life It can also alter the set pointsof regulation when they are not xed by thermodynamicchemical or geophysical constraints (Lenton amp Lovelock2000) Complexity theory may provide a framework fordeveloping Gaia theory by synthesizing principles fromcybernetics and evolutionary biology

4 COMPLEXITY THEORY

Complexity theory is a general theory of complexdynamic systems The Latin complexus comes from theGreek pleko meaning to plait or twine Thus a complexsystem is literally one consisting of interwoven partsComplex can also mean dif cult to understand or analyseA broad de nition of a complex system is one whoseproperties are not fully explained by an understanding of

Phil Trans R Soc Lond B (2002)

dynamical

systems

complex

ordered

critical

chaotic

simple

Figure 3 A subdivision of dynamical systems in terms ofbehaviour

its component parts (Gallagher amp Appenzeller 1999) Bycontrast simple systems are ones whose properties arefully explained by the properties of their component parts(eg a pendulum) Emergence describes the collectivebehaviour of complex systems It can be local or globalLocal emergent properties are well studied in physicswhere they are often termed lsquointensive propertiesrsquo (egpressure and temperature of an ideal gas) Global emer-gent properties are the more original focus of complexitytheory

Complexity theory aims to understand the origin oforganization In doing so it adopts different modellingmethodologies to those commonly used to study speci csystems For example rather than predicting the dynamicsof a given organization rules of interaction between allpossible objects are speci ed and it is left open whichobjects appear in a given simulation An example of thisapproach is the use of CA Attempts to simulate lsquoAlifersquocommunities and ecosystems are also particularly relevantto Gaia

The relationship between complexity theory and otherdisciplines can be viewed in terms of a behavioural classi- cation of systems ( gure 3) In this case complex sys-tems are a subset of dynamical systems and complexitytheory is part of dynamic systems theory which also con-siders simple systems Complex systems can be subdividedinto ordered systems critical systems and chaotic systemsChaos describes unpredictable behaviour emerging fromnonlinear equations giving high sensitivity to initial con-ditions Order describes a tendency to reside in one stateor limit cycle between a limited number of states Betweenfrozen order and unpredictable chaos much interest hasbeen focused on a critical regime dubbed lsquothe edge ofchaosrsquo Complexity theory can be seen as an extension ofcybernetics (control theory) which focuses on feedbackand feed-forward systems with predictable behaviour Italso encompasses AI and lsquoAlifersquo research By contrastchaos theory focuses on systems with unpredictablebehaviour

This special issue focuses on the subset of CAS A lsquobot-tom-uprsquo de nition of a CAS has been given (Levin 1998)based on three essential elements (i) sustained diversityand individuality of components (ii) localized interactionamong those components and (iii) an autonomous pro-cess that selects from among these components based onthe results of local interactions a subset for replication orenhancement From these essential elements it is argued(Levin 1998) that the following properties (Holland 1995)emerge (1) continual adaptation (2) absence of a globalcontroller (3) hierarchical organization (4) generation of

688 T M Lenton and M van Oijen Gaia as a complex adaptive system

Table 1 Orders of control in complex systems (after Joslashrgensen amp Straskraba 2000)

order scope for adaptation example system discussed in text

rst xed parameters and structure original Daisyworld modelsecond variable parameters xed structure CA Daisyworldthird variable structure and parameters lsquoAlifersquo Guild modelfourth change of goal functions Gaia ()

perpetual novelty and (5) far-from-equilibrium dynamicsCommonly given examples of CASs are cells individualorganisms and ecosystems

What is the typical behaviour of a CAS First they dis-play lsquoself-organizationrsquo in the sense of emergence ofordered behaviour and structure from many parts withsuf cient connections independent of natural selection(Kauffman 1993) The concept was inspired by the resultsof mathematical models which starting from arbitraryinitial conditions and obeying only simple local rules pro-duced large-scale order The second law of thermody-namics forbids true self-organization increasing order isonly possible in thermodynamically open systems Thusself-organization is dissipative requiring free energy inputand producing high-entropy output CASs may also showlsquoself-organized criticalityrsquo (Bak et al 1987) meaning atendency to reside in the edge of chaos regime allowingchange without getting locked into frozen order A power-law distribution of responses is thought to be characteristicof self-organized critical systems but may occur morewidely in nature

Complex systems can be described in terms of theirorder of dynamics and control (Joslashrgensen amp Straskraba2000 table 1) First-order dynamical systems have xedparameters and structure and hence can only achievefeedback control Second-order dynamical systems havevariable parameters as well as states but xed structureThird-order systems have variable structure as well asparameters and states The distinction in fourth-order sys-tems is that changes in states parameters and structurelead to a change in the goal functions that determine thelong-term behaviour of a system (Wilhelm amp Bruggemann2000) How do CASs t into this classi cation Theelement of replication or enhancement indicates that theirstructure is variable allowing third-order control Thegeneration of continual adaptation suggests that CASs arefourth order with internally generated changes in goalfunctions

In what sense are such behaviours adaptive Adaptationhas two common meanings in biology (i) in evolution itis a change in the structure or functioning of organismsthat makes them better suited to their environment and(ii) in physiology it is an alteration in an organismrsquosresponse to its environment Evolutionary adaptation (i) isusually thought of as the consequence of natural selectionacting on heritable variation The capacity for physiologi-cal adaptation (ii) can be the product of evolutionaryadaptation (i) lsquoAdaptiversquo is used in complexity theory todescribe system development as well as response and isoften applied to systems that are not subject to naturalselection as a whole (although their parts may be) Hencelsquoadaptiversquo behaviours described by complexity theoristsare not necessarily lsquoadaptationsrsquo in the sense used by evo-

Phil Trans R Soc Lond B (2002)

lutionary biologists (i) or physiologists (ii) One way outof this semantic mine eld is to consider natural selectionas just one (rather than the only) form of selection Otherforms of selection can emerge at levels above that of natu-ral selection acting on heritable variation eg in the pro-cess of foraging by social insect colonies utilizingpheromone signals (stigmurgy) or in models of the evo-lution of altruism as a consequence of emergent spatialpatterns (Paolo 2000) If selection can be broader thanjust natural selection then there can be lsquoadaptiversquo behav-iours that are not necessarily the product of natural selec-tion

5 IS GAIA A COMPLEX ADAPTIVE SYSTEM

Gaia is a complex system in that it has many interwovenparts and properties that are not fully explained by anunderstanding of the parts for example the stability ofcomponents of the atmosphere Gaia also ful ls the CAScriteria given previously (Levin 1998) as it contains sus-tained diversity and individuality of components (egorganisms) localized interaction among these compo-nents and at least one autonomous selection process(natural selection) Gaia also possesses non-local interac-tion of components because there is global mixing of theatmosphere and oceans This gives rise to globally mixedvariables atmospheric gases with lifetimes longer thanatmospheric mixing (ca 1 yr) and dissolved chemicalspecies in the ocean with lifetimes longer than ocean mix-ing (ca 1000 yr) There are also non-local interactions inthe climate system described as lsquoteleconnectionsrsquo

If Gaia is a CAS we can expect it to display character-istic properties and behaviour Gaia does indeed sharegeneric CAS properties (Holland 1995) far-from equilib-rium dynamics (of life the atmosphere and aspects ofocean chemistry) generation of perpetual novelty(through evolution) hierarchical organization (eg organ-isms ecosystems Gaia) and absence of a global control-ler However non-local interaction simpli es the systemand offers the possibility that from its many complexcomponents Gaia could display emergent simplicity in itsbehaviour In what sense might Gaia be adaptive Gaiahas not evolved by natural selection at the whole systemlevel but various types of selection operate within the sys-tem The system can be viewed physiologically as cap-tured in the term lsquogeophysiologyrsquo (Lovelock 1986) andmay respond to forcing in a manner resembling physio-logical adaptation There is change at the system level andthere may also be developmental trends that enhance lifeas a whole eg an increase global gross primary pro-ductivity with time

Is Gaia self-organizing It is often said that Gaia is self-regulating but what order of control (table 1) is actually

Gaia as a complex adaptive system T M Lenton and M van Oijen 689

achieved There are many examples of rst-order feed-back control (examples in sect 3) Gaia also contains evo-lution which continually reshapes the system and thusallows higher levels of system control The evolution ofresponses to prevailing environmental conditions and theevolution of environment-altering traits represent changesin the parameters and structure of the system allowing forsecond- and third-order control For example the coloniz-ation of the land surface by vascular plants altered the cli-mate in a self-bene cial manner (Betts 1999) and led toa reorganization of biogeochemical cycles including adrop in carbon dioxide (Berner 1998) global cooling anda rise in oxygen (Lenton 2001) Changes in the Earthrsquoshistory such as the switch from anaerobic to aerobic con-ditions as oxygen rose ca 2 Gyr ago and the resultingincrease in free-energy availability to the biota could beviewed as fourth-order control a change in goal functionfrom an anaerobic lsquoupside-downrsquo biosphere (Walker1987) to an aerobic attractor state that allowed the pro-liferation of new types of life Thus Gaia may be viewedas self-organizing and more in terms of the levels of con-trol achieved

Is Gaia in a self-organized critical state If one contraststhe current state of Gaia with that of Mars or Venus orthe suggested lsquosnowball Earthrsquo state Gaia is more com-plex and less lsquofrozenrsquo into order (of course Mars is literallyfrozen as would be the snowball Earth) It has been sug-gested that the Earthrsquos biota is in a self-organized criticalstate on the basis that extinction events have a distributionclosely approximated by a power law (Kauffman 1993)Proponents of complexity theory propose that the majorityof all extinction events are internally generated by thedynamics of coevolution of species If so this would indi-cate criticality of the biota but not necessarily criticalityof Gaia An alternative hypothesis is that the majority ofextinction events are caused by external perturbation Inthe case of mass extinctions there is good evidence for acausative asteroid impact at the CretaceousndashTertiaryboundary 65 Myr ago (Alvarez et al 1980) Simple mod-els of coevolution (Bak amp Sneppen 1993) or of environ-mental stress (Newman 1997) (without speciesinteraction) as the cause of extinction both exhibit apower law Of the two the environmental stress modelhas an exponent much closer to actual data We concludethat although some extinction may result from coevo-lution there is not yet a convincing case that the biota isin a critical state To test whether Gaia is in a critical statea frequency response analysis of environmental recordsmight be more appropriate For example the carbondioxide and methane records in the Vostok ice core(Petit et al 1999)

6 EMERGENCE OF GAIA

Complexity theory stimulates us to search for a com-plexity threshold for a planet with life beyond which theemergence of self-organization (including self-regulation)and adaptive behaviour becomes likely in other wordsa planetary analogue for the emergence of auto-catalyticnetworks (Kauffman 1993) In coupled open systems oflife and environment does self-organization become vastlymore probable beyond a critical lsquosizersquo (eg number of

Phil Trans R Soc Lond B (2002)

organisms) Also can we pinpoint a particular time in theEarthrsquos history when Gaia emerged

Once life arose it must soon have depleted its surround-ings of substrates thus posing a pressing need for recy-cling Key biogeochemical transformations of essentialelements are present deep in the tree of life among theancient kingdoms of archaea and bacteria supporting aview that nutrient recycling evolved early One furtherrequirement is important for the emergence of planetaryscale self-organization in order to achieve global signi -cance life must have an abundant source of free energyThe earliest types of photosynthesis used relatively scarcesubstrates such as H2S Once oxygenic photosynthesisemerged using the abundant H2O as a substrate then the ux of free energy captured by the biota increased mas-sively (DesMarais 2000) Thus we suggest the genesis ofGaia came with the origin of widespread oxygenic photo-synthesis This occurred at least 28 Gyr ago (DesMarais2000) and possibly as early as 38 Gyr ago (Schidlowski1988)

A remarkable property of Gaia that demands an expla-nation is that its abiotic state variables have stayed at lev-els that support abundant life for most of the last 38 GyrEarly strong versions of the Gaia hypothesis suggestedthat all life-forbidding state variable levels are unreachablebecause there is selection against the processes that wouldlead there Selection at the level of the system as a wholeseems untenable (Doolittle 1981 Dawkins 1983) How-ever it may still be the case that life-forbidding state-vari-able levels are dif cult to reach for at least two reasons(i) if an organism is driving an environmental variabletowards an uninhabitable state its growth and spread willbe suppressed (by negative feedback) such that the systemwill stabilize within the habitable regime and (ii) when-ever organisms become so abundant that the side-effectsof their metabolism become life-threatening on a globalscale different organisms will evolve for which the abun-dant pollutants and the polluters themselves becomeresources If natural selection has enough substrate(genotypic variation) on which to operate such checksand balances are always likely to evolve and make extremeconditions unreachable This old idea (originating fromSmith 1776) could explain the likelihood of regulation atliveable levels as a side-effect of evolution in suf cientlydiverse biota

Uninhabitable or barely habitable states (with life inrefugia) can be reached because of global scale environ-mental perturbation eg massive asteroid impact (Watson1999) or extreme external forcing eg future increases insolar luminosity (Lovelock amp Whit eld 1982 Lenton ampVon Bloh 2001) It is also possible that the evolution ofparticularly strong biotic effects could lsquoovershootrsquo anddrive the environment into a barely habitable stateespecially if there is a time-delay in self-limiting negativefeedback (this is a counter argument to (i) above) Fur-thermore variables that cannot function as a resource toany organism may be able to build up to toxic levels (acounter argument to (ii) above) However useless anddangerous waste products may generally kill off their pro-ducers before disrupting the functioning of Gaia as awhole

Gaia has suffered massive perturbations (asteroidimpacts) and lsquosnowball Earthrsquo states may have occurred

690 T M Lenton and M van Oijen Gaia as a complex adaptive system

in which life only hung on in refugia However abundantlife has always reappeared sometimes remarkably quickly(DrsquoHondt et al 1998) New types of life appear in thewake of mass extinction but there is also a system lsquomem-oryrsquo carried in the gene pool This suggests an interestingpossibility if in response to perturbation a new traitevolves that contributes to recovery then if it remains inthe gene pool and a similar perturbation occurs again thesystem may recover faster the second time In this senseGaia may gain from experience

7 SIMULATING PLANETARY SCALE EMERGENCEWITH DAISYWORLDS

The persistence of life and recovery of Gaia from per-turbation suggest that self-regulation occurs We wouldlike to know how it can emerge and whether it is a chanceor a highly probable outcome of lifendashenvironment coup-ling The feasibility and probability of the emergence ofplanetary scale lsquoself-organizationrsquo andor lsquoadaptive behav-iourrsquo can be evaluated using a synthetic approach of math-ematical modelling

The rst such attempt to simulate the emergence ofplanetary scale self-regulation was the Daisyworld model(Watson amp Lovelock 1983) In Daisyworld global tem-perature regulation emerges automatically from feedbackcoupling between life and its environment with selectionat the component (individual organism) but not the sys-tem (whole planet) level In Daisyworld the environmentis reduced to one variable temperature and life is reducedto two types black and white daisies inhabiting bareground The daisies share the same optimum temperaturefor growth of 225 degC and outer limits to growth of 5 degCand 40 degC The daisy types affect their environment inopposite ways by virtue of their different re ectivity(albedo) The white daisies re ect more solar radiationthan bare ground whilst the black daisies absorb moreHence the local temperature of the daisies differs blackdaisies are always warmer and white daisies are alwayscooler than bare ground The system is forced by a gradualincrease in solar luminosity as has occurred on the Earth

With only one type of daisy present there is a range offorcing for which negative feedback occurs and a point atwhich positive feedback occurs In the case of black daisiesonly when they can establish their spread is ampli ed bypositive environmental feedback (similar to gure 2c butthe effect of life on the environment is stronger) As lumi-nosity increases the population of black daisies declinesthus providing negative feedback on temperature In thecase of white daisies only when they can germinate theirspread is immediately suppressed by their cooling effectAs luminosity increases their population increases pro-viding negative feedback on temperature A regime isentered where white daisies maintain the planet in a habit-able state when otherwise it would be uninhabitable( gure 2d) Eventually they collapse catastrophically withpositive feedback With both types of daisy present thereis a range of forcing for which global temperature actuallydecreases as forcing increases This is an example oflsquosuper-negativersquo feedback (the sign of response is oppositeto that of the forcing (Sardeshmukh 2000))

The Daisyworld model has been portrayed as a CAS(Lewin 1993) but this deserves closer examination It

Phil Trans R Soc Lond B (2002)

possesses rst-order feedback control (table 1) and theregime of super-negative feedback was unexpected fromits parts However the original model does not explicitlyinclude interacting local components The system isdescribed by coupled equations and its behaviour can beunderstood analytically (Saunders 1994 Weber 2001)

If time-delays are introduced into the population andtemperature equations of Daisyworld then apparentlychaotic behaviour can be generated (Zeng et al 1990)Varying the time-delay reveals a series of period doublingscharacteristic of the transition from order to deterministicchaos (De Gregorio et al 1992ab) There is no real-worldjusti cation for the time-delays and it has been shownthat the average of the lsquochaoticrsquo solutions is close to thetemperature regulation in the original model (Jascourt ampRaymond 1992) Introducing an unrealistically large heatcapacity to Daisyworld generates limit cycle oscillations ofthe two daisy populations and temperature (Nevison et al1999) (ie generates the rst period doubling) Thesestudies show that the original Daisyworld model resideswell into the ordered regime and is not in a critical state

Subsequent versions of Daisyworld arguably show theemergence of higher-order control (although the nal prop-erty of temperature regulation is similar in each case)Variants of the model with adaptation of the optimumgrowth temperature of the daisies (Robertson amp Robinson1998 Lenton amp Lovelock 2000) include alteration ofparameters but this is enforced through further para-meters A more fully second-order control system is a Dai-syworld with random mutation of daisy albedo (some ofthe parameters) and subsequent selection (Lenton 1998Lenton amp Lovelock 2001) The structure of this modelcould be said to change in that new daisy lsquospeciesrsquo appearThis suggests there may be some third- and fourth-ordercontrol

8 CA DAISYWORLDS

To ful l the CAS criteria models must include localinteraction of components CA provide a tool for thisHence we have followed the lead of others (Von Bloh etal 1997) and constructed a CA version of Daisyworld toexplore the effects of local interaction and the capacity foradaptive system behaviour The original equations(Watson amp Lovelock 1983) are retained where possibleThe CA grid and rules are simply used to replace thepopulation equations We consider a square grid witheight neighbours to each cell rather than four nearestneighbours (Von Bloh et al 1997) There is no diffusivetemperature eld just the original equations for local tem-peratures of daisies (determined by albedo global tem-perature and insulation parameter q) and globaltemperature (determined by average albedo of the systemand luminosity forcing) Seeding is used to enable popu-lations to establish (but once they are established it haslittle impact) First we consider the original case of popu-lations of lsquoblackrsquo (albedo aB = 025) and lsquowhitersquo (albedoaW = 075) daisies covering bare ground (albedo aG = 05)For an empty cell with nB black neighbours each withgrowth rate b B and nW white neighbours each with growthrate b W the following colonization rules apply

The probability that black will colonize when only theyare present is

Gaia as a complex adaptive system T M Lenton and M van Oijen 691

P(B|nW = 0) = 1 2 (1 2 b B)nB (81)

The probability that white will colonize when only theyare present is

P(W|nB = 0) = 1 2 (1 2 b W )nW (82)

The probability that the cell remains empty is

P(E) = (1 2 P(B|nW = 0))(1 2 P(W|nB = 0)) (83)

The probability that black will colonize when both arepresent is

P(B) = (1 2 P(E))P(B|nW = 0)

P(B|nW = 0) 1 P(W|nB = 0) (84)

The probability that white will colonize when both arepresent is

P(W) = (1 2 P(E))P(W|nB = 0)

P(B|nW = 0) 1 P(W|nB = 0) (85)

The probability of seeding an empty cell is xed

P(S) = h ( h = 0001 in the results shown) (86)

The probability of death at an occupied cell is also xed

P(D) = g ( g = 03 as in the original model) (87)

The 2D CA model has less smooth dynamics than theoriginal zero-dimensional model in that it can exhibitbifurcations and limit cycling ( gure 4) The growth equa-tions are such that for one type alone ( gure 4ac) it canreach carrying capacity on the grid even when its localtemperature and growth rate are sub-optimal This isbecause the presence of many identical neighbours canmake colonization of an empty cell highly probable evenwhen growth rate is suppressed by temperature (equations(81) or (82)) For black daisies alone ( gure 4ab) asforcing is increased a bifurcation point is reached wherethe global temperature is such that the local temperatureof black daisies becomes uninhabitable (b B = 0 when thetemperature of black daisies TB = 40 degC) This generatespartial collapse (ca 30 die-back of the daisies) immedi-ate recovery and resulting oscillations of temperature andpopulation As forcing is increased further a second bifur-cation point is reached Then the trajectories combinebefore the black daisies disappear For white daisies alone( gure 4cd) there are two period doublings and thebeginnings of a third (inset in gure 4d) before a returnto a single trajectory

The one daisy-type model illustrates an lsquoovershootrsquoproblem for Gaia life may develop the capacity to drivean environmental variable into an uninhabitable or barelyhabitable state if the environmental effect is strong andlocal interactions that encourage growth outweigh nega-tive feedback on growth from the environment The modeldoes not include natural selection in that all the daisiesare identical and are always equally t in terms of growthrate (although in the initial growth phase clusters formand cells at the edge of clusters are better able to spreadthan those within clusters) The model does include a sys-tem selection process between bare ground and one daisytype under a certain range of forcing daisies are selectedover bare ground outside that range bare ground willsuccessfully take over from daisies

Phil Trans R Soc Lond B (2002)

When black and white types can both arise the limitcycle regimes are removed and the solution resembles theoriginal zero-dimensional model ( gure 4ef ) The twodifferent daisy types have different growth rates and hence tness thus adding a crude form of natural selection tothe model (although there is no evolution) With thisadditional selective process the model stays more rmlyin the ordered regime The system is stabilized by at leastthree effects (i) if one daisy type reaches an uninhabitabletemperature the other may still be able to spread (becausetheir local temperatures differ) (ii) in the mid-range offorcing a combination of black and white generates a glo-bal temperature closer to optimal and (iii) the presenceof one daisy type reduces the area available to the otherto expand into

We have introduced random mutation of albedo to themodel generalizing the colonization equations (81)ndash(85)to deal with any albedo type Mutation is assumed alwaysto occur in the process of colonization of an empty cell(asexual reproduction that always generates mutatedoffspring) Albedo can mutate within a parameterizedwidth of the parent albedo (plusmn D a) Within this rangeeither side of the parent albedo an offspring albedo is ran-domly chosen Limits to mutation are set at am in = 0 andam ax = 1

With mutation and natural selection within the modelsystem ( gure 5) its behaviour could be said to be lsquoadap-tiversquo in that it lsquoevolvesrsquo to counteract forcing When themodel is seeded with the original lsquoblackrsquo daisies(aB = 025) and these are allowed to mutate as forcingincreases progressively paler daisies evolve cooling theplanet and then maintaining the temperature close to con-stant Increasing D a brings the average planetary tempera-ture more rapidly towards the optimum for daisy growthThe tendency for bifurcation ( gure 4a) is removed byincreasing D a ( gure 5) because this tends to generate anearly increase in average albedo In a sensitivity analysisof the stabilizing effect of albedo diversity am ax ndash am in wasprogressively increased around a central value ofaB = 025 without any mutation and this was also foundto remove the bifurcations Albedo mutation extends therange of temperature regulation beyond that in the originalmodel because paler types than the original lsquowhitersquo onescan arise The latter result has been found in other vari-ants of Daisyworld (Stocker 1995 Von Bloh et al 1997Lenton amp Lovelock 2001)

A more complex 2D CA version of Daisyworld has pre-viously been formulated with albedo mutation and a con-tinuous temperature eld (Von Bloh et al 1997) Thissystem exhibits the remarkable property that underenforced habitat fragmentation using a percolating fractalthe system is able to regulate temperature unimpaired upto a lsquocriticalrsquo threshold at which daisy areas become iso-lated and regulation starts to break down Once uninhabi-ted land forms a spanning cluster regulation is completelyremoved By contrast trivial reductions in habitat (eg agrowing square of lsquoconcretersquo) impair temperature regu-lation in a linear fashion In the former case adjacent dai-sies can affect the temperature of small uninhabited areasbut overall temperature regulation depends on compe-tition among daisies across an entire connected space Inother words the emergent property of global temperatureregulation relies on uninhibited local interaction tting

692 T M Lenton and M van Oijen Gaia as a complex adaptive system

100

50

0

80

60

40

20

0

plusmn20

100

50

0

100

50

0

80

60

40

20

0

plusmn20

80

60

40

20

0

plusmn20

05 10 15 20

05 10 15 20

05 10 15 20 05 10 15 20

05 10 15 20

05 10 15 20

solar luminosity (_) solar luminosity (_)

solar luminosity (_) solar luminosity (_)

solar luminosity (_) solar luminosity (_)

gri

d c

over

(

)g

rid

cov

er (

)

gri

d c

ov

er (

)

glo

bal

tem

per

ature

(degC

)g

lob

al t

emp

erat

ure

(degC

)g

lob

al t

emper

atu

re (

degC)

15

plusmn508 11

(a) (b)

(c) (d)

(e) ( f )

Figure 4 Simulations of xed albedo populations in a simple CA Daisyworld (64 acute 64 grid) Parameters are as in the originalmodel (Watson amp Lovelock 1983) and the CA rules are described in sect 8 Solar luminosity (in normalized units) is increased insteps of 0004 at each of which the model is updated The left-hand graphs show percentage grid cover by the daisies versusluminosity and the right-hand graphs show global average temperature (degC) versus luminosity Temperature is a function ofluminosity and the albedo a and grid cover of daises and empty cells (ab) Seeding with lsquoblackrsquo daisies (aB = 025) denotedby lled circles (cd) Seeding with lsquowhitersquo daisies (aW= 075) denoted by open circles (ef ) Seeding with both black and whitedaisies (albedo of each seed chosen at random) The inset in (d ) shows the period doubling in the temperature trajectory withonly white daisies

in nicely with the criteria for a CAS The system is self-organizing and may arguably be in a critical state near thelimit at which daisy areas become disconnected

9 FEASIBILITY TESTS OF GAIA USING lsquoALIFErsquo

A key criticism of Daisyworld is that it is limited in onlyconsidering one predetermined type of interactionbetween the local and the global and it is one that will

Phil Trans R Soc Lond B (2002)

tend to generate regulation The daisies affect theirenvironment in the same way at the local and the globalscale Hence what is selected for at the individual leveltends to be bene cial at the global level With two or moredaisy types present there is negative selective feedbackmaking regulation likely (Lenton 1998)

lsquoAlifersquo techniques offer a promising way of makingunbiased tests of the potential for emergence of planetaryscale self-organization The model environment lsquoTierrarsquo

Gaia as a complex adaptive system T M Lenton and M van Oijen 693

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

0

20151005

solar luminosity (ndash)

grid

cov

er (

)

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

(a) (b)

(c)(d)

( f )(e)

Figure 5 CA Daisyworld simulations with albedo mutation (64 acute 64 grid) In each simulation there is seeding with theoriginal lsquoblackrsquo daisies (aB = 025) which fall in the range coloured in blue The model is updated with each increase in solarluminosity of 0004 normalized units and at each update empty cells can be colonized with offspring cells that differ at mostby plusmn D a from the albedo of their parent cell Left- and right-hand graphs show grid cover by daisy populations () and globalaverage temperature (degC) respectively The albedo colour scheme in the left-hand graphs is 0ndash02 black 02ndash04 blue 04ndash06 green 06ndash08 orange 08ndash10 red The graphs show the effect of increasing mutation range (ab) D a = 001 (cd) D a =002 (ef ) D a = 01

(Ray 1991) evolved a community of arti cial life-formsthat reproduce in different ways including parasiticallyThe model lsquolife-formsrsquo compete for resource (processortime) but they do not produce waste products Hencetheir interaction with their environment is not thermody-namically complete in the way that it is for real life-formswhich can only maintain an ordered (low entropy) stateby transforming matter as well as energy

The evolution of matter recycling is addressed usinglsquoAlifersquo techniques in the Guild model (Downing amp Zvirin-sky 1999) From one ancestral lsquospeciesrsquo a communityevolves which is able to recycle a given set of lsquochemicalsrsquo(which can be thought of as different molecular forms ofthe same key nutrient element) Such recycling enablesgreatly enhanced productivity in real ecosystems and Gaia

Phil Trans R Soc Lond B (2002)

(Volk 1998) The mechanism of emergence of recyclingis quite different from the spontaneous emergence of auto-catalytic cycles in systems of very large numbers of chemi-cal reactions (Kauffman 1993) In the Guild model lsquoAlifersquochances upon closed recycling of a small set of chemicalsand this is reinforced by selection This illustrates part ofthe mechanism (ii) that we highlighted in sect 6

The main criticisms of the original Guild model are thatthere is no treatment of energy in the system and that adeviation of the local environment from the global isassumed that may not be justi ed for some real world ana-logues A lsquoGuild IIrsquo model is being developed (K Down-ing personal communication) that includes free energyand entropy in the abstract chemistry (eg it takes freeenergy to build larger molecules) and makes the local

694 T M Lenton and M van Oijen Gaia as a complex adaptive system

environment the interior of proto-cells In this modeldespite a relatively small input of free energy in chemicalform recycling and regulation can emerge

An ideal model world for testing Gaia would containarti cial life-forms that transform lsquomatterrsquo and lsquoenergyrsquoare lsquothermodynamicallyrsquo constrained grow and replicatewith a heritable genome subject to random mutationinteract with one another and evolve new ways of alteringtheir environment related to their internal functioningThe environment would contain many lsquophysicalrsquo andlsquochemicalrsquo variables some homogeneous (well mixed) andothers heterogeneous The resulting system behaviourwould be observable and testable by perturbation

10 CONCLUSIONS

Many scientists now accept that planetary regulationinvolving the biota occurs (Longhurst 1998) However westill have to determine whether Gaiarsquos coming into exis-tence and survival was coincidental or probable and howfragile or robust the system is at present We have arguedthat Gaia is a complex system with self-organizing andadaptive behaviour but that it does not reside in a criticalstate Complexity theory modelling approaches havehelped us simulate and understand the emergence of plan-etary order lsquoAlifersquo techniques can take this further andhelp in assessing the probability of emergence of planetaryregulatory properties Our attempts to apply complexitytheory to Gaia have yielded a broader view of selectionthan previously encompassed in the Gaia theory (Lenton1998) Gene-based natural selection is just one type andlevel of selection operating within Gaia and it is not anecessary condition for regulation The existence of differ-ent types of selection operating at different levels makes iteasier to understand how planetary-scale self-regulationcan arise It also makes it easier to accept that a Gaia-likesystem may be a probable outcome once there is abundantlife on a planet with the capacity for large-scale freeenergy capture

We thank Ricard Sole and Simon Levin for the invitation towrite this article

REFERENCES

Alvarez L W Alvarez W Asaro F amp Michel H V 1980Extraterrestrial cause for the CretaceousndashTertiary extinctionScience 208 1095ndash1108

Bak P amp Sneppen K 1993 Punctuated equilibrium and criti-cality in a simple model of evolution Phys Rev Lett 714083ndash4086

Bak P Tang C amp Wiesenfeld K 1987 Self-organized criti-calitymdashan explanation of 1f noise Phys Rev Lett 59381ndash384

Berner R A 1998 The carbon cycle and CO2 over Phanero-zoic time the role of land plants Phil Trans R SocLond B 353 75ndash82 (DOI 101098rstb19980192)

Betts R A 1999 Self-bene cial effects of vegetation on cli-mate in an oceanndashatmosphere general circulation modelGeophys Res Lett 26 1457ndash1460

Bonan G B Pollard D amp Thompson S L 1992 Effects ofboreal forest vegetation on global climate Nature 359716ndash718

Budyko M I 1968 The effect of solar radiation variations onthe climate of the Earth Tellus 21 611ndash619

Phil Trans R Soc Lond B (2002)

Dawkins R 1983 The extended phenotype Oxford UniversityPress

De Gregorio S Pielke R A amp Dalu G A 1992a Feedbackbetween a simple biosystem and the temperature of theEarth J Nonlinear Sci 2 263ndash292

De Gregorio S Pielke R A amp Dalu G A 1992b A delayedbiophysical system for the Earthrsquos climate J Nonlinear Sci2 293ndash318

DesMarais D J 2000 When did photosynthesis emerge onEarth Science 289 1703ndash1705

DrsquoHondt S Donaghay P Zachos J C Luttenberg D ampLindinger M 1998 Organic carbon uxes and ecologicalrecovery from the CretaceousndashTertiary mass extinctionScience 282 276ndash279

Doolittle W F 1981 Is nature really motherly The CoEvol-ution Q Spring 58ndash63

Downing K amp Zvirinsky P 1999 The simulated evolutionof biochemical guilds reconciling Gaia theory and naturalselection Artif Life 5 291ndash318

Ehrlich P 1991 Coevolution and its applicability to the Gaiahypothesis In Scientists on Gaia (ed S H Schneider amp PJ Boston) pp 118ndash120 London MIT Press

Gallagher R amp Appenzeller T 1999 Beyond reductionismScience 284 79

Hamilton W D 1995 Ecology in the large Gaia and GenghisKhan J Appl Ecol 32 451ndash453

Hamilton W D 1996 Gaiarsquos bene ts New Scientist 15162ndash63

Hamilton W D amp Lenton T M 1998 Spora and Gaia howmicrobes y with their clouds Ethol Ecol Evol 10 1ndash16

Han T-M amp Runnegar B 1992 Megascopic eukaryotic algaefrom the 21 billion-year-old Negaunee iron-formationMichigan Science 257 232ndash235

Hoffman P F Kaufman A J Halverson G P amp SchragD P 1998 A Neoproterozoic snowball earth Science 2811342ndash1346

Holland J 1995 Hidden order how adaptation builds complexityReading MA Addison-Wesley

Hyde W T Crowley T J Baum S K amp Peltier W R2000 Neoproterozoic lsquosnowball Earthrsquo simulations with acoupled climateice-sheet model Nature 405 425ndash429

Imshenetsky A A Lysenko S V amp Kazakov G A 1978Upper boundary of the biosphere Appl Environ Microbiol35 1ndash5

Isaacs A Daintith J amp Martin E (eds) 1996 Concise sciencedictionary Oxford University Press

Jascourt S D amp Raymond W H 1992 Comments on lsquoChaosin daisyworldrsquo by X Zeng et al Tellus 44B 243ndash246

Joslashrgensen S E amp Straskraba M 2000 Ecosystems as cyber-netic systems In Handbook of ecosystem theories and manage-ment (ed S E Joslashrgensen amp F Muller) pp 249ndash264London Lewis Publishers

Kasting J F 1991 Box models for the evolution of atmo-spheric oxygen an update Global and Planetary Change 97125ndash131

Kauffman S A 1993 The origins of order self-organization andselection in evolution Oxford University Press

Kleidon A 2002 Testing the effect of life on Earthrsquos func-tioning how Gaian is the Earth system Climatic Change 52383ndash389

Klinger L F 1991 Peatland formation and ice ages a possibleGaian mechanism related to community succession InScientists on Gaia (ed S H Schneider amp P J Boston) pp247ndash255 London MIT Press

Koeslag J H Saunders P T amp Wessels J A 1997 Glucosehomeostasis with in nite gain further lessons from theDaisyworld parable J Endocrinol 154 187ndash192

Lenton T M 1998 Gaia and natural selection Nature 394439ndash447

Gaia as a complex adaptive system T M Lenton and M van Oijen 685

face has remained habitable for more than 385 Gyr(Mojzsis et al 1996) The relatively stable organic carboncontent and isotopic composition of the crust indicate thatlife has been abundant for most of the past 38 Gyr(Schidlowski 1988) Life has been invoked to explainmany of the Earthrsquos remarkable physical and chemicalproperties The abundance of oxygen in the presentatmosphere is almost entirely a biological product Atmo-spheric oxygen has increased in a stepwise fashion frompO2 0002 atm more than 22 Gyr ago and has beensuf cient to support eukaryotes (pO2 001 atm) for atleast the last 2 Gyr (Han amp Runnegar 1992) The stabilityof O2 over the past 350 Myr has enabled the continuouspersistence of large metazoa (requiring O2 ca 015 atm)and slowly regenerating trees (requiring O2 ca 03 atm)(Lenton amp Watson 2000b) The scarcity of carbon dioxidein the atmosphere and consequent cooling of the planetis due to biologically ampli ed silicate rock weatheringwhich drives the dominant sink in the long-term carboncycle (Lovelock amp Watson 1982 Schwartzman 1999)Within Gaia there is greatly enhanced cycling of matterespecially of the elements essential to life For examplephosphorus is cycled an average of 46 times through aterrestrial ecosystem before being lost to the ocean whereit is cycled an average of 280 times before being nallyburied in new rocks (Volk 1998) Return of water to theatmosphere is increased approximately three times by thepresence of vascular plants on the land surface (Betts1999 Kleidon 2002) These recycling effects greatlyincrease global gross primary productivity (Volk 1998Kleidon 2002)

3 GAIA THEORY

The Gaia theory seeks to explain the remarkable proper-ties of the system just described especially its far-from-equilibrium ordered state dynamic stability habitability ourishing of life and pattern of change over time(Lovelock 1988 Lenton 1998) From the outset Gaia hasbeen viewed as a cybernetic (feedback control) system(Lovelock amp Margulis 1974) The essential elements ofthe theory are (i) life affects its environment all organ-isms alter their environment by taking in free energy andexcreting high-entropy waste products in order to main-tain a low internal entropy (Schrodinger 1944) (ii) growth(including reproduction) organisms grow and multiplypotentially exponentially (iii) environment constrains lifefor each environmental variable there is a level or rangeat which growth of a particular organism is maximizedand (iv) natural selection once a planet contains differenttypes of life (phenotypes) with faithfully replicated heri-table variation (genotypes) growing in an environment of nite resources natural selection determines that the typesof life that leave the most descendants come to dominatetheir environment

The overall behaviour of Gaia is governed by a combi-nation of positive and negative feedback Positive feedbacktends to add to change while negative feedback tends tocounteract change Growth is intrinsically a positive feed-back process (the more life there is the more life it canbeget) The growth of life drives lifersquos effects on itsenvironment to become global in scale The extreme ther-modynamic disequilibrium of the Earthrsquos atmosphere

Phil Trans R Soc Lond B (2002)

biotic

abiotic

environmental

feedback

selection

growth

Figure 1 A subdivision of types of environmental feedback

indicates that this has occurred The fact that life altersits environment and is also constrained by it means thatenvironmental feedback is inevitable Environmental feed-back arises at the local level (eg due to the evolution ofenvironment-altering traits) With growth environmentalfeedback has the potential to become global in scale Thetypes of environmental feedback can be classi ed in a hier-archy (Lenton 1998)

The rst distinction is between abiotic and biotic feed-back to the environment ( gure 1) The response of lifeto a particular environmental variable includes habitabilitybounds for the organisms in question whereas abioticresponses have no automatic correlation with what is hab-itable for life Abiotic responses to a particular environ-mental variable are typically simple increasing ordecreasing functions ( gure 2ab) If they also affect thevariable in question then either negative feedback or posi-tive feedback will result Negative abiotic feedback ( gure2a) can stabilize the environment in either a habitable oran uninhabitable state Positive abiotic feedback ( gure2b) can drive the environment into an uninhabitable statealthough in many cases it is not suf ciently strong to doso By contrast organisms tend to have a peaked growthresponse to many environmental variables ( gure 2cd) Ifthey also affect a particular environmental variable thenthe resulting system will have both negative and positivefeedback regimes either side of the optimum for growthand for a range of forcing it will by de nition tend to sta-bilize in a habitable state For a weak biotic effect on theenvironment ( gure 2c) the stable state can be in eitherthe negative or the positive feedback regime For a strongbiotic effect on the environment ( gure 2d) the systemwill tend to transit the positive feedback regime and stabil-ize in the negative feedback regime For some forcing (eg gure 2d) multiple solutions can occur such that life main-tains the environment in a habitable state when otherwiseit would be uninhabitable If the system is forced beyondthe unstable solution in the positive feedback regime thenlife will collapse catastrophically

Biotic environmental feedback can be subdivided( gure 1) into feedback on growth and feedback on selec-tion (Lenton 1998) Non-selective feedback on growthoccurs when the effect of a trait on the environment altersthe growth rate of the organisms carrying it but theenvironmental alteration is a side-effect of the trait thatdoes not hamper its selective advantage Feedback onselection occurs when the effect of a trait on the environ-ment alters the forces of selection determining its value

An important example of negative feedback on growth( gure 2d) is that resulting from plant-induced ampli -cation of rock weathering This inadvertently tends to

686 T M Lenton and M van Oijen Gaia as a complex adaptive system

environment variable (E) environment variable (E)

environment variable (E)environment variable (E)

abio

tic

var

iable

(A

)ab

ioti

c v

aria

ble

(A

)

life

var

iable

(L

)li

fe v

aria

ble

(L

)

E = f (A) A = f (E)

E = f (L)

L= f (E)

L= f (E)

E = f (L)

A = f (E)

E = f (A)

(a)

(b)

(c)

(d )

Figure 2 General representations of types of environmental feedback for xed forcing (a) abiotic negative feedback (b)abiotic positive feedback (c) weak biotic feedback and (d) strong biotic feedback Large open circles indicate stable statesSmall lled circles indicate unstable states The arrows indicate the general direction of change for starting states withineach regime The schematic diagrams are loosely based on the following global cases described in more detail in the text(a) abiotic silicate weathering rate and temperature (b) ice cover and temperature (c) boreal forest cover and temperature(d) growth rate of rock weathering organisms and temperature

decrease atmospheric CO2 and cool the planet DecliningCO2 and cooling below optimum growth temperaturetend to suppress plant growth closing the feedback loopRock weathering traits are probably selected for as ameans of acquiring rock-bound nutrients (especiallyphosphorus) and changes in CO2 and temperature do notaffect this requirement or the resulting selection (It ismore likely that local build-up of phosphorus in soil woulddo that) The feedback from changing CO2 and tempera-ture is very slow and requires a global spread of the traitover many generations before it affects growth Howeverit is key to the long-term regulation of atmospheric CO2

and temperature and can thus be bene cial to plantgrowth in the long term In particular it counteractsincreasing solar luminosity that could otherwise drive theEarthrsquos surface temperature above optimal levels Someabiotic negative feedback ( gure 2a) would exist in aworld without life but with tectonics and a hydrologicalcycle (Walker et al 1981) However rock-weatheringorganisms greatly strengthen the feedback (Lovelock ampWatson 1982 Schwartzman amp Volk 1989) They maythus extend their own future persistence on Earth(Lenton amp Von Bloh 2001)

An example of positive feedback on growth ( gure 2c)is that resulting from the dark snow-shedding foliage oftrees in the boreal forest By absorbing solar radiation thetrees are warmed (especially relative to snow cover) andtheir growth is enhanced This warms their surroundingsthus further enhancing growth (Bonan et al 1992) Thepositive feedback is constrained in that temperatures inthe boreal regions remain below the optimum for growthfor much of the year but they are increased such that

Phil Trans R Soc Lond B (2002)

forest is able to persist over large regions that would other-wise be too cold for growth (Betts 1999)

An example of negative feedback on selection is thatresulting from nitrogen xation in the worldrsquos oceansmany terrestrial ecosystems and some freshwater lakesNitrogen xation is an energetically demanding processwhich will only be selected for when there is a lack ofavailable nitrogen relative to other potentially growth-lim-iting nutrients By xing nitrogen the responsible organ-isms ultimately increase the amount of nitrogen availablein their environment for non-nitrogen- xers Thisremoves the selective advantage of being a nitrogen xerand hence the proliferation of nitrogen xation is self-lim-ited This mechanism regulates the nitrate content of theworldrsquos oceans relative to the phosphate content in a pro-portion close to organismsrsquo requirements (Red eld 1958Lenton amp Watson 2000a)

An example of positive feedback on selection is thatresulting from the ability of sphagnum moss to acidify soilThis environmental change gives the moss a selectiveadvantage relative to other potential invading plants andencourages succession to a peat bog (Klinger 1991Hamilton 1996) There are probably other self-limiting(negative) feedbacks on bog growth given that we do notlive in a world dominated by peat bogs (although theauthors live in a country dominated by them) Interest-ingly examples of positive feedback on selection tend tobe more localized than examples of negative feedbackon selection

One of the possible fates for Gaia is for abiotic positivefeedback ( gure 2b) to take the planet into an uninhabit-able or barely habitable state In the ice-albedo positive

Gaia as a complex adaptive system T M Lenton and M van Oijen 687

feedback effect snow and ice form surfaces that are highlyre ective (high albedo) to solar radiation thus coolingtheir surroundings and encouraging the spread of snowicecover In simple models a modest reduction in solar inputis ampli ed by this feedback to cause complete ice coverof the Earth (Budyko 1968 Sellers 1969) the so-calledlsquosnowball Earthrsquo (Hoffman et al 1998) Recent simula-tions suggest that a lsquoslushball Earthrsquo state with open waterin equatorial oceans may be more realistic and less fatalto life (Hyde et al 2000) If a snowball Earth attractorexists it should be unstable because CO2 input from vol-canoes can gradually accumulate in the atmosphere untilradiative forcing is suf cient to melt continental ice cover

A key challenge to Gaia theory from evolutionary biol-ogists is to explain how order especially self-regulationcan arise at the global scale without invoking teleology orselection at the level of the planet (Doolittle 1981 Daw-kins 1983) Such criticisms inspired the formulation of theDaisyworld model (Lovelock 1983 Watson amp Lovelock1983) which demonstrates that self-regulation canemerge automatically from competing populations alter-ing their local environments in different ways (see sect 7 andsect 8) The idea that evolution within Gaia could have pro-duced organisms that contribute to regulating the planetis still variously criticised as untenable altruism vulnerableto cheats or demanding large-scale group selection(Hamilton 1995) It is sometimes argued that randomvariation and natural selection are necessary and suf cientto explain the self-regulation of organisms and candidatesuper-organisms (eg temperature regulated social insectcolonies Ehrlich 1991) in which case self-regulation ofGaia could not occur However regulation can emergeautomatically (Saunders 1994 Watson 1999) and hencethe mechanisms by which regulation emerges in physi-ology may have parallels at the planetary scale (Koeslaget al 1997 Saunders et al 1998) even though planetaryregulation cannot be re ned by selection We think thatwith an appreciation of feedback principles the theoriesof Gaia and natural selection can be reconciled (Lenton1998)

Equally there is a need to extend the original cyberneticview of Gaia to encompass evolution The continuousgeneration and selection of different environment-alteringtraits ensures that the feedback structure of Gaia remainsdynamic Evolution within the biota drives changes in thestate parameters and structure of the system (eg the riseof atmospheric oxygen) This in turn facilitates the evolu-tion of new forms of life It can also alter the set pointsof regulation when they are not xed by thermodynamicchemical or geophysical constraints (Lenton amp Lovelock2000) Complexity theory may provide a framework fordeveloping Gaia theory by synthesizing principles fromcybernetics and evolutionary biology

4 COMPLEXITY THEORY

Complexity theory is a general theory of complexdynamic systems The Latin complexus comes from theGreek pleko meaning to plait or twine Thus a complexsystem is literally one consisting of interwoven partsComplex can also mean dif cult to understand or analyseA broad de nition of a complex system is one whoseproperties are not fully explained by an understanding of

Phil Trans R Soc Lond B (2002)

dynamical

systems

complex

ordered

critical

chaotic

simple

Figure 3 A subdivision of dynamical systems in terms ofbehaviour

its component parts (Gallagher amp Appenzeller 1999) Bycontrast simple systems are ones whose properties arefully explained by the properties of their component parts(eg a pendulum) Emergence describes the collectivebehaviour of complex systems It can be local or globalLocal emergent properties are well studied in physicswhere they are often termed lsquointensive propertiesrsquo (egpressure and temperature of an ideal gas) Global emer-gent properties are the more original focus of complexitytheory

Complexity theory aims to understand the origin oforganization In doing so it adopts different modellingmethodologies to those commonly used to study speci csystems For example rather than predicting the dynamicsof a given organization rules of interaction between allpossible objects are speci ed and it is left open whichobjects appear in a given simulation An example of thisapproach is the use of CA Attempts to simulate lsquoAlifersquocommunities and ecosystems are also particularly relevantto Gaia

The relationship between complexity theory and otherdisciplines can be viewed in terms of a behavioural classi- cation of systems ( gure 3) In this case complex sys-tems are a subset of dynamical systems and complexitytheory is part of dynamic systems theory which also con-siders simple systems Complex systems can be subdividedinto ordered systems critical systems and chaotic systemsChaos describes unpredictable behaviour emerging fromnonlinear equations giving high sensitivity to initial con-ditions Order describes a tendency to reside in one stateor limit cycle between a limited number of states Betweenfrozen order and unpredictable chaos much interest hasbeen focused on a critical regime dubbed lsquothe edge ofchaosrsquo Complexity theory can be seen as an extension ofcybernetics (control theory) which focuses on feedbackand feed-forward systems with predictable behaviour Italso encompasses AI and lsquoAlifersquo research By contrastchaos theory focuses on systems with unpredictablebehaviour

This special issue focuses on the subset of CAS A lsquobot-tom-uprsquo de nition of a CAS has been given (Levin 1998)based on three essential elements (i) sustained diversityand individuality of components (ii) localized interactionamong those components and (iii) an autonomous pro-cess that selects from among these components based onthe results of local interactions a subset for replication orenhancement From these essential elements it is argued(Levin 1998) that the following properties (Holland 1995)emerge (1) continual adaptation (2) absence of a globalcontroller (3) hierarchical organization (4) generation of

688 T M Lenton and M van Oijen Gaia as a complex adaptive system

Table 1 Orders of control in complex systems (after Joslashrgensen amp Straskraba 2000)

order scope for adaptation example system discussed in text

rst xed parameters and structure original Daisyworld modelsecond variable parameters xed structure CA Daisyworldthird variable structure and parameters lsquoAlifersquo Guild modelfourth change of goal functions Gaia ()

perpetual novelty and (5) far-from-equilibrium dynamicsCommonly given examples of CASs are cells individualorganisms and ecosystems

What is the typical behaviour of a CAS First they dis-play lsquoself-organizationrsquo in the sense of emergence ofordered behaviour and structure from many parts withsuf cient connections independent of natural selection(Kauffman 1993) The concept was inspired by the resultsof mathematical models which starting from arbitraryinitial conditions and obeying only simple local rules pro-duced large-scale order The second law of thermody-namics forbids true self-organization increasing order isonly possible in thermodynamically open systems Thusself-organization is dissipative requiring free energy inputand producing high-entropy output CASs may also showlsquoself-organized criticalityrsquo (Bak et al 1987) meaning atendency to reside in the edge of chaos regime allowingchange without getting locked into frozen order A power-law distribution of responses is thought to be characteristicof self-organized critical systems but may occur morewidely in nature

Complex systems can be described in terms of theirorder of dynamics and control (Joslashrgensen amp Straskraba2000 table 1) First-order dynamical systems have xedparameters and structure and hence can only achievefeedback control Second-order dynamical systems havevariable parameters as well as states but xed structureThird-order systems have variable structure as well asparameters and states The distinction in fourth-order sys-tems is that changes in states parameters and structurelead to a change in the goal functions that determine thelong-term behaviour of a system (Wilhelm amp Bruggemann2000) How do CASs t into this classi cation Theelement of replication or enhancement indicates that theirstructure is variable allowing third-order control Thegeneration of continual adaptation suggests that CASs arefourth order with internally generated changes in goalfunctions

In what sense are such behaviours adaptive Adaptationhas two common meanings in biology (i) in evolution itis a change in the structure or functioning of organismsthat makes them better suited to their environment and(ii) in physiology it is an alteration in an organismrsquosresponse to its environment Evolutionary adaptation (i) isusually thought of as the consequence of natural selectionacting on heritable variation The capacity for physiologi-cal adaptation (ii) can be the product of evolutionaryadaptation (i) lsquoAdaptiversquo is used in complexity theory todescribe system development as well as response and isoften applied to systems that are not subject to naturalselection as a whole (although their parts may be) Hencelsquoadaptiversquo behaviours described by complexity theoristsare not necessarily lsquoadaptationsrsquo in the sense used by evo-

Phil Trans R Soc Lond B (2002)

lutionary biologists (i) or physiologists (ii) One way outof this semantic mine eld is to consider natural selectionas just one (rather than the only) form of selection Otherforms of selection can emerge at levels above that of natu-ral selection acting on heritable variation eg in the pro-cess of foraging by social insect colonies utilizingpheromone signals (stigmurgy) or in models of the evo-lution of altruism as a consequence of emergent spatialpatterns (Paolo 2000) If selection can be broader thanjust natural selection then there can be lsquoadaptiversquo behav-iours that are not necessarily the product of natural selec-tion

5 IS GAIA A COMPLEX ADAPTIVE SYSTEM

Gaia is a complex system in that it has many interwovenparts and properties that are not fully explained by anunderstanding of the parts for example the stability ofcomponents of the atmosphere Gaia also ful ls the CAScriteria given previously (Levin 1998) as it contains sus-tained diversity and individuality of components (egorganisms) localized interaction among these compo-nents and at least one autonomous selection process(natural selection) Gaia also possesses non-local interac-tion of components because there is global mixing of theatmosphere and oceans This gives rise to globally mixedvariables atmospheric gases with lifetimes longer thanatmospheric mixing (ca 1 yr) and dissolved chemicalspecies in the ocean with lifetimes longer than ocean mix-ing (ca 1000 yr) There are also non-local interactions inthe climate system described as lsquoteleconnectionsrsquo

If Gaia is a CAS we can expect it to display character-istic properties and behaviour Gaia does indeed sharegeneric CAS properties (Holland 1995) far-from equilib-rium dynamics (of life the atmosphere and aspects ofocean chemistry) generation of perpetual novelty(through evolution) hierarchical organization (eg organ-isms ecosystems Gaia) and absence of a global control-ler However non-local interaction simpli es the systemand offers the possibility that from its many complexcomponents Gaia could display emergent simplicity in itsbehaviour In what sense might Gaia be adaptive Gaiahas not evolved by natural selection at the whole systemlevel but various types of selection operate within the sys-tem The system can be viewed physiologically as cap-tured in the term lsquogeophysiologyrsquo (Lovelock 1986) andmay respond to forcing in a manner resembling physio-logical adaptation There is change at the system level andthere may also be developmental trends that enhance lifeas a whole eg an increase global gross primary pro-ductivity with time

Is Gaia self-organizing It is often said that Gaia is self-regulating but what order of control (table 1) is actually

Gaia as a complex adaptive system T M Lenton and M van Oijen 689

achieved There are many examples of rst-order feed-back control (examples in sect 3) Gaia also contains evo-lution which continually reshapes the system and thusallows higher levels of system control The evolution ofresponses to prevailing environmental conditions and theevolution of environment-altering traits represent changesin the parameters and structure of the system allowing forsecond- and third-order control For example the coloniz-ation of the land surface by vascular plants altered the cli-mate in a self-bene cial manner (Betts 1999) and led toa reorganization of biogeochemical cycles including adrop in carbon dioxide (Berner 1998) global cooling anda rise in oxygen (Lenton 2001) Changes in the Earthrsquoshistory such as the switch from anaerobic to aerobic con-ditions as oxygen rose ca 2 Gyr ago and the resultingincrease in free-energy availability to the biota could beviewed as fourth-order control a change in goal functionfrom an anaerobic lsquoupside-downrsquo biosphere (Walker1987) to an aerobic attractor state that allowed the pro-liferation of new types of life Thus Gaia may be viewedas self-organizing and more in terms of the levels of con-trol achieved

Is Gaia in a self-organized critical state If one contraststhe current state of Gaia with that of Mars or Venus orthe suggested lsquosnowball Earthrsquo state Gaia is more com-plex and less lsquofrozenrsquo into order (of course Mars is literallyfrozen as would be the snowball Earth) It has been sug-gested that the Earthrsquos biota is in a self-organized criticalstate on the basis that extinction events have a distributionclosely approximated by a power law (Kauffman 1993)Proponents of complexity theory propose that the majorityof all extinction events are internally generated by thedynamics of coevolution of species If so this would indi-cate criticality of the biota but not necessarily criticalityof Gaia An alternative hypothesis is that the majority ofextinction events are caused by external perturbation Inthe case of mass extinctions there is good evidence for acausative asteroid impact at the CretaceousndashTertiaryboundary 65 Myr ago (Alvarez et al 1980) Simple mod-els of coevolution (Bak amp Sneppen 1993) or of environ-mental stress (Newman 1997) (without speciesinteraction) as the cause of extinction both exhibit apower law Of the two the environmental stress modelhas an exponent much closer to actual data We concludethat although some extinction may result from coevo-lution there is not yet a convincing case that the biota isin a critical state To test whether Gaia is in a critical statea frequency response analysis of environmental recordsmight be more appropriate For example the carbondioxide and methane records in the Vostok ice core(Petit et al 1999)

6 EMERGENCE OF GAIA

Complexity theory stimulates us to search for a com-plexity threshold for a planet with life beyond which theemergence of self-organization (including self-regulation)and adaptive behaviour becomes likely in other wordsa planetary analogue for the emergence of auto-catalyticnetworks (Kauffman 1993) In coupled open systems oflife and environment does self-organization become vastlymore probable beyond a critical lsquosizersquo (eg number of

Phil Trans R Soc Lond B (2002)

organisms) Also can we pinpoint a particular time in theEarthrsquos history when Gaia emerged

Once life arose it must soon have depleted its surround-ings of substrates thus posing a pressing need for recy-cling Key biogeochemical transformations of essentialelements are present deep in the tree of life among theancient kingdoms of archaea and bacteria supporting aview that nutrient recycling evolved early One furtherrequirement is important for the emergence of planetaryscale self-organization in order to achieve global signi -cance life must have an abundant source of free energyThe earliest types of photosynthesis used relatively scarcesubstrates such as H2S Once oxygenic photosynthesisemerged using the abundant H2O as a substrate then the ux of free energy captured by the biota increased mas-sively (DesMarais 2000) Thus we suggest the genesis ofGaia came with the origin of widespread oxygenic photo-synthesis This occurred at least 28 Gyr ago (DesMarais2000) and possibly as early as 38 Gyr ago (Schidlowski1988)

A remarkable property of Gaia that demands an expla-nation is that its abiotic state variables have stayed at lev-els that support abundant life for most of the last 38 GyrEarly strong versions of the Gaia hypothesis suggestedthat all life-forbidding state variable levels are unreachablebecause there is selection against the processes that wouldlead there Selection at the level of the system as a wholeseems untenable (Doolittle 1981 Dawkins 1983) How-ever it may still be the case that life-forbidding state-vari-able levels are dif cult to reach for at least two reasons(i) if an organism is driving an environmental variabletowards an uninhabitable state its growth and spread willbe suppressed (by negative feedback) such that the systemwill stabilize within the habitable regime and (ii) when-ever organisms become so abundant that the side-effectsof their metabolism become life-threatening on a globalscale different organisms will evolve for which the abun-dant pollutants and the polluters themselves becomeresources If natural selection has enough substrate(genotypic variation) on which to operate such checksand balances are always likely to evolve and make extremeconditions unreachable This old idea (originating fromSmith 1776) could explain the likelihood of regulation atliveable levels as a side-effect of evolution in suf cientlydiverse biota

Uninhabitable or barely habitable states (with life inrefugia) can be reached because of global scale environ-mental perturbation eg massive asteroid impact (Watson1999) or extreme external forcing eg future increases insolar luminosity (Lovelock amp Whit eld 1982 Lenton ampVon Bloh 2001) It is also possible that the evolution ofparticularly strong biotic effects could lsquoovershootrsquo anddrive the environment into a barely habitable stateespecially if there is a time-delay in self-limiting negativefeedback (this is a counter argument to (i) above) Fur-thermore variables that cannot function as a resource toany organism may be able to build up to toxic levels (acounter argument to (ii) above) However useless anddangerous waste products may generally kill off their pro-ducers before disrupting the functioning of Gaia as awhole

Gaia has suffered massive perturbations (asteroidimpacts) and lsquosnowball Earthrsquo states may have occurred

690 T M Lenton and M van Oijen Gaia as a complex adaptive system

in which life only hung on in refugia However abundantlife has always reappeared sometimes remarkably quickly(DrsquoHondt et al 1998) New types of life appear in thewake of mass extinction but there is also a system lsquomem-oryrsquo carried in the gene pool This suggests an interestingpossibility if in response to perturbation a new traitevolves that contributes to recovery then if it remains inthe gene pool and a similar perturbation occurs again thesystem may recover faster the second time In this senseGaia may gain from experience

7 SIMULATING PLANETARY SCALE EMERGENCEWITH DAISYWORLDS

The persistence of life and recovery of Gaia from per-turbation suggest that self-regulation occurs We wouldlike to know how it can emerge and whether it is a chanceor a highly probable outcome of lifendashenvironment coup-ling The feasibility and probability of the emergence ofplanetary scale lsquoself-organizationrsquo andor lsquoadaptive behav-iourrsquo can be evaluated using a synthetic approach of math-ematical modelling

The rst such attempt to simulate the emergence ofplanetary scale self-regulation was the Daisyworld model(Watson amp Lovelock 1983) In Daisyworld global tem-perature regulation emerges automatically from feedbackcoupling between life and its environment with selectionat the component (individual organism) but not the sys-tem (whole planet) level In Daisyworld the environmentis reduced to one variable temperature and life is reducedto two types black and white daisies inhabiting bareground The daisies share the same optimum temperaturefor growth of 225 degC and outer limits to growth of 5 degCand 40 degC The daisy types affect their environment inopposite ways by virtue of their different re ectivity(albedo) The white daisies re ect more solar radiationthan bare ground whilst the black daisies absorb moreHence the local temperature of the daisies differs blackdaisies are always warmer and white daisies are alwayscooler than bare ground The system is forced by a gradualincrease in solar luminosity as has occurred on the Earth

With only one type of daisy present there is a range offorcing for which negative feedback occurs and a point atwhich positive feedback occurs In the case of black daisiesonly when they can establish their spread is ampli ed bypositive environmental feedback (similar to gure 2c butthe effect of life on the environment is stronger) As lumi-nosity increases the population of black daisies declinesthus providing negative feedback on temperature In thecase of white daisies only when they can germinate theirspread is immediately suppressed by their cooling effectAs luminosity increases their population increases pro-viding negative feedback on temperature A regime isentered where white daisies maintain the planet in a habit-able state when otherwise it would be uninhabitable( gure 2d) Eventually they collapse catastrophically withpositive feedback With both types of daisy present thereis a range of forcing for which global temperature actuallydecreases as forcing increases This is an example oflsquosuper-negativersquo feedback (the sign of response is oppositeto that of the forcing (Sardeshmukh 2000))

The Daisyworld model has been portrayed as a CAS(Lewin 1993) but this deserves closer examination It

Phil Trans R Soc Lond B (2002)

possesses rst-order feedback control (table 1) and theregime of super-negative feedback was unexpected fromits parts However the original model does not explicitlyinclude interacting local components The system isdescribed by coupled equations and its behaviour can beunderstood analytically (Saunders 1994 Weber 2001)

If time-delays are introduced into the population andtemperature equations of Daisyworld then apparentlychaotic behaviour can be generated (Zeng et al 1990)Varying the time-delay reveals a series of period doublingscharacteristic of the transition from order to deterministicchaos (De Gregorio et al 1992ab) There is no real-worldjusti cation for the time-delays and it has been shownthat the average of the lsquochaoticrsquo solutions is close to thetemperature regulation in the original model (Jascourt ampRaymond 1992) Introducing an unrealistically large heatcapacity to Daisyworld generates limit cycle oscillations ofthe two daisy populations and temperature (Nevison et al1999) (ie generates the rst period doubling) Thesestudies show that the original Daisyworld model resideswell into the ordered regime and is not in a critical state

Subsequent versions of Daisyworld arguably show theemergence of higher-order control (although the nal prop-erty of temperature regulation is similar in each case)Variants of the model with adaptation of the optimumgrowth temperature of the daisies (Robertson amp Robinson1998 Lenton amp Lovelock 2000) include alteration ofparameters but this is enforced through further para-meters A more fully second-order control system is a Dai-syworld with random mutation of daisy albedo (some ofthe parameters) and subsequent selection (Lenton 1998Lenton amp Lovelock 2001) The structure of this modelcould be said to change in that new daisy lsquospeciesrsquo appearThis suggests there may be some third- and fourth-ordercontrol

8 CA DAISYWORLDS

To ful l the CAS criteria models must include localinteraction of components CA provide a tool for thisHence we have followed the lead of others (Von Bloh etal 1997) and constructed a CA version of Daisyworld toexplore the effects of local interaction and the capacity foradaptive system behaviour The original equations(Watson amp Lovelock 1983) are retained where possibleThe CA grid and rules are simply used to replace thepopulation equations We consider a square grid witheight neighbours to each cell rather than four nearestneighbours (Von Bloh et al 1997) There is no diffusivetemperature eld just the original equations for local tem-peratures of daisies (determined by albedo global tem-perature and insulation parameter q) and globaltemperature (determined by average albedo of the systemand luminosity forcing) Seeding is used to enable popu-lations to establish (but once they are established it haslittle impact) First we consider the original case of popu-lations of lsquoblackrsquo (albedo aB = 025) and lsquowhitersquo (albedoaW = 075) daisies covering bare ground (albedo aG = 05)For an empty cell with nB black neighbours each withgrowth rate b B and nW white neighbours each with growthrate b W the following colonization rules apply

The probability that black will colonize when only theyare present is

Gaia as a complex adaptive system T M Lenton and M van Oijen 691

P(B|nW = 0) = 1 2 (1 2 b B)nB (81)

The probability that white will colonize when only theyare present is

P(W|nB = 0) = 1 2 (1 2 b W )nW (82)

The probability that the cell remains empty is

P(E) = (1 2 P(B|nW = 0))(1 2 P(W|nB = 0)) (83)

The probability that black will colonize when both arepresent is

P(B) = (1 2 P(E))P(B|nW = 0)

P(B|nW = 0) 1 P(W|nB = 0) (84)

The probability that white will colonize when both arepresent is

P(W) = (1 2 P(E))P(W|nB = 0)

P(B|nW = 0) 1 P(W|nB = 0) (85)

The probability of seeding an empty cell is xed

P(S) = h ( h = 0001 in the results shown) (86)

The probability of death at an occupied cell is also xed

P(D) = g ( g = 03 as in the original model) (87)

The 2D CA model has less smooth dynamics than theoriginal zero-dimensional model in that it can exhibitbifurcations and limit cycling ( gure 4) The growth equa-tions are such that for one type alone ( gure 4ac) it canreach carrying capacity on the grid even when its localtemperature and growth rate are sub-optimal This isbecause the presence of many identical neighbours canmake colonization of an empty cell highly probable evenwhen growth rate is suppressed by temperature (equations(81) or (82)) For black daisies alone ( gure 4ab) asforcing is increased a bifurcation point is reached wherethe global temperature is such that the local temperatureof black daisies becomes uninhabitable (b B = 0 when thetemperature of black daisies TB = 40 degC) This generatespartial collapse (ca 30 die-back of the daisies) immedi-ate recovery and resulting oscillations of temperature andpopulation As forcing is increased further a second bifur-cation point is reached Then the trajectories combinebefore the black daisies disappear For white daisies alone( gure 4cd) there are two period doublings and thebeginnings of a third (inset in gure 4d) before a returnto a single trajectory

The one daisy-type model illustrates an lsquoovershootrsquoproblem for Gaia life may develop the capacity to drivean environmental variable into an uninhabitable or barelyhabitable state if the environmental effect is strong andlocal interactions that encourage growth outweigh nega-tive feedback on growth from the environment The modeldoes not include natural selection in that all the daisiesare identical and are always equally t in terms of growthrate (although in the initial growth phase clusters formand cells at the edge of clusters are better able to spreadthan those within clusters) The model does include a sys-tem selection process between bare ground and one daisytype under a certain range of forcing daisies are selectedover bare ground outside that range bare ground willsuccessfully take over from daisies

Phil Trans R Soc Lond B (2002)

When black and white types can both arise the limitcycle regimes are removed and the solution resembles theoriginal zero-dimensional model ( gure 4ef ) The twodifferent daisy types have different growth rates and hence tness thus adding a crude form of natural selection tothe model (although there is no evolution) With thisadditional selective process the model stays more rmlyin the ordered regime The system is stabilized by at leastthree effects (i) if one daisy type reaches an uninhabitabletemperature the other may still be able to spread (becausetheir local temperatures differ) (ii) in the mid-range offorcing a combination of black and white generates a glo-bal temperature closer to optimal and (iii) the presenceof one daisy type reduces the area available to the otherto expand into

We have introduced random mutation of albedo to themodel generalizing the colonization equations (81)ndash(85)to deal with any albedo type Mutation is assumed alwaysto occur in the process of colonization of an empty cell(asexual reproduction that always generates mutatedoffspring) Albedo can mutate within a parameterizedwidth of the parent albedo (plusmn D a) Within this rangeeither side of the parent albedo an offspring albedo is ran-domly chosen Limits to mutation are set at am in = 0 andam ax = 1

With mutation and natural selection within the modelsystem ( gure 5) its behaviour could be said to be lsquoadap-tiversquo in that it lsquoevolvesrsquo to counteract forcing When themodel is seeded with the original lsquoblackrsquo daisies(aB = 025) and these are allowed to mutate as forcingincreases progressively paler daisies evolve cooling theplanet and then maintaining the temperature close to con-stant Increasing D a brings the average planetary tempera-ture more rapidly towards the optimum for daisy growthThe tendency for bifurcation ( gure 4a) is removed byincreasing D a ( gure 5) because this tends to generate anearly increase in average albedo In a sensitivity analysisof the stabilizing effect of albedo diversity am ax ndash am in wasprogressively increased around a central value ofaB = 025 without any mutation and this was also foundto remove the bifurcations Albedo mutation extends therange of temperature regulation beyond that in the originalmodel because paler types than the original lsquowhitersquo onescan arise The latter result has been found in other vari-ants of Daisyworld (Stocker 1995 Von Bloh et al 1997Lenton amp Lovelock 2001)

A more complex 2D CA version of Daisyworld has pre-viously been formulated with albedo mutation and a con-tinuous temperature eld (Von Bloh et al 1997) Thissystem exhibits the remarkable property that underenforced habitat fragmentation using a percolating fractalthe system is able to regulate temperature unimpaired upto a lsquocriticalrsquo threshold at which daisy areas become iso-lated and regulation starts to break down Once uninhabi-ted land forms a spanning cluster regulation is completelyremoved By contrast trivial reductions in habitat (eg agrowing square of lsquoconcretersquo) impair temperature regu-lation in a linear fashion In the former case adjacent dai-sies can affect the temperature of small uninhabited areasbut overall temperature regulation depends on compe-tition among daisies across an entire connected space Inother words the emergent property of global temperatureregulation relies on uninhibited local interaction tting

692 T M Lenton and M van Oijen Gaia as a complex adaptive system

100

50

0

80

60

40

20

0

plusmn20

100

50

0

100

50

0

80

60

40

20

0

plusmn20

80

60

40

20

0

plusmn20

05 10 15 20

05 10 15 20

05 10 15 20 05 10 15 20

05 10 15 20

05 10 15 20

solar luminosity (_) solar luminosity (_)

solar luminosity (_) solar luminosity (_)

solar luminosity (_) solar luminosity (_)

gri

d c

over

(

)g

rid

cov

er (

)

gri

d c

ov

er (

)

glo

bal

tem

per

ature

(degC

)g

lob

al t

emp

erat

ure

(degC

)g

lob

al t

emper

atu

re (

degC)

15

plusmn508 11

(a) (b)

(c) (d)

(e) ( f )

Figure 4 Simulations of xed albedo populations in a simple CA Daisyworld (64 acute 64 grid) Parameters are as in the originalmodel (Watson amp Lovelock 1983) and the CA rules are described in sect 8 Solar luminosity (in normalized units) is increased insteps of 0004 at each of which the model is updated The left-hand graphs show percentage grid cover by the daisies versusluminosity and the right-hand graphs show global average temperature (degC) versus luminosity Temperature is a function ofluminosity and the albedo a and grid cover of daises and empty cells (ab) Seeding with lsquoblackrsquo daisies (aB = 025) denotedby lled circles (cd) Seeding with lsquowhitersquo daisies (aW= 075) denoted by open circles (ef ) Seeding with both black and whitedaisies (albedo of each seed chosen at random) The inset in (d ) shows the period doubling in the temperature trajectory withonly white daisies

in nicely with the criteria for a CAS The system is self-organizing and may arguably be in a critical state near thelimit at which daisy areas become disconnected

9 FEASIBILITY TESTS OF GAIA USING lsquoALIFErsquo

A key criticism of Daisyworld is that it is limited in onlyconsidering one predetermined type of interactionbetween the local and the global and it is one that will

Phil Trans R Soc Lond B (2002)

tend to generate regulation The daisies affect theirenvironment in the same way at the local and the globalscale Hence what is selected for at the individual leveltends to be bene cial at the global level With two or moredaisy types present there is negative selective feedbackmaking regulation likely (Lenton 1998)

lsquoAlifersquo techniques offer a promising way of makingunbiased tests of the potential for emergence of planetaryscale self-organization The model environment lsquoTierrarsquo

Gaia as a complex adaptive system T M Lenton and M van Oijen 693

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

0

20151005

solar luminosity (ndash)

grid

cov

er (

)

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

(a) (b)

(c)(d)

( f )(e)

Figure 5 CA Daisyworld simulations with albedo mutation (64 acute 64 grid) In each simulation there is seeding with theoriginal lsquoblackrsquo daisies (aB = 025) which fall in the range coloured in blue The model is updated with each increase in solarluminosity of 0004 normalized units and at each update empty cells can be colonized with offspring cells that differ at mostby plusmn D a from the albedo of their parent cell Left- and right-hand graphs show grid cover by daisy populations () and globalaverage temperature (degC) respectively The albedo colour scheme in the left-hand graphs is 0ndash02 black 02ndash04 blue 04ndash06 green 06ndash08 orange 08ndash10 red The graphs show the effect of increasing mutation range (ab) D a = 001 (cd) D a =002 (ef ) D a = 01

(Ray 1991) evolved a community of arti cial life-formsthat reproduce in different ways including parasiticallyThe model lsquolife-formsrsquo compete for resource (processortime) but they do not produce waste products Hencetheir interaction with their environment is not thermody-namically complete in the way that it is for real life-formswhich can only maintain an ordered (low entropy) stateby transforming matter as well as energy

The evolution of matter recycling is addressed usinglsquoAlifersquo techniques in the Guild model (Downing amp Zvirin-sky 1999) From one ancestral lsquospeciesrsquo a communityevolves which is able to recycle a given set of lsquochemicalsrsquo(which can be thought of as different molecular forms ofthe same key nutrient element) Such recycling enablesgreatly enhanced productivity in real ecosystems and Gaia

Phil Trans R Soc Lond B (2002)

(Volk 1998) The mechanism of emergence of recyclingis quite different from the spontaneous emergence of auto-catalytic cycles in systems of very large numbers of chemi-cal reactions (Kauffman 1993) In the Guild model lsquoAlifersquochances upon closed recycling of a small set of chemicalsand this is reinforced by selection This illustrates part ofthe mechanism (ii) that we highlighted in sect 6

The main criticisms of the original Guild model are thatthere is no treatment of energy in the system and that adeviation of the local environment from the global isassumed that may not be justi ed for some real world ana-logues A lsquoGuild IIrsquo model is being developed (K Down-ing personal communication) that includes free energyand entropy in the abstract chemistry (eg it takes freeenergy to build larger molecules) and makes the local

694 T M Lenton and M van Oijen Gaia as a complex adaptive system

environment the interior of proto-cells In this modeldespite a relatively small input of free energy in chemicalform recycling and regulation can emerge

An ideal model world for testing Gaia would containarti cial life-forms that transform lsquomatterrsquo and lsquoenergyrsquoare lsquothermodynamicallyrsquo constrained grow and replicatewith a heritable genome subject to random mutationinteract with one another and evolve new ways of alteringtheir environment related to their internal functioningThe environment would contain many lsquophysicalrsquo andlsquochemicalrsquo variables some homogeneous (well mixed) andothers heterogeneous The resulting system behaviourwould be observable and testable by perturbation

10 CONCLUSIONS

Many scientists now accept that planetary regulationinvolving the biota occurs (Longhurst 1998) However westill have to determine whether Gaiarsquos coming into exis-tence and survival was coincidental or probable and howfragile or robust the system is at present We have arguedthat Gaia is a complex system with self-organizing andadaptive behaviour but that it does not reside in a criticalstate Complexity theory modelling approaches havehelped us simulate and understand the emergence of plan-etary order lsquoAlifersquo techniques can take this further andhelp in assessing the probability of emergence of planetaryregulatory properties Our attempts to apply complexitytheory to Gaia have yielded a broader view of selectionthan previously encompassed in the Gaia theory (Lenton1998) Gene-based natural selection is just one type andlevel of selection operating within Gaia and it is not anecessary condition for regulation The existence of differ-ent types of selection operating at different levels makes iteasier to understand how planetary-scale self-regulationcan arise It also makes it easier to accept that a Gaia-likesystem may be a probable outcome once there is abundantlife on a planet with the capacity for large-scale freeenergy capture

We thank Ricard Sole and Simon Levin for the invitation towrite this article

REFERENCES

Alvarez L W Alvarez W Asaro F amp Michel H V 1980Extraterrestrial cause for the CretaceousndashTertiary extinctionScience 208 1095ndash1108

Bak P amp Sneppen K 1993 Punctuated equilibrium and criti-cality in a simple model of evolution Phys Rev Lett 714083ndash4086

Bak P Tang C amp Wiesenfeld K 1987 Self-organized criti-calitymdashan explanation of 1f noise Phys Rev Lett 59381ndash384

Berner R A 1998 The carbon cycle and CO2 over Phanero-zoic time the role of land plants Phil Trans R SocLond B 353 75ndash82 (DOI 101098rstb19980192)

Betts R A 1999 Self-bene cial effects of vegetation on cli-mate in an oceanndashatmosphere general circulation modelGeophys Res Lett 26 1457ndash1460

Bonan G B Pollard D amp Thompson S L 1992 Effects ofboreal forest vegetation on global climate Nature 359716ndash718

Budyko M I 1968 The effect of solar radiation variations onthe climate of the Earth Tellus 21 611ndash619

Phil Trans R Soc Lond B (2002)

Dawkins R 1983 The extended phenotype Oxford UniversityPress

De Gregorio S Pielke R A amp Dalu G A 1992a Feedbackbetween a simple biosystem and the temperature of theEarth J Nonlinear Sci 2 263ndash292

De Gregorio S Pielke R A amp Dalu G A 1992b A delayedbiophysical system for the Earthrsquos climate J Nonlinear Sci2 293ndash318

DesMarais D J 2000 When did photosynthesis emerge onEarth Science 289 1703ndash1705

DrsquoHondt S Donaghay P Zachos J C Luttenberg D ampLindinger M 1998 Organic carbon uxes and ecologicalrecovery from the CretaceousndashTertiary mass extinctionScience 282 276ndash279

Doolittle W F 1981 Is nature really motherly The CoEvol-ution Q Spring 58ndash63

Downing K amp Zvirinsky P 1999 The simulated evolutionof biochemical guilds reconciling Gaia theory and naturalselection Artif Life 5 291ndash318

Ehrlich P 1991 Coevolution and its applicability to the Gaiahypothesis In Scientists on Gaia (ed S H Schneider amp PJ Boston) pp 118ndash120 London MIT Press

Gallagher R amp Appenzeller T 1999 Beyond reductionismScience 284 79

Hamilton W D 1995 Ecology in the large Gaia and GenghisKhan J Appl Ecol 32 451ndash453

Hamilton W D 1996 Gaiarsquos bene ts New Scientist 15162ndash63

Hamilton W D amp Lenton T M 1998 Spora and Gaia howmicrobes y with their clouds Ethol Ecol Evol 10 1ndash16

Han T-M amp Runnegar B 1992 Megascopic eukaryotic algaefrom the 21 billion-year-old Negaunee iron-formationMichigan Science 257 232ndash235

Hoffman P F Kaufman A J Halverson G P amp SchragD P 1998 A Neoproterozoic snowball earth Science 2811342ndash1346

Holland J 1995 Hidden order how adaptation builds complexityReading MA Addison-Wesley

Hyde W T Crowley T J Baum S K amp Peltier W R2000 Neoproterozoic lsquosnowball Earthrsquo simulations with acoupled climateice-sheet model Nature 405 425ndash429

Imshenetsky A A Lysenko S V amp Kazakov G A 1978Upper boundary of the biosphere Appl Environ Microbiol35 1ndash5

Isaacs A Daintith J amp Martin E (eds) 1996 Concise sciencedictionary Oxford University Press

Jascourt S D amp Raymond W H 1992 Comments on lsquoChaosin daisyworldrsquo by X Zeng et al Tellus 44B 243ndash246

Joslashrgensen S E amp Straskraba M 2000 Ecosystems as cyber-netic systems In Handbook of ecosystem theories and manage-ment (ed S E Joslashrgensen amp F Muller) pp 249ndash264London Lewis Publishers

Kasting J F 1991 Box models for the evolution of atmo-spheric oxygen an update Global and Planetary Change 97125ndash131

Kauffman S A 1993 The origins of order self-organization andselection in evolution Oxford University Press

Kleidon A 2002 Testing the effect of life on Earthrsquos func-tioning how Gaian is the Earth system Climatic Change 52383ndash389

Klinger L F 1991 Peatland formation and ice ages a possibleGaian mechanism related to community succession InScientists on Gaia (ed S H Schneider amp P J Boston) pp247ndash255 London MIT Press

Koeslag J H Saunders P T amp Wessels J A 1997 Glucosehomeostasis with in nite gain further lessons from theDaisyworld parable J Endocrinol 154 187ndash192

Lenton T M 1998 Gaia and natural selection Nature 394439ndash447

686 T M Lenton and M van Oijen Gaia as a complex adaptive system

environment variable (E) environment variable (E)

environment variable (E)environment variable (E)

abio

tic

var

iable

(A

)ab

ioti

c v

aria

ble

(A

)

life

var

iable

(L

)li

fe v

aria

ble

(L

)

E = f (A) A = f (E)

E = f (L)

L= f (E)

L= f (E)

E = f (L)

A = f (E)

E = f (A)

(a)

(b)

(c)

(d )

Figure 2 General representations of types of environmental feedback for xed forcing (a) abiotic negative feedback (b)abiotic positive feedback (c) weak biotic feedback and (d) strong biotic feedback Large open circles indicate stable statesSmall lled circles indicate unstable states The arrows indicate the general direction of change for starting states withineach regime The schematic diagrams are loosely based on the following global cases described in more detail in the text(a) abiotic silicate weathering rate and temperature (b) ice cover and temperature (c) boreal forest cover and temperature(d) growth rate of rock weathering organisms and temperature

decrease atmospheric CO2 and cool the planet DecliningCO2 and cooling below optimum growth temperaturetend to suppress plant growth closing the feedback loopRock weathering traits are probably selected for as ameans of acquiring rock-bound nutrients (especiallyphosphorus) and changes in CO2 and temperature do notaffect this requirement or the resulting selection (It ismore likely that local build-up of phosphorus in soil woulddo that) The feedback from changing CO2 and tempera-ture is very slow and requires a global spread of the traitover many generations before it affects growth Howeverit is key to the long-term regulation of atmospheric CO2

and temperature and can thus be bene cial to plantgrowth in the long term In particular it counteractsincreasing solar luminosity that could otherwise drive theEarthrsquos surface temperature above optimal levels Someabiotic negative feedback ( gure 2a) would exist in aworld without life but with tectonics and a hydrologicalcycle (Walker et al 1981) However rock-weatheringorganisms greatly strengthen the feedback (Lovelock ampWatson 1982 Schwartzman amp Volk 1989) They maythus extend their own future persistence on Earth(Lenton amp Von Bloh 2001)

An example of positive feedback on growth ( gure 2c)is that resulting from the dark snow-shedding foliage oftrees in the boreal forest By absorbing solar radiation thetrees are warmed (especially relative to snow cover) andtheir growth is enhanced This warms their surroundingsthus further enhancing growth (Bonan et al 1992) Thepositive feedback is constrained in that temperatures inthe boreal regions remain below the optimum for growthfor much of the year but they are increased such that

Phil Trans R Soc Lond B (2002)

forest is able to persist over large regions that would other-wise be too cold for growth (Betts 1999)

An example of negative feedback on selection is thatresulting from nitrogen xation in the worldrsquos oceansmany terrestrial ecosystems and some freshwater lakesNitrogen xation is an energetically demanding processwhich will only be selected for when there is a lack ofavailable nitrogen relative to other potentially growth-lim-iting nutrients By xing nitrogen the responsible organ-isms ultimately increase the amount of nitrogen availablein their environment for non-nitrogen- xers Thisremoves the selective advantage of being a nitrogen xerand hence the proliferation of nitrogen xation is self-lim-ited This mechanism regulates the nitrate content of theworldrsquos oceans relative to the phosphate content in a pro-portion close to organismsrsquo requirements (Red eld 1958Lenton amp Watson 2000a)

An example of positive feedback on selection is thatresulting from the ability of sphagnum moss to acidify soilThis environmental change gives the moss a selectiveadvantage relative to other potential invading plants andencourages succession to a peat bog (Klinger 1991Hamilton 1996) There are probably other self-limiting(negative) feedbacks on bog growth given that we do notlive in a world dominated by peat bogs (although theauthors live in a country dominated by them) Interest-ingly examples of positive feedback on selection tend tobe more localized than examples of negative feedbackon selection

One of the possible fates for Gaia is for abiotic positivefeedback ( gure 2b) to take the planet into an uninhabit-able or barely habitable state In the ice-albedo positive

Gaia as a complex adaptive system T M Lenton and M van Oijen 687

feedback effect snow and ice form surfaces that are highlyre ective (high albedo) to solar radiation thus coolingtheir surroundings and encouraging the spread of snowicecover In simple models a modest reduction in solar inputis ampli ed by this feedback to cause complete ice coverof the Earth (Budyko 1968 Sellers 1969) the so-calledlsquosnowball Earthrsquo (Hoffman et al 1998) Recent simula-tions suggest that a lsquoslushball Earthrsquo state with open waterin equatorial oceans may be more realistic and less fatalto life (Hyde et al 2000) If a snowball Earth attractorexists it should be unstable because CO2 input from vol-canoes can gradually accumulate in the atmosphere untilradiative forcing is suf cient to melt continental ice cover

A key challenge to Gaia theory from evolutionary biol-ogists is to explain how order especially self-regulationcan arise at the global scale without invoking teleology orselection at the level of the planet (Doolittle 1981 Daw-kins 1983) Such criticisms inspired the formulation of theDaisyworld model (Lovelock 1983 Watson amp Lovelock1983) which demonstrates that self-regulation canemerge automatically from competing populations alter-ing their local environments in different ways (see sect 7 andsect 8) The idea that evolution within Gaia could have pro-duced organisms that contribute to regulating the planetis still variously criticised as untenable altruism vulnerableto cheats or demanding large-scale group selection(Hamilton 1995) It is sometimes argued that randomvariation and natural selection are necessary and suf cientto explain the self-regulation of organisms and candidatesuper-organisms (eg temperature regulated social insectcolonies Ehrlich 1991) in which case self-regulation ofGaia could not occur However regulation can emergeautomatically (Saunders 1994 Watson 1999) and hencethe mechanisms by which regulation emerges in physi-ology may have parallels at the planetary scale (Koeslaget al 1997 Saunders et al 1998) even though planetaryregulation cannot be re ned by selection We think thatwith an appreciation of feedback principles the theoriesof Gaia and natural selection can be reconciled (Lenton1998)

Equally there is a need to extend the original cyberneticview of Gaia to encompass evolution The continuousgeneration and selection of different environment-alteringtraits ensures that the feedback structure of Gaia remainsdynamic Evolution within the biota drives changes in thestate parameters and structure of the system (eg the riseof atmospheric oxygen) This in turn facilitates the evolu-tion of new forms of life It can also alter the set pointsof regulation when they are not xed by thermodynamicchemical or geophysical constraints (Lenton amp Lovelock2000) Complexity theory may provide a framework fordeveloping Gaia theory by synthesizing principles fromcybernetics and evolutionary biology

4 COMPLEXITY THEORY

Complexity theory is a general theory of complexdynamic systems The Latin complexus comes from theGreek pleko meaning to plait or twine Thus a complexsystem is literally one consisting of interwoven partsComplex can also mean dif cult to understand or analyseA broad de nition of a complex system is one whoseproperties are not fully explained by an understanding of

Phil Trans R Soc Lond B (2002)

dynamical

systems

complex

ordered

critical

chaotic

simple

Figure 3 A subdivision of dynamical systems in terms ofbehaviour

its component parts (Gallagher amp Appenzeller 1999) Bycontrast simple systems are ones whose properties arefully explained by the properties of their component parts(eg a pendulum) Emergence describes the collectivebehaviour of complex systems It can be local or globalLocal emergent properties are well studied in physicswhere they are often termed lsquointensive propertiesrsquo (egpressure and temperature of an ideal gas) Global emer-gent properties are the more original focus of complexitytheory

Complexity theory aims to understand the origin oforganization In doing so it adopts different modellingmethodologies to those commonly used to study speci csystems For example rather than predicting the dynamicsof a given organization rules of interaction between allpossible objects are speci ed and it is left open whichobjects appear in a given simulation An example of thisapproach is the use of CA Attempts to simulate lsquoAlifersquocommunities and ecosystems are also particularly relevantto Gaia

The relationship between complexity theory and otherdisciplines can be viewed in terms of a behavioural classi- cation of systems ( gure 3) In this case complex sys-tems are a subset of dynamical systems and complexitytheory is part of dynamic systems theory which also con-siders simple systems Complex systems can be subdividedinto ordered systems critical systems and chaotic systemsChaos describes unpredictable behaviour emerging fromnonlinear equations giving high sensitivity to initial con-ditions Order describes a tendency to reside in one stateor limit cycle between a limited number of states Betweenfrozen order and unpredictable chaos much interest hasbeen focused on a critical regime dubbed lsquothe edge ofchaosrsquo Complexity theory can be seen as an extension ofcybernetics (control theory) which focuses on feedbackand feed-forward systems with predictable behaviour Italso encompasses AI and lsquoAlifersquo research By contrastchaos theory focuses on systems with unpredictablebehaviour

This special issue focuses on the subset of CAS A lsquobot-tom-uprsquo de nition of a CAS has been given (Levin 1998)based on three essential elements (i) sustained diversityand individuality of components (ii) localized interactionamong those components and (iii) an autonomous pro-cess that selects from among these components based onthe results of local interactions a subset for replication orenhancement From these essential elements it is argued(Levin 1998) that the following properties (Holland 1995)emerge (1) continual adaptation (2) absence of a globalcontroller (3) hierarchical organization (4) generation of

688 T M Lenton and M van Oijen Gaia as a complex adaptive system

Table 1 Orders of control in complex systems (after Joslashrgensen amp Straskraba 2000)

order scope for adaptation example system discussed in text

rst xed parameters and structure original Daisyworld modelsecond variable parameters xed structure CA Daisyworldthird variable structure and parameters lsquoAlifersquo Guild modelfourth change of goal functions Gaia ()

perpetual novelty and (5) far-from-equilibrium dynamicsCommonly given examples of CASs are cells individualorganisms and ecosystems

What is the typical behaviour of a CAS First they dis-play lsquoself-organizationrsquo in the sense of emergence ofordered behaviour and structure from many parts withsuf cient connections independent of natural selection(Kauffman 1993) The concept was inspired by the resultsof mathematical models which starting from arbitraryinitial conditions and obeying only simple local rules pro-duced large-scale order The second law of thermody-namics forbids true self-organization increasing order isonly possible in thermodynamically open systems Thusself-organization is dissipative requiring free energy inputand producing high-entropy output CASs may also showlsquoself-organized criticalityrsquo (Bak et al 1987) meaning atendency to reside in the edge of chaos regime allowingchange without getting locked into frozen order A power-law distribution of responses is thought to be characteristicof self-organized critical systems but may occur morewidely in nature

Complex systems can be described in terms of theirorder of dynamics and control (Joslashrgensen amp Straskraba2000 table 1) First-order dynamical systems have xedparameters and structure and hence can only achievefeedback control Second-order dynamical systems havevariable parameters as well as states but xed structureThird-order systems have variable structure as well asparameters and states The distinction in fourth-order sys-tems is that changes in states parameters and structurelead to a change in the goal functions that determine thelong-term behaviour of a system (Wilhelm amp Bruggemann2000) How do CASs t into this classi cation Theelement of replication or enhancement indicates that theirstructure is variable allowing third-order control Thegeneration of continual adaptation suggests that CASs arefourth order with internally generated changes in goalfunctions

In what sense are such behaviours adaptive Adaptationhas two common meanings in biology (i) in evolution itis a change in the structure or functioning of organismsthat makes them better suited to their environment and(ii) in physiology it is an alteration in an organismrsquosresponse to its environment Evolutionary adaptation (i) isusually thought of as the consequence of natural selectionacting on heritable variation The capacity for physiologi-cal adaptation (ii) can be the product of evolutionaryadaptation (i) lsquoAdaptiversquo is used in complexity theory todescribe system development as well as response and isoften applied to systems that are not subject to naturalselection as a whole (although their parts may be) Hencelsquoadaptiversquo behaviours described by complexity theoristsare not necessarily lsquoadaptationsrsquo in the sense used by evo-

Phil Trans R Soc Lond B (2002)

lutionary biologists (i) or physiologists (ii) One way outof this semantic mine eld is to consider natural selectionas just one (rather than the only) form of selection Otherforms of selection can emerge at levels above that of natu-ral selection acting on heritable variation eg in the pro-cess of foraging by social insect colonies utilizingpheromone signals (stigmurgy) or in models of the evo-lution of altruism as a consequence of emergent spatialpatterns (Paolo 2000) If selection can be broader thanjust natural selection then there can be lsquoadaptiversquo behav-iours that are not necessarily the product of natural selec-tion

5 IS GAIA A COMPLEX ADAPTIVE SYSTEM

Gaia is a complex system in that it has many interwovenparts and properties that are not fully explained by anunderstanding of the parts for example the stability ofcomponents of the atmosphere Gaia also ful ls the CAScriteria given previously (Levin 1998) as it contains sus-tained diversity and individuality of components (egorganisms) localized interaction among these compo-nents and at least one autonomous selection process(natural selection) Gaia also possesses non-local interac-tion of components because there is global mixing of theatmosphere and oceans This gives rise to globally mixedvariables atmospheric gases with lifetimes longer thanatmospheric mixing (ca 1 yr) and dissolved chemicalspecies in the ocean with lifetimes longer than ocean mix-ing (ca 1000 yr) There are also non-local interactions inthe climate system described as lsquoteleconnectionsrsquo

If Gaia is a CAS we can expect it to display character-istic properties and behaviour Gaia does indeed sharegeneric CAS properties (Holland 1995) far-from equilib-rium dynamics (of life the atmosphere and aspects ofocean chemistry) generation of perpetual novelty(through evolution) hierarchical organization (eg organ-isms ecosystems Gaia) and absence of a global control-ler However non-local interaction simpli es the systemand offers the possibility that from its many complexcomponents Gaia could display emergent simplicity in itsbehaviour In what sense might Gaia be adaptive Gaiahas not evolved by natural selection at the whole systemlevel but various types of selection operate within the sys-tem The system can be viewed physiologically as cap-tured in the term lsquogeophysiologyrsquo (Lovelock 1986) andmay respond to forcing in a manner resembling physio-logical adaptation There is change at the system level andthere may also be developmental trends that enhance lifeas a whole eg an increase global gross primary pro-ductivity with time

Is Gaia self-organizing It is often said that Gaia is self-regulating but what order of control (table 1) is actually

Gaia as a complex adaptive system T M Lenton and M van Oijen 689

achieved There are many examples of rst-order feed-back control (examples in sect 3) Gaia also contains evo-lution which continually reshapes the system and thusallows higher levels of system control The evolution ofresponses to prevailing environmental conditions and theevolution of environment-altering traits represent changesin the parameters and structure of the system allowing forsecond- and third-order control For example the coloniz-ation of the land surface by vascular plants altered the cli-mate in a self-bene cial manner (Betts 1999) and led toa reorganization of biogeochemical cycles including adrop in carbon dioxide (Berner 1998) global cooling anda rise in oxygen (Lenton 2001) Changes in the Earthrsquoshistory such as the switch from anaerobic to aerobic con-ditions as oxygen rose ca 2 Gyr ago and the resultingincrease in free-energy availability to the biota could beviewed as fourth-order control a change in goal functionfrom an anaerobic lsquoupside-downrsquo biosphere (Walker1987) to an aerobic attractor state that allowed the pro-liferation of new types of life Thus Gaia may be viewedas self-organizing and more in terms of the levels of con-trol achieved

Is Gaia in a self-organized critical state If one contraststhe current state of Gaia with that of Mars or Venus orthe suggested lsquosnowball Earthrsquo state Gaia is more com-plex and less lsquofrozenrsquo into order (of course Mars is literallyfrozen as would be the snowball Earth) It has been sug-gested that the Earthrsquos biota is in a self-organized criticalstate on the basis that extinction events have a distributionclosely approximated by a power law (Kauffman 1993)Proponents of complexity theory propose that the majorityof all extinction events are internally generated by thedynamics of coevolution of species If so this would indi-cate criticality of the biota but not necessarily criticalityof Gaia An alternative hypothesis is that the majority ofextinction events are caused by external perturbation Inthe case of mass extinctions there is good evidence for acausative asteroid impact at the CretaceousndashTertiaryboundary 65 Myr ago (Alvarez et al 1980) Simple mod-els of coevolution (Bak amp Sneppen 1993) or of environ-mental stress (Newman 1997) (without speciesinteraction) as the cause of extinction both exhibit apower law Of the two the environmental stress modelhas an exponent much closer to actual data We concludethat although some extinction may result from coevo-lution there is not yet a convincing case that the biota isin a critical state To test whether Gaia is in a critical statea frequency response analysis of environmental recordsmight be more appropriate For example the carbondioxide and methane records in the Vostok ice core(Petit et al 1999)

6 EMERGENCE OF GAIA

Complexity theory stimulates us to search for a com-plexity threshold for a planet with life beyond which theemergence of self-organization (including self-regulation)and adaptive behaviour becomes likely in other wordsa planetary analogue for the emergence of auto-catalyticnetworks (Kauffman 1993) In coupled open systems oflife and environment does self-organization become vastlymore probable beyond a critical lsquosizersquo (eg number of

Phil Trans R Soc Lond B (2002)

organisms) Also can we pinpoint a particular time in theEarthrsquos history when Gaia emerged

Once life arose it must soon have depleted its surround-ings of substrates thus posing a pressing need for recy-cling Key biogeochemical transformations of essentialelements are present deep in the tree of life among theancient kingdoms of archaea and bacteria supporting aview that nutrient recycling evolved early One furtherrequirement is important for the emergence of planetaryscale self-organization in order to achieve global signi -cance life must have an abundant source of free energyThe earliest types of photosynthesis used relatively scarcesubstrates such as H2S Once oxygenic photosynthesisemerged using the abundant H2O as a substrate then the ux of free energy captured by the biota increased mas-sively (DesMarais 2000) Thus we suggest the genesis ofGaia came with the origin of widespread oxygenic photo-synthesis This occurred at least 28 Gyr ago (DesMarais2000) and possibly as early as 38 Gyr ago (Schidlowski1988)

A remarkable property of Gaia that demands an expla-nation is that its abiotic state variables have stayed at lev-els that support abundant life for most of the last 38 GyrEarly strong versions of the Gaia hypothesis suggestedthat all life-forbidding state variable levels are unreachablebecause there is selection against the processes that wouldlead there Selection at the level of the system as a wholeseems untenable (Doolittle 1981 Dawkins 1983) How-ever it may still be the case that life-forbidding state-vari-able levels are dif cult to reach for at least two reasons(i) if an organism is driving an environmental variabletowards an uninhabitable state its growth and spread willbe suppressed (by negative feedback) such that the systemwill stabilize within the habitable regime and (ii) when-ever organisms become so abundant that the side-effectsof their metabolism become life-threatening on a globalscale different organisms will evolve for which the abun-dant pollutants and the polluters themselves becomeresources If natural selection has enough substrate(genotypic variation) on which to operate such checksand balances are always likely to evolve and make extremeconditions unreachable This old idea (originating fromSmith 1776) could explain the likelihood of regulation atliveable levels as a side-effect of evolution in suf cientlydiverse biota

Uninhabitable or barely habitable states (with life inrefugia) can be reached because of global scale environ-mental perturbation eg massive asteroid impact (Watson1999) or extreme external forcing eg future increases insolar luminosity (Lovelock amp Whit eld 1982 Lenton ampVon Bloh 2001) It is also possible that the evolution ofparticularly strong biotic effects could lsquoovershootrsquo anddrive the environment into a barely habitable stateespecially if there is a time-delay in self-limiting negativefeedback (this is a counter argument to (i) above) Fur-thermore variables that cannot function as a resource toany organism may be able to build up to toxic levels (acounter argument to (ii) above) However useless anddangerous waste products may generally kill off their pro-ducers before disrupting the functioning of Gaia as awhole

Gaia has suffered massive perturbations (asteroidimpacts) and lsquosnowball Earthrsquo states may have occurred

690 T M Lenton and M van Oijen Gaia as a complex adaptive system

in which life only hung on in refugia However abundantlife has always reappeared sometimes remarkably quickly(DrsquoHondt et al 1998) New types of life appear in thewake of mass extinction but there is also a system lsquomem-oryrsquo carried in the gene pool This suggests an interestingpossibility if in response to perturbation a new traitevolves that contributes to recovery then if it remains inthe gene pool and a similar perturbation occurs again thesystem may recover faster the second time In this senseGaia may gain from experience

7 SIMULATING PLANETARY SCALE EMERGENCEWITH DAISYWORLDS

The persistence of life and recovery of Gaia from per-turbation suggest that self-regulation occurs We wouldlike to know how it can emerge and whether it is a chanceor a highly probable outcome of lifendashenvironment coup-ling The feasibility and probability of the emergence ofplanetary scale lsquoself-organizationrsquo andor lsquoadaptive behav-iourrsquo can be evaluated using a synthetic approach of math-ematical modelling

The rst such attempt to simulate the emergence ofplanetary scale self-regulation was the Daisyworld model(Watson amp Lovelock 1983) In Daisyworld global tem-perature regulation emerges automatically from feedbackcoupling between life and its environment with selectionat the component (individual organism) but not the sys-tem (whole planet) level In Daisyworld the environmentis reduced to one variable temperature and life is reducedto two types black and white daisies inhabiting bareground The daisies share the same optimum temperaturefor growth of 225 degC and outer limits to growth of 5 degCand 40 degC The daisy types affect their environment inopposite ways by virtue of their different re ectivity(albedo) The white daisies re ect more solar radiationthan bare ground whilst the black daisies absorb moreHence the local temperature of the daisies differs blackdaisies are always warmer and white daisies are alwayscooler than bare ground The system is forced by a gradualincrease in solar luminosity as has occurred on the Earth

With only one type of daisy present there is a range offorcing for which negative feedback occurs and a point atwhich positive feedback occurs In the case of black daisiesonly when they can establish their spread is ampli ed bypositive environmental feedback (similar to gure 2c butthe effect of life on the environment is stronger) As lumi-nosity increases the population of black daisies declinesthus providing negative feedback on temperature In thecase of white daisies only when they can germinate theirspread is immediately suppressed by their cooling effectAs luminosity increases their population increases pro-viding negative feedback on temperature A regime isentered where white daisies maintain the planet in a habit-able state when otherwise it would be uninhabitable( gure 2d) Eventually they collapse catastrophically withpositive feedback With both types of daisy present thereis a range of forcing for which global temperature actuallydecreases as forcing increases This is an example oflsquosuper-negativersquo feedback (the sign of response is oppositeto that of the forcing (Sardeshmukh 2000))

The Daisyworld model has been portrayed as a CAS(Lewin 1993) but this deserves closer examination It

Phil Trans R Soc Lond B (2002)

possesses rst-order feedback control (table 1) and theregime of super-negative feedback was unexpected fromits parts However the original model does not explicitlyinclude interacting local components The system isdescribed by coupled equations and its behaviour can beunderstood analytically (Saunders 1994 Weber 2001)

If time-delays are introduced into the population andtemperature equations of Daisyworld then apparentlychaotic behaviour can be generated (Zeng et al 1990)Varying the time-delay reveals a series of period doublingscharacteristic of the transition from order to deterministicchaos (De Gregorio et al 1992ab) There is no real-worldjusti cation for the time-delays and it has been shownthat the average of the lsquochaoticrsquo solutions is close to thetemperature regulation in the original model (Jascourt ampRaymond 1992) Introducing an unrealistically large heatcapacity to Daisyworld generates limit cycle oscillations ofthe two daisy populations and temperature (Nevison et al1999) (ie generates the rst period doubling) Thesestudies show that the original Daisyworld model resideswell into the ordered regime and is not in a critical state

Subsequent versions of Daisyworld arguably show theemergence of higher-order control (although the nal prop-erty of temperature regulation is similar in each case)Variants of the model with adaptation of the optimumgrowth temperature of the daisies (Robertson amp Robinson1998 Lenton amp Lovelock 2000) include alteration ofparameters but this is enforced through further para-meters A more fully second-order control system is a Dai-syworld with random mutation of daisy albedo (some ofthe parameters) and subsequent selection (Lenton 1998Lenton amp Lovelock 2001) The structure of this modelcould be said to change in that new daisy lsquospeciesrsquo appearThis suggests there may be some third- and fourth-ordercontrol

8 CA DAISYWORLDS

To ful l the CAS criteria models must include localinteraction of components CA provide a tool for thisHence we have followed the lead of others (Von Bloh etal 1997) and constructed a CA version of Daisyworld toexplore the effects of local interaction and the capacity foradaptive system behaviour The original equations(Watson amp Lovelock 1983) are retained where possibleThe CA grid and rules are simply used to replace thepopulation equations We consider a square grid witheight neighbours to each cell rather than four nearestneighbours (Von Bloh et al 1997) There is no diffusivetemperature eld just the original equations for local tem-peratures of daisies (determined by albedo global tem-perature and insulation parameter q) and globaltemperature (determined by average albedo of the systemand luminosity forcing) Seeding is used to enable popu-lations to establish (but once they are established it haslittle impact) First we consider the original case of popu-lations of lsquoblackrsquo (albedo aB = 025) and lsquowhitersquo (albedoaW = 075) daisies covering bare ground (albedo aG = 05)For an empty cell with nB black neighbours each withgrowth rate b B and nW white neighbours each with growthrate b W the following colonization rules apply

The probability that black will colonize when only theyare present is

Gaia as a complex adaptive system T M Lenton and M van Oijen 691

P(B|nW = 0) = 1 2 (1 2 b B)nB (81)

The probability that white will colonize when only theyare present is

P(W|nB = 0) = 1 2 (1 2 b W )nW (82)

The probability that the cell remains empty is

P(E) = (1 2 P(B|nW = 0))(1 2 P(W|nB = 0)) (83)

The probability that black will colonize when both arepresent is

P(B) = (1 2 P(E))P(B|nW = 0)

P(B|nW = 0) 1 P(W|nB = 0) (84)

The probability that white will colonize when both arepresent is

P(W) = (1 2 P(E))P(W|nB = 0)

P(B|nW = 0) 1 P(W|nB = 0) (85)

The probability of seeding an empty cell is xed

P(S) = h ( h = 0001 in the results shown) (86)

The probability of death at an occupied cell is also xed

P(D) = g ( g = 03 as in the original model) (87)

The 2D CA model has less smooth dynamics than theoriginal zero-dimensional model in that it can exhibitbifurcations and limit cycling ( gure 4) The growth equa-tions are such that for one type alone ( gure 4ac) it canreach carrying capacity on the grid even when its localtemperature and growth rate are sub-optimal This isbecause the presence of many identical neighbours canmake colonization of an empty cell highly probable evenwhen growth rate is suppressed by temperature (equations(81) or (82)) For black daisies alone ( gure 4ab) asforcing is increased a bifurcation point is reached wherethe global temperature is such that the local temperatureof black daisies becomes uninhabitable (b B = 0 when thetemperature of black daisies TB = 40 degC) This generatespartial collapse (ca 30 die-back of the daisies) immedi-ate recovery and resulting oscillations of temperature andpopulation As forcing is increased further a second bifur-cation point is reached Then the trajectories combinebefore the black daisies disappear For white daisies alone( gure 4cd) there are two period doublings and thebeginnings of a third (inset in gure 4d) before a returnto a single trajectory

The one daisy-type model illustrates an lsquoovershootrsquoproblem for Gaia life may develop the capacity to drivean environmental variable into an uninhabitable or barelyhabitable state if the environmental effect is strong andlocal interactions that encourage growth outweigh nega-tive feedback on growth from the environment The modeldoes not include natural selection in that all the daisiesare identical and are always equally t in terms of growthrate (although in the initial growth phase clusters formand cells at the edge of clusters are better able to spreadthan those within clusters) The model does include a sys-tem selection process between bare ground and one daisytype under a certain range of forcing daisies are selectedover bare ground outside that range bare ground willsuccessfully take over from daisies

Phil Trans R Soc Lond B (2002)

When black and white types can both arise the limitcycle regimes are removed and the solution resembles theoriginal zero-dimensional model ( gure 4ef ) The twodifferent daisy types have different growth rates and hence tness thus adding a crude form of natural selection tothe model (although there is no evolution) With thisadditional selective process the model stays more rmlyin the ordered regime The system is stabilized by at leastthree effects (i) if one daisy type reaches an uninhabitabletemperature the other may still be able to spread (becausetheir local temperatures differ) (ii) in the mid-range offorcing a combination of black and white generates a glo-bal temperature closer to optimal and (iii) the presenceof one daisy type reduces the area available to the otherto expand into

We have introduced random mutation of albedo to themodel generalizing the colonization equations (81)ndash(85)to deal with any albedo type Mutation is assumed alwaysto occur in the process of colonization of an empty cell(asexual reproduction that always generates mutatedoffspring) Albedo can mutate within a parameterizedwidth of the parent albedo (plusmn D a) Within this rangeeither side of the parent albedo an offspring albedo is ran-domly chosen Limits to mutation are set at am in = 0 andam ax = 1

With mutation and natural selection within the modelsystem ( gure 5) its behaviour could be said to be lsquoadap-tiversquo in that it lsquoevolvesrsquo to counteract forcing When themodel is seeded with the original lsquoblackrsquo daisies(aB = 025) and these are allowed to mutate as forcingincreases progressively paler daisies evolve cooling theplanet and then maintaining the temperature close to con-stant Increasing D a brings the average planetary tempera-ture more rapidly towards the optimum for daisy growthThe tendency for bifurcation ( gure 4a) is removed byincreasing D a ( gure 5) because this tends to generate anearly increase in average albedo In a sensitivity analysisof the stabilizing effect of albedo diversity am ax ndash am in wasprogressively increased around a central value ofaB = 025 without any mutation and this was also foundto remove the bifurcations Albedo mutation extends therange of temperature regulation beyond that in the originalmodel because paler types than the original lsquowhitersquo onescan arise The latter result has been found in other vari-ants of Daisyworld (Stocker 1995 Von Bloh et al 1997Lenton amp Lovelock 2001)

A more complex 2D CA version of Daisyworld has pre-viously been formulated with albedo mutation and a con-tinuous temperature eld (Von Bloh et al 1997) Thissystem exhibits the remarkable property that underenforced habitat fragmentation using a percolating fractalthe system is able to regulate temperature unimpaired upto a lsquocriticalrsquo threshold at which daisy areas become iso-lated and regulation starts to break down Once uninhabi-ted land forms a spanning cluster regulation is completelyremoved By contrast trivial reductions in habitat (eg agrowing square of lsquoconcretersquo) impair temperature regu-lation in a linear fashion In the former case adjacent dai-sies can affect the temperature of small uninhabited areasbut overall temperature regulation depends on compe-tition among daisies across an entire connected space Inother words the emergent property of global temperatureregulation relies on uninhibited local interaction tting

692 T M Lenton and M van Oijen Gaia as a complex adaptive system

100

50

0

80

60

40

20

0

plusmn20

100

50

0

100

50

0

80

60

40

20

0

plusmn20

80

60

40

20

0

plusmn20

05 10 15 20

05 10 15 20

05 10 15 20 05 10 15 20

05 10 15 20

05 10 15 20

solar luminosity (_) solar luminosity (_)

solar luminosity (_) solar luminosity (_)

solar luminosity (_) solar luminosity (_)

gri

d c

over

(

)g

rid

cov

er (

)

gri

d c

ov

er (

)

glo

bal

tem

per

ature

(degC

)g

lob

al t

emp

erat

ure

(degC

)g

lob

al t

emper

atu

re (

degC)

15

plusmn508 11

(a) (b)

(c) (d)

(e) ( f )

Figure 4 Simulations of xed albedo populations in a simple CA Daisyworld (64 acute 64 grid) Parameters are as in the originalmodel (Watson amp Lovelock 1983) and the CA rules are described in sect 8 Solar luminosity (in normalized units) is increased insteps of 0004 at each of which the model is updated The left-hand graphs show percentage grid cover by the daisies versusluminosity and the right-hand graphs show global average temperature (degC) versus luminosity Temperature is a function ofluminosity and the albedo a and grid cover of daises and empty cells (ab) Seeding with lsquoblackrsquo daisies (aB = 025) denotedby lled circles (cd) Seeding with lsquowhitersquo daisies (aW= 075) denoted by open circles (ef ) Seeding with both black and whitedaisies (albedo of each seed chosen at random) The inset in (d ) shows the period doubling in the temperature trajectory withonly white daisies

in nicely with the criteria for a CAS The system is self-organizing and may arguably be in a critical state near thelimit at which daisy areas become disconnected

9 FEASIBILITY TESTS OF GAIA USING lsquoALIFErsquo

A key criticism of Daisyworld is that it is limited in onlyconsidering one predetermined type of interactionbetween the local and the global and it is one that will

Phil Trans R Soc Lond B (2002)

tend to generate regulation The daisies affect theirenvironment in the same way at the local and the globalscale Hence what is selected for at the individual leveltends to be bene cial at the global level With two or moredaisy types present there is negative selective feedbackmaking regulation likely (Lenton 1998)

lsquoAlifersquo techniques offer a promising way of makingunbiased tests of the potential for emergence of planetaryscale self-organization The model environment lsquoTierrarsquo

Gaia as a complex adaptive system T M Lenton and M van Oijen 693

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

0

20151005

solar luminosity (ndash)

grid

cov

er (

)

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

(a) (b)

(c)(d)

( f )(e)

Figure 5 CA Daisyworld simulations with albedo mutation (64 acute 64 grid) In each simulation there is seeding with theoriginal lsquoblackrsquo daisies (aB = 025) which fall in the range coloured in blue The model is updated with each increase in solarluminosity of 0004 normalized units and at each update empty cells can be colonized with offspring cells that differ at mostby plusmn D a from the albedo of their parent cell Left- and right-hand graphs show grid cover by daisy populations () and globalaverage temperature (degC) respectively The albedo colour scheme in the left-hand graphs is 0ndash02 black 02ndash04 blue 04ndash06 green 06ndash08 orange 08ndash10 red The graphs show the effect of increasing mutation range (ab) D a = 001 (cd) D a =002 (ef ) D a = 01

(Ray 1991) evolved a community of arti cial life-formsthat reproduce in different ways including parasiticallyThe model lsquolife-formsrsquo compete for resource (processortime) but they do not produce waste products Hencetheir interaction with their environment is not thermody-namically complete in the way that it is for real life-formswhich can only maintain an ordered (low entropy) stateby transforming matter as well as energy

The evolution of matter recycling is addressed usinglsquoAlifersquo techniques in the Guild model (Downing amp Zvirin-sky 1999) From one ancestral lsquospeciesrsquo a communityevolves which is able to recycle a given set of lsquochemicalsrsquo(which can be thought of as different molecular forms ofthe same key nutrient element) Such recycling enablesgreatly enhanced productivity in real ecosystems and Gaia

Phil Trans R Soc Lond B (2002)

(Volk 1998) The mechanism of emergence of recyclingis quite different from the spontaneous emergence of auto-catalytic cycles in systems of very large numbers of chemi-cal reactions (Kauffman 1993) In the Guild model lsquoAlifersquochances upon closed recycling of a small set of chemicalsand this is reinforced by selection This illustrates part ofthe mechanism (ii) that we highlighted in sect 6

The main criticisms of the original Guild model are thatthere is no treatment of energy in the system and that adeviation of the local environment from the global isassumed that may not be justi ed for some real world ana-logues A lsquoGuild IIrsquo model is being developed (K Down-ing personal communication) that includes free energyand entropy in the abstract chemistry (eg it takes freeenergy to build larger molecules) and makes the local

694 T M Lenton and M van Oijen Gaia as a complex adaptive system

environment the interior of proto-cells In this modeldespite a relatively small input of free energy in chemicalform recycling and regulation can emerge

An ideal model world for testing Gaia would containarti cial life-forms that transform lsquomatterrsquo and lsquoenergyrsquoare lsquothermodynamicallyrsquo constrained grow and replicatewith a heritable genome subject to random mutationinteract with one another and evolve new ways of alteringtheir environment related to their internal functioningThe environment would contain many lsquophysicalrsquo andlsquochemicalrsquo variables some homogeneous (well mixed) andothers heterogeneous The resulting system behaviourwould be observable and testable by perturbation

10 CONCLUSIONS

Many scientists now accept that planetary regulationinvolving the biota occurs (Longhurst 1998) However westill have to determine whether Gaiarsquos coming into exis-tence and survival was coincidental or probable and howfragile or robust the system is at present We have arguedthat Gaia is a complex system with self-organizing andadaptive behaviour but that it does not reside in a criticalstate Complexity theory modelling approaches havehelped us simulate and understand the emergence of plan-etary order lsquoAlifersquo techniques can take this further andhelp in assessing the probability of emergence of planetaryregulatory properties Our attempts to apply complexitytheory to Gaia have yielded a broader view of selectionthan previously encompassed in the Gaia theory (Lenton1998) Gene-based natural selection is just one type andlevel of selection operating within Gaia and it is not anecessary condition for regulation The existence of differ-ent types of selection operating at different levels makes iteasier to understand how planetary-scale self-regulationcan arise It also makes it easier to accept that a Gaia-likesystem may be a probable outcome once there is abundantlife on a planet with the capacity for large-scale freeenergy capture

We thank Ricard Sole and Simon Levin for the invitation towrite this article

REFERENCES

Alvarez L W Alvarez W Asaro F amp Michel H V 1980Extraterrestrial cause for the CretaceousndashTertiary extinctionScience 208 1095ndash1108

Bak P amp Sneppen K 1993 Punctuated equilibrium and criti-cality in a simple model of evolution Phys Rev Lett 714083ndash4086

Bak P Tang C amp Wiesenfeld K 1987 Self-organized criti-calitymdashan explanation of 1f noise Phys Rev Lett 59381ndash384

Berner R A 1998 The carbon cycle and CO2 over Phanero-zoic time the role of land plants Phil Trans R SocLond B 353 75ndash82 (DOI 101098rstb19980192)

Betts R A 1999 Self-bene cial effects of vegetation on cli-mate in an oceanndashatmosphere general circulation modelGeophys Res Lett 26 1457ndash1460

Bonan G B Pollard D amp Thompson S L 1992 Effects ofboreal forest vegetation on global climate Nature 359716ndash718

Budyko M I 1968 The effect of solar radiation variations onthe climate of the Earth Tellus 21 611ndash619

Phil Trans R Soc Lond B (2002)

Dawkins R 1983 The extended phenotype Oxford UniversityPress

De Gregorio S Pielke R A amp Dalu G A 1992a Feedbackbetween a simple biosystem and the temperature of theEarth J Nonlinear Sci 2 263ndash292

De Gregorio S Pielke R A amp Dalu G A 1992b A delayedbiophysical system for the Earthrsquos climate J Nonlinear Sci2 293ndash318

DesMarais D J 2000 When did photosynthesis emerge onEarth Science 289 1703ndash1705

DrsquoHondt S Donaghay P Zachos J C Luttenberg D ampLindinger M 1998 Organic carbon uxes and ecologicalrecovery from the CretaceousndashTertiary mass extinctionScience 282 276ndash279

Doolittle W F 1981 Is nature really motherly The CoEvol-ution Q Spring 58ndash63

Downing K amp Zvirinsky P 1999 The simulated evolutionof biochemical guilds reconciling Gaia theory and naturalselection Artif Life 5 291ndash318

Ehrlich P 1991 Coevolution and its applicability to the Gaiahypothesis In Scientists on Gaia (ed S H Schneider amp PJ Boston) pp 118ndash120 London MIT Press

Gallagher R amp Appenzeller T 1999 Beyond reductionismScience 284 79

Hamilton W D 1995 Ecology in the large Gaia and GenghisKhan J Appl Ecol 32 451ndash453

Hamilton W D 1996 Gaiarsquos bene ts New Scientist 15162ndash63

Hamilton W D amp Lenton T M 1998 Spora and Gaia howmicrobes y with their clouds Ethol Ecol Evol 10 1ndash16

Han T-M amp Runnegar B 1992 Megascopic eukaryotic algaefrom the 21 billion-year-old Negaunee iron-formationMichigan Science 257 232ndash235

Hoffman P F Kaufman A J Halverson G P amp SchragD P 1998 A Neoproterozoic snowball earth Science 2811342ndash1346

Holland J 1995 Hidden order how adaptation builds complexityReading MA Addison-Wesley

Hyde W T Crowley T J Baum S K amp Peltier W R2000 Neoproterozoic lsquosnowball Earthrsquo simulations with acoupled climateice-sheet model Nature 405 425ndash429

Imshenetsky A A Lysenko S V amp Kazakov G A 1978Upper boundary of the biosphere Appl Environ Microbiol35 1ndash5

Isaacs A Daintith J amp Martin E (eds) 1996 Concise sciencedictionary Oxford University Press

Jascourt S D amp Raymond W H 1992 Comments on lsquoChaosin daisyworldrsquo by X Zeng et al Tellus 44B 243ndash246

Joslashrgensen S E amp Straskraba M 2000 Ecosystems as cyber-netic systems In Handbook of ecosystem theories and manage-ment (ed S E Joslashrgensen amp F Muller) pp 249ndash264London Lewis Publishers

Kasting J F 1991 Box models for the evolution of atmo-spheric oxygen an update Global and Planetary Change 97125ndash131

Kauffman S A 1993 The origins of order self-organization andselection in evolution Oxford University Press

Kleidon A 2002 Testing the effect of life on Earthrsquos func-tioning how Gaian is the Earth system Climatic Change 52383ndash389

Klinger L F 1991 Peatland formation and ice ages a possibleGaian mechanism related to community succession InScientists on Gaia (ed S H Schneider amp P J Boston) pp247ndash255 London MIT Press

Koeslag J H Saunders P T amp Wessels J A 1997 Glucosehomeostasis with in nite gain further lessons from theDaisyworld parable J Endocrinol 154 187ndash192

Lenton T M 1998 Gaia and natural selection Nature 394439ndash447

Gaia as a complex adaptive system T M Lenton and M van Oijen 687

feedback effect snow and ice form surfaces that are highlyre ective (high albedo) to solar radiation thus coolingtheir surroundings and encouraging the spread of snowicecover In simple models a modest reduction in solar inputis ampli ed by this feedback to cause complete ice coverof the Earth (Budyko 1968 Sellers 1969) the so-calledlsquosnowball Earthrsquo (Hoffman et al 1998) Recent simula-tions suggest that a lsquoslushball Earthrsquo state with open waterin equatorial oceans may be more realistic and less fatalto life (Hyde et al 2000) If a snowball Earth attractorexists it should be unstable because CO2 input from vol-canoes can gradually accumulate in the atmosphere untilradiative forcing is suf cient to melt continental ice cover

A key challenge to Gaia theory from evolutionary biol-ogists is to explain how order especially self-regulationcan arise at the global scale without invoking teleology orselection at the level of the planet (Doolittle 1981 Daw-kins 1983) Such criticisms inspired the formulation of theDaisyworld model (Lovelock 1983 Watson amp Lovelock1983) which demonstrates that self-regulation canemerge automatically from competing populations alter-ing their local environments in different ways (see sect 7 andsect 8) The idea that evolution within Gaia could have pro-duced organisms that contribute to regulating the planetis still variously criticised as untenable altruism vulnerableto cheats or demanding large-scale group selection(Hamilton 1995) It is sometimes argued that randomvariation and natural selection are necessary and suf cientto explain the self-regulation of organisms and candidatesuper-organisms (eg temperature regulated social insectcolonies Ehrlich 1991) in which case self-regulation ofGaia could not occur However regulation can emergeautomatically (Saunders 1994 Watson 1999) and hencethe mechanisms by which regulation emerges in physi-ology may have parallels at the planetary scale (Koeslaget al 1997 Saunders et al 1998) even though planetaryregulation cannot be re ned by selection We think thatwith an appreciation of feedback principles the theoriesof Gaia and natural selection can be reconciled (Lenton1998)

Equally there is a need to extend the original cyberneticview of Gaia to encompass evolution The continuousgeneration and selection of different environment-alteringtraits ensures that the feedback structure of Gaia remainsdynamic Evolution within the biota drives changes in thestate parameters and structure of the system (eg the riseof atmospheric oxygen) This in turn facilitates the evolu-tion of new forms of life It can also alter the set pointsof regulation when they are not xed by thermodynamicchemical or geophysical constraints (Lenton amp Lovelock2000) Complexity theory may provide a framework fordeveloping Gaia theory by synthesizing principles fromcybernetics and evolutionary biology

4 COMPLEXITY THEORY

Complexity theory is a general theory of complexdynamic systems The Latin complexus comes from theGreek pleko meaning to plait or twine Thus a complexsystem is literally one consisting of interwoven partsComplex can also mean dif cult to understand or analyseA broad de nition of a complex system is one whoseproperties are not fully explained by an understanding of

Phil Trans R Soc Lond B (2002)

dynamical

systems

complex

ordered

critical

chaotic

simple

Figure 3 A subdivision of dynamical systems in terms ofbehaviour

its component parts (Gallagher amp Appenzeller 1999) Bycontrast simple systems are ones whose properties arefully explained by the properties of their component parts(eg a pendulum) Emergence describes the collectivebehaviour of complex systems It can be local or globalLocal emergent properties are well studied in physicswhere they are often termed lsquointensive propertiesrsquo (egpressure and temperature of an ideal gas) Global emer-gent properties are the more original focus of complexitytheory

Complexity theory aims to understand the origin oforganization In doing so it adopts different modellingmethodologies to those commonly used to study speci csystems For example rather than predicting the dynamicsof a given organization rules of interaction between allpossible objects are speci ed and it is left open whichobjects appear in a given simulation An example of thisapproach is the use of CA Attempts to simulate lsquoAlifersquocommunities and ecosystems are also particularly relevantto Gaia

The relationship between complexity theory and otherdisciplines can be viewed in terms of a behavioural classi- cation of systems ( gure 3) In this case complex sys-tems are a subset of dynamical systems and complexitytheory is part of dynamic systems theory which also con-siders simple systems Complex systems can be subdividedinto ordered systems critical systems and chaotic systemsChaos describes unpredictable behaviour emerging fromnonlinear equations giving high sensitivity to initial con-ditions Order describes a tendency to reside in one stateor limit cycle between a limited number of states Betweenfrozen order and unpredictable chaos much interest hasbeen focused on a critical regime dubbed lsquothe edge ofchaosrsquo Complexity theory can be seen as an extension ofcybernetics (control theory) which focuses on feedbackand feed-forward systems with predictable behaviour Italso encompasses AI and lsquoAlifersquo research By contrastchaos theory focuses on systems with unpredictablebehaviour

This special issue focuses on the subset of CAS A lsquobot-tom-uprsquo de nition of a CAS has been given (Levin 1998)based on three essential elements (i) sustained diversityand individuality of components (ii) localized interactionamong those components and (iii) an autonomous pro-cess that selects from among these components based onthe results of local interactions a subset for replication orenhancement From these essential elements it is argued(Levin 1998) that the following properties (Holland 1995)emerge (1) continual adaptation (2) absence of a globalcontroller (3) hierarchical organization (4) generation of

688 T M Lenton and M van Oijen Gaia as a complex adaptive system

Table 1 Orders of control in complex systems (after Joslashrgensen amp Straskraba 2000)

order scope for adaptation example system discussed in text

rst xed parameters and structure original Daisyworld modelsecond variable parameters xed structure CA Daisyworldthird variable structure and parameters lsquoAlifersquo Guild modelfourth change of goal functions Gaia ()

perpetual novelty and (5) far-from-equilibrium dynamicsCommonly given examples of CASs are cells individualorganisms and ecosystems

What is the typical behaviour of a CAS First they dis-play lsquoself-organizationrsquo in the sense of emergence ofordered behaviour and structure from many parts withsuf cient connections independent of natural selection(Kauffman 1993) The concept was inspired by the resultsof mathematical models which starting from arbitraryinitial conditions and obeying only simple local rules pro-duced large-scale order The second law of thermody-namics forbids true self-organization increasing order isonly possible in thermodynamically open systems Thusself-organization is dissipative requiring free energy inputand producing high-entropy output CASs may also showlsquoself-organized criticalityrsquo (Bak et al 1987) meaning atendency to reside in the edge of chaos regime allowingchange without getting locked into frozen order A power-law distribution of responses is thought to be characteristicof self-organized critical systems but may occur morewidely in nature

Complex systems can be described in terms of theirorder of dynamics and control (Joslashrgensen amp Straskraba2000 table 1) First-order dynamical systems have xedparameters and structure and hence can only achievefeedback control Second-order dynamical systems havevariable parameters as well as states but xed structureThird-order systems have variable structure as well asparameters and states The distinction in fourth-order sys-tems is that changes in states parameters and structurelead to a change in the goal functions that determine thelong-term behaviour of a system (Wilhelm amp Bruggemann2000) How do CASs t into this classi cation Theelement of replication or enhancement indicates that theirstructure is variable allowing third-order control Thegeneration of continual adaptation suggests that CASs arefourth order with internally generated changes in goalfunctions

In what sense are such behaviours adaptive Adaptationhas two common meanings in biology (i) in evolution itis a change in the structure or functioning of organismsthat makes them better suited to their environment and(ii) in physiology it is an alteration in an organismrsquosresponse to its environment Evolutionary adaptation (i) isusually thought of as the consequence of natural selectionacting on heritable variation The capacity for physiologi-cal adaptation (ii) can be the product of evolutionaryadaptation (i) lsquoAdaptiversquo is used in complexity theory todescribe system development as well as response and isoften applied to systems that are not subject to naturalselection as a whole (although their parts may be) Hencelsquoadaptiversquo behaviours described by complexity theoristsare not necessarily lsquoadaptationsrsquo in the sense used by evo-

Phil Trans R Soc Lond B (2002)

lutionary biologists (i) or physiologists (ii) One way outof this semantic mine eld is to consider natural selectionas just one (rather than the only) form of selection Otherforms of selection can emerge at levels above that of natu-ral selection acting on heritable variation eg in the pro-cess of foraging by social insect colonies utilizingpheromone signals (stigmurgy) or in models of the evo-lution of altruism as a consequence of emergent spatialpatterns (Paolo 2000) If selection can be broader thanjust natural selection then there can be lsquoadaptiversquo behav-iours that are not necessarily the product of natural selec-tion

5 IS GAIA A COMPLEX ADAPTIVE SYSTEM

Gaia is a complex system in that it has many interwovenparts and properties that are not fully explained by anunderstanding of the parts for example the stability ofcomponents of the atmosphere Gaia also ful ls the CAScriteria given previously (Levin 1998) as it contains sus-tained diversity and individuality of components (egorganisms) localized interaction among these compo-nents and at least one autonomous selection process(natural selection) Gaia also possesses non-local interac-tion of components because there is global mixing of theatmosphere and oceans This gives rise to globally mixedvariables atmospheric gases with lifetimes longer thanatmospheric mixing (ca 1 yr) and dissolved chemicalspecies in the ocean with lifetimes longer than ocean mix-ing (ca 1000 yr) There are also non-local interactions inthe climate system described as lsquoteleconnectionsrsquo

If Gaia is a CAS we can expect it to display character-istic properties and behaviour Gaia does indeed sharegeneric CAS properties (Holland 1995) far-from equilib-rium dynamics (of life the atmosphere and aspects ofocean chemistry) generation of perpetual novelty(through evolution) hierarchical organization (eg organ-isms ecosystems Gaia) and absence of a global control-ler However non-local interaction simpli es the systemand offers the possibility that from its many complexcomponents Gaia could display emergent simplicity in itsbehaviour In what sense might Gaia be adaptive Gaiahas not evolved by natural selection at the whole systemlevel but various types of selection operate within the sys-tem The system can be viewed physiologically as cap-tured in the term lsquogeophysiologyrsquo (Lovelock 1986) andmay respond to forcing in a manner resembling physio-logical adaptation There is change at the system level andthere may also be developmental trends that enhance lifeas a whole eg an increase global gross primary pro-ductivity with time

Is Gaia self-organizing It is often said that Gaia is self-regulating but what order of control (table 1) is actually

Gaia as a complex adaptive system T M Lenton and M van Oijen 689

achieved There are many examples of rst-order feed-back control (examples in sect 3) Gaia also contains evo-lution which continually reshapes the system and thusallows higher levels of system control The evolution ofresponses to prevailing environmental conditions and theevolution of environment-altering traits represent changesin the parameters and structure of the system allowing forsecond- and third-order control For example the coloniz-ation of the land surface by vascular plants altered the cli-mate in a self-bene cial manner (Betts 1999) and led toa reorganization of biogeochemical cycles including adrop in carbon dioxide (Berner 1998) global cooling anda rise in oxygen (Lenton 2001) Changes in the Earthrsquoshistory such as the switch from anaerobic to aerobic con-ditions as oxygen rose ca 2 Gyr ago and the resultingincrease in free-energy availability to the biota could beviewed as fourth-order control a change in goal functionfrom an anaerobic lsquoupside-downrsquo biosphere (Walker1987) to an aerobic attractor state that allowed the pro-liferation of new types of life Thus Gaia may be viewedas self-organizing and more in terms of the levels of con-trol achieved

Is Gaia in a self-organized critical state If one contraststhe current state of Gaia with that of Mars or Venus orthe suggested lsquosnowball Earthrsquo state Gaia is more com-plex and less lsquofrozenrsquo into order (of course Mars is literallyfrozen as would be the snowball Earth) It has been sug-gested that the Earthrsquos biota is in a self-organized criticalstate on the basis that extinction events have a distributionclosely approximated by a power law (Kauffman 1993)Proponents of complexity theory propose that the majorityof all extinction events are internally generated by thedynamics of coevolution of species If so this would indi-cate criticality of the biota but not necessarily criticalityof Gaia An alternative hypothesis is that the majority ofextinction events are caused by external perturbation Inthe case of mass extinctions there is good evidence for acausative asteroid impact at the CretaceousndashTertiaryboundary 65 Myr ago (Alvarez et al 1980) Simple mod-els of coevolution (Bak amp Sneppen 1993) or of environ-mental stress (Newman 1997) (without speciesinteraction) as the cause of extinction both exhibit apower law Of the two the environmental stress modelhas an exponent much closer to actual data We concludethat although some extinction may result from coevo-lution there is not yet a convincing case that the biota isin a critical state To test whether Gaia is in a critical statea frequency response analysis of environmental recordsmight be more appropriate For example the carbondioxide and methane records in the Vostok ice core(Petit et al 1999)

6 EMERGENCE OF GAIA

Complexity theory stimulates us to search for a com-plexity threshold for a planet with life beyond which theemergence of self-organization (including self-regulation)and adaptive behaviour becomes likely in other wordsa planetary analogue for the emergence of auto-catalyticnetworks (Kauffman 1993) In coupled open systems oflife and environment does self-organization become vastlymore probable beyond a critical lsquosizersquo (eg number of

Phil Trans R Soc Lond B (2002)

organisms) Also can we pinpoint a particular time in theEarthrsquos history when Gaia emerged

Once life arose it must soon have depleted its surround-ings of substrates thus posing a pressing need for recy-cling Key biogeochemical transformations of essentialelements are present deep in the tree of life among theancient kingdoms of archaea and bacteria supporting aview that nutrient recycling evolved early One furtherrequirement is important for the emergence of planetaryscale self-organization in order to achieve global signi -cance life must have an abundant source of free energyThe earliest types of photosynthesis used relatively scarcesubstrates such as H2S Once oxygenic photosynthesisemerged using the abundant H2O as a substrate then the ux of free energy captured by the biota increased mas-sively (DesMarais 2000) Thus we suggest the genesis ofGaia came with the origin of widespread oxygenic photo-synthesis This occurred at least 28 Gyr ago (DesMarais2000) and possibly as early as 38 Gyr ago (Schidlowski1988)

A remarkable property of Gaia that demands an expla-nation is that its abiotic state variables have stayed at lev-els that support abundant life for most of the last 38 GyrEarly strong versions of the Gaia hypothesis suggestedthat all life-forbidding state variable levels are unreachablebecause there is selection against the processes that wouldlead there Selection at the level of the system as a wholeseems untenable (Doolittle 1981 Dawkins 1983) How-ever it may still be the case that life-forbidding state-vari-able levels are dif cult to reach for at least two reasons(i) if an organism is driving an environmental variabletowards an uninhabitable state its growth and spread willbe suppressed (by negative feedback) such that the systemwill stabilize within the habitable regime and (ii) when-ever organisms become so abundant that the side-effectsof their metabolism become life-threatening on a globalscale different organisms will evolve for which the abun-dant pollutants and the polluters themselves becomeresources If natural selection has enough substrate(genotypic variation) on which to operate such checksand balances are always likely to evolve and make extremeconditions unreachable This old idea (originating fromSmith 1776) could explain the likelihood of regulation atliveable levels as a side-effect of evolution in suf cientlydiverse biota

Uninhabitable or barely habitable states (with life inrefugia) can be reached because of global scale environ-mental perturbation eg massive asteroid impact (Watson1999) or extreme external forcing eg future increases insolar luminosity (Lovelock amp Whit eld 1982 Lenton ampVon Bloh 2001) It is also possible that the evolution ofparticularly strong biotic effects could lsquoovershootrsquo anddrive the environment into a barely habitable stateespecially if there is a time-delay in self-limiting negativefeedback (this is a counter argument to (i) above) Fur-thermore variables that cannot function as a resource toany organism may be able to build up to toxic levels (acounter argument to (ii) above) However useless anddangerous waste products may generally kill off their pro-ducers before disrupting the functioning of Gaia as awhole

Gaia has suffered massive perturbations (asteroidimpacts) and lsquosnowball Earthrsquo states may have occurred

690 T M Lenton and M van Oijen Gaia as a complex adaptive system

in which life only hung on in refugia However abundantlife has always reappeared sometimes remarkably quickly(DrsquoHondt et al 1998) New types of life appear in thewake of mass extinction but there is also a system lsquomem-oryrsquo carried in the gene pool This suggests an interestingpossibility if in response to perturbation a new traitevolves that contributes to recovery then if it remains inthe gene pool and a similar perturbation occurs again thesystem may recover faster the second time In this senseGaia may gain from experience

7 SIMULATING PLANETARY SCALE EMERGENCEWITH DAISYWORLDS

The persistence of life and recovery of Gaia from per-turbation suggest that self-regulation occurs We wouldlike to know how it can emerge and whether it is a chanceor a highly probable outcome of lifendashenvironment coup-ling The feasibility and probability of the emergence ofplanetary scale lsquoself-organizationrsquo andor lsquoadaptive behav-iourrsquo can be evaluated using a synthetic approach of math-ematical modelling

The rst such attempt to simulate the emergence ofplanetary scale self-regulation was the Daisyworld model(Watson amp Lovelock 1983) In Daisyworld global tem-perature regulation emerges automatically from feedbackcoupling between life and its environment with selectionat the component (individual organism) but not the sys-tem (whole planet) level In Daisyworld the environmentis reduced to one variable temperature and life is reducedto two types black and white daisies inhabiting bareground The daisies share the same optimum temperaturefor growth of 225 degC and outer limits to growth of 5 degCand 40 degC The daisy types affect their environment inopposite ways by virtue of their different re ectivity(albedo) The white daisies re ect more solar radiationthan bare ground whilst the black daisies absorb moreHence the local temperature of the daisies differs blackdaisies are always warmer and white daisies are alwayscooler than bare ground The system is forced by a gradualincrease in solar luminosity as has occurred on the Earth

With only one type of daisy present there is a range offorcing for which negative feedback occurs and a point atwhich positive feedback occurs In the case of black daisiesonly when they can establish their spread is ampli ed bypositive environmental feedback (similar to gure 2c butthe effect of life on the environment is stronger) As lumi-nosity increases the population of black daisies declinesthus providing negative feedback on temperature In thecase of white daisies only when they can germinate theirspread is immediately suppressed by their cooling effectAs luminosity increases their population increases pro-viding negative feedback on temperature A regime isentered where white daisies maintain the planet in a habit-able state when otherwise it would be uninhabitable( gure 2d) Eventually they collapse catastrophically withpositive feedback With both types of daisy present thereis a range of forcing for which global temperature actuallydecreases as forcing increases This is an example oflsquosuper-negativersquo feedback (the sign of response is oppositeto that of the forcing (Sardeshmukh 2000))

The Daisyworld model has been portrayed as a CAS(Lewin 1993) but this deserves closer examination It

Phil Trans R Soc Lond B (2002)

possesses rst-order feedback control (table 1) and theregime of super-negative feedback was unexpected fromits parts However the original model does not explicitlyinclude interacting local components The system isdescribed by coupled equations and its behaviour can beunderstood analytically (Saunders 1994 Weber 2001)

If time-delays are introduced into the population andtemperature equations of Daisyworld then apparentlychaotic behaviour can be generated (Zeng et al 1990)Varying the time-delay reveals a series of period doublingscharacteristic of the transition from order to deterministicchaos (De Gregorio et al 1992ab) There is no real-worldjusti cation for the time-delays and it has been shownthat the average of the lsquochaoticrsquo solutions is close to thetemperature regulation in the original model (Jascourt ampRaymond 1992) Introducing an unrealistically large heatcapacity to Daisyworld generates limit cycle oscillations ofthe two daisy populations and temperature (Nevison et al1999) (ie generates the rst period doubling) Thesestudies show that the original Daisyworld model resideswell into the ordered regime and is not in a critical state

Subsequent versions of Daisyworld arguably show theemergence of higher-order control (although the nal prop-erty of temperature regulation is similar in each case)Variants of the model with adaptation of the optimumgrowth temperature of the daisies (Robertson amp Robinson1998 Lenton amp Lovelock 2000) include alteration ofparameters but this is enforced through further para-meters A more fully second-order control system is a Dai-syworld with random mutation of daisy albedo (some ofthe parameters) and subsequent selection (Lenton 1998Lenton amp Lovelock 2001) The structure of this modelcould be said to change in that new daisy lsquospeciesrsquo appearThis suggests there may be some third- and fourth-ordercontrol

8 CA DAISYWORLDS

To ful l the CAS criteria models must include localinteraction of components CA provide a tool for thisHence we have followed the lead of others (Von Bloh etal 1997) and constructed a CA version of Daisyworld toexplore the effects of local interaction and the capacity foradaptive system behaviour The original equations(Watson amp Lovelock 1983) are retained where possibleThe CA grid and rules are simply used to replace thepopulation equations We consider a square grid witheight neighbours to each cell rather than four nearestneighbours (Von Bloh et al 1997) There is no diffusivetemperature eld just the original equations for local tem-peratures of daisies (determined by albedo global tem-perature and insulation parameter q) and globaltemperature (determined by average albedo of the systemand luminosity forcing) Seeding is used to enable popu-lations to establish (but once they are established it haslittle impact) First we consider the original case of popu-lations of lsquoblackrsquo (albedo aB = 025) and lsquowhitersquo (albedoaW = 075) daisies covering bare ground (albedo aG = 05)For an empty cell with nB black neighbours each withgrowth rate b B and nW white neighbours each with growthrate b W the following colonization rules apply

The probability that black will colonize when only theyare present is

Gaia as a complex adaptive system T M Lenton and M van Oijen 691

P(B|nW = 0) = 1 2 (1 2 b B)nB (81)

The probability that white will colonize when only theyare present is

P(W|nB = 0) = 1 2 (1 2 b W )nW (82)

The probability that the cell remains empty is

P(E) = (1 2 P(B|nW = 0))(1 2 P(W|nB = 0)) (83)

The probability that black will colonize when both arepresent is

P(B) = (1 2 P(E))P(B|nW = 0)

P(B|nW = 0) 1 P(W|nB = 0) (84)

The probability that white will colonize when both arepresent is

P(W) = (1 2 P(E))P(W|nB = 0)

P(B|nW = 0) 1 P(W|nB = 0) (85)

The probability of seeding an empty cell is xed

P(S) = h ( h = 0001 in the results shown) (86)

The probability of death at an occupied cell is also xed

P(D) = g ( g = 03 as in the original model) (87)

The 2D CA model has less smooth dynamics than theoriginal zero-dimensional model in that it can exhibitbifurcations and limit cycling ( gure 4) The growth equa-tions are such that for one type alone ( gure 4ac) it canreach carrying capacity on the grid even when its localtemperature and growth rate are sub-optimal This isbecause the presence of many identical neighbours canmake colonization of an empty cell highly probable evenwhen growth rate is suppressed by temperature (equations(81) or (82)) For black daisies alone ( gure 4ab) asforcing is increased a bifurcation point is reached wherethe global temperature is such that the local temperatureof black daisies becomes uninhabitable (b B = 0 when thetemperature of black daisies TB = 40 degC) This generatespartial collapse (ca 30 die-back of the daisies) immedi-ate recovery and resulting oscillations of temperature andpopulation As forcing is increased further a second bifur-cation point is reached Then the trajectories combinebefore the black daisies disappear For white daisies alone( gure 4cd) there are two period doublings and thebeginnings of a third (inset in gure 4d) before a returnto a single trajectory

The one daisy-type model illustrates an lsquoovershootrsquoproblem for Gaia life may develop the capacity to drivean environmental variable into an uninhabitable or barelyhabitable state if the environmental effect is strong andlocal interactions that encourage growth outweigh nega-tive feedback on growth from the environment The modeldoes not include natural selection in that all the daisiesare identical and are always equally t in terms of growthrate (although in the initial growth phase clusters formand cells at the edge of clusters are better able to spreadthan those within clusters) The model does include a sys-tem selection process between bare ground and one daisytype under a certain range of forcing daisies are selectedover bare ground outside that range bare ground willsuccessfully take over from daisies

Phil Trans R Soc Lond B (2002)

When black and white types can both arise the limitcycle regimes are removed and the solution resembles theoriginal zero-dimensional model ( gure 4ef ) The twodifferent daisy types have different growth rates and hence tness thus adding a crude form of natural selection tothe model (although there is no evolution) With thisadditional selective process the model stays more rmlyin the ordered regime The system is stabilized by at leastthree effects (i) if one daisy type reaches an uninhabitabletemperature the other may still be able to spread (becausetheir local temperatures differ) (ii) in the mid-range offorcing a combination of black and white generates a glo-bal temperature closer to optimal and (iii) the presenceof one daisy type reduces the area available to the otherto expand into

We have introduced random mutation of albedo to themodel generalizing the colonization equations (81)ndash(85)to deal with any albedo type Mutation is assumed alwaysto occur in the process of colonization of an empty cell(asexual reproduction that always generates mutatedoffspring) Albedo can mutate within a parameterizedwidth of the parent albedo (plusmn D a) Within this rangeeither side of the parent albedo an offspring albedo is ran-domly chosen Limits to mutation are set at am in = 0 andam ax = 1

With mutation and natural selection within the modelsystem ( gure 5) its behaviour could be said to be lsquoadap-tiversquo in that it lsquoevolvesrsquo to counteract forcing When themodel is seeded with the original lsquoblackrsquo daisies(aB = 025) and these are allowed to mutate as forcingincreases progressively paler daisies evolve cooling theplanet and then maintaining the temperature close to con-stant Increasing D a brings the average planetary tempera-ture more rapidly towards the optimum for daisy growthThe tendency for bifurcation ( gure 4a) is removed byincreasing D a ( gure 5) because this tends to generate anearly increase in average albedo In a sensitivity analysisof the stabilizing effect of albedo diversity am ax ndash am in wasprogressively increased around a central value ofaB = 025 without any mutation and this was also foundto remove the bifurcations Albedo mutation extends therange of temperature regulation beyond that in the originalmodel because paler types than the original lsquowhitersquo onescan arise The latter result has been found in other vari-ants of Daisyworld (Stocker 1995 Von Bloh et al 1997Lenton amp Lovelock 2001)

A more complex 2D CA version of Daisyworld has pre-viously been formulated with albedo mutation and a con-tinuous temperature eld (Von Bloh et al 1997) Thissystem exhibits the remarkable property that underenforced habitat fragmentation using a percolating fractalthe system is able to regulate temperature unimpaired upto a lsquocriticalrsquo threshold at which daisy areas become iso-lated and regulation starts to break down Once uninhabi-ted land forms a spanning cluster regulation is completelyremoved By contrast trivial reductions in habitat (eg agrowing square of lsquoconcretersquo) impair temperature regu-lation in a linear fashion In the former case adjacent dai-sies can affect the temperature of small uninhabited areasbut overall temperature regulation depends on compe-tition among daisies across an entire connected space Inother words the emergent property of global temperatureregulation relies on uninhibited local interaction tting

692 T M Lenton and M van Oijen Gaia as a complex adaptive system

100

50

0

80

60

40

20

0

plusmn20

100

50

0

100

50

0

80

60

40

20

0

plusmn20

80

60

40

20

0

plusmn20

05 10 15 20

05 10 15 20

05 10 15 20 05 10 15 20

05 10 15 20

05 10 15 20

solar luminosity (_) solar luminosity (_)

solar luminosity (_) solar luminosity (_)

solar luminosity (_) solar luminosity (_)

gri

d c

over

(

)g

rid

cov

er (

)

gri

d c

ov

er (

)

glo

bal

tem

per

ature

(degC

)g

lob

al t

emp

erat

ure

(degC

)g

lob

al t

emper

atu

re (

degC)

15

plusmn508 11

(a) (b)

(c) (d)

(e) ( f )

Figure 4 Simulations of xed albedo populations in a simple CA Daisyworld (64 acute 64 grid) Parameters are as in the originalmodel (Watson amp Lovelock 1983) and the CA rules are described in sect 8 Solar luminosity (in normalized units) is increased insteps of 0004 at each of which the model is updated The left-hand graphs show percentage grid cover by the daisies versusluminosity and the right-hand graphs show global average temperature (degC) versus luminosity Temperature is a function ofluminosity and the albedo a and grid cover of daises and empty cells (ab) Seeding with lsquoblackrsquo daisies (aB = 025) denotedby lled circles (cd) Seeding with lsquowhitersquo daisies (aW= 075) denoted by open circles (ef ) Seeding with both black and whitedaisies (albedo of each seed chosen at random) The inset in (d ) shows the period doubling in the temperature trajectory withonly white daisies

in nicely with the criteria for a CAS The system is self-organizing and may arguably be in a critical state near thelimit at which daisy areas become disconnected

9 FEASIBILITY TESTS OF GAIA USING lsquoALIFErsquo

A key criticism of Daisyworld is that it is limited in onlyconsidering one predetermined type of interactionbetween the local and the global and it is one that will

Phil Trans R Soc Lond B (2002)

tend to generate regulation The daisies affect theirenvironment in the same way at the local and the globalscale Hence what is selected for at the individual leveltends to be bene cial at the global level With two or moredaisy types present there is negative selective feedbackmaking regulation likely (Lenton 1998)

lsquoAlifersquo techniques offer a promising way of makingunbiased tests of the potential for emergence of planetaryscale self-organization The model environment lsquoTierrarsquo

Gaia as a complex adaptive system T M Lenton and M van Oijen 693

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

0

20151005

solar luminosity (ndash)

grid

cov

er (

)

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

(a) (b)

(c)(d)

( f )(e)

Figure 5 CA Daisyworld simulations with albedo mutation (64 acute 64 grid) In each simulation there is seeding with theoriginal lsquoblackrsquo daisies (aB = 025) which fall in the range coloured in blue The model is updated with each increase in solarluminosity of 0004 normalized units and at each update empty cells can be colonized with offspring cells that differ at mostby plusmn D a from the albedo of their parent cell Left- and right-hand graphs show grid cover by daisy populations () and globalaverage temperature (degC) respectively The albedo colour scheme in the left-hand graphs is 0ndash02 black 02ndash04 blue 04ndash06 green 06ndash08 orange 08ndash10 red The graphs show the effect of increasing mutation range (ab) D a = 001 (cd) D a =002 (ef ) D a = 01

(Ray 1991) evolved a community of arti cial life-formsthat reproduce in different ways including parasiticallyThe model lsquolife-formsrsquo compete for resource (processortime) but they do not produce waste products Hencetheir interaction with their environment is not thermody-namically complete in the way that it is for real life-formswhich can only maintain an ordered (low entropy) stateby transforming matter as well as energy

The evolution of matter recycling is addressed usinglsquoAlifersquo techniques in the Guild model (Downing amp Zvirin-sky 1999) From one ancestral lsquospeciesrsquo a communityevolves which is able to recycle a given set of lsquochemicalsrsquo(which can be thought of as different molecular forms ofthe same key nutrient element) Such recycling enablesgreatly enhanced productivity in real ecosystems and Gaia

Phil Trans R Soc Lond B (2002)

(Volk 1998) The mechanism of emergence of recyclingis quite different from the spontaneous emergence of auto-catalytic cycles in systems of very large numbers of chemi-cal reactions (Kauffman 1993) In the Guild model lsquoAlifersquochances upon closed recycling of a small set of chemicalsand this is reinforced by selection This illustrates part ofthe mechanism (ii) that we highlighted in sect 6

The main criticisms of the original Guild model are thatthere is no treatment of energy in the system and that adeviation of the local environment from the global isassumed that may not be justi ed for some real world ana-logues A lsquoGuild IIrsquo model is being developed (K Down-ing personal communication) that includes free energyand entropy in the abstract chemistry (eg it takes freeenergy to build larger molecules) and makes the local

694 T M Lenton and M van Oijen Gaia as a complex adaptive system

environment the interior of proto-cells In this modeldespite a relatively small input of free energy in chemicalform recycling and regulation can emerge

An ideal model world for testing Gaia would containarti cial life-forms that transform lsquomatterrsquo and lsquoenergyrsquoare lsquothermodynamicallyrsquo constrained grow and replicatewith a heritable genome subject to random mutationinteract with one another and evolve new ways of alteringtheir environment related to their internal functioningThe environment would contain many lsquophysicalrsquo andlsquochemicalrsquo variables some homogeneous (well mixed) andothers heterogeneous The resulting system behaviourwould be observable and testable by perturbation

10 CONCLUSIONS

Many scientists now accept that planetary regulationinvolving the biota occurs (Longhurst 1998) However westill have to determine whether Gaiarsquos coming into exis-tence and survival was coincidental or probable and howfragile or robust the system is at present We have arguedthat Gaia is a complex system with self-organizing andadaptive behaviour but that it does not reside in a criticalstate Complexity theory modelling approaches havehelped us simulate and understand the emergence of plan-etary order lsquoAlifersquo techniques can take this further andhelp in assessing the probability of emergence of planetaryregulatory properties Our attempts to apply complexitytheory to Gaia have yielded a broader view of selectionthan previously encompassed in the Gaia theory (Lenton1998) Gene-based natural selection is just one type andlevel of selection operating within Gaia and it is not anecessary condition for regulation The existence of differ-ent types of selection operating at different levels makes iteasier to understand how planetary-scale self-regulationcan arise It also makes it easier to accept that a Gaia-likesystem may be a probable outcome once there is abundantlife on a planet with the capacity for large-scale freeenergy capture

We thank Ricard Sole and Simon Levin for the invitation towrite this article

REFERENCES

Alvarez L W Alvarez W Asaro F amp Michel H V 1980Extraterrestrial cause for the CretaceousndashTertiary extinctionScience 208 1095ndash1108

Bak P amp Sneppen K 1993 Punctuated equilibrium and criti-cality in a simple model of evolution Phys Rev Lett 714083ndash4086

Bak P Tang C amp Wiesenfeld K 1987 Self-organized criti-calitymdashan explanation of 1f noise Phys Rev Lett 59381ndash384

Berner R A 1998 The carbon cycle and CO2 over Phanero-zoic time the role of land plants Phil Trans R SocLond B 353 75ndash82 (DOI 101098rstb19980192)

Betts R A 1999 Self-bene cial effects of vegetation on cli-mate in an oceanndashatmosphere general circulation modelGeophys Res Lett 26 1457ndash1460

Bonan G B Pollard D amp Thompson S L 1992 Effects ofboreal forest vegetation on global climate Nature 359716ndash718

Budyko M I 1968 The effect of solar radiation variations onthe climate of the Earth Tellus 21 611ndash619

Phil Trans R Soc Lond B (2002)

Dawkins R 1983 The extended phenotype Oxford UniversityPress

De Gregorio S Pielke R A amp Dalu G A 1992a Feedbackbetween a simple biosystem and the temperature of theEarth J Nonlinear Sci 2 263ndash292

De Gregorio S Pielke R A amp Dalu G A 1992b A delayedbiophysical system for the Earthrsquos climate J Nonlinear Sci2 293ndash318

DesMarais D J 2000 When did photosynthesis emerge onEarth Science 289 1703ndash1705

DrsquoHondt S Donaghay P Zachos J C Luttenberg D ampLindinger M 1998 Organic carbon uxes and ecologicalrecovery from the CretaceousndashTertiary mass extinctionScience 282 276ndash279

Doolittle W F 1981 Is nature really motherly The CoEvol-ution Q Spring 58ndash63

Downing K amp Zvirinsky P 1999 The simulated evolutionof biochemical guilds reconciling Gaia theory and naturalselection Artif Life 5 291ndash318

Ehrlich P 1991 Coevolution and its applicability to the Gaiahypothesis In Scientists on Gaia (ed S H Schneider amp PJ Boston) pp 118ndash120 London MIT Press

Gallagher R amp Appenzeller T 1999 Beyond reductionismScience 284 79

Hamilton W D 1995 Ecology in the large Gaia and GenghisKhan J Appl Ecol 32 451ndash453

Hamilton W D 1996 Gaiarsquos bene ts New Scientist 15162ndash63

Hamilton W D amp Lenton T M 1998 Spora and Gaia howmicrobes y with their clouds Ethol Ecol Evol 10 1ndash16

Han T-M amp Runnegar B 1992 Megascopic eukaryotic algaefrom the 21 billion-year-old Negaunee iron-formationMichigan Science 257 232ndash235

Hoffman P F Kaufman A J Halverson G P amp SchragD P 1998 A Neoproterozoic snowball earth Science 2811342ndash1346

Holland J 1995 Hidden order how adaptation builds complexityReading MA Addison-Wesley

Hyde W T Crowley T J Baum S K amp Peltier W R2000 Neoproterozoic lsquosnowball Earthrsquo simulations with acoupled climateice-sheet model Nature 405 425ndash429

Imshenetsky A A Lysenko S V amp Kazakov G A 1978Upper boundary of the biosphere Appl Environ Microbiol35 1ndash5

Isaacs A Daintith J amp Martin E (eds) 1996 Concise sciencedictionary Oxford University Press

Jascourt S D amp Raymond W H 1992 Comments on lsquoChaosin daisyworldrsquo by X Zeng et al Tellus 44B 243ndash246

Joslashrgensen S E amp Straskraba M 2000 Ecosystems as cyber-netic systems In Handbook of ecosystem theories and manage-ment (ed S E Joslashrgensen amp F Muller) pp 249ndash264London Lewis Publishers

Kasting J F 1991 Box models for the evolution of atmo-spheric oxygen an update Global and Planetary Change 97125ndash131

Kauffman S A 1993 The origins of order self-organization andselection in evolution Oxford University Press

Kleidon A 2002 Testing the effect of life on Earthrsquos func-tioning how Gaian is the Earth system Climatic Change 52383ndash389

Klinger L F 1991 Peatland formation and ice ages a possibleGaian mechanism related to community succession InScientists on Gaia (ed S H Schneider amp P J Boston) pp247ndash255 London MIT Press

Koeslag J H Saunders P T amp Wessels J A 1997 Glucosehomeostasis with in nite gain further lessons from theDaisyworld parable J Endocrinol 154 187ndash192

Lenton T M 1998 Gaia and natural selection Nature 394439ndash447

688 T M Lenton and M van Oijen Gaia as a complex adaptive system

Table 1 Orders of control in complex systems (after Joslashrgensen amp Straskraba 2000)

order scope for adaptation example system discussed in text

rst xed parameters and structure original Daisyworld modelsecond variable parameters xed structure CA Daisyworldthird variable structure and parameters lsquoAlifersquo Guild modelfourth change of goal functions Gaia ()

perpetual novelty and (5) far-from-equilibrium dynamicsCommonly given examples of CASs are cells individualorganisms and ecosystems

What is the typical behaviour of a CAS First they dis-play lsquoself-organizationrsquo in the sense of emergence ofordered behaviour and structure from many parts withsuf cient connections independent of natural selection(Kauffman 1993) The concept was inspired by the resultsof mathematical models which starting from arbitraryinitial conditions and obeying only simple local rules pro-duced large-scale order The second law of thermody-namics forbids true self-organization increasing order isonly possible in thermodynamically open systems Thusself-organization is dissipative requiring free energy inputand producing high-entropy output CASs may also showlsquoself-organized criticalityrsquo (Bak et al 1987) meaning atendency to reside in the edge of chaos regime allowingchange without getting locked into frozen order A power-law distribution of responses is thought to be characteristicof self-organized critical systems but may occur morewidely in nature

Complex systems can be described in terms of theirorder of dynamics and control (Joslashrgensen amp Straskraba2000 table 1) First-order dynamical systems have xedparameters and structure and hence can only achievefeedback control Second-order dynamical systems havevariable parameters as well as states but xed structureThird-order systems have variable structure as well asparameters and states The distinction in fourth-order sys-tems is that changes in states parameters and structurelead to a change in the goal functions that determine thelong-term behaviour of a system (Wilhelm amp Bruggemann2000) How do CASs t into this classi cation Theelement of replication or enhancement indicates that theirstructure is variable allowing third-order control Thegeneration of continual adaptation suggests that CASs arefourth order with internally generated changes in goalfunctions

In what sense are such behaviours adaptive Adaptationhas two common meanings in biology (i) in evolution itis a change in the structure or functioning of organismsthat makes them better suited to their environment and(ii) in physiology it is an alteration in an organismrsquosresponse to its environment Evolutionary adaptation (i) isusually thought of as the consequence of natural selectionacting on heritable variation The capacity for physiologi-cal adaptation (ii) can be the product of evolutionaryadaptation (i) lsquoAdaptiversquo is used in complexity theory todescribe system development as well as response and isoften applied to systems that are not subject to naturalselection as a whole (although their parts may be) Hencelsquoadaptiversquo behaviours described by complexity theoristsare not necessarily lsquoadaptationsrsquo in the sense used by evo-

Phil Trans R Soc Lond B (2002)

lutionary biologists (i) or physiologists (ii) One way outof this semantic mine eld is to consider natural selectionas just one (rather than the only) form of selection Otherforms of selection can emerge at levels above that of natu-ral selection acting on heritable variation eg in the pro-cess of foraging by social insect colonies utilizingpheromone signals (stigmurgy) or in models of the evo-lution of altruism as a consequence of emergent spatialpatterns (Paolo 2000) If selection can be broader thanjust natural selection then there can be lsquoadaptiversquo behav-iours that are not necessarily the product of natural selec-tion

5 IS GAIA A COMPLEX ADAPTIVE SYSTEM

Gaia is a complex system in that it has many interwovenparts and properties that are not fully explained by anunderstanding of the parts for example the stability ofcomponents of the atmosphere Gaia also ful ls the CAScriteria given previously (Levin 1998) as it contains sus-tained diversity and individuality of components (egorganisms) localized interaction among these compo-nents and at least one autonomous selection process(natural selection) Gaia also possesses non-local interac-tion of components because there is global mixing of theatmosphere and oceans This gives rise to globally mixedvariables atmospheric gases with lifetimes longer thanatmospheric mixing (ca 1 yr) and dissolved chemicalspecies in the ocean with lifetimes longer than ocean mix-ing (ca 1000 yr) There are also non-local interactions inthe climate system described as lsquoteleconnectionsrsquo

If Gaia is a CAS we can expect it to display character-istic properties and behaviour Gaia does indeed sharegeneric CAS properties (Holland 1995) far-from equilib-rium dynamics (of life the atmosphere and aspects ofocean chemistry) generation of perpetual novelty(through evolution) hierarchical organization (eg organ-isms ecosystems Gaia) and absence of a global control-ler However non-local interaction simpli es the systemand offers the possibility that from its many complexcomponents Gaia could display emergent simplicity in itsbehaviour In what sense might Gaia be adaptive Gaiahas not evolved by natural selection at the whole systemlevel but various types of selection operate within the sys-tem The system can be viewed physiologically as cap-tured in the term lsquogeophysiologyrsquo (Lovelock 1986) andmay respond to forcing in a manner resembling physio-logical adaptation There is change at the system level andthere may also be developmental trends that enhance lifeas a whole eg an increase global gross primary pro-ductivity with time

Is Gaia self-organizing It is often said that Gaia is self-regulating but what order of control (table 1) is actually

Gaia as a complex adaptive system T M Lenton and M van Oijen 689

achieved There are many examples of rst-order feed-back control (examples in sect 3) Gaia also contains evo-lution which continually reshapes the system and thusallows higher levels of system control The evolution ofresponses to prevailing environmental conditions and theevolution of environment-altering traits represent changesin the parameters and structure of the system allowing forsecond- and third-order control For example the coloniz-ation of the land surface by vascular plants altered the cli-mate in a self-bene cial manner (Betts 1999) and led toa reorganization of biogeochemical cycles including adrop in carbon dioxide (Berner 1998) global cooling anda rise in oxygen (Lenton 2001) Changes in the Earthrsquoshistory such as the switch from anaerobic to aerobic con-ditions as oxygen rose ca 2 Gyr ago and the resultingincrease in free-energy availability to the biota could beviewed as fourth-order control a change in goal functionfrom an anaerobic lsquoupside-downrsquo biosphere (Walker1987) to an aerobic attractor state that allowed the pro-liferation of new types of life Thus Gaia may be viewedas self-organizing and more in terms of the levels of con-trol achieved

Is Gaia in a self-organized critical state If one contraststhe current state of Gaia with that of Mars or Venus orthe suggested lsquosnowball Earthrsquo state Gaia is more com-plex and less lsquofrozenrsquo into order (of course Mars is literallyfrozen as would be the snowball Earth) It has been sug-gested that the Earthrsquos biota is in a self-organized criticalstate on the basis that extinction events have a distributionclosely approximated by a power law (Kauffman 1993)Proponents of complexity theory propose that the majorityof all extinction events are internally generated by thedynamics of coevolution of species If so this would indi-cate criticality of the biota but not necessarily criticalityof Gaia An alternative hypothesis is that the majority ofextinction events are caused by external perturbation Inthe case of mass extinctions there is good evidence for acausative asteroid impact at the CretaceousndashTertiaryboundary 65 Myr ago (Alvarez et al 1980) Simple mod-els of coevolution (Bak amp Sneppen 1993) or of environ-mental stress (Newman 1997) (without speciesinteraction) as the cause of extinction both exhibit apower law Of the two the environmental stress modelhas an exponent much closer to actual data We concludethat although some extinction may result from coevo-lution there is not yet a convincing case that the biota isin a critical state To test whether Gaia is in a critical statea frequency response analysis of environmental recordsmight be more appropriate For example the carbondioxide and methane records in the Vostok ice core(Petit et al 1999)

6 EMERGENCE OF GAIA

Complexity theory stimulates us to search for a com-plexity threshold for a planet with life beyond which theemergence of self-organization (including self-regulation)and adaptive behaviour becomes likely in other wordsa planetary analogue for the emergence of auto-catalyticnetworks (Kauffman 1993) In coupled open systems oflife and environment does self-organization become vastlymore probable beyond a critical lsquosizersquo (eg number of

Phil Trans R Soc Lond B (2002)

organisms) Also can we pinpoint a particular time in theEarthrsquos history when Gaia emerged

Once life arose it must soon have depleted its surround-ings of substrates thus posing a pressing need for recy-cling Key biogeochemical transformations of essentialelements are present deep in the tree of life among theancient kingdoms of archaea and bacteria supporting aview that nutrient recycling evolved early One furtherrequirement is important for the emergence of planetaryscale self-organization in order to achieve global signi -cance life must have an abundant source of free energyThe earliest types of photosynthesis used relatively scarcesubstrates such as H2S Once oxygenic photosynthesisemerged using the abundant H2O as a substrate then the ux of free energy captured by the biota increased mas-sively (DesMarais 2000) Thus we suggest the genesis ofGaia came with the origin of widespread oxygenic photo-synthesis This occurred at least 28 Gyr ago (DesMarais2000) and possibly as early as 38 Gyr ago (Schidlowski1988)

A remarkable property of Gaia that demands an expla-nation is that its abiotic state variables have stayed at lev-els that support abundant life for most of the last 38 GyrEarly strong versions of the Gaia hypothesis suggestedthat all life-forbidding state variable levels are unreachablebecause there is selection against the processes that wouldlead there Selection at the level of the system as a wholeseems untenable (Doolittle 1981 Dawkins 1983) How-ever it may still be the case that life-forbidding state-vari-able levels are dif cult to reach for at least two reasons(i) if an organism is driving an environmental variabletowards an uninhabitable state its growth and spread willbe suppressed (by negative feedback) such that the systemwill stabilize within the habitable regime and (ii) when-ever organisms become so abundant that the side-effectsof their metabolism become life-threatening on a globalscale different organisms will evolve for which the abun-dant pollutants and the polluters themselves becomeresources If natural selection has enough substrate(genotypic variation) on which to operate such checksand balances are always likely to evolve and make extremeconditions unreachable This old idea (originating fromSmith 1776) could explain the likelihood of regulation atliveable levels as a side-effect of evolution in suf cientlydiverse biota

Uninhabitable or barely habitable states (with life inrefugia) can be reached because of global scale environ-mental perturbation eg massive asteroid impact (Watson1999) or extreme external forcing eg future increases insolar luminosity (Lovelock amp Whit eld 1982 Lenton ampVon Bloh 2001) It is also possible that the evolution ofparticularly strong biotic effects could lsquoovershootrsquo anddrive the environment into a barely habitable stateespecially if there is a time-delay in self-limiting negativefeedback (this is a counter argument to (i) above) Fur-thermore variables that cannot function as a resource toany organism may be able to build up to toxic levels (acounter argument to (ii) above) However useless anddangerous waste products may generally kill off their pro-ducers before disrupting the functioning of Gaia as awhole

Gaia has suffered massive perturbations (asteroidimpacts) and lsquosnowball Earthrsquo states may have occurred

690 T M Lenton and M van Oijen Gaia as a complex adaptive system

in which life only hung on in refugia However abundantlife has always reappeared sometimes remarkably quickly(DrsquoHondt et al 1998) New types of life appear in thewake of mass extinction but there is also a system lsquomem-oryrsquo carried in the gene pool This suggests an interestingpossibility if in response to perturbation a new traitevolves that contributes to recovery then if it remains inthe gene pool and a similar perturbation occurs again thesystem may recover faster the second time In this senseGaia may gain from experience

7 SIMULATING PLANETARY SCALE EMERGENCEWITH DAISYWORLDS

The persistence of life and recovery of Gaia from per-turbation suggest that self-regulation occurs We wouldlike to know how it can emerge and whether it is a chanceor a highly probable outcome of lifendashenvironment coup-ling The feasibility and probability of the emergence ofplanetary scale lsquoself-organizationrsquo andor lsquoadaptive behav-iourrsquo can be evaluated using a synthetic approach of math-ematical modelling

The rst such attempt to simulate the emergence ofplanetary scale self-regulation was the Daisyworld model(Watson amp Lovelock 1983) In Daisyworld global tem-perature regulation emerges automatically from feedbackcoupling between life and its environment with selectionat the component (individual organism) but not the sys-tem (whole planet) level In Daisyworld the environmentis reduced to one variable temperature and life is reducedto two types black and white daisies inhabiting bareground The daisies share the same optimum temperaturefor growth of 225 degC and outer limits to growth of 5 degCand 40 degC The daisy types affect their environment inopposite ways by virtue of their different re ectivity(albedo) The white daisies re ect more solar radiationthan bare ground whilst the black daisies absorb moreHence the local temperature of the daisies differs blackdaisies are always warmer and white daisies are alwayscooler than bare ground The system is forced by a gradualincrease in solar luminosity as has occurred on the Earth

With only one type of daisy present there is a range offorcing for which negative feedback occurs and a point atwhich positive feedback occurs In the case of black daisiesonly when they can establish their spread is ampli ed bypositive environmental feedback (similar to gure 2c butthe effect of life on the environment is stronger) As lumi-nosity increases the population of black daisies declinesthus providing negative feedback on temperature In thecase of white daisies only when they can germinate theirspread is immediately suppressed by their cooling effectAs luminosity increases their population increases pro-viding negative feedback on temperature A regime isentered where white daisies maintain the planet in a habit-able state when otherwise it would be uninhabitable( gure 2d) Eventually they collapse catastrophically withpositive feedback With both types of daisy present thereis a range of forcing for which global temperature actuallydecreases as forcing increases This is an example oflsquosuper-negativersquo feedback (the sign of response is oppositeto that of the forcing (Sardeshmukh 2000))

The Daisyworld model has been portrayed as a CAS(Lewin 1993) but this deserves closer examination It

Phil Trans R Soc Lond B (2002)

possesses rst-order feedback control (table 1) and theregime of super-negative feedback was unexpected fromits parts However the original model does not explicitlyinclude interacting local components The system isdescribed by coupled equations and its behaviour can beunderstood analytically (Saunders 1994 Weber 2001)

If time-delays are introduced into the population andtemperature equations of Daisyworld then apparentlychaotic behaviour can be generated (Zeng et al 1990)Varying the time-delay reveals a series of period doublingscharacteristic of the transition from order to deterministicchaos (De Gregorio et al 1992ab) There is no real-worldjusti cation for the time-delays and it has been shownthat the average of the lsquochaoticrsquo solutions is close to thetemperature regulation in the original model (Jascourt ampRaymond 1992) Introducing an unrealistically large heatcapacity to Daisyworld generates limit cycle oscillations ofthe two daisy populations and temperature (Nevison et al1999) (ie generates the rst period doubling) Thesestudies show that the original Daisyworld model resideswell into the ordered regime and is not in a critical state

Subsequent versions of Daisyworld arguably show theemergence of higher-order control (although the nal prop-erty of temperature regulation is similar in each case)Variants of the model with adaptation of the optimumgrowth temperature of the daisies (Robertson amp Robinson1998 Lenton amp Lovelock 2000) include alteration ofparameters but this is enforced through further para-meters A more fully second-order control system is a Dai-syworld with random mutation of daisy albedo (some ofthe parameters) and subsequent selection (Lenton 1998Lenton amp Lovelock 2001) The structure of this modelcould be said to change in that new daisy lsquospeciesrsquo appearThis suggests there may be some third- and fourth-ordercontrol

8 CA DAISYWORLDS

To ful l the CAS criteria models must include localinteraction of components CA provide a tool for thisHence we have followed the lead of others (Von Bloh etal 1997) and constructed a CA version of Daisyworld toexplore the effects of local interaction and the capacity foradaptive system behaviour The original equations(Watson amp Lovelock 1983) are retained where possibleThe CA grid and rules are simply used to replace thepopulation equations We consider a square grid witheight neighbours to each cell rather than four nearestneighbours (Von Bloh et al 1997) There is no diffusivetemperature eld just the original equations for local tem-peratures of daisies (determined by albedo global tem-perature and insulation parameter q) and globaltemperature (determined by average albedo of the systemand luminosity forcing) Seeding is used to enable popu-lations to establish (but once they are established it haslittle impact) First we consider the original case of popu-lations of lsquoblackrsquo (albedo aB = 025) and lsquowhitersquo (albedoaW = 075) daisies covering bare ground (albedo aG = 05)For an empty cell with nB black neighbours each withgrowth rate b B and nW white neighbours each with growthrate b W the following colonization rules apply

The probability that black will colonize when only theyare present is

Gaia as a complex adaptive system T M Lenton and M van Oijen 691

P(B|nW = 0) = 1 2 (1 2 b B)nB (81)

The probability that white will colonize when only theyare present is

P(W|nB = 0) = 1 2 (1 2 b W )nW (82)

The probability that the cell remains empty is

P(E) = (1 2 P(B|nW = 0))(1 2 P(W|nB = 0)) (83)

The probability that black will colonize when both arepresent is

P(B) = (1 2 P(E))P(B|nW = 0)

P(B|nW = 0) 1 P(W|nB = 0) (84)

The probability that white will colonize when both arepresent is

P(W) = (1 2 P(E))P(W|nB = 0)

P(B|nW = 0) 1 P(W|nB = 0) (85)

The probability of seeding an empty cell is xed

P(S) = h ( h = 0001 in the results shown) (86)

The probability of death at an occupied cell is also xed

P(D) = g ( g = 03 as in the original model) (87)

The 2D CA model has less smooth dynamics than theoriginal zero-dimensional model in that it can exhibitbifurcations and limit cycling ( gure 4) The growth equa-tions are such that for one type alone ( gure 4ac) it canreach carrying capacity on the grid even when its localtemperature and growth rate are sub-optimal This isbecause the presence of many identical neighbours canmake colonization of an empty cell highly probable evenwhen growth rate is suppressed by temperature (equations(81) or (82)) For black daisies alone ( gure 4ab) asforcing is increased a bifurcation point is reached wherethe global temperature is such that the local temperatureof black daisies becomes uninhabitable (b B = 0 when thetemperature of black daisies TB = 40 degC) This generatespartial collapse (ca 30 die-back of the daisies) immedi-ate recovery and resulting oscillations of temperature andpopulation As forcing is increased further a second bifur-cation point is reached Then the trajectories combinebefore the black daisies disappear For white daisies alone( gure 4cd) there are two period doublings and thebeginnings of a third (inset in gure 4d) before a returnto a single trajectory

The one daisy-type model illustrates an lsquoovershootrsquoproblem for Gaia life may develop the capacity to drivean environmental variable into an uninhabitable or barelyhabitable state if the environmental effect is strong andlocal interactions that encourage growth outweigh nega-tive feedback on growth from the environment The modeldoes not include natural selection in that all the daisiesare identical and are always equally t in terms of growthrate (although in the initial growth phase clusters formand cells at the edge of clusters are better able to spreadthan those within clusters) The model does include a sys-tem selection process between bare ground and one daisytype under a certain range of forcing daisies are selectedover bare ground outside that range bare ground willsuccessfully take over from daisies

Phil Trans R Soc Lond B (2002)

When black and white types can both arise the limitcycle regimes are removed and the solution resembles theoriginal zero-dimensional model ( gure 4ef ) The twodifferent daisy types have different growth rates and hence tness thus adding a crude form of natural selection tothe model (although there is no evolution) With thisadditional selective process the model stays more rmlyin the ordered regime The system is stabilized by at leastthree effects (i) if one daisy type reaches an uninhabitabletemperature the other may still be able to spread (becausetheir local temperatures differ) (ii) in the mid-range offorcing a combination of black and white generates a glo-bal temperature closer to optimal and (iii) the presenceof one daisy type reduces the area available to the otherto expand into

We have introduced random mutation of albedo to themodel generalizing the colonization equations (81)ndash(85)to deal with any albedo type Mutation is assumed alwaysto occur in the process of colonization of an empty cell(asexual reproduction that always generates mutatedoffspring) Albedo can mutate within a parameterizedwidth of the parent albedo (plusmn D a) Within this rangeeither side of the parent albedo an offspring albedo is ran-domly chosen Limits to mutation are set at am in = 0 andam ax = 1

With mutation and natural selection within the modelsystem ( gure 5) its behaviour could be said to be lsquoadap-tiversquo in that it lsquoevolvesrsquo to counteract forcing When themodel is seeded with the original lsquoblackrsquo daisies(aB = 025) and these are allowed to mutate as forcingincreases progressively paler daisies evolve cooling theplanet and then maintaining the temperature close to con-stant Increasing D a brings the average planetary tempera-ture more rapidly towards the optimum for daisy growthThe tendency for bifurcation ( gure 4a) is removed byincreasing D a ( gure 5) because this tends to generate anearly increase in average albedo In a sensitivity analysisof the stabilizing effect of albedo diversity am ax ndash am in wasprogressively increased around a central value ofaB = 025 without any mutation and this was also foundto remove the bifurcations Albedo mutation extends therange of temperature regulation beyond that in the originalmodel because paler types than the original lsquowhitersquo onescan arise The latter result has been found in other vari-ants of Daisyworld (Stocker 1995 Von Bloh et al 1997Lenton amp Lovelock 2001)

A more complex 2D CA version of Daisyworld has pre-viously been formulated with albedo mutation and a con-tinuous temperature eld (Von Bloh et al 1997) Thissystem exhibits the remarkable property that underenforced habitat fragmentation using a percolating fractalthe system is able to regulate temperature unimpaired upto a lsquocriticalrsquo threshold at which daisy areas become iso-lated and regulation starts to break down Once uninhabi-ted land forms a spanning cluster regulation is completelyremoved By contrast trivial reductions in habitat (eg agrowing square of lsquoconcretersquo) impair temperature regu-lation in a linear fashion In the former case adjacent dai-sies can affect the temperature of small uninhabited areasbut overall temperature regulation depends on compe-tition among daisies across an entire connected space Inother words the emergent property of global temperatureregulation relies on uninhibited local interaction tting

692 T M Lenton and M van Oijen Gaia as a complex adaptive system

100

50

0

80

60

40

20

0

plusmn20

100

50

0

100

50

0

80

60

40

20

0

plusmn20

80

60

40

20

0

plusmn20

05 10 15 20

05 10 15 20

05 10 15 20 05 10 15 20

05 10 15 20

05 10 15 20

solar luminosity (_) solar luminosity (_)

solar luminosity (_) solar luminosity (_)

solar luminosity (_) solar luminosity (_)

gri

d c

over

(

)g

rid

cov

er (

)

gri

d c

ov

er (

)

glo

bal

tem

per

ature

(degC

)g

lob

al t

emp

erat

ure

(degC

)g

lob

al t

emper

atu

re (

degC)

15

plusmn508 11

(a) (b)

(c) (d)

(e) ( f )

Figure 4 Simulations of xed albedo populations in a simple CA Daisyworld (64 acute 64 grid) Parameters are as in the originalmodel (Watson amp Lovelock 1983) and the CA rules are described in sect 8 Solar luminosity (in normalized units) is increased insteps of 0004 at each of which the model is updated The left-hand graphs show percentage grid cover by the daisies versusluminosity and the right-hand graphs show global average temperature (degC) versus luminosity Temperature is a function ofluminosity and the albedo a and grid cover of daises and empty cells (ab) Seeding with lsquoblackrsquo daisies (aB = 025) denotedby lled circles (cd) Seeding with lsquowhitersquo daisies (aW= 075) denoted by open circles (ef ) Seeding with both black and whitedaisies (albedo of each seed chosen at random) The inset in (d ) shows the period doubling in the temperature trajectory withonly white daisies

in nicely with the criteria for a CAS The system is self-organizing and may arguably be in a critical state near thelimit at which daisy areas become disconnected

9 FEASIBILITY TESTS OF GAIA USING lsquoALIFErsquo

A key criticism of Daisyworld is that it is limited in onlyconsidering one predetermined type of interactionbetween the local and the global and it is one that will

Phil Trans R Soc Lond B (2002)

tend to generate regulation The daisies affect theirenvironment in the same way at the local and the globalscale Hence what is selected for at the individual leveltends to be bene cial at the global level With two or moredaisy types present there is negative selective feedbackmaking regulation likely (Lenton 1998)

lsquoAlifersquo techniques offer a promising way of makingunbiased tests of the potential for emergence of planetaryscale self-organization The model environment lsquoTierrarsquo

Gaia as a complex adaptive system T M Lenton and M van Oijen 693

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

0

20151005

solar luminosity (ndash)

grid

cov

er (

)

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

(a) (b)

(c)(d)

( f )(e)

Figure 5 CA Daisyworld simulations with albedo mutation (64 acute 64 grid) In each simulation there is seeding with theoriginal lsquoblackrsquo daisies (aB = 025) which fall in the range coloured in blue The model is updated with each increase in solarluminosity of 0004 normalized units and at each update empty cells can be colonized with offspring cells that differ at mostby plusmn D a from the albedo of their parent cell Left- and right-hand graphs show grid cover by daisy populations () and globalaverage temperature (degC) respectively The albedo colour scheme in the left-hand graphs is 0ndash02 black 02ndash04 blue 04ndash06 green 06ndash08 orange 08ndash10 red The graphs show the effect of increasing mutation range (ab) D a = 001 (cd) D a =002 (ef ) D a = 01

(Ray 1991) evolved a community of arti cial life-formsthat reproduce in different ways including parasiticallyThe model lsquolife-formsrsquo compete for resource (processortime) but they do not produce waste products Hencetheir interaction with their environment is not thermody-namically complete in the way that it is for real life-formswhich can only maintain an ordered (low entropy) stateby transforming matter as well as energy

The evolution of matter recycling is addressed usinglsquoAlifersquo techniques in the Guild model (Downing amp Zvirin-sky 1999) From one ancestral lsquospeciesrsquo a communityevolves which is able to recycle a given set of lsquochemicalsrsquo(which can be thought of as different molecular forms ofthe same key nutrient element) Such recycling enablesgreatly enhanced productivity in real ecosystems and Gaia

Phil Trans R Soc Lond B (2002)

(Volk 1998) The mechanism of emergence of recyclingis quite different from the spontaneous emergence of auto-catalytic cycles in systems of very large numbers of chemi-cal reactions (Kauffman 1993) In the Guild model lsquoAlifersquochances upon closed recycling of a small set of chemicalsand this is reinforced by selection This illustrates part ofthe mechanism (ii) that we highlighted in sect 6

The main criticisms of the original Guild model are thatthere is no treatment of energy in the system and that adeviation of the local environment from the global isassumed that may not be justi ed for some real world ana-logues A lsquoGuild IIrsquo model is being developed (K Down-ing personal communication) that includes free energyand entropy in the abstract chemistry (eg it takes freeenergy to build larger molecules) and makes the local

694 T M Lenton and M van Oijen Gaia as a complex adaptive system

environment the interior of proto-cells In this modeldespite a relatively small input of free energy in chemicalform recycling and regulation can emerge

An ideal model world for testing Gaia would containarti cial life-forms that transform lsquomatterrsquo and lsquoenergyrsquoare lsquothermodynamicallyrsquo constrained grow and replicatewith a heritable genome subject to random mutationinteract with one another and evolve new ways of alteringtheir environment related to their internal functioningThe environment would contain many lsquophysicalrsquo andlsquochemicalrsquo variables some homogeneous (well mixed) andothers heterogeneous The resulting system behaviourwould be observable and testable by perturbation

10 CONCLUSIONS

Many scientists now accept that planetary regulationinvolving the biota occurs (Longhurst 1998) However westill have to determine whether Gaiarsquos coming into exis-tence and survival was coincidental or probable and howfragile or robust the system is at present We have arguedthat Gaia is a complex system with self-organizing andadaptive behaviour but that it does not reside in a criticalstate Complexity theory modelling approaches havehelped us simulate and understand the emergence of plan-etary order lsquoAlifersquo techniques can take this further andhelp in assessing the probability of emergence of planetaryregulatory properties Our attempts to apply complexitytheory to Gaia have yielded a broader view of selectionthan previously encompassed in the Gaia theory (Lenton1998) Gene-based natural selection is just one type andlevel of selection operating within Gaia and it is not anecessary condition for regulation The existence of differ-ent types of selection operating at different levels makes iteasier to understand how planetary-scale self-regulationcan arise It also makes it easier to accept that a Gaia-likesystem may be a probable outcome once there is abundantlife on a planet with the capacity for large-scale freeenergy capture

We thank Ricard Sole and Simon Levin for the invitation towrite this article

REFERENCES

Alvarez L W Alvarez W Asaro F amp Michel H V 1980Extraterrestrial cause for the CretaceousndashTertiary extinctionScience 208 1095ndash1108

Bak P amp Sneppen K 1993 Punctuated equilibrium and criti-cality in a simple model of evolution Phys Rev Lett 714083ndash4086

Bak P Tang C amp Wiesenfeld K 1987 Self-organized criti-calitymdashan explanation of 1f noise Phys Rev Lett 59381ndash384

Berner R A 1998 The carbon cycle and CO2 over Phanero-zoic time the role of land plants Phil Trans R SocLond B 353 75ndash82 (DOI 101098rstb19980192)

Betts R A 1999 Self-bene cial effects of vegetation on cli-mate in an oceanndashatmosphere general circulation modelGeophys Res Lett 26 1457ndash1460

Bonan G B Pollard D amp Thompson S L 1992 Effects ofboreal forest vegetation on global climate Nature 359716ndash718

Budyko M I 1968 The effect of solar radiation variations onthe climate of the Earth Tellus 21 611ndash619

Phil Trans R Soc Lond B (2002)

Dawkins R 1983 The extended phenotype Oxford UniversityPress

De Gregorio S Pielke R A amp Dalu G A 1992a Feedbackbetween a simple biosystem and the temperature of theEarth J Nonlinear Sci 2 263ndash292

De Gregorio S Pielke R A amp Dalu G A 1992b A delayedbiophysical system for the Earthrsquos climate J Nonlinear Sci2 293ndash318

DesMarais D J 2000 When did photosynthesis emerge onEarth Science 289 1703ndash1705

DrsquoHondt S Donaghay P Zachos J C Luttenberg D ampLindinger M 1998 Organic carbon uxes and ecologicalrecovery from the CretaceousndashTertiary mass extinctionScience 282 276ndash279

Doolittle W F 1981 Is nature really motherly The CoEvol-ution Q Spring 58ndash63

Downing K amp Zvirinsky P 1999 The simulated evolutionof biochemical guilds reconciling Gaia theory and naturalselection Artif Life 5 291ndash318

Ehrlich P 1991 Coevolution and its applicability to the Gaiahypothesis In Scientists on Gaia (ed S H Schneider amp PJ Boston) pp 118ndash120 London MIT Press

Gallagher R amp Appenzeller T 1999 Beyond reductionismScience 284 79

Hamilton W D 1995 Ecology in the large Gaia and GenghisKhan J Appl Ecol 32 451ndash453

Hamilton W D 1996 Gaiarsquos bene ts New Scientist 15162ndash63

Hamilton W D amp Lenton T M 1998 Spora and Gaia howmicrobes y with their clouds Ethol Ecol Evol 10 1ndash16

Han T-M amp Runnegar B 1992 Megascopic eukaryotic algaefrom the 21 billion-year-old Negaunee iron-formationMichigan Science 257 232ndash235

Hoffman P F Kaufman A J Halverson G P amp SchragD P 1998 A Neoproterozoic snowball earth Science 2811342ndash1346

Holland J 1995 Hidden order how adaptation builds complexityReading MA Addison-Wesley

Hyde W T Crowley T J Baum S K amp Peltier W R2000 Neoproterozoic lsquosnowball Earthrsquo simulations with acoupled climateice-sheet model Nature 405 425ndash429

Imshenetsky A A Lysenko S V amp Kazakov G A 1978Upper boundary of the biosphere Appl Environ Microbiol35 1ndash5

Isaacs A Daintith J amp Martin E (eds) 1996 Concise sciencedictionary Oxford University Press

Jascourt S D amp Raymond W H 1992 Comments on lsquoChaosin daisyworldrsquo by X Zeng et al Tellus 44B 243ndash246

Joslashrgensen S E amp Straskraba M 2000 Ecosystems as cyber-netic systems In Handbook of ecosystem theories and manage-ment (ed S E Joslashrgensen amp F Muller) pp 249ndash264London Lewis Publishers

Kasting J F 1991 Box models for the evolution of atmo-spheric oxygen an update Global and Planetary Change 97125ndash131

Kauffman S A 1993 The origins of order self-organization andselection in evolution Oxford University Press

Kleidon A 2002 Testing the effect of life on Earthrsquos func-tioning how Gaian is the Earth system Climatic Change 52383ndash389

Klinger L F 1991 Peatland formation and ice ages a possibleGaian mechanism related to community succession InScientists on Gaia (ed S H Schneider amp P J Boston) pp247ndash255 London MIT Press

Koeslag J H Saunders P T amp Wessels J A 1997 Glucosehomeostasis with in nite gain further lessons from theDaisyworld parable J Endocrinol 154 187ndash192

Lenton T M 1998 Gaia and natural selection Nature 394439ndash447

Gaia as a complex adaptive system T M Lenton and M van Oijen 689

achieved There are many examples of rst-order feed-back control (examples in sect 3) Gaia also contains evo-lution which continually reshapes the system and thusallows higher levels of system control The evolution ofresponses to prevailing environmental conditions and theevolution of environment-altering traits represent changesin the parameters and structure of the system allowing forsecond- and third-order control For example the coloniz-ation of the land surface by vascular plants altered the cli-mate in a self-bene cial manner (Betts 1999) and led toa reorganization of biogeochemical cycles including adrop in carbon dioxide (Berner 1998) global cooling anda rise in oxygen (Lenton 2001) Changes in the Earthrsquoshistory such as the switch from anaerobic to aerobic con-ditions as oxygen rose ca 2 Gyr ago and the resultingincrease in free-energy availability to the biota could beviewed as fourth-order control a change in goal functionfrom an anaerobic lsquoupside-downrsquo biosphere (Walker1987) to an aerobic attractor state that allowed the pro-liferation of new types of life Thus Gaia may be viewedas self-organizing and more in terms of the levels of con-trol achieved

Is Gaia in a self-organized critical state If one contraststhe current state of Gaia with that of Mars or Venus orthe suggested lsquosnowball Earthrsquo state Gaia is more com-plex and less lsquofrozenrsquo into order (of course Mars is literallyfrozen as would be the snowball Earth) It has been sug-gested that the Earthrsquos biota is in a self-organized criticalstate on the basis that extinction events have a distributionclosely approximated by a power law (Kauffman 1993)Proponents of complexity theory propose that the majorityof all extinction events are internally generated by thedynamics of coevolution of species If so this would indi-cate criticality of the biota but not necessarily criticalityof Gaia An alternative hypothesis is that the majority ofextinction events are caused by external perturbation Inthe case of mass extinctions there is good evidence for acausative asteroid impact at the CretaceousndashTertiaryboundary 65 Myr ago (Alvarez et al 1980) Simple mod-els of coevolution (Bak amp Sneppen 1993) or of environ-mental stress (Newman 1997) (without speciesinteraction) as the cause of extinction both exhibit apower law Of the two the environmental stress modelhas an exponent much closer to actual data We concludethat although some extinction may result from coevo-lution there is not yet a convincing case that the biota isin a critical state To test whether Gaia is in a critical statea frequency response analysis of environmental recordsmight be more appropriate For example the carbondioxide and methane records in the Vostok ice core(Petit et al 1999)

6 EMERGENCE OF GAIA

Complexity theory stimulates us to search for a com-plexity threshold for a planet with life beyond which theemergence of self-organization (including self-regulation)and adaptive behaviour becomes likely in other wordsa planetary analogue for the emergence of auto-catalyticnetworks (Kauffman 1993) In coupled open systems oflife and environment does self-organization become vastlymore probable beyond a critical lsquosizersquo (eg number of

Phil Trans R Soc Lond B (2002)

organisms) Also can we pinpoint a particular time in theEarthrsquos history when Gaia emerged

Once life arose it must soon have depleted its surround-ings of substrates thus posing a pressing need for recy-cling Key biogeochemical transformations of essentialelements are present deep in the tree of life among theancient kingdoms of archaea and bacteria supporting aview that nutrient recycling evolved early One furtherrequirement is important for the emergence of planetaryscale self-organization in order to achieve global signi -cance life must have an abundant source of free energyThe earliest types of photosynthesis used relatively scarcesubstrates such as H2S Once oxygenic photosynthesisemerged using the abundant H2O as a substrate then the ux of free energy captured by the biota increased mas-sively (DesMarais 2000) Thus we suggest the genesis ofGaia came with the origin of widespread oxygenic photo-synthesis This occurred at least 28 Gyr ago (DesMarais2000) and possibly as early as 38 Gyr ago (Schidlowski1988)

A remarkable property of Gaia that demands an expla-nation is that its abiotic state variables have stayed at lev-els that support abundant life for most of the last 38 GyrEarly strong versions of the Gaia hypothesis suggestedthat all life-forbidding state variable levels are unreachablebecause there is selection against the processes that wouldlead there Selection at the level of the system as a wholeseems untenable (Doolittle 1981 Dawkins 1983) How-ever it may still be the case that life-forbidding state-vari-able levels are dif cult to reach for at least two reasons(i) if an organism is driving an environmental variabletowards an uninhabitable state its growth and spread willbe suppressed (by negative feedback) such that the systemwill stabilize within the habitable regime and (ii) when-ever organisms become so abundant that the side-effectsof their metabolism become life-threatening on a globalscale different organisms will evolve for which the abun-dant pollutants and the polluters themselves becomeresources If natural selection has enough substrate(genotypic variation) on which to operate such checksand balances are always likely to evolve and make extremeconditions unreachable This old idea (originating fromSmith 1776) could explain the likelihood of regulation atliveable levels as a side-effect of evolution in suf cientlydiverse biota

Uninhabitable or barely habitable states (with life inrefugia) can be reached because of global scale environ-mental perturbation eg massive asteroid impact (Watson1999) or extreme external forcing eg future increases insolar luminosity (Lovelock amp Whit eld 1982 Lenton ampVon Bloh 2001) It is also possible that the evolution ofparticularly strong biotic effects could lsquoovershootrsquo anddrive the environment into a barely habitable stateespecially if there is a time-delay in self-limiting negativefeedback (this is a counter argument to (i) above) Fur-thermore variables that cannot function as a resource toany organism may be able to build up to toxic levels (acounter argument to (ii) above) However useless anddangerous waste products may generally kill off their pro-ducers before disrupting the functioning of Gaia as awhole

Gaia has suffered massive perturbations (asteroidimpacts) and lsquosnowball Earthrsquo states may have occurred

690 T M Lenton and M van Oijen Gaia as a complex adaptive system

in which life only hung on in refugia However abundantlife has always reappeared sometimes remarkably quickly(DrsquoHondt et al 1998) New types of life appear in thewake of mass extinction but there is also a system lsquomem-oryrsquo carried in the gene pool This suggests an interestingpossibility if in response to perturbation a new traitevolves that contributes to recovery then if it remains inthe gene pool and a similar perturbation occurs again thesystem may recover faster the second time In this senseGaia may gain from experience

7 SIMULATING PLANETARY SCALE EMERGENCEWITH DAISYWORLDS

The persistence of life and recovery of Gaia from per-turbation suggest that self-regulation occurs We wouldlike to know how it can emerge and whether it is a chanceor a highly probable outcome of lifendashenvironment coup-ling The feasibility and probability of the emergence ofplanetary scale lsquoself-organizationrsquo andor lsquoadaptive behav-iourrsquo can be evaluated using a synthetic approach of math-ematical modelling

The rst such attempt to simulate the emergence ofplanetary scale self-regulation was the Daisyworld model(Watson amp Lovelock 1983) In Daisyworld global tem-perature regulation emerges automatically from feedbackcoupling between life and its environment with selectionat the component (individual organism) but not the sys-tem (whole planet) level In Daisyworld the environmentis reduced to one variable temperature and life is reducedto two types black and white daisies inhabiting bareground The daisies share the same optimum temperaturefor growth of 225 degC and outer limits to growth of 5 degCand 40 degC The daisy types affect their environment inopposite ways by virtue of their different re ectivity(albedo) The white daisies re ect more solar radiationthan bare ground whilst the black daisies absorb moreHence the local temperature of the daisies differs blackdaisies are always warmer and white daisies are alwayscooler than bare ground The system is forced by a gradualincrease in solar luminosity as has occurred on the Earth

With only one type of daisy present there is a range offorcing for which negative feedback occurs and a point atwhich positive feedback occurs In the case of black daisiesonly when they can establish their spread is ampli ed bypositive environmental feedback (similar to gure 2c butthe effect of life on the environment is stronger) As lumi-nosity increases the population of black daisies declinesthus providing negative feedback on temperature In thecase of white daisies only when they can germinate theirspread is immediately suppressed by their cooling effectAs luminosity increases their population increases pro-viding negative feedback on temperature A regime isentered where white daisies maintain the planet in a habit-able state when otherwise it would be uninhabitable( gure 2d) Eventually they collapse catastrophically withpositive feedback With both types of daisy present thereis a range of forcing for which global temperature actuallydecreases as forcing increases This is an example oflsquosuper-negativersquo feedback (the sign of response is oppositeto that of the forcing (Sardeshmukh 2000))

The Daisyworld model has been portrayed as a CAS(Lewin 1993) but this deserves closer examination It

Phil Trans R Soc Lond B (2002)

possesses rst-order feedback control (table 1) and theregime of super-negative feedback was unexpected fromits parts However the original model does not explicitlyinclude interacting local components The system isdescribed by coupled equations and its behaviour can beunderstood analytically (Saunders 1994 Weber 2001)

If time-delays are introduced into the population andtemperature equations of Daisyworld then apparentlychaotic behaviour can be generated (Zeng et al 1990)Varying the time-delay reveals a series of period doublingscharacteristic of the transition from order to deterministicchaos (De Gregorio et al 1992ab) There is no real-worldjusti cation for the time-delays and it has been shownthat the average of the lsquochaoticrsquo solutions is close to thetemperature regulation in the original model (Jascourt ampRaymond 1992) Introducing an unrealistically large heatcapacity to Daisyworld generates limit cycle oscillations ofthe two daisy populations and temperature (Nevison et al1999) (ie generates the rst period doubling) Thesestudies show that the original Daisyworld model resideswell into the ordered regime and is not in a critical state

Subsequent versions of Daisyworld arguably show theemergence of higher-order control (although the nal prop-erty of temperature regulation is similar in each case)Variants of the model with adaptation of the optimumgrowth temperature of the daisies (Robertson amp Robinson1998 Lenton amp Lovelock 2000) include alteration ofparameters but this is enforced through further para-meters A more fully second-order control system is a Dai-syworld with random mutation of daisy albedo (some ofthe parameters) and subsequent selection (Lenton 1998Lenton amp Lovelock 2001) The structure of this modelcould be said to change in that new daisy lsquospeciesrsquo appearThis suggests there may be some third- and fourth-ordercontrol

8 CA DAISYWORLDS

To ful l the CAS criteria models must include localinteraction of components CA provide a tool for thisHence we have followed the lead of others (Von Bloh etal 1997) and constructed a CA version of Daisyworld toexplore the effects of local interaction and the capacity foradaptive system behaviour The original equations(Watson amp Lovelock 1983) are retained where possibleThe CA grid and rules are simply used to replace thepopulation equations We consider a square grid witheight neighbours to each cell rather than four nearestneighbours (Von Bloh et al 1997) There is no diffusivetemperature eld just the original equations for local tem-peratures of daisies (determined by albedo global tem-perature and insulation parameter q) and globaltemperature (determined by average albedo of the systemand luminosity forcing) Seeding is used to enable popu-lations to establish (but once they are established it haslittle impact) First we consider the original case of popu-lations of lsquoblackrsquo (albedo aB = 025) and lsquowhitersquo (albedoaW = 075) daisies covering bare ground (albedo aG = 05)For an empty cell with nB black neighbours each withgrowth rate b B and nW white neighbours each with growthrate b W the following colonization rules apply

The probability that black will colonize when only theyare present is

Gaia as a complex adaptive system T M Lenton and M van Oijen 691

P(B|nW = 0) = 1 2 (1 2 b B)nB (81)

The probability that white will colonize when only theyare present is

P(W|nB = 0) = 1 2 (1 2 b W )nW (82)

The probability that the cell remains empty is

P(E) = (1 2 P(B|nW = 0))(1 2 P(W|nB = 0)) (83)

The probability that black will colonize when both arepresent is

P(B) = (1 2 P(E))P(B|nW = 0)

P(B|nW = 0) 1 P(W|nB = 0) (84)

The probability that white will colonize when both arepresent is

P(W) = (1 2 P(E))P(W|nB = 0)

P(B|nW = 0) 1 P(W|nB = 0) (85)

The probability of seeding an empty cell is xed

P(S) = h ( h = 0001 in the results shown) (86)

The probability of death at an occupied cell is also xed

P(D) = g ( g = 03 as in the original model) (87)

The 2D CA model has less smooth dynamics than theoriginal zero-dimensional model in that it can exhibitbifurcations and limit cycling ( gure 4) The growth equa-tions are such that for one type alone ( gure 4ac) it canreach carrying capacity on the grid even when its localtemperature and growth rate are sub-optimal This isbecause the presence of many identical neighbours canmake colonization of an empty cell highly probable evenwhen growth rate is suppressed by temperature (equations(81) or (82)) For black daisies alone ( gure 4ab) asforcing is increased a bifurcation point is reached wherethe global temperature is such that the local temperatureof black daisies becomes uninhabitable (b B = 0 when thetemperature of black daisies TB = 40 degC) This generatespartial collapse (ca 30 die-back of the daisies) immedi-ate recovery and resulting oscillations of temperature andpopulation As forcing is increased further a second bifur-cation point is reached Then the trajectories combinebefore the black daisies disappear For white daisies alone( gure 4cd) there are two period doublings and thebeginnings of a third (inset in gure 4d) before a returnto a single trajectory

The one daisy-type model illustrates an lsquoovershootrsquoproblem for Gaia life may develop the capacity to drivean environmental variable into an uninhabitable or barelyhabitable state if the environmental effect is strong andlocal interactions that encourage growth outweigh nega-tive feedback on growth from the environment The modeldoes not include natural selection in that all the daisiesare identical and are always equally t in terms of growthrate (although in the initial growth phase clusters formand cells at the edge of clusters are better able to spreadthan those within clusters) The model does include a sys-tem selection process between bare ground and one daisytype under a certain range of forcing daisies are selectedover bare ground outside that range bare ground willsuccessfully take over from daisies

Phil Trans R Soc Lond B (2002)

When black and white types can both arise the limitcycle regimes are removed and the solution resembles theoriginal zero-dimensional model ( gure 4ef ) The twodifferent daisy types have different growth rates and hence tness thus adding a crude form of natural selection tothe model (although there is no evolution) With thisadditional selective process the model stays more rmlyin the ordered regime The system is stabilized by at leastthree effects (i) if one daisy type reaches an uninhabitabletemperature the other may still be able to spread (becausetheir local temperatures differ) (ii) in the mid-range offorcing a combination of black and white generates a glo-bal temperature closer to optimal and (iii) the presenceof one daisy type reduces the area available to the otherto expand into

We have introduced random mutation of albedo to themodel generalizing the colonization equations (81)ndash(85)to deal with any albedo type Mutation is assumed alwaysto occur in the process of colonization of an empty cell(asexual reproduction that always generates mutatedoffspring) Albedo can mutate within a parameterizedwidth of the parent albedo (plusmn D a) Within this rangeeither side of the parent albedo an offspring albedo is ran-domly chosen Limits to mutation are set at am in = 0 andam ax = 1

With mutation and natural selection within the modelsystem ( gure 5) its behaviour could be said to be lsquoadap-tiversquo in that it lsquoevolvesrsquo to counteract forcing When themodel is seeded with the original lsquoblackrsquo daisies(aB = 025) and these are allowed to mutate as forcingincreases progressively paler daisies evolve cooling theplanet and then maintaining the temperature close to con-stant Increasing D a brings the average planetary tempera-ture more rapidly towards the optimum for daisy growthThe tendency for bifurcation ( gure 4a) is removed byincreasing D a ( gure 5) because this tends to generate anearly increase in average albedo In a sensitivity analysisof the stabilizing effect of albedo diversity am ax ndash am in wasprogressively increased around a central value ofaB = 025 without any mutation and this was also foundto remove the bifurcations Albedo mutation extends therange of temperature regulation beyond that in the originalmodel because paler types than the original lsquowhitersquo onescan arise The latter result has been found in other vari-ants of Daisyworld (Stocker 1995 Von Bloh et al 1997Lenton amp Lovelock 2001)

A more complex 2D CA version of Daisyworld has pre-viously been formulated with albedo mutation and a con-tinuous temperature eld (Von Bloh et al 1997) Thissystem exhibits the remarkable property that underenforced habitat fragmentation using a percolating fractalthe system is able to regulate temperature unimpaired upto a lsquocriticalrsquo threshold at which daisy areas become iso-lated and regulation starts to break down Once uninhabi-ted land forms a spanning cluster regulation is completelyremoved By contrast trivial reductions in habitat (eg agrowing square of lsquoconcretersquo) impair temperature regu-lation in a linear fashion In the former case adjacent dai-sies can affect the temperature of small uninhabited areasbut overall temperature regulation depends on compe-tition among daisies across an entire connected space Inother words the emergent property of global temperatureregulation relies on uninhibited local interaction tting

692 T M Lenton and M van Oijen Gaia as a complex adaptive system

100

50

0

80

60

40

20

0

plusmn20

100

50

0

100

50

0

80

60

40

20

0

plusmn20

80

60

40

20

0

plusmn20

05 10 15 20

05 10 15 20

05 10 15 20 05 10 15 20

05 10 15 20

05 10 15 20

solar luminosity (_) solar luminosity (_)

solar luminosity (_) solar luminosity (_)

solar luminosity (_) solar luminosity (_)

gri

d c

over

(

)g

rid

cov

er (

)

gri

d c

ov

er (

)

glo

bal

tem

per

ature

(degC

)g

lob

al t

emp

erat

ure

(degC

)g

lob

al t

emper

atu

re (

degC)

15

plusmn508 11

(a) (b)

(c) (d)

(e) ( f )

Figure 4 Simulations of xed albedo populations in a simple CA Daisyworld (64 acute 64 grid) Parameters are as in the originalmodel (Watson amp Lovelock 1983) and the CA rules are described in sect 8 Solar luminosity (in normalized units) is increased insteps of 0004 at each of which the model is updated The left-hand graphs show percentage grid cover by the daisies versusluminosity and the right-hand graphs show global average temperature (degC) versus luminosity Temperature is a function ofluminosity and the albedo a and grid cover of daises and empty cells (ab) Seeding with lsquoblackrsquo daisies (aB = 025) denotedby lled circles (cd) Seeding with lsquowhitersquo daisies (aW= 075) denoted by open circles (ef ) Seeding with both black and whitedaisies (albedo of each seed chosen at random) The inset in (d ) shows the period doubling in the temperature trajectory withonly white daisies

in nicely with the criteria for a CAS The system is self-organizing and may arguably be in a critical state near thelimit at which daisy areas become disconnected

9 FEASIBILITY TESTS OF GAIA USING lsquoALIFErsquo

A key criticism of Daisyworld is that it is limited in onlyconsidering one predetermined type of interactionbetween the local and the global and it is one that will

Phil Trans R Soc Lond B (2002)

tend to generate regulation The daisies affect theirenvironment in the same way at the local and the globalscale Hence what is selected for at the individual leveltends to be bene cial at the global level With two or moredaisy types present there is negative selective feedbackmaking regulation likely (Lenton 1998)

lsquoAlifersquo techniques offer a promising way of makingunbiased tests of the potential for emergence of planetaryscale self-organization The model environment lsquoTierrarsquo

Gaia as a complex adaptive system T M Lenton and M van Oijen 693

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

0

20151005

solar luminosity (ndash)

grid

cov

er (

)

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

(a) (b)

(c)(d)

( f )(e)

Figure 5 CA Daisyworld simulations with albedo mutation (64 acute 64 grid) In each simulation there is seeding with theoriginal lsquoblackrsquo daisies (aB = 025) which fall in the range coloured in blue The model is updated with each increase in solarluminosity of 0004 normalized units and at each update empty cells can be colonized with offspring cells that differ at mostby plusmn D a from the albedo of their parent cell Left- and right-hand graphs show grid cover by daisy populations () and globalaverage temperature (degC) respectively The albedo colour scheme in the left-hand graphs is 0ndash02 black 02ndash04 blue 04ndash06 green 06ndash08 orange 08ndash10 red The graphs show the effect of increasing mutation range (ab) D a = 001 (cd) D a =002 (ef ) D a = 01

(Ray 1991) evolved a community of arti cial life-formsthat reproduce in different ways including parasiticallyThe model lsquolife-formsrsquo compete for resource (processortime) but they do not produce waste products Hencetheir interaction with their environment is not thermody-namically complete in the way that it is for real life-formswhich can only maintain an ordered (low entropy) stateby transforming matter as well as energy

The evolution of matter recycling is addressed usinglsquoAlifersquo techniques in the Guild model (Downing amp Zvirin-sky 1999) From one ancestral lsquospeciesrsquo a communityevolves which is able to recycle a given set of lsquochemicalsrsquo(which can be thought of as different molecular forms ofthe same key nutrient element) Such recycling enablesgreatly enhanced productivity in real ecosystems and Gaia

Phil Trans R Soc Lond B (2002)

(Volk 1998) The mechanism of emergence of recyclingis quite different from the spontaneous emergence of auto-catalytic cycles in systems of very large numbers of chemi-cal reactions (Kauffman 1993) In the Guild model lsquoAlifersquochances upon closed recycling of a small set of chemicalsand this is reinforced by selection This illustrates part ofthe mechanism (ii) that we highlighted in sect 6

The main criticisms of the original Guild model are thatthere is no treatment of energy in the system and that adeviation of the local environment from the global isassumed that may not be justi ed for some real world ana-logues A lsquoGuild IIrsquo model is being developed (K Down-ing personal communication) that includes free energyand entropy in the abstract chemistry (eg it takes freeenergy to build larger molecules) and makes the local

694 T M Lenton and M van Oijen Gaia as a complex adaptive system

environment the interior of proto-cells In this modeldespite a relatively small input of free energy in chemicalform recycling and regulation can emerge

An ideal model world for testing Gaia would containarti cial life-forms that transform lsquomatterrsquo and lsquoenergyrsquoare lsquothermodynamicallyrsquo constrained grow and replicatewith a heritable genome subject to random mutationinteract with one another and evolve new ways of alteringtheir environment related to their internal functioningThe environment would contain many lsquophysicalrsquo andlsquochemicalrsquo variables some homogeneous (well mixed) andothers heterogeneous The resulting system behaviourwould be observable and testable by perturbation

10 CONCLUSIONS

Many scientists now accept that planetary regulationinvolving the biota occurs (Longhurst 1998) However westill have to determine whether Gaiarsquos coming into exis-tence and survival was coincidental or probable and howfragile or robust the system is at present We have arguedthat Gaia is a complex system with self-organizing andadaptive behaviour but that it does not reside in a criticalstate Complexity theory modelling approaches havehelped us simulate and understand the emergence of plan-etary order lsquoAlifersquo techniques can take this further andhelp in assessing the probability of emergence of planetaryregulatory properties Our attempts to apply complexitytheory to Gaia have yielded a broader view of selectionthan previously encompassed in the Gaia theory (Lenton1998) Gene-based natural selection is just one type andlevel of selection operating within Gaia and it is not anecessary condition for regulation The existence of differ-ent types of selection operating at different levels makes iteasier to understand how planetary-scale self-regulationcan arise It also makes it easier to accept that a Gaia-likesystem may be a probable outcome once there is abundantlife on a planet with the capacity for large-scale freeenergy capture

We thank Ricard Sole and Simon Levin for the invitation towrite this article

REFERENCES

Alvarez L W Alvarez W Asaro F amp Michel H V 1980Extraterrestrial cause for the CretaceousndashTertiary extinctionScience 208 1095ndash1108

Bak P amp Sneppen K 1993 Punctuated equilibrium and criti-cality in a simple model of evolution Phys Rev Lett 714083ndash4086

Bak P Tang C amp Wiesenfeld K 1987 Self-organized criti-calitymdashan explanation of 1f noise Phys Rev Lett 59381ndash384

Berner R A 1998 The carbon cycle and CO2 over Phanero-zoic time the role of land plants Phil Trans R SocLond B 353 75ndash82 (DOI 101098rstb19980192)

Betts R A 1999 Self-bene cial effects of vegetation on cli-mate in an oceanndashatmosphere general circulation modelGeophys Res Lett 26 1457ndash1460

Bonan G B Pollard D amp Thompson S L 1992 Effects ofboreal forest vegetation on global climate Nature 359716ndash718

Budyko M I 1968 The effect of solar radiation variations onthe climate of the Earth Tellus 21 611ndash619

Phil Trans R Soc Lond B (2002)

Dawkins R 1983 The extended phenotype Oxford UniversityPress

De Gregorio S Pielke R A amp Dalu G A 1992a Feedbackbetween a simple biosystem and the temperature of theEarth J Nonlinear Sci 2 263ndash292

De Gregorio S Pielke R A amp Dalu G A 1992b A delayedbiophysical system for the Earthrsquos climate J Nonlinear Sci2 293ndash318

DesMarais D J 2000 When did photosynthesis emerge onEarth Science 289 1703ndash1705

DrsquoHondt S Donaghay P Zachos J C Luttenberg D ampLindinger M 1998 Organic carbon uxes and ecologicalrecovery from the CretaceousndashTertiary mass extinctionScience 282 276ndash279

Doolittle W F 1981 Is nature really motherly The CoEvol-ution Q Spring 58ndash63

Downing K amp Zvirinsky P 1999 The simulated evolutionof biochemical guilds reconciling Gaia theory and naturalselection Artif Life 5 291ndash318

Ehrlich P 1991 Coevolution and its applicability to the Gaiahypothesis In Scientists on Gaia (ed S H Schneider amp PJ Boston) pp 118ndash120 London MIT Press

Gallagher R amp Appenzeller T 1999 Beyond reductionismScience 284 79

Hamilton W D 1995 Ecology in the large Gaia and GenghisKhan J Appl Ecol 32 451ndash453

Hamilton W D 1996 Gaiarsquos bene ts New Scientist 15162ndash63

Hamilton W D amp Lenton T M 1998 Spora and Gaia howmicrobes y with their clouds Ethol Ecol Evol 10 1ndash16

Han T-M amp Runnegar B 1992 Megascopic eukaryotic algaefrom the 21 billion-year-old Negaunee iron-formationMichigan Science 257 232ndash235

Hoffman P F Kaufman A J Halverson G P amp SchragD P 1998 A Neoproterozoic snowball earth Science 2811342ndash1346

Holland J 1995 Hidden order how adaptation builds complexityReading MA Addison-Wesley

Hyde W T Crowley T J Baum S K amp Peltier W R2000 Neoproterozoic lsquosnowball Earthrsquo simulations with acoupled climateice-sheet model Nature 405 425ndash429

Imshenetsky A A Lysenko S V amp Kazakov G A 1978Upper boundary of the biosphere Appl Environ Microbiol35 1ndash5

Isaacs A Daintith J amp Martin E (eds) 1996 Concise sciencedictionary Oxford University Press

Jascourt S D amp Raymond W H 1992 Comments on lsquoChaosin daisyworldrsquo by X Zeng et al Tellus 44B 243ndash246

Joslashrgensen S E amp Straskraba M 2000 Ecosystems as cyber-netic systems In Handbook of ecosystem theories and manage-ment (ed S E Joslashrgensen amp F Muller) pp 249ndash264London Lewis Publishers

Kasting J F 1991 Box models for the evolution of atmo-spheric oxygen an update Global and Planetary Change 97125ndash131

Kauffman S A 1993 The origins of order self-organization andselection in evolution Oxford University Press

Kleidon A 2002 Testing the effect of life on Earthrsquos func-tioning how Gaian is the Earth system Climatic Change 52383ndash389

Klinger L F 1991 Peatland formation and ice ages a possibleGaian mechanism related to community succession InScientists on Gaia (ed S H Schneider amp P J Boston) pp247ndash255 London MIT Press

Koeslag J H Saunders P T amp Wessels J A 1997 Glucosehomeostasis with in nite gain further lessons from theDaisyworld parable J Endocrinol 154 187ndash192

Lenton T M 1998 Gaia and natural selection Nature 394439ndash447

690 T M Lenton and M van Oijen Gaia as a complex adaptive system

in which life only hung on in refugia However abundantlife has always reappeared sometimes remarkably quickly(DrsquoHondt et al 1998) New types of life appear in thewake of mass extinction but there is also a system lsquomem-oryrsquo carried in the gene pool This suggests an interestingpossibility if in response to perturbation a new traitevolves that contributes to recovery then if it remains inthe gene pool and a similar perturbation occurs again thesystem may recover faster the second time In this senseGaia may gain from experience

7 SIMULATING PLANETARY SCALE EMERGENCEWITH DAISYWORLDS

The persistence of life and recovery of Gaia from per-turbation suggest that self-regulation occurs We wouldlike to know how it can emerge and whether it is a chanceor a highly probable outcome of lifendashenvironment coup-ling The feasibility and probability of the emergence ofplanetary scale lsquoself-organizationrsquo andor lsquoadaptive behav-iourrsquo can be evaluated using a synthetic approach of math-ematical modelling

The rst such attempt to simulate the emergence ofplanetary scale self-regulation was the Daisyworld model(Watson amp Lovelock 1983) In Daisyworld global tem-perature regulation emerges automatically from feedbackcoupling between life and its environment with selectionat the component (individual organism) but not the sys-tem (whole planet) level In Daisyworld the environmentis reduced to one variable temperature and life is reducedto two types black and white daisies inhabiting bareground The daisies share the same optimum temperaturefor growth of 225 degC and outer limits to growth of 5 degCand 40 degC The daisy types affect their environment inopposite ways by virtue of their different re ectivity(albedo) The white daisies re ect more solar radiationthan bare ground whilst the black daisies absorb moreHence the local temperature of the daisies differs blackdaisies are always warmer and white daisies are alwayscooler than bare ground The system is forced by a gradualincrease in solar luminosity as has occurred on the Earth

With only one type of daisy present there is a range offorcing for which negative feedback occurs and a point atwhich positive feedback occurs In the case of black daisiesonly when they can establish their spread is ampli ed bypositive environmental feedback (similar to gure 2c butthe effect of life on the environment is stronger) As lumi-nosity increases the population of black daisies declinesthus providing negative feedback on temperature In thecase of white daisies only when they can germinate theirspread is immediately suppressed by their cooling effectAs luminosity increases their population increases pro-viding negative feedback on temperature A regime isentered where white daisies maintain the planet in a habit-able state when otherwise it would be uninhabitable( gure 2d) Eventually they collapse catastrophically withpositive feedback With both types of daisy present thereis a range of forcing for which global temperature actuallydecreases as forcing increases This is an example oflsquosuper-negativersquo feedback (the sign of response is oppositeto that of the forcing (Sardeshmukh 2000))

The Daisyworld model has been portrayed as a CAS(Lewin 1993) but this deserves closer examination It

Phil Trans R Soc Lond B (2002)

possesses rst-order feedback control (table 1) and theregime of super-negative feedback was unexpected fromits parts However the original model does not explicitlyinclude interacting local components The system isdescribed by coupled equations and its behaviour can beunderstood analytically (Saunders 1994 Weber 2001)

If time-delays are introduced into the population andtemperature equations of Daisyworld then apparentlychaotic behaviour can be generated (Zeng et al 1990)Varying the time-delay reveals a series of period doublingscharacteristic of the transition from order to deterministicchaos (De Gregorio et al 1992ab) There is no real-worldjusti cation for the time-delays and it has been shownthat the average of the lsquochaoticrsquo solutions is close to thetemperature regulation in the original model (Jascourt ampRaymond 1992) Introducing an unrealistically large heatcapacity to Daisyworld generates limit cycle oscillations ofthe two daisy populations and temperature (Nevison et al1999) (ie generates the rst period doubling) Thesestudies show that the original Daisyworld model resideswell into the ordered regime and is not in a critical state

Subsequent versions of Daisyworld arguably show theemergence of higher-order control (although the nal prop-erty of temperature regulation is similar in each case)Variants of the model with adaptation of the optimumgrowth temperature of the daisies (Robertson amp Robinson1998 Lenton amp Lovelock 2000) include alteration ofparameters but this is enforced through further para-meters A more fully second-order control system is a Dai-syworld with random mutation of daisy albedo (some ofthe parameters) and subsequent selection (Lenton 1998Lenton amp Lovelock 2001) The structure of this modelcould be said to change in that new daisy lsquospeciesrsquo appearThis suggests there may be some third- and fourth-ordercontrol

8 CA DAISYWORLDS

To ful l the CAS criteria models must include localinteraction of components CA provide a tool for thisHence we have followed the lead of others (Von Bloh etal 1997) and constructed a CA version of Daisyworld toexplore the effects of local interaction and the capacity foradaptive system behaviour The original equations(Watson amp Lovelock 1983) are retained where possibleThe CA grid and rules are simply used to replace thepopulation equations We consider a square grid witheight neighbours to each cell rather than four nearestneighbours (Von Bloh et al 1997) There is no diffusivetemperature eld just the original equations for local tem-peratures of daisies (determined by albedo global tem-perature and insulation parameter q) and globaltemperature (determined by average albedo of the systemand luminosity forcing) Seeding is used to enable popu-lations to establish (but once they are established it haslittle impact) First we consider the original case of popu-lations of lsquoblackrsquo (albedo aB = 025) and lsquowhitersquo (albedoaW = 075) daisies covering bare ground (albedo aG = 05)For an empty cell with nB black neighbours each withgrowth rate b B and nW white neighbours each with growthrate b W the following colonization rules apply

The probability that black will colonize when only theyare present is

Gaia as a complex adaptive system T M Lenton and M van Oijen 691

P(B|nW = 0) = 1 2 (1 2 b B)nB (81)

The probability that white will colonize when only theyare present is

P(W|nB = 0) = 1 2 (1 2 b W )nW (82)

The probability that the cell remains empty is

P(E) = (1 2 P(B|nW = 0))(1 2 P(W|nB = 0)) (83)

The probability that black will colonize when both arepresent is

P(B) = (1 2 P(E))P(B|nW = 0)

P(B|nW = 0) 1 P(W|nB = 0) (84)

The probability that white will colonize when both arepresent is

P(W) = (1 2 P(E))P(W|nB = 0)

P(B|nW = 0) 1 P(W|nB = 0) (85)

The probability of seeding an empty cell is xed

P(S) = h ( h = 0001 in the results shown) (86)

The probability of death at an occupied cell is also xed

P(D) = g ( g = 03 as in the original model) (87)

The 2D CA model has less smooth dynamics than theoriginal zero-dimensional model in that it can exhibitbifurcations and limit cycling ( gure 4) The growth equa-tions are such that for one type alone ( gure 4ac) it canreach carrying capacity on the grid even when its localtemperature and growth rate are sub-optimal This isbecause the presence of many identical neighbours canmake colonization of an empty cell highly probable evenwhen growth rate is suppressed by temperature (equations(81) or (82)) For black daisies alone ( gure 4ab) asforcing is increased a bifurcation point is reached wherethe global temperature is such that the local temperatureof black daisies becomes uninhabitable (b B = 0 when thetemperature of black daisies TB = 40 degC) This generatespartial collapse (ca 30 die-back of the daisies) immedi-ate recovery and resulting oscillations of temperature andpopulation As forcing is increased further a second bifur-cation point is reached Then the trajectories combinebefore the black daisies disappear For white daisies alone( gure 4cd) there are two period doublings and thebeginnings of a third (inset in gure 4d) before a returnto a single trajectory

The one daisy-type model illustrates an lsquoovershootrsquoproblem for Gaia life may develop the capacity to drivean environmental variable into an uninhabitable or barelyhabitable state if the environmental effect is strong andlocal interactions that encourage growth outweigh nega-tive feedback on growth from the environment The modeldoes not include natural selection in that all the daisiesare identical and are always equally t in terms of growthrate (although in the initial growth phase clusters formand cells at the edge of clusters are better able to spreadthan those within clusters) The model does include a sys-tem selection process between bare ground and one daisytype under a certain range of forcing daisies are selectedover bare ground outside that range bare ground willsuccessfully take over from daisies

Phil Trans R Soc Lond B (2002)

When black and white types can both arise the limitcycle regimes are removed and the solution resembles theoriginal zero-dimensional model ( gure 4ef ) The twodifferent daisy types have different growth rates and hence tness thus adding a crude form of natural selection tothe model (although there is no evolution) With thisadditional selective process the model stays more rmlyin the ordered regime The system is stabilized by at leastthree effects (i) if one daisy type reaches an uninhabitabletemperature the other may still be able to spread (becausetheir local temperatures differ) (ii) in the mid-range offorcing a combination of black and white generates a glo-bal temperature closer to optimal and (iii) the presenceof one daisy type reduces the area available to the otherto expand into

We have introduced random mutation of albedo to themodel generalizing the colonization equations (81)ndash(85)to deal with any albedo type Mutation is assumed alwaysto occur in the process of colonization of an empty cell(asexual reproduction that always generates mutatedoffspring) Albedo can mutate within a parameterizedwidth of the parent albedo (plusmn D a) Within this rangeeither side of the parent albedo an offspring albedo is ran-domly chosen Limits to mutation are set at am in = 0 andam ax = 1

With mutation and natural selection within the modelsystem ( gure 5) its behaviour could be said to be lsquoadap-tiversquo in that it lsquoevolvesrsquo to counteract forcing When themodel is seeded with the original lsquoblackrsquo daisies(aB = 025) and these are allowed to mutate as forcingincreases progressively paler daisies evolve cooling theplanet and then maintaining the temperature close to con-stant Increasing D a brings the average planetary tempera-ture more rapidly towards the optimum for daisy growthThe tendency for bifurcation ( gure 4a) is removed byincreasing D a ( gure 5) because this tends to generate anearly increase in average albedo In a sensitivity analysisof the stabilizing effect of albedo diversity am ax ndash am in wasprogressively increased around a central value ofaB = 025 without any mutation and this was also foundto remove the bifurcations Albedo mutation extends therange of temperature regulation beyond that in the originalmodel because paler types than the original lsquowhitersquo onescan arise The latter result has been found in other vari-ants of Daisyworld (Stocker 1995 Von Bloh et al 1997Lenton amp Lovelock 2001)

A more complex 2D CA version of Daisyworld has pre-viously been formulated with albedo mutation and a con-tinuous temperature eld (Von Bloh et al 1997) Thissystem exhibits the remarkable property that underenforced habitat fragmentation using a percolating fractalthe system is able to regulate temperature unimpaired upto a lsquocriticalrsquo threshold at which daisy areas become iso-lated and regulation starts to break down Once uninhabi-ted land forms a spanning cluster regulation is completelyremoved By contrast trivial reductions in habitat (eg agrowing square of lsquoconcretersquo) impair temperature regu-lation in a linear fashion In the former case adjacent dai-sies can affect the temperature of small uninhabited areasbut overall temperature regulation depends on compe-tition among daisies across an entire connected space Inother words the emergent property of global temperatureregulation relies on uninhibited local interaction tting

692 T M Lenton and M van Oijen Gaia as a complex adaptive system

100

50

0

80

60

40

20

0

plusmn20

100

50

0

100

50

0

80

60

40

20

0

plusmn20

80

60

40

20

0

plusmn20

05 10 15 20

05 10 15 20

05 10 15 20 05 10 15 20

05 10 15 20

05 10 15 20

solar luminosity (_) solar luminosity (_)

solar luminosity (_) solar luminosity (_)

solar luminosity (_) solar luminosity (_)

gri

d c

over

(

)g

rid

cov

er (

)

gri

d c

ov

er (

)

glo

bal

tem

per

ature

(degC

)g

lob

al t

emp

erat

ure

(degC

)g

lob

al t

emper

atu

re (

degC)

15

plusmn508 11

(a) (b)

(c) (d)

(e) ( f )

Figure 4 Simulations of xed albedo populations in a simple CA Daisyworld (64 acute 64 grid) Parameters are as in the originalmodel (Watson amp Lovelock 1983) and the CA rules are described in sect 8 Solar luminosity (in normalized units) is increased insteps of 0004 at each of which the model is updated The left-hand graphs show percentage grid cover by the daisies versusluminosity and the right-hand graphs show global average temperature (degC) versus luminosity Temperature is a function ofluminosity and the albedo a and grid cover of daises and empty cells (ab) Seeding with lsquoblackrsquo daisies (aB = 025) denotedby lled circles (cd) Seeding with lsquowhitersquo daisies (aW= 075) denoted by open circles (ef ) Seeding with both black and whitedaisies (albedo of each seed chosen at random) The inset in (d ) shows the period doubling in the temperature trajectory withonly white daisies

in nicely with the criteria for a CAS The system is self-organizing and may arguably be in a critical state near thelimit at which daisy areas become disconnected

9 FEASIBILITY TESTS OF GAIA USING lsquoALIFErsquo

A key criticism of Daisyworld is that it is limited in onlyconsidering one predetermined type of interactionbetween the local and the global and it is one that will

Phil Trans R Soc Lond B (2002)

tend to generate regulation The daisies affect theirenvironment in the same way at the local and the globalscale Hence what is selected for at the individual leveltends to be bene cial at the global level With two or moredaisy types present there is negative selective feedbackmaking regulation likely (Lenton 1998)

lsquoAlifersquo techniques offer a promising way of makingunbiased tests of the potential for emergence of planetaryscale self-organization The model environment lsquoTierrarsquo

Gaia as a complex adaptive system T M Lenton and M van Oijen 693

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

0

20151005

solar luminosity (ndash)

grid

cov

er (

)

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

(a) (b)

(c)(d)

( f )(e)

Figure 5 CA Daisyworld simulations with albedo mutation (64 acute 64 grid) In each simulation there is seeding with theoriginal lsquoblackrsquo daisies (aB = 025) which fall in the range coloured in blue The model is updated with each increase in solarluminosity of 0004 normalized units and at each update empty cells can be colonized with offspring cells that differ at mostby plusmn D a from the albedo of their parent cell Left- and right-hand graphs show grid cover by daisy populations () and globalaverage temperature (degC) respectively The albedo colour scheme in the left-hand graphs is 0ndash02 black 02ndash04 blue 04ndash06 green 06ndash08 orange 08ndash10 red The graphs show the effect of increasing mutation range (ab) D a = 001 (cd) D a =002 (ef ) D a = 01

(Ray 1991) evolved a community of arti cial life-formsthat reproduce in different ways including parasiticallyThe model lsquolife-formsrsquo compete for resource (processortime) but they do not produce waste products Hencetheir interaction with their environment is not thermody-namically complete in the way that it is for real life-formswhich can only maintain an ordered (low entropy) stateby transforming matter as well as energy

The evolution of matter recycling is addressed usinglsquoAlifersquo techniques in the Guild model (Downing amp Zvirin-sky 1999) From one ancestral lsquospeciesrsquo a communityevolves which is able to recycle a given set of lsquochemicalsrsquo(which can be thought of as different molecular forms ofthe same key nutrient element) Such recycling enablesgreatly enhanced productivity in real ecosystems and Gaia

Phil Trans R Soc Lond B (2002)

(Volk 1998) The mechanism of emergence of recyclingis quite different from the spontaneous emergence of auto-catalytic cycles in systems of very large numbers of chemi-cal reactions (Kauffman 1993) In the Guild model lsquoAlifersquochances upon closed recycling of a small set of chemicalsand this is reinforced by selection This illustrates part ofthe mechanism (ii) that we highlighted in sect 6

The main criticisms of the original Guild model are thatthere is no treatment of energy in the system and that adeviation of the local environment from the global isassumed that may not be justi ed for some real world ana-logues A lsquoGuild IIrsquo model is being developed (K Down-ing personal communication) that includes free energyand entropy in the abstract chemistry (eg it takes freeenergy to build larger molecules) and makes the local

694 T M Lenton and M van Oijen Gaia as a complex adaptive system

environment the interior of proto-cells In this modeldespite a relatively small input of free energy in chemicalform recycling and regulation can emerge

An ideal model world for testing Gaia would containarti cial life-forms that transform lsquomatterrsquo and lsquoenergyrsquoare lsquothermodynamicallyrsquo constrained grow and replicatewith a heritable genome subject to random mutationinteract with one another and evolve new ways of alteringtheir environment related to their internal functioningThe environment would contain many lsquophysicalrsquo andlsquochemicalrsquo variables some homogeneous (well mixed) andothers heterogeneous The resulting system behaviourwould be observable and testable by perturbation

10 CONCLUSIONS

Many scientists now accept that planetary regulationinvolving the biota occurs (Longhurst 1998) However westill have to determine whether Gaiarsquos coming into exis-tence and survival was coincidental or probable and howfragile or robust the system is at present We have arguedthat Gaia is a complex system with self-organizing andadaptive behaviour but that it does not reside in a criticalstate Complexity theory modelling approaches havehelped us simulate and understand the emergence of plan-etary order lsquoAlifersquo techniques can take this further andhelp in assessing the probability of emergence of planetaryregulatory properties Our attempts to apply complexitytheory to Gaia have yielded a broader view of selectionthan previously encompassed in the Gaia theory (Lenton1998) Gene-based natural selection is just one type andlevel of selection operating within Gaia and it is not anecessary condition for regulation The existence of differ-ent types of selection operating at different levels makes iteasier to understand how planetary-scale self-regulationcan arise It also makes it easier to accept that a Gaia-likesystem may be a probable outcome once there is abundantlife on a planet with the capacity for large-scale freeenergy capture

We thank Ricard Sole and Simon Levin for the invitation towrite this article

REFERENCES

Alvarez L W Alvarez W Asaro F amp Michel H V 1980Extraterrestrial cause for the CretaceousndashTertiary extinctionScience 208 1095ndash1108

Bak P amp Sneppen K 1993 Punctuated equilibrium and criti-cality in a simple model of evolution Phys Rev Lett 714083ndash4086

Bak P Tang C amp Wiesenfeld K 1987 Self-organized criti-calitymdashan explanation of 1f noise Phys Rev Lett 59381ndash384

Berner R A 1998 The carbon cycle and CO2 over Phanero-zoic time the role of land plants Phil Trans R SocLond B 353 75ndash82 (DOI 101098rstb19980192)

Betts R A 1999 Self-bene cial effects of vegetation on cli-mate in an oceanndashatmosphere general circulation modelGeophys Res Lett 26 1457ndash1460

Bonan G B Pollard D amp Thompson S L 1992 Effects ofboreal forest vegetation on global climate Nature 359716ndash718

Budyko M I 1968 The effect of solar radiation variations onthe climate of the Earth Tellus 21 611ndash619

Phil Trans R Soc Lond B (2002)

Dawkins R 1983 The extended phenotype Oxford UniversityPress

De Gregorio S Pielke R A amp Dalu G A 1992a Feedbackbetween a simple biosystem and the temperature of theEarth J Nonlinear Sci 2 263ndash292

De Gregorio S Pielke R A amp Dalu G A 1992b A delayedbiophysical system for the Earthrsquos climate J Nonlinear Sci2 293ndash318

DesMarais D J 2000 When did photosynthesis emerge onEarth Science 289 1703ndash1705

DrsquoHondt S Donaghay P Zachos J C Luttenberg D ampLindinger M 1998 Organic carbon uxes and ecologicalrecovery from the CretaceousndashTertiary mass extinctionScience 282 276ndash279

Doolittle W F 1981 Is nature really motherly The CoEvol-ution Q Spring 58ndash63

Downing K amp Zvirinsky P 1999 The simulated evolutionof biochemical guilds reconciling Gaia theory and naturalselection Artif Life 5 291ndash318

Ehrlich P 1991 Coevolution and its applicability to the Gaiahypothesis In Scientists on Gaia (ed S H Schneider amp PJ Boston) pp 118ndash120 London MIT Press

Gallagher R amp Appenzeller T 1999 Beyond reductionismScience 284 79

Hamilton W D 1995 Ecology in the large Gaia and GenghisKhan J Appl Ecol 32 451ndash453

Hamilton W D 1996 Gaiarsquos bene ts New Scientist 15162ndash63

Hamilton W D amp Lenton T M 1998 Spora and Gaia howmicrobes y with their clouds Ethol Ecol Evol 10 1ndash16

Han T-M amp Runnegar B 1992 Megascopic eukaryotic algaefrom the 21 billion-year-old Negaunee iron-formationMichigan Science 257 232ndash235

Hoffman P F Kaufman A J Halverson G P amp SchragD P 1998 A Neoproterozoic snowball earth Science 2811342ndash1346

Holland J 1995 Hidden order how adaptation builds complexityReading MA Addison-Wesley

Hyde W T Crowley T J Baum S K amp Peltier W R2000 Neoproterozoic lsquosnowball Earthrsquo simulations with acoupled climateice-sheet model Nature 405 425ndash429

Imshenetsky A A Lysenko S V amp Kazakov G A 1978Upper boundary of the biosphere Appl Environ Microbiol35 1ndash5

Isaacs A Daintith J amp Martin E (eds) 1996 Concise sciencedictionary Oxford University Press

Jascourt S D amp Raymond W H 1992 Comments on lsquoChaosin daisyworldrsquo by X Zeng et al Tellus 44B 243ndash246

Joslashrgensen S E amp Straskraba M 2000 Ecosystems as cyber-netic systems In Handbook of ecosystem theories and manage-ment (ed S E Joslashrgensen amp F Muller) pp 249ndash264London Lewis Publishers

Kasting J F 1991 Box models for the evolution of atmo-spheric oxygen an update Global and Planetary Change 97125ndash131

Kauffman S A 1993 The origins of order self-organization andselection in evolution Oxford University Press

Kleidon A 2002 Testing the effect of life on Earthrsquos func-tioning how Gaian is the Earth system Climatic Change 52383ndash389

Klinger L F 1991 Peatland formation and ice ages a possibleGaian mechanism related to community succession InScientists on Gaia (ed S H Schneider amp P J Boston) pp247ndash255 London MIT Press

Koeslag J H Saunders P T amp Wessels J A 1997 Glucosehomeostasis with in nite gain further lessons from theDaisyworld parable J Endocrinol 154 187ndash192

Lenton T M 1998 Gaia and natural selection Nature 394439ndash447

Gaia as a complex adaptive system T M Lenton and M van Oijen 691

P(B|nW = 0) = 1 2 (1 2 b B)nB (81)

The probability that white will colonize when only theyare present is

P(W|nB = 0) = 1 2 (1 2 b W )nW (82)

The probability that the cell remains empty is

P(E) = (1 2 P(B|nW = 0))(1 2 P(W|nB = 0)) (83)

The probability that black will colonize when both arepresent is

P(B) = (1 2 P(E))P(B|nW = 0)

P(B|nW = 0) 1 P(W|nB = 0) (84)

The probability that white will colonize when both arepresent is

P(W) = (1 2 P(E))P(W|nB = 0)

P(B|nW = 0) 1 P(W|nB = 0) (85)

The probability of seeding an empty cell is xed

P(S) = h ( h = 0001 in the results shown) (86)

The probability of death at an occupied cell is also xed

P(D) = g ( g = 03 as in the original model) (87)

The 2D CA model has less smooth dynamics than theoriginal zero-dimensional model in that it can exhibitbifurcations and limit cycling ( gure 4) The growth equa-tions are such that for one type alone ( gure 4ac) it canreach carrying capacity on the grid even when its localtemperature and growth rate are sub-optimal This isbecause the presence of many identical neighbours canmake colonization of an empty cell highly probable evenwhen growth rate is suppressed by temperature (equations(81) or (82)) For black daisies alone ( gure 4ab) asforcing is increased a bifurcation point is reached wherethe global temperature is such that the local temperatureof black daisies becomes uninhabitable (b B = 0 when thetemperature of black daisies TB = 40 degC) This generatespartial collapse (ca 30 die-back of the daisies) immedi-ate recovery and resulting oscillations of temperature andpopulation As forcing is increased further a second bifur-cation point is reached Then the trajectories combinebefore the black daisies disappear For white daisies alone( gure 4cd) there are two period doublings and thebeginnings of a third (inset in gure 4d) before a returnto a single trajectory

The one daisy-type model illustrates an lsquoovershootrsquoproblem for Gaia life may develop the capacity to drivean environmental variable into an uninhabitable or barelyhabitable state if the environmental effect is strong andlocal interactions that encourage growth outweigh nega-tive feedback on growth from the environment The modeldoes not include natural selection in that all the daisiesare identical and are always equally t in terms of growthrate (although in the initial growth phase clusters formand cells at the edge of clusters are better able to spreadthan those within clusters) The model does include a sys-tem selection process between bare ground and one daisytype under a certain range of forcing daisies are selectedover bare ground outside that range bare ground willsuccessfully take over from daisies

Phil Trans R Soc Lond B (2002)

When black and white types can both arise the limitcycle regimes are removed and the solution resembles theoriginal zero-dimensional model ( gure 4ef ) The twodifferent daisy types have different growth rates and hence tness thus adding a crude form of natural selection tothe model (although there is no evolution) With thisadditional selective process the model stays more rmlyin the ordered regime The system is stabilized by at leastthree effects (i) if one daisy type reaches an uninhabitabletemperature the other may still be able to spread (becausetheir local temperatures differ) (ii) in the mid-range offorcing a combination of black and white generates a glo-bal temperature closer to optimal and (iii) the presenceof one daisy type reduces the area available to the otherto expand into

We have introduced random mutation of albedo to themodel generalizing the colonization equations (81)ndash(85)to deal with any albedo type Mutation is assumed alwaysto occur in the process of colonization of an empty cell(asexual reproduction that always generates mutatedoffspring) Albedo can mutate within a parameterizedwidth of the parent albedo (plusmn D a) Within this rangeeither side of the parent albedo an offspring albedo is ran-domly chosen Limits to mutation are set at am in = 0 andam ax = 1

With mutation and natural selection within the modelsystem ( gure 5) its behaviour could be said to be lsquoadap-tiversquo in that it lsquoevolvesrsquo to counteract forcing When themodel is seeded with the original lsquoblackrsquo daisies(aB = 025) and these are allowed to mutate as forcingincreases progressively paler daisies evolve cooling theplanet and then maintaining the temperature close to con-stant Increasing D a brings the average planetary tempera-ture more rapidly towards the optimum for daisy growthThe tendency for bifurcation ( gure 4a) is removed byincreasing D a ( gure 5) because this tends to generate anearly increase in average albedo In a sensitivity analysisof the stabilizing effect of albedo diversity am ax ndash am in wasprogressively increased around a central value ofaB = 025 without any mutation and this was also foundto remove the bifurcations Albedo mutation extends therange of temperature regulation beyond that in the originalmodel because paler types than the original lsquowhitersquo onescan arise The latter result has been found in other vari-ants of Daisyworld (Stocker 1995 Von Bloh et al 1997Lenton amp Lovelock 2001)

A more complex 2D CA version of Daisyworld has pre-viously been formulated with albedo mutation and a con-tinuous temperature eld (Von Bloh et al 1997) Thissystem exhibits the remarkable property that underenforced habitat fragmentation using a percolating fractalthe system is able to regulate temperature unimpaired upto a lsquocriticalrsquo threshold at which daisy areas become iso-lated and regulation starts to break down Once uninhabi-ted land forms a spanning cluster regulation is completelyremoved By contrast trivial reductions in habitat (eg agrowing square of lsquoconcretersquo) impair temperature regu-lation in a linear fashion In the former case adjacent dai-sies can affect the temperature of small uninhabited areasbut overall temperature regulation depends on compe-tition among daisies across an entire connected space Inother words the emergent property of global temperatureregulation relies on uninhibited local interaction tting

692 T M Lenton and M van Oijen Gaia as a complex adaptive system

100

50

0

80

60

40

20

0

plusmn20

100

50

0

100

50

0

80

60

40

20

0

plusmn20

80

60

40

20

0

plusmn20

05 10 15 20

05 10 15 20

05 10 15 20 05 10 15 20

05 10 15 20

05 10 15 20

solar luminosity (_) solar luminosity (_)

solar luminosity (_) solar luminosity (_)

solar luminosity (_) solar luminosity (_)

gri

d c

over

(

)g

rid

cov

er (

)

gri

d c

ov

er (

)

glo

bal

tem

per

ature

(degC

)g

lob

al t

emp

erat

ure

(degC

)g

lob

al t

emper

atu

re (

degC)

15

plusmn508 11

(a) (b)

(c) (d)

(e) ( f )

Figure 4 Simulations of xed albedo populations in a simple CA Daisyworld (64 acute 64 grid) Parameters are as in the originalmodel (Watson amp Lovelock 1983) and the CA rules are described in sect 8 Solar luminosity (in normalized units) is increased insteps of 0004 at each of which the model is updated The left-hand graphs show percentage grid cover by the daisies versusluminosity and the right-hand graphs show global average temperature (degC) versus luminosity Temperature is a function ofluminosity and the albedo a and grid cover of daises and empty cells (ab) Seeding with lsquoblackrsquo daisies (aB = 025) denotedby lled circles (cd) Seeding with lsquowhitersquo daisies (aW= 075) denoted by open circles (ef ) Seeding with both black and whitedaisies (albedo of each seed chosen at random) The inset in (d ) shows the period doubling in the temperature trajectory withonly white daisies

in nicely with the criteria for a CAS The system is self-organizing and may arguably be in a critical state near thelimit at which daisy areas become disconnected

9 FEASIBILITY TESTS OF GAIA USING lsquoALIFErsquo

A key criticism of Daisyworld is that it is limited in onlyconsidering one predetermined type of interactionbetween the local and the global and it is one that will

Phil Trans R Soc Lond B (2002)

tend to generate regulation The daisies affect theirenvironment in the same way at the local and the globalscale Hence what is selected for at the individual leveltends to be bene cial at the global level With two or moredaisy types present there is negative selective feedbackmaking regulation likely (Lenton 1998)

lsquoAlifersquo techniques offer a promising way of makingunbiased tests of the potential for emergence of planetaryscale self-organization The model environment lsquoTierrarsquo

Gaia as a complex adaptive system T M Lenton and M van Oijen 693

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

0

20151005

solar luminosity (ndash)

grid

cov

er (

)

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

(a) (b)

(c)(d)

( f )(e)

Figure 5 CA Daisyworld simulations with albedo mutation (64 acute 64 grid) In each simulation there is seeding with theoriginal lsquoblackrsquo daisies (aB = 025) which fall in the range coloured in blue The model is updated with each increase in solarluminosity of 0004 normalized units and at each update empty cells can be colonized with offspring cells that differ at mostby plusmn D a from the albedo of their parent cell Left- and right-hand graphs show grid cover by daisy populations () and globalaverage temperature (degC) respectively The albedo colour scheme in the left-hand graphs is 0ndash02 black 02ndash04 blue 04ndash06 green 06ndash08 orange 08ndash10 red The graphs show the effect of increasing mutation range (ab) D a = 001 (cd) D a =002 (ef ) D a = 01

(Ray 1991) evolved a community of arti cial life-formsthat reproduce in different ways including parasiticallyThe model lsquolife-formsrsquo compete for resource (processortime) but they do not produce waste products Hencetheir interaction with their environment is not thermody-namically complete in the way that it is for real life-formswhich can only maintain an ordered (low entropy) stateby transforming matter as well as energy

The evolution of matter recycling is addressed usinglsquoAlifersquo techniques in the Guild model (Downing amp Zvirin-sky 1999) From one ancestral lsquospeciesrsquo a communityevolves which is able to recycle a given set of lsquochemicalsrsquo(which can be thought of as different molecular forms ofthe same key nutrient element) Such recycling enablesgreatly enhanced productivity in real ecosystems and Gaia

Phil Trans R Soc Lond B (2002)

(Volk 1998) The mechanism of emergence of recyclingis quite different from the spontaneous emergence of auto-catalytic cycles in systems of very large numbers of chemi-cal reactions (Kauffman 1993) In the Guild model lsquoAlifersquochances upon closed recycling of a small set of chemicalsand this is reinforced by selection This illustrates part ofthe mechanism (ii) that we highlighted in sect 6

The main criticisms of the original Guild model are thatthere is no treatment of energy in the system and that adeviation of the local environment from the global isassumed that may not be justi ed for some real world ana-logues A lsquoGuild IIrsquo model is being developed (K Down-ing personal communication) that includes free energyand entropy in the abstract chemistry (eg it takes freeenergy to build larger molecules) and makes the local

694 T M Lenton and M van Oijen Gaia as a complex adaptive system

environment the interior of proto-cells In this modeldespite a relatively small input of free energy in chemicalform recycling and regulation can emerge

An ideal model world for testing Gaia would containarti cial life-forms that transform lsquomatterrsquo and lsquoenergyrsquoare lsquothermodynamicallyrsquo constrained grow and replicatewith a heritable genome subject to random mutationinteract with one another and evolve new ways of alteringtheir environment related to their internal functioningThe environment would contain many lsquophysicalrsquo andlsquochemicalrsquo variables some homogeneous (well mixed) andothers heterogeneous The resulting system behaviourwould be observable and testable by perturbation

10 CONCLUSIONS

Many scientists now accept that planetary regulationinvolving the biota occurs (Longhurst 1998) However westill have to determine whether Gaiarsquos coming into exis-tence and survival was coincidental or probable and howfragile or robust the system is at present We have arguedthat Gaia is a complex system with self-organizing andadaptive behaviour but that it does not reside in a criticalstate Complexity theory modelling approaches havehelped us simulate and understand the emergence of plan-etary order lsquoAlifersquo techniques can take this further andhelp in assessing the probability of emergence of planetaryregulatory properties Our attempts to apply complexitytheory to Gaia have yielded a broader view of selectionthan previously encompassed in the Gaia theory (Lenton1998) Gene-based natural selection is just one type andlevel of selection operating within Gaia and it is not anecessary condition for regulation The existence of differ-ent types of selection operating at different levels makes iteasier to understand how planetary-scale self-regulationcan arise It also makes it easier to accept that a Gaia-likesystem may be a probable outcome once there is abundantlife on a planet with the capacity for large-scale freeenergy capture

We thank Ricard Sole and Simon Levin for the invitation towrite this article

REFERENCES

Alvarez L W Alvarez W Asaro F amp Michel H V 1980Extraterrestrial cause for the CretaceousndashTertiary extinctionScience 208 1095ndash1108

Bak P amp Sneppen K 1993 Punctuated equilibrium and criti-cality in a simple model of evolution Phys Rev Lett 714083ndash4086

Bak P Tang C amp Wiesenfeld K 1987 Self-organized criti-calitymdashan explanation of 1f noise Phys Rev Lett 59381ndash384

Berner R A 1998 The carbon cycle and CO2 over Phanero-zoic time the role of land plants Phil Trans R SocLond B 353 75ndash82 (DOI 101098rstb19980192)

Betts R A 1999 Self-bene cial effects of vegetation on cli-mate in an oceanndashatmosphere general circulation modelGeophys Res Lett 26 1457ndash1460

Bonan G B Pollard D amp Thompson S L 1992 Effects ofboreal forest vegetation on global climate Nature 359716ndash718

Budyko M I 1968 The effect of solar radiation variations onthe climate of the Earth Tellus 21 611ndash619

Phil Trans R Soc Lond B (2002)

Dawkins R 1983 The extended phenotype Oxford UniversityPress

De Gregorio S Pielke R A amp Dalu G A 1992a Feedbackbetween a simple biosystem and the temperature of theEarth J Nonlinear Sci 2 263ndash292

De Gregorio S Pielke R A amp Dalu G A 1992b A delayedbiophysical system for the Earthrsquos climate J Nonlinear Sci2 293ndash318

DesMarais D J 2000 When did photosynthesis emerge onEarth Science 289 1703ndash1705

DrsquoHondt S Donaghay P Zachos J C Luttenberg D ampLindinger M 1998 Organic carbon uxes and ecologicalrecovery from the CretaceousndashTertiary mass extinctionScience 282 276ndash279

Doolittle W F 1981 Is nature really motherly The CoEvol-ution Q Spring 58ndash63

Downing K amp Zvirinsky P 1999 The simulated evolutionof biochemical guilds reconciling Gaia theory and naturalselection Artif Life 5 291ndash318

Ehrlich P 1991 Coevolution and its applicability to the Gaiahypothesis In Scientists on Gaia (ed S H Schneider amp PJ Boston) pp 118ndash120 London MIT Press

Gallagher R amp Appenzeller T 1999 Beyond reductionismScience 284 79

Hamilton W D 1995 Ecology in the large Gaia and GenghisKhan J Appl Ecol 32 451ndash453

Hamilton W D 1996 Gaiarsquos bene ts New Scientist 15162ndash63

Hamilton W D amp Lenton T M 1998 Spora and Gaia howmicrobes y with their clouds Ethol Ecol Evol 10 1ndash16

Han T-M amp Runnegar B 1992 Megascopic eukaryotic algaefrom the 21 billion-year-old Negaunee iron-formationMichigan Science 257 232ndash235

Hoffman P F Kaufman A J Halverson G P amp SchragD P 1998 A Neoproterozoic snowball earth Science 2811342ndash1346

Holland J 1995 Hidden order how adaptation builds complexityReading MA Addison-Wesley

Hyde W T Crowley T J Baum S K amp Peltier W R2000 Neoproterozoic lsquosnowball Earthrsquo simulations with acoupled climateice-sheet model Nature 405 425ndash429

Imshenetsky A A Lysenko S V amp Kazakov G A 1978Upper boundary of the biosphere Appl Environ Microbiol35 1ndash5

Isaacs A Daintith J amp Martin E (eds) 1996 Concise sciencedictionary Oxford University Press

Jascourt S D amp Raymond W H 1992 Comments on lsquoChaosin daisyworldrsquo by X Zeng et al Tellus 44B 243ndash246

Joslashrgensen S E amp Straskraba M 2000 Ecosystems as cyber-netic systems In Handbook of ecosystem theories and manage-ment (ed S E Joslashrgensen amp F Muller) pp 249ndash264London Lewis Publishers

Kasting J F 1991 Box models for the evolution of atmo-spheric oxygen an update Global and Planetary Change 97125ndash131

Kauffman S A 1993 The origins of order self-organization andselection in evolution Oxford University Press

Kleidon A 2002 Testing the effect of life on Earthrsquos func-tioning how Gaian is the Earth system Climatic Change 52383ndash389

Klinger L F 1991 Peatland formation and ice ages a possibleGaian mechanism related to community succession InScientists on Gaia (ed S H Schneider amp P J Boston) pp247ndash255 London MIT Press

Koeslag J H Saunders P T amp Wessels J A 1997 Glucosehomeostasis with in nite gain further lessons from theDaisyworld parable J Endocrinol 154 187ndash192

Lenton T M 1998 Gaia and natural selection Nature 394439ndash447

692 T M Lenton and M van Oijen Gaia as a complex adaptive system

100

50

0

80

60

40

20

0

plusmn20

100

50

0

100

50

0

80

60

40

20

0

plusmn20

80

60

40

20

0

plusmn20

05 10 15 20

05 10 15 20

05 10 15 20 05 10 15 20

05 10 15 20

05 10 15 20

solar luminosity (_) solar luminosity (_)

solar luminosity (_) solar luminosity (_)

solar luminosity (_) solar luminosity (_)

gri

d c

over

(

)g

rid

cov

er (

)

gri

d c

ov

er (

)

glo

bal

tem

per

ature

(degC

)g

lob

al t

emp

erat

ure

(degC

)g

lob

al t

emper

atu

re (

degC)

15

plusmn508 11

(a) (b)

(c) (d)

(e) ( f )

Figure 4 Simulations of xed albedo populations in a simple CA Daisyworld (64 acute 64 grid) Parameters are as in the originalmodel (Watson amp Lovelock 1983) and the CA rules are described in sect 8 Solar luminosity (in normalized units) is increased insteps of 0004 at each of which the model is updated The left-hand graphs show percentage grid cover by the daisies versusluminosity and the right-hand graphs show global average temperature (degC) versus luminosity Temperature is a function ofluminosity and the albedo a and grid cover of daises and empty cells (ab) Seeding with lsquoblackrsquo daisies (aB = 025) denotedby lled circles (cd) Seeding with lsquowhitersquo daisies (aW= 075) denoted by open circles (ef ) Seeding with both black and whitedaisies (albedo of each seed chosen at random) The inset in (d ) shows the period doubling in the temperature trajectory withonly white daisies

in nicely with the criteria for a CAS The system is self-organizing and may arguably be in a critical state near thelimit at which daisy areas become disconnected

9 FEASIBILITY TESTS OF GAIA USING lsquoALIFErsquo

A key criticism of Daisyworld is that it is limited in onlyconsidering one predetermined type of interactionbetween the local and the global and it is one that will

Phil Trans R Soc Lond B (2002)

tend to generate regulation The daisies affect theirenvironment in the same way at the local and the globalscale Hence what is selected for at the individual leveltends to be bene cial at the global level With two or moredaisy types present there is negative selective feedbackmaking regulation likely (Lenton 1998)

lsquoAlifersquo techniques offer a promising way of makingunbiased tests of the potential for emergence of planetaryscale self-organization The model environment lsquoTierrarsquo

Gaia as a complex adaptive system T M Lenton and M van Oijen 693

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

0

20151005

solar luminosity (ndash)

grid

cov

er (

)

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

(a) (b)

(c)(d)

( f )(e)

Figure 5 CA Daisyworld simulations with albedo mutation (64 acute 64 grid) In each simulation there is seeding with theoriginal lsquoblackrsquo daisies (aB = 025) which fall in the range coloured in blue The model is updated with each increase in solarluminosity of 0004 normalized units and at each update empty cells can be colonized with offspring cells that differ at mostby plusmn D a from the albedo of their parent cell Left- and right-hand graphs show grid cover by daisy populations () and globalaverage temperature (degC) respectively The albedo colour scheme in the left-hand graphs is 0ndash02 black 02ndash04 blue 04ndash06 green 06ndash08 orange 08ndash10 red The graphs show the effect of increasing mutation range (ab) D a = 001 (cd) D a =002 (ef ) D a = 01

(Ray 1991) evolved a community of arti cial life-formsthat reproduce in different ways including parasiticallyThe model lsquolife-formsrsquo compete for resource (processortime) but they do not produce waste products Hencetheir interaction with their environment is not thermody-namically complete in the way that it is for real life-formswhich can only maintain an ordered (low entropy) stateby transforming matter as well as energy

The evolution of matter recycling is addressed usinglsquoAlifersquo techniques in the Guild model (Downing amp Zvirin-sky 1999) From one ancestral lsquospeciesrsquo a communityevolves which is able to recycle a given set of lsquochemicalsrsquo(which can be thought of as different molecular forms ofthe same key nutrient element) Such recycling enablesgreatly enhanced productivity in real ecosystems and Gaia

Phil Trans R Soc Lond B (2002)

(Volk 1998) The mechanism of emergence of recyclingis quite different from the spontaneous emergence of auto-catalytic cycles in systems of very large numbers of chemi-cal reactions (Kauffman 1993) In the Guild model lsquoAlifersquochances upon closed recycling of a small set of chemicalsand this is reinforced by selection This illustrates part ofthe mechanism (ii) that we highlighted in sect 6

The main criticisms of the original Guild model are thatthere is no treatment of energy in the system and that adeviation of the local environment from the global isassumed that may not be justi ed for some real world ana-logues A lsquoGuild IIrsquo model is being developed (K Down-ing personal communication) that includes free energyand entropy in the abstract chemistry (eg it takes freeenergy to build larger molecules) and makes the local

694 T M Lenton and M van Oijen Gaia as a complex adaptive system

environment the interior of proto-cells In this modeldespite a relatively small input of free energy in chemicalform recycling and regulation can emerge

An ideal model world for testing Gaia would containarti cial life-forms that transform lsquomatterrsquo and lsquoenergyrsquoare lsquothermodynamicallyrsquo constrained grow and replicatewith a heritable genome subject to random mutationinteract with one another and evolve new ways of alteringtheir environment related to their internal functioningThe environment would contain many lsquophysicalrsquo andlsquochemicalrsquo variables some homogeneous (well mixed) andothers heterogeneous The resulting system behaviourwould be observable and testable by perturbation

10 CONCLUSIONS

Many scientists now accept that planetary regulationinvolving the biota occurs (Longhurst 1998) However westill have to determine whether Gaiarsquos coming into exis-tence and survival was coincidental or probable and howfragile or robust the system is at present We have arguedthat Gaia is a complex system with self-organizing andadaptive behaviour but that it does not reside in a criticalstate Complexity theory modelling approaches havehelped us simulate and understand the emergence of plan-etary order lsquoAlifersquo techniques can take this further andhelp in assessing the probability of emergence of planetaryregulatory properties Our attempts to apply complexitytheory to Gaia have yielded a broader view of selectionthan previously encompassed in the Gaia theory (Lenton1998) Gene-based natural selection is just one type andlevel of selection operating within Gaia and it is not anecessary condition for regulation The existence of differ-ent types of selection operating at different levels makes iteasier to understand how planetary-scale self-regulationcan arise It also makes it easier to accept that a Gaia-likesystem may be a probable outcome once there is abundantlife on a planet with the capacity for large-scale freeenergy capture

We thank Ricard Sole and Simon Levin for the invitation towrite this article

REFERENCES

Alvarez L W Alvarez W Asaro F amp Michel H V 1980Extraterrestrial cause for the CretaceousndashTertiary extinctionScience 208 1095ndash1108

Bak P amp Sneppen K 1993 Punctuated equilibrium and criti-cality in a simple model of evolution Phys Rev Lett 714083ndash4086

Bak P Tang C amp Wiesenfeld K 1987 Self-organized criti-calitymdashan explanation of 1f noise Phys Rev Lett 59381ndash384

Berner R A 1998 The carbon cycle and CO2 over Phanero-zoic time the role of land plants Phil Trans R SocLond B 353 75ndash82 (DOI 101098rstb19980192)

Betts R A 1999 Self-bene cial effects of vegetation on cli-mate in an oceanndashatmosphere general circulation modelGeophys Res Lett 26 1457ndash1460

Bonan G B Pollard D amp Thompson S L 1992 Effects ofboreal forest vegetation on global climate Nature 359716ndash718

Budyko M I 1968 The effect of solar radiation variations onthe climate of the Earth Tellus 21 611ndash619

Phil Trans R Soc Lond B (2002)

Dawkins R 1983 The extended phenotype Oxford UniversityPress

De Gregorio S Pielke R A amp Dalu G A 1992a Feedbackbetween a simple biosystem and the temperature of theEarth J Nonlinear Sci 2 263ndash292

De Gregorio S Pielke R A amp Dalu G A 1992b A delayedbiophysical system for the Earthrsquos climate J Nonlinear Sci2 293ndash318

DesMarais D J 2000 When did photosynthesis emerge onEarth Science 289 1703ndash1705

DrsquoHondt S Donaghay P Zachos J C Luttenberg D ampLindinger M 1998 Organic carbon uxes and ecologicalrecovery from the CretaceousndashTertiary mass extinctionScience 282 276ndash279

Doolittle W F 1981 Is nature really motherly The CoEvol-ution Q Spring 58ndash63

Downing K amp Zvirinsky P 1999 The simulated evolutionof biochemical guilds reconciling Gaia theory and naturalselection Artif Life 5 291ndash318

Ehrlich P 1991 Coevolution and its applicability to the Gaiahypothesis In Scientists on Gaia (ed S H Schneider amp PJ Boston) pp 118ndash120 London MIT Press

Gallagher R amp Appenzeller T 1999 Beyond reductionismScience 284 79

Hamilton W D 1995 Ecology in the large Gaia and GenghisKhan J Appl Ecol 32 451ndash453

Hamilton W D 1996 Gaiarsquos bene ts New Scientist 15162ndash63

Hamilton W D amp Lenton T M 1998 Spora and Gaia howmicrobes y with their clouds Ethol Ecol Evol 10 1ndash16

Han T-M amp Runnegar B 1992 Megascopic eukaryotic algaefrom the 21 billion-year-old Negaunee iron-formationMichigan Science 257 232ndash235

Hoffman P F Kaufman A J Halverson G P amp SchragD P 1998 A Neoproterozoic snowball earth Science 2811342ndash1346

Holland J 1995 Hidden order how adaptation builds complexityReading MA Addison-Wesley

Hyde W T Crowley T J Baum S K amp Peltier W R2000 Neoproterozoic lsquosnowball Earthrsquo simulations with acoupled climateice-sheet model Nature 405 425ndash429

Imshenetsky A A Lysenko S V amp Kazakov G A 1978Upper boundary of the biosphere Appl Environ Microbiol35 1ndash5

Isaacs A Daintith J amp Martin E (eds) 1996 Concise sciencedictionary Oxford University Press

Jascourt S D amp Raymond W H 1992 Comments on lsquoChaosin daisyworldrsquo by X Zeng et al Tellus 44B 243ndash246

Joslashrgensen S E amp Straskraba M 2000 Ecosystems as cyber-netic systems In Handbook of ecosystem theories and manage-ment (ed S E Joslashrgensen amp F Muller) pp 249ndash264London Lewis Publishers

Kasting J F 1991 Box models for the evolution of atmo-spheric oxygen an update Global and Planetary Change 97125ndash131

Kauffman S A 1993 The origins of order self-organization andselection in evolution Oxford University Press

Kleidon A 2002 Testing the effect of life on Earthrsquos func-tioning how Gaian is the Earth system Climatic Change 52383ndash389

Klinger L F 1991 Peatland formation and ice ages a possibleGaian mechanism related to community succession InScientists on Gaia (ed S H Schneider amp P J Boston) pp247ndash255 London MIT Press

Koeslag J H Saunders P T amp Wessels J A 1997 Glucosehomeostasis with in nite gain further lessons from theDaisyworld parable J Endocrinol 154 187ndash192

Lenton T M 1998 Gaia and natural selection Nature 394439ndash447

Gaia as a complex adaptive system T M Lenton and M van Oijen 693

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

020151005

solar luminosity (ndash)

grid

cov

er (

)

100

50

0

20151005

solar luminosity (ndash)

grid

cov

er (

)

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

20151005

solar luminosity (ndash)

80

60

40

20

0

ndash20

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

glob

al te

mpe

ratu

re (

degC)

(a) (b)

(c)(d)

( f )(e)

Figure 5 CA Daisyworld simulations with albedo mutation (64 acute 64 grid) In each simulation there is seeding with theoriginal lsquoblackrsquo daisies (aB = 025) which fall in the range coloured in blue The model is updated with each increase in solarluminosity of 0004 normalized units and at each update empty cells can be colonized with offspring cells that differ at mostby plusmn D a from the albedo of their parent cell Left- and right-hand graphs show grid cover by daisy populations () and globalaverage temperature (degC) respectively The albedo colour scheme in the left-hand graphs is 0ndash02 black 02ndash04 blue 04ndash06 green 06ndash08 orange 08ndash10 red The graphs show the effect of increasing mutation range (ab) D a = 001 (cd) D a =002 (ef ) D a = 01

(Ray 1991) evolved a community of arti cial life-formsthat reproduce in different ways including parasiticallyThe model lsquolife-formsrsquo compete for resource (processortime) but they do not produce waste products Hencetheir interaction with their environment is not thermody-namically complete in the way that it is for real life-formswhich can only maintain an ordered (low entropy) stateby transforming matter as well as energy

The evolution of matter recycling is addressed usinglsquoAlifersquo techniques in the Guild model (Downing amp Zvirin-sky 1999) From one ancestral lsquospeciesrsquo a communityevolves which is able to recycle a given set of lsquochemicalsrsquo(which can be thought of as different molecular forms ofthe same key nutrient element) Such recycling enablesgreatly enhanced productivity in real ecosystems and Gaia

Phil Trans R Soc Lond B (2002)

(Volk 1998) The mechanism of emergence of recyclingis quite different from the spontaneous emergence of auto-catalytic cycles in systems of very large numbers of chemi-cal reactions (Kauffman 1993) In the Guild model lsquoAlifersquochances upon closed recycling of a small set of chemicalsand this is reinforced by selection This illustrates part ofthe mechanism (ii) that we highlighted in sect 6

The main criticisms of the original Guild model are thatthere is no treatment of energy in the system and that adeviation of the local environment from the global isassumed that may not be justi ed for some real world ana-logues A lsquoGuild IIrsquo model is being developed (K Down-ing personal communication) that includes free energyand entropy in the abstract chemistry (eg it takes freeenergy to build larger molecules) and makes the local

694 T M Lenton and M van Oijen Gaia as a complex adaptive system

environment the interior of proto-cells In this modeldespite a relatively small input of free energy in chemicalform recycling and regulation can emerge

An ideal model world for testing Gaia would containarti cial life-forms that transform lsquomatterrsquo and lsquoenergyrsquoare lsquothermodynamicallyrsquo constrained grow and replicatewith a heritable genome subject to random mutationinteract with one another and evolve new ways of alteringtheir environment related to their internal functioningThe environment would contain many lsquophysicalrsquo andlsquochemicalrsquo variables some homogeneous (well mixed) andothers heterogeneous The resulting system behaviourwould be observable and testable by perturbation

10 CONCLUSIONS

Many scientists now accept that planetary regulationinvolving the biota occurs (Longhurst 1998) However westill have to determine whether Gaiarsquos coming into exis-tence and survival was coincidental or probable and howfragile or robust the system is at present We have arguedthat Gaia is a complex system with self-organizing andadaptive behaviour but that it does not reside in a criticalstate Complexity theory modelling approaches havehelped us simulate and understand the emergence of plan-etary order lsquoAlifersquo techniques can take this further andhelp in assessing the probability of emergence of planetaryregulatory properties Our attempts to apply complexitytheory to Gaia have yielded a broader view of selectionthan previously encompassed in the Gaia theory (Lenton1998) Gene-based natural selection is just one type andlevel of selection operating within Gaia and it is not anecessary condition for regulation The existence of differ-ent types of selection operating at different levels makes iteasier to understand how planetary-scale self-regulationcan arise It also makes it easier to accept that a Gaia-likesystem may be a probable outcome once there is abundantlife on a planet with the capacity for large-scale freeenergy capture

We thank Ricard Sole and Simon Levin for the invitation towrite this article

REFERENCES

Alvarez L W Alvarez W Asaro F amp Michel H V 1980Extraterrestrial cause for the CretaceousndashTertiary extinctionScience 208 1095ndash1108

Bak P amp Sneppen K 1993 Punctuated equilibrium and criti-cality in a simple model of evolution Phys Rev Lett 714083ndash4086

Bak P Tang C amp Wiesenfeld K 1987 Self-organized criti-calitymdashan explanation of 1f noise Phys Rev Lett 59381ndash384

Berner R A 1998 The carbon cycle and CO2 over Phanero-zoic time the role of land plants Phil Trans R SocLond B 353 75ndash82 (DOI 101098rstb19980192)

Betts R A 1999 Self-bene cial effects of vegetation on cli-mate in an oceanndashatmosphere general circulation modelGeophys Res Lett 26 1457ndash1460

Bonan G B Pollard D amp Thompson S L 1992 Effects ofboreal forest vegetation on global climate Nature 359716ndash718

Budyko M I 1968 The effect of solar radiation variations onthe climate of the Earth Tellus 21 611ndash619

Phil Trans R Soc Lond B (2002)

Dawkins R 1983 The extended phenotype Oxford UniversityPress

De Gregorio S Pielke R A amp Dalu G A 1992a Feedbackbetween a simple biosystem and the temperature of theEarth J Nonlinear Sci 2 263ndash292

De Gregorio S Pielke R A amp Dalu G A 1992b A delayedbiophysical system for the Earthrsquos climate J Nonlinear Sci2 293ndash318

DesMarais D J 2000 When did photosynthesis emerge onEarth Science 289 1703ndash1705

DrsquoHondt S Donaghay P Zachos J C Luttenberg D ampLindinger M 1998 Organic carbon uxes and ecologicalrecovery from the CretaceousndashTertiary mass extinctionScience 282 276ndash279

Doolittle W F 1981 Is nature really motherly The CoEvol-ution Q Spring 58ndash63

Downing K amp Zvirinsky P 1999 The simulated evolutionof biochemical guilds reconciling Gaia theory and naturalselection Artif Life 5 291ndash318

Ehrlich P 1991 Coevolution and its applicability to the Gaiahypothesis In Scientists on Gaia (ed S H Schneider amp PJ Boston) pp 118ndash120 London MIT Press

Gallagher R amp Appenzeller T 1999 Beyond reductionismScience 284 79

Hamilton W D 1995 Ecology in the large Gaia and GenghisKhan J Appl Ecol 32 451ndash453

Hamilton W D 1996 Gaiarsquos bene ts New Scientist 15162ndash63

Hamilton W D amp Lenton T M 1998 Spora and Gaia howmicrobes y with their clouds Ethol Ecol Evol 10 1ndash16

Han T-M amp Runnegar B 1992 Megascopic eukaryotic algaefrom the 21 billion-year-old Negaunee iron-formationMichigan Science 257 232ndash235

Hoffman P F Kaufman A J Halverson G P amp SchragD P 1998 A Neoproterozoic snowball earth Science 2811342ndash1346

Holland J 1995 Hidden order how adaptation builds complexityReading MA Addison-Wesley

Hyde W T Crowley T J Baum S K amp Peltier W R2000 Neoproterozoic lsquosnowball Earthrsquo simulations with acoupled climateice-sheet model Nature 405 425ndash429

Imshenetsky A A Lysenko S V amp Kazakov G A 1978Upper boundary of the biosphere Appl Environ Microbiol35 1ndash5

Isaacs A Daintith J amp Martin E (eds) 1996 Concise sciencedictionary Oxford University Press

Jascourt S D amp Raymond W H 1992 Comments on lsquoChaosin daisyworldrsquo by X Zeng et al Tellus 44B 243ndash246

Joslashrgensen S E amp Straskraba M 2000 Ecosystems as cyber-netic systems In Handbook of ecosystem theories and manage-ment (ed S E Joslashrgensen amp F Muller) pp 249ndash264London Lewis Publishers

Kasting J F 1991 Box models for the evolution of atmo-spheric oxygen an update Global and Planetary Change 97125ndash131

Kauffman S A 1993 The origins of order self-organization andselection in evolution Oxford University Press

Kleidon A 2002 Testing the effect of life on Earthrsquos func-tioning how Gaian is the Earth system Climatic Change 52383ndash389

Klinger L F 1991 Peatland formation and ice ages a possibleGaian mechanism related to community succession InScientists on Gaia (ed S H Schneider amp P J Boston) pp247ndash255 London MIT Press

Koeslag J H Saunders P T amp Wessels J A 1997 Glucosehomeostasis with in nite gain further lessons from theDaisyworld parable J Endocrinol 154 187ndash192

Lenton T M 1998 Gaia and natural selection Nature 394439ndash447

694 T M Lenton and M van Oijen Gaia as a complex adaptive system

environment the interior of proto-cells In this modeldespite a relatively small input of free energy in chemicalform recycling and regulation can emerge

An ideal model world for testing Gaia would containarti cial life-forms that transform lsquomatterrsquo and lsquoenergyrsquoare lsquothermodynamicallyrsquo constrained grow and replicatewith a heritable genome subject to random mutationinteract with one another and evolve new ways of alteringtheir environment related to their internal functioningThe environment would contain many lsquophysicalrsquo andlsquochemicalrsquo variables some homogeneous (well mixed) andothers heterogeneous The resulting system behaviourwould be observable and testable by perturbation

10 CONCLUSIONS

Many scientists now accept that planetary regulationinvolving the biota occurs (Longhurst 1998) However westill have to determine whether Gaiarsquos coming into exis-tence and survival was coincidental or probable and howfragile or robust the system is at present We have arguedthat Gaia is a complex system with self-organizing andadaptive behaviour but that it does not reside in a criticalstate Complexity theory modelling approaches havehelped us simulate and understand the emergence of plan-etary order lsquoAlifersquo techniques can take this further andhelp in assessing the probability of emergence of planetaryregulatory properties Our attempts to apply complexitytheory to Gaia have yielded a broader view of selectionthan previously encompassed in the Gaia theory (Lenton1998) Gene-based natural selection is just one type andlevel of selection operating within Gaia and it is not anecessary condition for regulation The existence of differ-ent types of selection operating at different levels makes iteasier to understand how planetary-scale self-regulationcan arise It also makes it easier to accept that a Gaia-likesystem may be a probable outcome once there is abundantlife on a planet with the capacity for large-scale freeenergy capture

We thank Ricard Sole and Simon Levin for the invitation towrite this article

REFERENCES

Alvarez L W Alvarez W Asaro F amp Michel H V 1980Extraterrestrial cause for the CretaceousndashTertiary extinctionScience 208 1095ndash1108

Bak P amp Sneppen K 1993 Punctuated equilibrium and criti-cality in a simple model of evolution Phys Rev Lett 714083ndash4086

Bak P Tang C amp Wiesenfeld K 1987 Self-organized criti-calitymdashan explanation of 1f noise Phys Rev Lett 59381ndash384

Berner R A 1998 The carbon cycle and CO2 over Phanero-zoic time the role of land plants Phil Trans R SocLond B 353 75ndash82 (DOI 101098rstb19980192)

Betts R A 1999 Self-bene cial effects of vegetation on cli-mate in an oceanndashatmosphere general circulation modelGeophys Res Lett 26 1457ndash1460

Bonan G B Pollard D amp Thompson S L 1992 Effects ofboreal forest vegetation on global climate Nature 359716ndash718

Budyko M I 1968 The effect of solar radiation variations onthe climate of the Earth Tellus 21 611ndash619

Phil Trans R Soc Lond B (2002)

Dawkins R 1983 The extended phenotype Oxford UniversityPress

De Gregorio S Pielke R A amp Dalu G A 1992a Feedbackbetween a simple biosystem and the temperature of theEarth J Nonlinear Sci 2 263ndash292

De Gregorio S Pielke R A amp Dalu G A 1992b A delayedbiophysical system for the Earthrsquos climate J Nonlinear Sci2 293ndash318

DesMarais D J 2000 When did photosynthesis emerge onEarth Science 289 1703ndash1705

DrsquoHondt S Donaghay P Zachos J C Luttenberg D ampLindinger M 1998 Organic carbon uxes and ecologicalrecovery from the CretaceousndashTertiary mass extinctionScience 282 276ndash279

Doolittle W F 1981 Is nature really motherly The CoEvol-ution Q Spring 58ndash63

Downing K amp Zvirinsky P 1999 The simulated evolutionof biochemical guilds reconciling Gaia theory and naturalselection Artif Life 5 291ndash318

Ehrlich P 1991 Coevolution and its applicability to the Gaiahypothesis In Scientists on Gaia (ed S H Schneider amp PJ Boston) pp 118ndash120 London MIT Press

Gallagher R amp Appenzeller T 1999 Beyond reductionismScience 284 79

Hamilton W D 1995 Ecology in the large Gaia and GenghisKhan J Appl Ecol 32 451ndash453

Hamilton W D 1996 Gaiarsquos bene ts New Scientist 15162ndash63

Hamilton W D amp Lenton T M 1998 Spora and Gaia howmicrobes y with their clouds Ethol Ecol Evol 10 1ndash16

Han T-M amp Runnegar B 1992 Megascopic eukaryotic algaefrom the 21 billion-year-old Negaunee iron-formationMichigan Science 257 232ndash235

Hoffman P F Kaufman A J Halverson G P amp SchragD P 1998 A Neoproterozoic snowball earth Science 2811342ndash1346

Holland J 1995 Hidden order how adaptation builds complexityReading MA Addison-Wesley

Hyde W T Crowley T J Baum S K amp Peltier W R2000 Neoproterozoic lsquosnowball Earthrsquo simulations with acoupled climateice-sheet model Nature 405 425ndash429

Imshenetsky A A Lysenko S V amp Kazakov G A 1978Upper boundary of the biosphere Appl Environ Microbiol35 1ndash5

Isaacs A Daintith J amp Martin E (eds) 1996 Concise sciencedictionary Oxford University Press

Jascourt S D amp Raymond W H 1992 Comments on lsquoChaosin daisyworldrsquo by X Zeng et al Tellus 44B 243ndash246

Joslashrgensen S E amp Straskraba M 2000 Ecosystems as cyber-netic systems In Handbook of ecosystem theories and manage-ment (ed S E Joslashrgensen amp F Muller) pp 249ndash264London Lewis Publishers

Kasting J F 1991 Box models for the evolution of atmo-spheric oxygen an update Global and Planetary Change 97125ndash131

Kauffman S A 1993 The origins of order self-organization andselection in evolution Oxford University Press

Kleidon A 2002 Testing the effect of life on Earthrsquos func-tioning how Gaian is the Earth system Climatic Change 52383ndash389

Klinger L F 1991 Peatland formation and ice ages a possibleGaian mechanism related to community succession InScientists on Gaia (ed S H Schneider amp P J Boston) pp247ndash255 London MIT Press

Koeslag J H Saunders P T amp Wessels J A 1997 Glucosehomeostasis with in nite gain further lessons from theDaisyworld parable J Endocrinol 154 187ndash192

Lenton T M 1998 Gaia and natural selection Nature 394439ndash447

Gaia as a complex adaptive system T M Lenton and M van Oijen 695

Lenton T M 2001 The role of land plants phosphorusweathering and re in the rise and regulation of atmosphericoxygen Global Change Biology 7 613ndash629

Lenton T M 2002 Testing Gaia the effect of life on Earthrsquoshabitability and regulation Climatic Change 52 409ndash422

Lenton T M amp Lovelock J E 2000 Daisyworld is Darwin-ian constraints on adaptation are important for planetaryself-regulation J Theor Biol 206 109ndash114

Lenton T M amp Lovelock J E 2001 Daisyworld revisitedquantifying biological effects on planetary self-regulationTellus 53B 288ndash305

Lenton T M amp Von Bloh W 2001 Biotic feedback extendsthe lifespan of the biosphere Geophys Res Lett 28 1715ndash1718

Lenton T M amp Watson A J 2000a Red eld revisited 1Regulation of nitrate phosphate and oxygen in the oceanGlobal Biogeochemical Cycles 14 225ndash248

Lenton T M amp Watson A J 2000b Red eld revisited 2What regulates the oxygen content of the atmosphere GlobalBiogeochemical Cycles 14 249ndash268

Levin S A 1998 Ecosystems and the biosphere as complexadaptive systems Ecosystems 1 431ndash436

Lewin R 1993 Complexity life at the edge of chaos LondonPhoenix

Lewis G N amp Randall N 1923 Thermodynamics and the freeenergy of chemical substrates New York McGraw-Hill

Longhurst A 1998 Too intelligent for our own good Nature395 9

Lovelock J E 1972 Gaia as seen through the atmosphereAtmos Environ 6 579ndash580

Lovelock J E 1975 Thermodynamics and the recognition ofalien biospheres Proc R Soc Lond 189 167ndash181

Lovelock J E 1983 Daisyworldmdasha cybernetic proof of theGaia hypothesis The CoEvolution Q Summer 66ndash72

Lovelock J E 1986 Geophysiology a new look at Earthscience Bull Am Meteorol Soc 67 392ndash397

Lovelock J E 1988 The ages of Gaiamdasha biography of our livingEarth The Commonwealth Fund Book Program NewYork W W Norton amp Co

Lovelock J E 1991 Gaiamdashthe practical science of planetarymedicine London Gaia Books

Lovelock J E amp Margulis L M 1974 Atmospheric homeo-stasis by and for the biosphere the Gaia hypothesis Tellus26 2ndash10

Lovelock J E amp Watson A J 1982 The regulation of carbondioxide and climate Gaia or geochemistry Planetary SpaceSci 30 795ndash802

Lovelock J E amp Whit eld M 1982 Life-span of the bio-sphere Nature 296 561ndash563

Mojzsis S J Arrhenius G McKeegan K D HarrisonT M Nutman A P amp Friend C R L 1996 Evidence forlife on Earth before 3800 million years ago Nature 38455ndash59

Nevison C Gupta V amp Klinger L 1999 Self-sustained tem-perature oscillations on Daisyworld Tellus 51B 806ndash814

Newman M E J 1997 A model of mass extinction J TheorBiol 189 235ndash252

Paolo E A D 2000 Ecological symmetry breaking can favourthe evolution of altruism in an action-response game JTheor Biol 203 135ndash152

Petit J R (and 18 others) 1999 Climate and atmospherichistory of the past 420 000 years from the Vostok ice coreAntarctica Nature 399 429ndash436

Rampino M R 1987 Impact cratering and ood basaltvolcanism Nature 327 468

Ray T S 1991 An approach to the synthesis of life In Arti-

Phil Trans R Soc Lond B (2002)

cial life II (ed C G Langton C Taylor J D Farmer ampS Rasmussen) pp 371ndash408 Redwood City CAAddison-Wesley

Red eld A C 1958 The biological control of chemical factorsin the environment Am Sci 46 205ndash221

Robertson D amp Robinson J 1998 Darwinian Daisyworld JTheor Biol 195 129ndash134

Sagan C Thompson W R Carlson R Gurnett D ampHord C 1993 A search for life on Earth from the Galileospacecraft Nature 365 715ndash721

Sardeshmukh P D 2000 Coupled systems with super-negative feedbacks Geophys Res Abstracts 2 421

Saunders P T 1994 Evolution without natural selectionfurther implications of the Daisyworld parable J TheorBiol 166 365ndash373

Saunders P T Koeslag J H amp Wessels J A 1998 Integralrein control in physiology J Theor Biol 194 163ndash173

Schidlowski M 1988 A 3800-million-year isotopic record oflife from carbon in sedimentary rocks Nature 333 313ndash318

Schrodinger E 1944 What is life Cambridge University PressSchwartzman D 1999 Life temperature and the earth the self-

organizing biosphere New York Columbia University PressSchwartzman D W amp Volk T 1989 Biotic enhancement of

weathering and the habitability of Earth Nature 340 457ndash460

Sellers W D 1969 A global climate model based on theenergy balance of the Earthndashatmosphere system J ApplMeteorol 8 386ndash400

Sillen L G 1967 How have sea water and air got their presentcompositions Chemistry in Britain 3 291ndash297

Smith A 1776 An inquiry into the nature and causes of the wealthof nations London W Strahan amp T Cadell

Stocker S 1995 Regarding mutations in Daisyworld modelsJ Theor Biol 175 495ndash501

Volk T 1998 Gaiarsquos bodymdashtoward a physiology of the EarthNew York Copernicus

Von Bloh W Block A amp Schellnhuber H J 1997 Self-stabi-lization of the biosphere under global change a tutorial geo-physiological approach Tellus 49B 249ndash262

Walker J C G 1987 Was the Archaean biosphere upsidedown Nature 329 710ndash712

Walker J C G Hays P B amp Kasting J F 1981 A negativefeedback mechanism for the long-term stabilisation ofEarthrsquos surface temperature J Geophys Res 86 9776ndash9782

Watson A J 1999 Coevolution of the Earthrsquos environmentand life Goldilocks Gaia and the anthropic principle InJames Huttonmdashpresent and future vol 150 (ed G Y Craig ampJ H Hull) pp 75ndash88 London Geological Society

Watson A J amp Lovelock J E 1983 Biological homeostasis ofthe global environment the parable of Daisyworld Tellus35B 284ndash289

Weber S L 2001 On homeostasis in Daisyworld ClimaticChange 48 465ndash485

Wilhelm T amp Bruggemann R 2000 Goal functions for thedevelopment of natural systems Ecol Model 132 231ndash246

Zeng X Pielke R A amp Eykholt R 1990 Chaos in Daisy-world Tellus 42B 309ndash318

GLOSSARY

2D two dimensionalAI arti cial intelligencelsquoAlifersquo arti cial lifeCA cellular automataCAS complex adaptive system