Hubbell, S. P. 2005 (Neutral Theory of Biodiversity and Biogeography)

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The neutral theory of biodiversity and biogeography and Stephen Jay GouldAuthor(s): Stephen P. HubbellSource: Paleobiology, 31(sp5):122-132. 2005.Published By: The Paleontological SocietyDOI: http://dx.doi.org/10.1666/0094-8373(2005)031[0122:TNTOBA]2.0.CO;2URL: http://www.bioone.org/doi/full/10.1666/0094-8373%282005%29031%5B0122%3ATNTOBA%5D2.0.CO%3B2

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Paleobiology, 31(2, Supplement), 2005, pp. 122132

The neutral theory of biodiversity and biogeography andStephen Jay Gould

Stephen P. Hubbell

Abstract.Neutral theory in ecology is based on the symmetry assumption that ecologically similarspecies in a community can be treated as demographically equivalent on a per capita basisequiv-alent in birth and death rates, in rates of dispersal, and even in the probability of speciating. Al-though only a first approximation, the symmetry assumption allows the development of a quan-titative neutral theory of relative species abundance and dynamic null hypotheses for the assemblyof communities in ecological time and for phylogeny and phylogeography in evolutionary time.Although Steve Gould was not a neutralist, he made use of ideas of symmetry and of null modelsin his science, both of which are fundamental to neutral theory in ecology. Here I give a brief over-view of the current status of neural theory in ecology and phylogeny and, where relevant, connectthese newer ideas to Goulds work. In particular, I focus on modes of speciation under neutrality,particularly peripheral isolate speciation, and their implications for relative species abundance andspecies life spans. Gould was one of the pioneers in the study of neutral models of phylogeny, butthe modern theory suggests that at least some of the conclusions from these early neutral modelswere premature. Modern neutral theory is a remarkably rich source of new ideas to test in ecologyand paleobiology, the potential of which has only begun to be realized.

Stephen P. Hubbell. Department of Plant Biology, University of Georgia, Athens, Georgia 30602, andSmithsonian Tropical Research Institute, Unit 0948, APO AA 34002-0948. E-mail:[email protected]

Accepted: 12 September 2004

Introduction

Many of Goulds ideas generated controver-sy, but one for which he was never criticizedwas being a neutralist, which he most defi-nitely was not. On the contrary, Gould arguedthat patterns of punctuated equilibria in phy-logeny can be explained only if natural selec-tion operates not just among individuals with-in populations, but also among species andhigher taxon levels (Gould 2002). Selection op-erating at levels above the individual would ofcourse imply that species and higher taxa dif-fer in fundamental ways that affect their rel-ative fitnesses on geological timescales, whichin turn affect their relative life spans in the fos-sil record.

Although Gould was not a neutralist, thereare at least two deep philosophical connec-tions between Gould and current neutral the-ory. The first is his recognition of the impor-tance of null models in science, and more spe-cifically Goulds pioneering work using neu-tral models to study phylogeny. The unifiedneutral theory of biodiversity and biogeogra-phy is a recent example of such models, and it

generates a set of formal null hypotheses forthe origin, maintenance, and loss of species inecological communities or in phylogenies(Hubbell 2001a). Gould understood the criti-cal importance of null models in his own sci-ence (Gould et al. 1977), and in science in gen-eral. He also understood their importance asa control on ones own preconceptions and bi-ases, and what can happen when such con-trols are absent or abused, as in the racist the-ories of human evolution, which Gould vig-orously refuted (Gould 1981). In the 1970s,Gould and his collaborators used null modelsof phylogeny as a means to evaluate whetherthe patterns generated solely by random birth-death processes were consistent with thepunctuated equilibrium hypothesis of evolu-tion, with busts of speciation interspersedwith long periods of relative quietude (Raupet al. 1973; Gould et al. 1977). They found thatrandomly generated patterns were not consis-tent with observed patterns, and so Gould andcompany concluded that non-neutral selectionprocesses must be at work in the phylogenieshe studied. As it turns out, however, theseconclusions were somewhat premature, be-

123GOULD AND NEUTRAL THEORY

cause there were several problems with theformulations of the models that were not im-mediately apparent at the time.

The other philosophical connection of neu-tral theory to Gould is through the concept ofsymmetry and symmetry breaking. In theneutral theory of biodiversity, all species aretreated as symmetric, which means that, to afirst approximation, all species are assumed tobe demographically identical on a per capitabasis. The principal use of the neutral theoryis to evaluate when, and to what degree, asym-metries among species are required to explainthe assembly of observed ecological commu-nities. Although Gould did not use this ter-minology, nevertheless the concepts he wroteabout were the same. Paleontology could bedescribed as the study of how morphologicalsymmetries are transmitted, broken, and re-established over evolutionary time. In phylog-enies, more closely related species are moresimilar (symmetric) than less related species(Harvey and Pagel 1991). At least for the livingspecies, the new tools of genomics and evo-lutionary developmental biology promise toanswer many if not all of the recalcitrant clas-sic questions in ontogeny and phylogeny(Gould 1977). These tools are revealing thatthe symmetries of life run far deeper than any-one ever supposed, as illustrated, for example,by the discovery of ancient and phylogeneti-cally pervasive homeobox master regulatorygenes (Carroll et al. 2001; Davidson 2001).

In this paper, I first present a brief synopsisof the neutral theory (Hubbell 2001a; Volkovet al. 2003). The current theory is best devel-oped for ecological scales of time and space.However, the unified neutral theory embodiesmore of a macroecological and deep-time per-spective than do most contemporary theoriesin ecology. This is because it is one of very fewtheories in ecology to incorporate a process ofspeciation explicitly. Here I focus mainly onthe results for speciation, particularly periph-eral isolate speciation, and its implications forbiodiversity, speciation rates, and species lifespans. I conclude with a brief prospect for thefuture of symmetric neutral theory in ecologyand paleobiology, and how new models withsymmetry broken in various ways promise tomove us forward.

The Neural Theory and RelativeSpecies Abundance

The origins of modern neutral theory inecology can be traced back to the theory of is-land biogeography (MacArthur and Wilson1963, 1967). The theory of island biogeogra-phy hypothesizes that ecological communitiesare assembled purely by dispersal. This andother dispersal assembly theories assert thatthe species richness on islands or in local com-munities represents a dynamic equilibriumbetween the rates of immigration of speciesinto the community and the rate of their sub-sequent local extinction. Thus, such theoriesassert that communities are in taxonomic non-equilibrium with continual species turnover.The theory of island biogeography is neutralbecause it assumes that species are identical(symmetric) in their probabilities of arrivaland survival. This theory was, and remains, aradical departure from most contemporarytheory in ecology, which says that ecologicalnature is fundamentally asymmetric, thatcommunities are equilibrium or near-equilib-rium assemblages of niche-differentiated spe-cies, each of which is the best competitor in itsown ecological niche (Chase and Leibold2003). There has been a persistent theoreticaltension in ecology between these two conflict-ing worldviews. Both perspectives havestrong elements of truth, although typically onvery different spatial and temporal scales(Hubbell 2001a). The theoretical quest hasbeen the search for ways to reconcile and com-bine these divergent perspectives into a singleseamless theory for ecology.

The unified neutral theory of biodiversitybegins to build a theoretical bridge betweenthese two perspectives by incorporating a dy-namic theory of relative species abundanceinto the theory of island biogeography (Hub-bell 2001a; Bell 2000, 2001). As in the originaltheory, the unified neutral theory treats spe-cies as identical (symmetric) in their per capitavital rates of birth, death, and migration. Un-like the theory of island biogeography, how-ever, the unified neutral theory makes theneutrality assumption at the individual level,not the species level, a change that allows spe-cies to differentiate in relative abundance

124 STEPHEN P. HUBBELL

FIGURE 1. The fit of the unified neutral theory to thedominance-diversity curve for tropical tree species in a50-ha permanent plot of rainforest in Lambir Hills Na-tional Park, Sarawak, Borneo. The dotted line extendingdiagonally down to the right is the best-fit metacom-munity curve for u 5 310, assuming no dispersal limi-tation (m 5 1). The relative abundance for the 50-ha plotwas best fit with u 5 310 and m 5 0.18. The error barsare 6 one standard deviation. The heavier solid line isthe observed dominance-diversity curve. Note the ex-cellent fit even for very rare species. This fit to 1197 spe-cies is achieved with just three parameters, u, m, and lo-cal community size J, the latter of which is known fromthe plot census data (J 5 324,592).

through ecological drift (demographic sto-chasticity). The persistence times of speciesunder drift are then dictated by their abun-dances, so that the extinction rate is a genuineprediction of the theory, not a free parameteras it was in the original theory of island bio-geography. In the unified neutral theory, themetacommunity replaces the mainlandsource area concept of the theory of island bio-geography. The metacommunity is the phy-logeographic unit within which most memberspecies spend their entire evolutionary life-times. The neutral theory also generates a nat-ural length scalethe biogeographic correla-tion lengththat measures the size of meta-communities. In the theory of island bioge-ography, however, the size of the source areais not defined.

Previous theories of relative species abun-dance have been largely static, phenomeno-logical models (e.g., Preston 1948, 1960) andinvolve fitting generic statistical distributionswhose parameters are not clearly derivablefrom first principles in population biology(Hubbell 2005). Because the previous modelsare not dynamic or mechanistic, they do notgenerate hypotheses about how basic demo-graphic processes affect species richness andthe distribution of relative species abundance.In contrast, the parameters of the neutral the-ory of relative species abundance all havestraightforward biological interpretations,such as per capita birth and death rates, dis-persal rates, and rates of speciation. Incorpo-rating a process of speciation was especiallykey to developing a neutral theory of relativespecies abundance. Lacking a speciationmechanism for generating new diversity, theolder phenomenological models have beengenerally unable to make predictions aboutthe expected patterns of relative species abun-dance on large biogeographic spatial scalesand evolutionary timescales. Fits of the neu-tral theory to relative abundance data are of-ten quite good, especially in species-rich com-munities such as tropical rain forests (Fig. 1).

The importance of studying relative speciesabundance, especially on large landscapescales, cannot be overstated. Apart from spe-cies richness, no other general attribute of eco-logical communities has received more theo-

retical and empirical attention in ecology thanrelative species abundance, attention that isfully justified. One of the most important in-sights gained from the unified neutral theoryis that speciation rates and patterns of relativespecies abundance on large spatio-temporalscales are inextricably and causally linked. Atlarge biogeographic scales and between punc-tuational events, the steady-state diversityand distribution of relative species abundanceare set by the balance between speciation andextinction rates. Relative species abundance isdirectly involved in this steady state becausespecies extinctions are not drawn at randomwith respect to the abundances of species.Both theoretically and empirically, we knowthat rare species are more extinction prone(Richter-Dyn and Goel 1972; Lande et al.1993). Although high global abundance ap-pears to offer little or no protection from theagents of mass extinction (Jablonski 2001,2002), there is evidence that abundant andgeographically widespread taxa are more per-sistent during normal times (Jablonski1995; Jackson 1995).

The correlation between global abundanceand taxon longevity implies that during nor-


mal times, the diversity steady state is main-tained principally by the balance between theorigination of new species and the extinctionof mostly rare species. This conclusion is im-portant in considering tests of the apparentdynamic quiescence of diversity betweenpunctuational events. If rare species are hard-er to find in the fossil record than commonspecies, there will be a built-in sampling biasthat will underestimate taxon turnover ratesduring these periods. As data sets improve forfossil assemblages to include ever rarer taxa, Ipredict that estimated turnover rates for pe-riods between punctuational events willsteadily rise. In studies of paleocommunities,relative species abundance has played a lessprominent role than species richness, but thissituation is changing as improved data setsbecome available (e.g., Kidwell 2001). How-ever, there are already data to support highrates of taxon turnover during periods of di-versity steady states in some taxa, even in theabsence of analyses of relative abundance data(e.g., Patzkowsky and Holland 1997).

Because relative species abundance is fun-damental to any discussion of speciation un-der the neutral theory, it is important to re-view briefly the formal connection betweenthe two subjects. Since publication of my book(Hubbell 2001a), there have been many signif-icant changes and improvements in the math-ematical framework of the theory (Houch-mandzadeh and Vallade 2003; Vallade andHouchmandzadeh 2003; Volkov et al. 2003;Etienne and Olff 2004; Hubbell 2004; McKaneet al. 2004). One of the advantages of the newframework is that several important problemsin the symmetric neutral theory that were ad-dressed only by simulations (numerical ex-periments) in my book are now tractable toanalytical solutions. In particular, we havemade substantial progress in understandingthe relationship of neutral theory to the twomost celebrated statistical distributions usedto describe the distribution of relative speciesabundance: the logseries (Fisher et al. 1943),and the lognormal (Preston 1948). The neutraltheory clarifies the situation and shows thatthe logseries is the fundamental distributionof relative species abundance expected atlarge spatiotemporal scales (the metacom-

munity) under the simplest mode of specia-tion (point mutation speciation; see below).However, this fundamental distribution be-comes modified on local scales under dispers-al limitation and on large spatial scales underdifferent modes of speciation, and these mod-ified distributions are more lognormal-like(Hubbell 2001a; Volkov et al. 2003; Hubbelland Borda-de-Agua 2004).

The formal connection between speciationand relative species abundance in the meta-community can be shown by simultaneouslyderiving the distribution of relative speciesabundance and the speciation rate from thefundamental dynamical equations of popula-tion growth under neutrality (see the Appen-dix for details). Under the metacommunitydistribution of relative species abundance,which is the log-series, the expected meannumber of species with n individuals ^fn& isgiven by

nx^f & 5 a ,n n

where parameter x is a positive number ,1,and a is the diversity parameter, known asFishers a. Fishers a (Fisher et al. 1943) is theoldest, most famous, and most widely usedmeasure of species diversity in ecology (Ma-gurran 1988). One reason it is used so widelyis that it is remarkably stable in the face of in-creasing sample sizes of relative abundancedata from communities. Until the unified neu-tral theory, however, there has been no cleartheoretical explanation for the stability anduniversality of Fishers a nor any biological in-terpretation of parameter x of the logseries.

Neutral theory explains that the diversityparameter, Fishers a, is so stable and univer-sal because it is a linear function of the averagespeciation rate across the entire metacommun-ity as well as of the size of the metacommun-ity, defined as the sum of the population sizesof all species in the metacommunity. Fishersacalled u by Hubbell (2001a)is a dimen-sionless, fundamental biodiversity numberthat crops up over and over again throughoutthe neutral theory. Neutral theory also dem-onstrates that parameter x of the logseries isequal to the ratio of the average per capitabirth rate to the average per capita death rate


of all species in the metacommunity (Volkovet al. 2003) (see Appendix). This ratio is veryslightly less than unity when the distributionof relative species abundance in the metacom-munity is in steady state. This means that atequilibrium diversity, there is a minute excessof deaths over births, and this small deficit inbirths is exactly balanced by the slow rate ofintroduction of new species into the metacom-munity. Thus, under the framework of theunified neutral theory, the fundamental dis-tribution of relative species abundance atlarge landscape scales is directly derivablefrom the speciation rate, the size of the meta-community, and the average rates of birth anddeath in the metacommunity.

The Neutral Theory and Speciation

Coyne and Orr (2004) have recently re-viewed current evidence in favor of variousmodes of speciation. They favor the biologicalspecies concept, which leads them naturally toa focus on the origin and maintenance of re-productive isolation. They conclude that, de-spite modest evidence for the hybrid origin ofsome species or for other mechanisms of sym-patric speciation, the vast majority of speciesarise through allopatric speciation, followingclosely the now classical model of Mayr(1963). The biological species concept is, ofcourse, not very useful in paleontology be-cause tests of reproductive isolation are notpossible. However, from the perspective ofneutral theory, the only question about speci-ation that matters is how the mode of specia-tion affects the mean size of the founding pop-ulation of new species. This is the critical ques-tion because initial population size deter-mines not only the mean life span of a species,but also steady-state species richness and rel-ative species abundance in the metacommun-ity.

In my book, I studied two modes of speci-ation, point mutation speciation and ran-dom fission speciation (Hubbell 2001a). Ichose to study these two modes because theyrepresent the end extremes of a speciationcontinuum in terms of the size of foundingpopulations and the predicted life spans ofnew species. Mean species life spans are veryshort under point mutation speciation, be-

cause under this mode, new species arise aslineages founded by single individuals, andmost of these lineages go extinct quickly.Random-fission speciation creates new spe-cies by the random uniform partition of an an-cestral species into two daughter species. Spe-cies life spans are much longer under ran-dom fission speciation because this modeproduces the largest average population sizeof new species. Large founding populationsizes buffer species from rapid extinction,which, in turn, increases the steady state spe-cies richness in the metacommunity. In mybook I suggested that random fission specia-tion is the analog to Mayrs allopatric specia-tion model (Hubbell 2001a). However, we nowhave a more complete and general formulationof the problem, in a mode of speciation we callperipheral isolate speciation (Hubbell andLake 2003), which is discussed below.

Ricklefs (2003) has recently argued thatthese two modes of speciation are unrealisticbecause point mutation speciation producestoo many short-lived species, whereas ran-dom fission speciation leads to overly long-lived species. In my response, (Hubbell 2003),I argued that the problems with point mu-tation speciation were easily resolved if oneviewed this mode as actually a model of thefate of all lineages, most of which die out rap-idly, and only a very few of which survive andbecome numerous enough to be discoveredand sufficiently reproductively isolated to becalled good species. The point mutationmode is the only known speciation mecha-nism that gives rise to Fishers a and the log-series distribution for the metacommunity.Whenever metacommunity relative speciesabundance distributions are observed to beconsistent with the logseries, such a findingnecessarily implies that the population sizes atorigination must be small to very small. Spe-cies that arise by sudden changes in ploidynumber or by hybridization are good candi-dates for origins by point mutation specia-tion.

Regarding random fission speciation,however, I think Ricklefss point is well taken,and certainly most current data seem to be in-consistent with the random fission mode. Inresponse to Ricklefs, Jeff Lake and I have ex-


FIGURE 2. As the initial size of species populations atorigination increases, more species are present at steadystate in the metacommunity, for a fixed speciation rate.The figure shows an example of the effect of varyingpopulation size at origination on the steady-state me-tacommunity species richness and distribution of rela-tive species abundance (dominance-diversitycurves), for a fixed value of the fundamental biodiver-sity number u (Fishers a) and for a metacommunity av-erage per capita birth/death ratio of x 5 0.9999. Thenumbers beside each dominance-diversity curve are theinitial population sizes at the origination of new species.The steepest dominance-diversity curve for a foundingpopulation size of unity corresponds to the logseriesdistribution for the limiting case of point mutationspeciation.

plored the consequences of a third and inter-mediate mode of speciation, dubbed periph-eral isolate speciation (Hubbell 2003; Hubbelland Lake 2003). Under this mode, foundingpopulations are not as small as singleton-founded lineages, nor as large as those underrandom fission, but nevertheless are fairlymodest in size. Peripheral isolate speciationis probably commonplace. Most species aredistributed as discontinuous metapopula-tions, and it seems likely that new speciesarise from one or more of the local isolateddemes of metapopulations. This mode of spe-ciation does indeed produce species havingintermediate life spans and equilibrium me-tacommunities with intermediate species rich-ness and relative species abundance distribu-tions (Hubbell and Lake 2003). If the incipientspecies originate in small populations, how-ever, empirically they may be difficult to dis-tinguish from point mutation speciationevents.

In my book, only the point mutationmode was solved analytically (Hubbell 2001a).Now, however, all three modes of speciation,including peripheral isolate speciation,have been solved analytically (I. Volkov per-sonal communication 2004). Although the an-alytical results will be reported elsewhere, wecan make three general statements about thefindings here. The first conclusion is that thegeneral case is peripheral isolate speciation;the other two modes are special cases of thisgeneral mode. The second conclusion con-firms the simulation results of Hubbell (2001a)and Hubbell and Lake (2003) that increasingthe size of the founding population greatly in-creases the steady-state species richness in themetacommunity. Figure 2 shows this effect fora value of Fishers a (Hubbells u) of 10, for abirth-death ratio of 0.9999, and for various val-ues of the size of the peripheral isolate at thepoint of speciation.

The third conclusion addresses one of themain concerns of Ricklefs (2003) about speci-ation rates that are too high under point mu-tation speciation. Because of the slower rateof extinction of new species under peripheralisolate speciation, a given level of speciesrichness in the metacommunity can be ex-plained by a much slower rate of speciation.

Thus, one will consistently overestimate thespeciation rate by fitting the point mutationspeciation equations to relative abundancedata. By how much the speciation rate is over-estimated will depend on the mean size of pe-ripheral isolate populations at origination.Figure 3 shows that speciation rates underperipheral isolate speciation are orders ofmagnitude smaller than those expected underpoint mutation speciation. The curves rep-resent the ratio of the speciation rate underperipheral isolate speciation to the specia-tion rate under point mutation speciationthat yields an equivalent metacommunity spe-cies richness, as a function of the populationsize of the isolate at speciation. Thus, the in-tercept for all curves is a ratio of 1.0 for an ini-tial population size of unity, which corre-sponds to the point mutation limiting case.A smaller and smaller speciation rate is re-quired to achieve the same metacommunitydiversity the larger the founding peripheralisolate population becomes, and the closer theaverage metacommunity birth/death rate ra-tio approaches unity.

Testing these predictions about speciationand relative species abundance in metacom-


FIGURE 3. Holding species richness in the metacom-munity constant, we can calculate the speciation rateunder peripheral isolate speciation that is necessaryto produce the same species richness relative to the spe-ciation rate required under point mutation speciation(initial size 5 1). These relative speciation rates are in-dependent of the starting value of the fundamental bio-diversity number u (Fishers a) under point mutationspeciation, but they do depend on the mean per capitabirth rate to death rate ratio, x. For large metacommun-ities, x is expected to be extremely close to unity, so thateven moderate-sized peripheral isolates will result in areduction of the effective speciation rate by several tomany orders of magnitude over than required underpoint mutation speciation to produce the same me-tacommunity diversity.

munities will be a considerable challenge. Thebest tests will involve independent measuresof speciation rates and metacommunity sizes,so that we have independently derived esti-mates of the fundamental biodiversity num-ber u. However, there are genuine empiricaldifficulties. One is that, if peripheral isolatespeciation is the dominant mode but the av-erage size of the founding populations issmall, then ecologists, and especially paleon-tologists, may have considerable difficulty infinding and recognizing these nascent species,leading us to underestimate the true specia-tion rates, potentially seriously. One possibleapproach to testing the theory relies on thefact that the structure of phylogenetic trees isexpected to be fractal with a single scaling do-main under point mutation speciation,whereas it is expected to be compound fractalunder peripheral isolate speciation (Hub-bell 2001b). In the former case, the neutral the-ory says that we should expect a linear rela-tionship between u and the fractal dimensionof the phylogeny (Hubbell 2001b). Because thedeep-time, higher taxonomic divisions of phy-logenetic clades leading to modern species arebetter sampled and known than the most re-

cent species-level taxa, an estimate of u fromthe deep-time structure of the phylogeny maybe more accurate, and this in turn may help usassess how much modern diversity we are stillmissing. Ironically, it may well be that fossilassemblages can be used to test these ideasbetter than living taxa can, providing a muchdeeper time perspective.

Goulds Contribution to Neutral Theoryand a Modern Update

As mentioned, Gould and a number of hiscolleagues made a pioneering contribution toneutral theory in their early studies of neutralphylogenies. After the publication of Eldredgeand Gould (1972) on the theory punctuatedequilibrium, one of the questions that arosewas whether randomly generated phylogenieswould produce patterns similar to those seenin the fossil record, which, depending on thetaxon, often exhibited sudden, episodic in-creases in diversity, separated by longer peri-ods of relatively calm and steady diversitylevels. In part to try to answer this question,Raup et al. (1973) and Gould et al. (1977) tooka demographic approach to phylogeny, inwhich they modeled monophyletic cladesevolving as a stochastic birth-death branchingprocess, picking up from the much earlierwork of Yule (1925). In these models, lineageswere assigned birth and death rates.When the birth rate exceeded the death rate,the general outcome of these models was ex-ponential growth in the number of descendantlineages, and somewhat slower growth if allextinct lineages were pruned out. In no casesdid the models yield the punctuational patternpostulated by Eldredge and Gould. In the lastdecade, in a series of elegant papers, Nee andhis collaborators have provided analytical so-lutions to these models to study the process ofphylogenetic reconstruction (e.g., Nee et al.1994). Nee argued that observed phylogeniesexhibit clades that are too bushy, with somesubclades containing too many species rela-tive to the predictions of the null models, andargued that this was strong evidence for non-random processes in clade evolution.

These models meshed very well withGoulds concepts about species, which he haslong argued can be treated as analogous to in-


dividuals when it comes to species-level selec-tion (Gould 2001). Indeed, in the unified neu-tral theory under point mutation speciation,the hypothesis that new species arise from in-dividually founded lineages blurs the distinc-tion between species and individuals. Thissaid, there is a fundamental difference be-tween species and individuals that led theoriginal neutral models of cladogenesis ofRaup et al. (1973) and Gould et al. (1977)andtheir analytical counterparts (Nee et al.1994)astray. The essential problem lies inthe failure to take the relative abundance oflineages into account: populations have abun-dances, individuals do not. In the models ofRaup, Gould, and Nee the evolutionary unit isthe lineage, and lineages have assigned prob-abilities of speciating or going extinct. How-ever, in the unified neutral theory, the evolu-tionary unit is the individual, and lineages perse have no preassigned speciation and extinc-tion rates. Instead, the probability of speciat-ing or going extinct is determined by lineageabundance, which is dictated in turn by thefundamental biodiversity number u (or Fish-ers a). In the models of Gould and Raup, lin-eage abundances are ignored completely, yetthe abundance of a lineage (i.e., a species) willhave a profound effect on the time to extinc-tion of the lineage. Models that are pure birth-death branding processes trace the fate of lin-eages as if they had equal probabilistic fates,but this is not true because the fate of globallyabundant lineages is very different on averagefrom the fate of rare and local endemics.

Including lineage abundance changes manyof the conclusions of the original neutral the-ory of phylogeny and suggests a series of test-able hypotheses. First, globally abundant spe-cies are expected to be much older on averagethan rare species, a result consistent with thenow classical theory of stochastic extinction(Richter-Dyn and Goel 1972). However, thereis no such expectation under Goulds theorybecause lineage abundance is not considered.Second, these globally abundant and wide-spread metacommunity species are expectedto be the ancestors of many more modern spe-cies than are rare and local species. This is aconsequence not only of their much longer ex-pected life spans, but also of their much high-

er total birth rate per unit time (opportunitiesfor speciation) than in the case of rare species.This effect will make certain subclades muchmore speciose than expected under Gould-type neutral models of phylogeny. Third, theunified neutral theory produces a genuine di-versity steady state at equilibrium betweenspeciation and extinction. As mentioned, thereis increasing evidence that these diversityequilibria between punctuational events (Eld-redge and Gould 1972, 1988) are dynamicsteady states with continual species turnover(Patzkowsky and Holland 1997). In contrast,Goulds neutral theory does not produce a di-versity steady state, but instead produces ex-ponential growth in the number of survivinglineages (Nee et al. 1994). This is because inGoulds theory, lineages have preassignedbirth and death rates that do not change withlineage abundance.

Current evidence gives equivocal supportto these various predictions of the unified neu-tral theory. As mentioned, there is evidencethat globally abundant taxa do indeed havelonger evolutionary life spans, at least duringnormal extinction times (Jablonski 1995;Jackson 1995), but this pattern breaks downduring mass extinctions (Jablonski 2001,2002). In molluscs and foraminifera, there arewell-established relationships between dis-persal ability and global abundance. However,there is also evidence that dispersal abilityand global abundance are negatively correlat-ed with rates of speciation, suggesting thatgene flow is a major cohesive force in main-taining the integrity of species (Jablonski andRoy 2003). It should be noted that increaseddispersal is expected to reduce the slope of thespecies-area relationship (Hubbell 2001a).This occurs for two reasons. One reason issimply more complete mixing. The other rea-son is extinctions of rare species caused by in-creased dispersal of common species and theoverwhelming mass effect of their greater ab-solute birth rates (even when per capita birthrates are the same). Thus, even in a fully neu-tral model at a per capita level, increasing dis-persal can cause a reduction of metacommun-ity diversity through increasing the extinctionrate of rare species (Hubbell 2001a).


Conclusions

Although the neutral theory is simple, itnevertheless fits many macroecological pat-terns as well as or better than current nichetheory in ecology. Perhaps the deepest ques-tion raised by neutral theory is why it per-forms so well despite its symmetry assump-tions. I expect that some of the best and mostrigorous tests will come from paleobiology.One of the most important conclusions fromneutral theory is that processes of speciationand macroecological patterns of species rich-ness and relative species abundance are inex-tricably and causally linked. This finding sug-gests that understanding relative speciesabundance in fossil communities better willprovide further insights into both speciationand extinction processes. There are encour-aging signs that major improvements in dataon patterns of relative species abundance infossil assemblages are possible (Kidwell2001), and this would be a major boon in test-ing the predictions of the unified neutral the-ory with fossil data. It is also extremely im-portant to obtain improved spatial data on thegeographic range of fossil communities.

Symmetric neutral theory will be a richsource of hypotheses and tests about com-munity assembly rules. I predict that one ofthe most productive uses of the unified neu-tral theory will be in testing when, how, andto what extent symmetry is broken in actualecological communities. The theory is still inits infancy; and there are many exciting, un-resolved theoretical challenges in and beyondthe unified neutral theory to tackle for yearsto come (Chave 2004). I also anticipate that thelegacy of the exciting, challenging, and stillunanswered questions left by Steve Gould inpaleobiology will continue to inspire majornew contributions to our understanding of theassembly of ecological communities, past andpresent.

Acknowledgments

I thank the National Science Foundation, theJohn D. and Catherine T. MacArthur Founda-tion, the Pew Charitable Trusts, the John Si-mon Guggenheim Foundation, and many oth-er donorsindividuals and private organiza-

tionswho have supported my ecological re-search over the past 25 years, and thedevelopment of the neutral theory over thepast ten years. I thank the Center for TropicalForest Science of the Smithsonian Tropical Re-search Institute for permission to analyze therelative species abundance data for tree spe-cies in the 52-hectare plot in Lambir Hills Na-tional Park, Sarawak (Fig. 1).

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Appendix

A full ecological explanation of Fishers logseries in terms ofpopulation dynamics is now available from new theoretical re-sults on the neutral theory of relative species abundance. Thisexplanation emerges from a more general theoretical formula-tion of the equations of demographic stochasticity that underpin

population dynamics under the unified neutral theory (Volkovet al. 2003). This new formulation incorporates birth and deathrates explicitly. Let bn,k and dn,k be the probabilities of birth anddeath of an arbitrary species k at abundance n. Let Pn,k(t) be theprobability that species k is at abundance n at time t. Then therate of change of this probability is given by

dp (t)n,k5 p (t)d 1 p (t)b 2 p (t)(b 1 d ). (A1)n11,k n11,k n21,k n21,k n,k n,k n,kdt

This equation is straightforward and easy to understand. Thefirst term on the right represents the transition from abundancen 1 1 to n, due to a death. The second term is the transition fromabundance n 2 1 to n due to a birth. The last two terms are lossesto Pn,k(t) because they are transitions away from abundance n toeither n 1 1 or n 2 1 through a birth or death, respectively. Onfirst consideration, equation (1) appears to be little more than abookkeeping exercise, but it is actually much more. Because it iswritten as a recursive function on abundance, it allows an equi-librium solution to be found for species of arbitrary abundancen. When all derivatives at all abundances are set equal to zero,then the solution is said to satisfy detailed balance, whichmeans that each abundance transition is in equilibrium. Now letPn,k denote this equilibrium. Then Pn,k 5 Pn21,k:(bn21,k/dn,k), andmore generally, this corresponds to a global equilibrium solu-tion for the metacommunity:

n21 bi,kP 5 P . (A2)Pn,k 0,k di50 i11,kNote that the probability of being at abundance n is a functionof the product of the ratios of birth rate to death rate over allabundances below n. Because the Pn,ks must sum to unity, wecan find the value of P0,k from this sum, and therefore all otherterms as well.

Now consider a symmetric neutral community of S speciesthat are all alike on a demographic basis, such that they all havethe same birth rates and death rates; that is, bn,k [ bn and dn,k [dn (i.e., the species identifier k doesnt matter, and we denote theprobabilities by Pn). We can introduce speciation by recognizinga special birth rate in this general metacommunity solution;i.e., b0 5 n, the speciation rate. The mean number of species withn individuals, ^fn&, in a community of S identical species is sim-ply proportional to Pn:

n21 bi^f & 5 SP . (A3)Pn 0 di50 i11

From equation (3) we are now in a position to derive Fisherslogseries under density independence. Density independencemeans that the birth rate of a species of current abundance n issimply n times the birth rate of a species with abundance 1; i.e.,bn 5 nb1, or density independence. Similarly, suppose that thedeath rates are density independent, dn 5 nd1. Substituting theseexpressions into equation (3), we immediately obtain Fisherslogseries:

nb b b x0 1 n21^f & 5 S P 5 u , (A4)n M M 0 d d d n1 2 n

where the subscript M refers to the metacommunity, x 5 bn/dn5 b1/d1 5 b/d, b0 5 n, and u 5 a 5 SmP0n/b of Fishers logseries.The derivation of equation (4) reveals that the mysterious pa-rameter x of the logseries is now biologically interpretable: x isthe ratio of the density-independent, per capita birth rate to percapita death rate. Note that when one introduces speciation, pa-rameter x must be slightly less than 1 to maintain a finite me-tacommunity size. At very large spatial scales, the total birthand death rates must be nearly in material balance, resulting ina metacommunity b/d ratio only infinitesimally less than unity.The very slight deficit in birth rates versus death rates at the


metacommunity biodiversity equilibrium is made up by thevery slow input of new species.

Thus, we now have a complete derivation of the logseries andits parameters u and x, from the neutral theory. It is interestingthat Hubbell (2001a) derived u following a completely differentroute from the one taken by Volkov et al. (2003), so we now havefurther insights into parametric relationships under the unifiedneutral theory. The greatest significance of this result, however,is demonstrating that the logseries relative species abundancedistribution arises at the metacommunity speciation-extinctionequilibrium when the birth and death rates are density inde-pendent and the metacommunity is symmetric (all species ex-hibit the same mean per capita rates).

The expected relative species abundance distribution on is-lands under dispersal limitation (the classical problem in thetheory of island biogeography) is not the logseries, however, butis a distribution that resembles a skewed lognormal (Hubbell2001a). The second advance in the unified neutral theory is thediscovery of an analytical solution for the relative species abun-dance distribution in a local community under immigrationfrom the metacommunity (Volkov et al. 2003), previously avail-able only by simulation (Hubbell 2001a). Once again, let ^fn& bethe mean number of species with n individuals. Then

J! G(g)^f & 5 un n!( J 2 n)! G( J 1 g)

g G(n 1 y) G( J 2 n 1 g 2 y) 2yu3 exp dy (A5)E 1 2G(1 1 y) G(g 2 y) g0

where G(z) 5 #`0 tz21e2t dt which is equal to z 2 1)! for integer z,and g 5 [m(J 2 1)]/(1 2 m). As in Hubbell 2001a, parameter mis the immigration rate. Equation (5) was derived by making thefollowing functional substitutions for the per capita birth anddeath rates in equation (2):

n J 2 n m nkb 5 (1 2 m) 1 m 1 2 andn,k 1 21 2 1 21 2J J 2 1 J JMn J 2 n m nkd 5 (1 2 m) 1 m 1 2 (A6)n,k 1 21 2 1 21 2J J 2 1 J JM

where mk is the abundance of the kth species in the metacom-munity under the logseries, and JM is the size of the metacom-munity. The first (second) term of bn,k and dn,k is the probabilityof an increase or decrease by one individual, the kth species inthe local community, as a function of whether an immigrationevent occurred (did not occur), respectively.

The expression in equation (5) can be solved numericallyquite accurately. Programs in C are attached electronically tothe paper by Hubbell and Borda-de-Agua (2004). As the im-migration rate m decreases, the relative species abundance dis-tribution in the local community given by equation (5) becomesprogressively more skewed. Thus, as islands or local commu-nities become more isolated, rare species become rarer and com-mon species become commoner. The degree of skewness of therelative species abundance distribution is also a function of lo-cal community size (Hubbell and Borda-de-Agua 2004).

Documents

Hubbell, S. P. 2005 (Neutral Theory of Biodiversity and Biogeography)