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Phil. Trans. R. Soc. B
doi:10.1098/rstb.2009.0004
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Rapid contemporary evolution and clonalfood web dynamics
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Laura E. Jones1, Lutz Becks1,†, Stephen P. Ellner1, Nelson G. Hairston Jr1,
Takehito Yoshida2 and Gregor F. Fussmann3,*
One con
*Autho† Presen25 Willc
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1Department of Ecology and Evolutionary Biology, Cornell University,Corson Hall, Ithaca, NY 14853-2701, USA
2Department of General Systems Studies, University of Tokyo, 3-8-1 Komaba, Meguro,Tokyo 153-8902, Japan
3Department of Biology, McGill University, 1205 Avenue Docteur-Penfield, Montreal,Quebec H3A 1B1, Canada
Character evolution that affects ecological community interactions often occurs contemporaneouslywith temporal changes in population size, potentially altering the very nature of those dynamics. Sucheco-evolutionary processes may be most readily explored in systems with short generations andsimple genetics. Asexual and cyclically parthenogenetic organisms such as microalgae, cladoceransand rotifers, which frequently dominate freshwater plankton communities, meet these requirements.Multiple clonal lines can coexist within each species over extended periods, until either fixationoccurs or a sexual phase reshuffles the genetic material. When clones differ in traits affectinginterspecific interactions, within-species clonal dynamics can have major effects on the populationdynamics. We first consider a simple predator–prey system with two prey genotypes, parametrizedwith data on a well-studied experimental system, and explore how the extent of differences in defenceagainst predation within the prey population determine dynamic stability versus instability of thesystem. We then explore how increased potential for evolution affects the community dynamics in amore general community model with multiple predator and multiple prey genotypes. These examplesillustrate how microevolutionary ‘details’ that enhance or limit the potential for heritable phenotypicchange can have significant effects on contemporaneous community-level dynamics and thepersistence and coexistence of species.
Keywords: predator–prey; eco-evolutionary; genetic diversity; rotifers; alga
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1. INTRODUCTIONThe last three decades have seen an accumulation ofstudies demonstrating that evolutionary change inecologically important organismal traits often takesplace at the same time and pace as ecological dynamics(‘eco-evolutionary dynamics’; Fussmann et al. 2007;Kinnison & Hairston 2007). Species as diverse assingle-celled algae, annual plants, birds, fishes, crus-taceans, insects and sheep are found to undergo rapidcontemporary evolutionary changes in traits that adaptthem within a few generations to changing or newenvironments (Reznick et al. 1997; Thompson 1998;Hairston et al. 1999; Sinervo et al. 2000; Cousyn et al.2001; Reznick & Ghalambor 2001; Grant & Grant2002; Heath et al. 2003; Yoshida et al. 2003; Olsenet al. 2004; Pelletier et al. 2007; Swain et al. 2007).Thus, the old assumption that evolutionary change isnegligible on the time scale of ecological interactionsis now demonstrably incorrect.
Ultimately, evolution has the potential to transformhow we think about and manage ecological systems,
tribution of 14 to a Theme Issue ‘Eco-evolutionary dynamics’.
r for correspondence ([email protected]).t address: Department of Ecology and Evolutionary Biology,ocks Street, Toronto, Ontario M5S 3B2, Canada.
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with implications for resource management (Heathet al. 2003; Swain et al. 2007; Strauss et al. 2008),
conservation of biodiversity (Ferriere & Couvert 2004;
Kinnison & Hairston 2007), invasive species manage-
ment (Lavergne & Molofsky 2007) and ecosystem
responses to environmental change (Hairston et al.2005; Strauss et al. 2008). However, virtually all of theecological theories developed to address these practical
issues invoke, tacitly or explicitly, a separation of time
scales between ecological and evolutionary dynamics
(see Ferriere & Couvert 2004). Frequently, that is
valid, of course, but the accumulating evidence
suggests that important questions may be answeredincorrectly if we fail to account for the fact that we are
studying and managing a ‘moving target’.
Here, we use the compound term ‘rapid contem-
porary evolution’ to refer to heritable changes within a
population which occur at a rate fast enough to affect
interspecific interactions while they are taking place.The descriptor ‘rapid’, by itself, leaves ambiguous the
frame over which evolutionary rates are compared
(rapid species diversification on a geological time scale
can be quite slow compared with the rate of heritable
changes within a population). The adjective ‘con-
temporary’ (Hendry & Kinnison 1999) identifies thetime scale that interests us, but permits the degree of
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This journal is q 2009 The Royal Society
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2 L. E. Jones et al. Rapid evolution in food webs
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change to be either negligible or dramatic. Our intent isto explore the effect of evolution that both occurswithin a few generations (the time scale of ecologicaldynamics) and is substantial (ecological interactionstrength is importantly altered), i.e. evolution that isboth contemporary and rapid.
Post & Palkovacs (in press) note that a system of eco-evolutionary feedbacks requires both that the pheno-types must affect the environment in which they liveand the environment must select on the distribution ofgenetically based phenotypes. A major component ofecological research has been the identification andmeasurement of interaction strengths among species,and between species and their chemical and physicalenvironments (e.g. Cain et al. 2008; Molles 2008), andPost & Palkovacs (in press) provide a table of fineexamples. At the same time, there is a growingliterature showing that heritable phenotypic differencesamong individuals have substantial importance for howcommunities and ecosystems function (e.g. Johnsonet al. 2006; Whitham et al. 2006; Urban et al. 2008;Palkovacs et al. in press). Finally, extensive reviews ofthe literature (Hendry & Kinnison 1999; Kinnison &Hendry 2001; Palumbi 2001) leave no doubt thatselection driven by strong ecological interactionsresults in marked adaptive evolutionary change thatfrequently takes place within a few generations.
A challenge, then, is to draw together each of thesecomponents within a single system to determine theimportance of rapid contemporary evolution to eco-logical dynamics. Hairston et al. (2005) proposed anapproach, first conceived by Monica Geber, in whichthe relative importance of temporal changes in a featureof the environment and heritable changes within apopulation are assessed in terms of the magnitudes andtheir contributions to ecological dynamics. Theyapplied it to data on Galapagos finches (Grant &Grant 2002), freshwater copepods (Ellner et al. 1999)and laboratory microcosms (Yoshida et al. 2003).Pelletier et al. (2007) applied a similar method toSoay sheep, and Ezard et al. (in press) have used thisapproach on five populations of ungulates. In eachcase, evolutionary contributions to ecological dynamicswere found to be substantial.
Some of the most striking examples of temporalecological dynamics in nature are found in consumer–resource interactions. Theory indicates and empiricaldata confirm that population abundances frequentlyoscillate substantially as interactions vary in strength,and in some cases sign, over time. Many of the clearestexamples of rapid contemporary evolution have beendocumented in these systems including predatory fishand their prey (Hairston & Walton 1986; Reznick et al.1997; Ellner et al. 1999; Hairston & De Meester2008), herbivorous insects and the plants theyconsume (Johnson et al. 2006, in press) and parasitesand pathogens and their hosts (Dube et al. 2002;Decaestecker et al. 2007; Duffy et al. 2007; Eldredet al. 2008). Owing to the propensity to oscillate,consumer–resource interactions are particularly goodmodel systems for detailed laboratory study of eco-evolutionary dynamics over both long (Lenski &Travisano 1994; Boraas et al. 1998) and short term(Meyer & Kassen 2007). Investigations using simple
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laboratory microcosms of real consumer and resourcespecies combined with mathematical models thatincorporate observed interactions and predict result-ing dynamics have proven to be particularly fruitful foruncovering some of the potential and diversity of eco-evolutionary dynamics (e.g. Yoshida et al. 2003, 2007;Meyer et al. 2006; Jones & Ellner 2007).
In this paper, we explore how evolutionary dynamicsin traits that influence the strength and nature ofinterspecific interactions affect the temporal dynamicsof species, and the reciprocal effects of populationdynamics on maintenance of the heritable variationthat allows evolution to continue. We begin byreviewing some of our relevant prior experimentaland theoretical work on rapid contemporary evolutionin predator–prey systems, and then use extensionsof our previous models to address the followinggeneral questions:
(i) How does evolution affect the dynamics ofecological communities, and their persistence,robustness and stability?
(ii) What are the dynamic possibilities when a widerange of heritable trait variation is present in asystem, and what are the consequences ofdiminished genetic diversity and the correspond-ingly reduced potential for evolutionary change?
Theory linking evolution and ecology has beenpublished for decades, but theory unfettered by datacan predict (and has predicted) any conceivableecological dynamics, including stability, instability,chaos and criticality (the boundary between twodifferent types of dynamics, e.g. stability versus cycles).To make specific predictions possible, our theory isclosely tied to our experimental work on predator–preychemostats that are laboratory analogues of freshwaterplanktonic food webs.
Natural freshwater plankton systems are oftendominated by obligately asexual or facultatively sexualspecies, so our models assume that trait evolutionoccurs through changes in the frequency of differentclonal lineages. However, models for quantitative traitdynamics in sexual species can be very similar to ourmodels for clone-frequency dynamics, and can even bemathematically identical (depending on assumptionsabout the genetic variance for the quantitative trait; seeAbrams & Matsuda 1997; Abrams 2005). As a result,our conclusions might also be relevant to sexuallyreproducing species. Models for clone-frequencychange are also mathematically equivalent to modelsfor multispecies interactions, but some predictionsabout clonal evolution result from constraints on thedifferences among clones within a species, whichtypically would not be realistic if we were modellingcompletely different species (Jones & Ellner 2007).
2. BACKGROUND: PREDATOR AND PREYIN THE CHEMOSTATIn laboratory microcosmscontaininga rotifer,Brachionuscalyciflorus, consuming an alga, Chlorella vulgaris, weobserved predator–prey cycles with the classic quarter-period phase lag between the peaks in prey and predator
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Figure 1. Comparison of theoretical and experimental results for rotifer–algal chemostats with the rotifer B. calyciflorus as thepredator (red circles) and the asexual green alga C. vulgaris as the prey (green circles). (a,b) Classical predator–prey cycles when algaeare monoclonal (one genotype) and so cannot evolve (red solid curve, predator, green dashed curve, prey and purple dotted curve,average prey vulnerability to predation with 1Zno defence and 0Zcomplete invulnerability to attack). Data from Yoshida et al.(2003). (c,d ) Evolutionary cycles when prey are genetically variable. Data from Fussmann et al. (2000). (e, f ) Cryptic cycles whenprey are genetically variable with low cost of defence. Data from Yoshida et al. (2007); spectral analysis confirms the presence ofperiodicity in the predator dynamics (P!0.01). Units: 106 cells mlK1 (algae), females mlK1 (rotifers) and mean palatability (preytrait). Additional experimental replicates for (b,d, f ) can be found in the publications cited as the source for the data.
Rapid evolution in food webs L. E. Jones et al. 3
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densities when the algal prey were genetically homo-
geneous. By contrast, with a genetically variable prey
population, cycle period increased three- to sixfold, and
predator and prey cycles were exactly out of phase
(Shertzer et al. 2002; Yoshida et al. 2003; figure 1), a
phenomenon that cannot be explained by conventional
predator–prey models. The algae in our microcosms
vary genetically along a trade-off curve between defence
against rotifer predation and ability to compete for
limiting nutrients (Yoshida et al. 2004). As a result, they
have an evolutionary response to fluctuations in rotifer
density and nutrient availability that qualitatively
changes the predator–prey dynamics.
To understand our experimental results, we for-
mulated and analysed a general model for a predator–
prey system with genetic variability in an asexually
reproducing prey species ( Yoshida et al. 2003, 2007;
Jones & Ellner 2004, 2007). Our results show that the
qualitative properties of evolution-driven cycles in our
experimental system are a general consequence of rapid
prey evolution in a predator–prey food chain, occurring
in a specific but biologically relevant region of
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parameter space. Specifically, genotypes with betterdefence against predation become more common whenpredators are abundant, and less common (due topoorer competitive ability) when predators are rare. Wethen confirmed this theoretical prediction experimen-tally, with close qualitative and quantitative agreementbetween experimental results and a refined versionof our evolutionary model (Yoshida et al. 2003;figure 1a–d ). Finally, we verified the postulated trade-off between defence against predation and ability tocompete for scarce nutrients (Yoshida et al. 2004).
A basic model for our experimental system is givenby equation (2.1) below; this model will be the startingpoint for the new theoretical results that we present inthis paper:
dS
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Figure 2. Bifurcation diagrams for a model with two preyclones having palatabilities p1 and p2Z1, with a linear trade-off between p and competitive ability. (a) The minimum andmaximum of prey (green circles) and predator (red circles)populations, once the populations have settled onto theirattractor (an equilibrium or limit cycle). EC, evolutionarycycles; SS, steady state; CRC, classical consumer–resourcecycles. (b) The minimum and maximum of the fraction of thedefended clone, p1, in the prey population.
4 L. E. Jones et al. Rapid evolution in food webs
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where x1, x2, y are the abundances of the two preyclones and the predator; S is the amount of a limitingsubstrate required for algal growth; and QZp1x1Cp2x2
is total prey ‘quality’ as perceived by the predator. Timehas been rescaled so that the dilution rate (the fractionof medium replaced each day) is 1, and state variableshave been rescaled so that the rate of substrate supply is1 and a unit of prey consumption yields one netpredator birth.
The prey types are assumed to be two genotypeswithin a single species, differing in two ways which wehave documented in our experimental systems: their‘palatability’ pi which determines their relative risk ofbeing attacked and consumed by the predator, and theirability to compete for scarce resources, representedby ki. There is a trade-off between defence againstpredation and the ability to compete for nutrients whennutrient concentration is low (Yoshida et al. 2004), sothe genotype with the lower value of p has the highervalue of k. The models fitted to our experimental dataalso include predator age structure (Fussmann et al.2000; Yoshida et al. 2003), mortality within thechemostat and a predator functional response thatbecomes linear (type-I) at low food density, but thesefeatures have no qualitative effect apart from stabilizingthe system at very low dilution rates (Jones & Ellner2007). The model’s main qualitative predictions aboutpotential effects of rapid contemporary prey evolutionon predator–prey cycles are also robust to changes in thefunctional forms of the prey and predator functionalresponses ( Jones & Ellner 2007). However, it isimportant for our results that the model does not allowthe predator to preferentially attack and consume theless defended prey type. Prey genotypes are attacked inproportion to their abundance, and better defencemeans a higher chance of surviving an attack. Theseassumptions have been verified experimentally for ourchemostat system (Meyer et al. 2006).
By mathematical and computational analysis of ageneral version of model (2.1), we have shown (Jones &Ellner 2007) that evolution-driven cycles occur whendefence against predation is effective but cheap: p1 ismuch smaller than p2, but k1 is not much larger thank2. When the cost of defence is extremely low, asurprising phenomenon occurs, which we have called‘cryptic dynamics’: the predator cycles in abundance,but the total prey population remains effectivelyconstant through time (figure 1e). We know that thecost of defence is quite low for some genotypes in ouralgal study species (Meyer et al. 2006), and the crypticdynamics predicted by the model have been observedin our experimental system (Yoshida et al. 2007;figure 1 f ). The constancy of total prey abundanceoccurs in the model due to near exact compensationbetween the defended and undefended genotypes.Each genotype is undergoing large changes in abun-dance, but as the cost of defence is made very low, theoscillations of the two genotypes become almost exactlyout of phase with each other, leading to near constancyof their sum (Jones & Ellner 2007). In addition, thecoefficient of variation in the trait becomes smaller andsmaller relative to the coefficient of variation in thepredators (compare the dotted curves in figure 1eversus figure 1c): only the predator continues to have
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cycles whose peaks are much higher than the troughs.Since defence is demonstrated to be cheap, or evenfree, in a number of natural and laboratory systems,especially those involving organisms with short gener-ation times (Andersson & Levin 1999; Yoshida et al.2004; Gagneux et al. 2006), cryptic dynamics may bemore common than hitherto anticipated.
3. RESULTS I: DYNAMIC EFFECTS OF PREYGENETIC VARIABILITYThe phenomenon of cryptic dynamics shows that thedynamics of a predator–prey interaction are not justdetermined by the presence or absence of contempor-ary evolution. The details matter, and the nature andextent of genetic variability for traits affecting theinteraction are important details.
Our goal in this paper is to explore theoretically howchanges in the suite of genotypes that are present in theprey and predator populations can affect dynamics atthe population and community levels. We begin, in thissection, by considering genetic variation in prey alone,with prey clones arrayed along a trade-off curvebetween competitive ability and defence againstpredation. Given a trade-off curve, how is thequalitative nature of the population-level dynamicsaffected by the presence or absence of specificgenotypes along the curve, such as the presence orabsence of well-defended types, or the number ofalternative clones filling in the range of variation fromlow to high levels of defence? And how does the shapeof the trade-off curve affect these predictions?
(a) Systems with two extreme prey types
A frequent outcome of competition between twoprey clones in our model is selection for two extremetypes: either the very least and most defended among
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Figure 3. Chemostat experiments (L. Becks, unpublisheddata) with the rotifer B. calyciflorus as the predator (red solidcurve and filled circles) and the asexual green algaChlamydomonas reinhardii as the prey (green dashed curveand open circles) ((a) weaker defence: SS and (b) strongerdefence: cycles). The circles and triangles are experimentalmeasurements, and the curves are a smooth of the data bylocal polynomial regression. The purple curve (dotted curveand triangles) shows the mean clump size of the algalpopulation. See the text for discussion of clumping as ananti-predator defence trait. Units are individuals mlK1 forpredator population density, 104 cells mlK1 for prey popu-lation density and mean number of cells per clump.
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the clones present in the population, or clones verynear to those extremes. In such cases, the range ofvariation present (the values of p1 and p2) determinesthe outcome, and the shape of the trade-off curveis irrelevant.
Figure 2 summarizes how the population dynamicsare affected by varying the range of palatability whenonly two extreme clones are present. When the better-defended clone has very effective defence ( p1%0.1),theory predicts the type of evolutionary cycles (EC,figure 2) observed by Yoshida et al. (2003), or possiblycryptic cycles (Yoshida et al. 2007), depending on thecost of defence. When defence is less effective, thesystem goes to a steady state (SS, figure 2). For anarrow range of p1-values (e.g. p1z0.14 in figure 2),both prey types coexist at SS: the fraction of thedefended prey clone is high but less than 100 per cent.This is followed by a substantial range of defence levelswhere the SS involves only the defended clone and thepredator. Eventually, for moderate to low levels ofdefence (0.3Rp1!p2 in figure 2), there are classicalconsumer–resource cycles (figure 2) with the predatorand only the defended clone. What happens whendefence is nearly ineffective ( p1zp2) is very sensitive tothe specifics of the trade-off curve. However, thequalitative pattern shown in figure 2 for high tomoderately effective defence is robust to changes inparameter values, and also to some qualitative changesin the model (i.e. the form of the predator functionalresponse, inclusion versus omission of predator agestructure ( Jones & Ellner 2004, 2007)).
The pattern predicted in figure 2 is somewhatcounter-intuitive, because it says that improveddefence by a defended clone is beneficial to theundefended clone. Specifically, an undefended clonecan persist in the system only when the defended cloneis nearly invulnerable to predation. What causes thispattern is indirect facilitation, a reversal of the familiar‘apparent competition’ scenario. Increased defence bythe defended prey (on its own) is bad for the predator,so it is good for undefended prey. As a prey lineageevolves better and better defence, eventually driving thepredator population to low numbers, it opens the wayfor a superior competitor that is not paying a cost(however, small) for anti-predator defence.
Some preliminary results (L. Becks, unpublisheddata; figure 3) from chemostat experiments withChlamydomonas reinhardii as the algal prey exhibit thepattern predicted by figure 2 with regard to EC versussteady-state coexistence. The Chlamydomonas systemhas the advantage that one prey defence trait, namelythe formation of clumps that are less easily consumedby the predator, is visible and easily quantified, so wecan track the dynamics of this trait along with thepopulation dynamics. We have shown that preyclumping reduces the ability of predators to consumethem, and that the tendency to clump is heritable(L. Becks, unpublished data). However, clumpingmay not be the only defence trait that these preycan evolve, so the degree of clumping may not bea complete indication of the level of prey defence.A direct indicator of the effectiveness of prey defence isthe relationship between prey abundance and predatorpopulation growth. The better defended the prey are,
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the lower the predator per capita rate of increase at anygiven prey abundance, and the higher the preyabundance required for the predator population toincrease rather than decrease.
In the experiment shown in figure 3a, the systemsettled to a SS with defended prey (as indicated by theoccurrence of clumping). The level of prey defence inthis experiment was such that the predator populationhad per capita rate of increase rz0 at algal density ofapproximately 105 mlK1 (days 45–58). The experimentshown in figure 3b was run under the same conditions,but was initialized with prey drawn from a populationthat had been exposed to predation for several months.The prey in this latter experiment developed far moreeffective defence than in the former experiment, as seenby the fact that (for example) at days 25 and 60 thepredator population was decreasing even though thealgal density was approximately 2!105 mlK1. Aspredicted in figure 2, stronger prey defence wasaccompanied by a shift from SS to EC. A completeanalysis of these experiments and additional replicateswill be presented elsewhere (Becks et al. in preparation).
(b) Systems with more than two prey types
The details of the trade-off between defence andcompetitive ability become important when morethan two prey types are initially present. Dependingon the shape of the trade-off curve, it may be possiblefor more than two prey types to coexist with thepredator. In that situation, the number of prey typespresent, the range of palatability between the least andmost defended types and the shape of the trade-offcurve together determine whether the system exhibits
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Figure 4. (a) Trade-off curves specified by equation (3.1). (b,c) Trajectories for a trade-off curve with bZ2, gZ1, for (b) NZ2,and (c) 32 initial prey types. Total prey are shown as dashed green curve and the predator is shown as solid red curve. A thin blackline denotes the mean predator density, which remains approximately 0.05 for all three scenarios in (a–c). The dilution rate isdZ0.7dK1, a setting for which we consistently observed cycles in our original experimental system (Jones & Ellner 2004). (d–f )Trajectories for a trade-off curve with bZ0.5, gZ1, for (d ) NZ2, (e) 4 and ( f ) 32 initial prey types. Total prey are shown ingreen and the predator is shown in red. A thin black line denotes the mean predator density, which is approximately 0.05, 0.07and 0.09, respectively, for the 2, 4 and 32 clone scenarios in (d–f ).
6 L. E. Jones et al. Rapid evolution in food webs
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stable limit cycles, transient cycling followed by acoexistence equilibrium of one or more types orexclusion of all but one prey genotype. The trade-offbetween defence against predation and competitiveability is modelled as follows:
kiðpiÞZk�
Cð1CgÞ
1Cgpbi
; i Z 1;2;.;N ; ð3:1Þ
where k�C is the half-saturation constant for the
completely undefended type; g is the cost of defence;and b sets the shape of the trade-off curve. Increaseddefence results in an increase in the half-saturationconstant ki( p), and thus a reduction in competitiveability relative to the undefended type in a predator-free environment. This curve (figure 4a) is only anexample of many trade-off formulations that produceconsistently similar results. For our purposes here,we set the minimum p-value as p1Z0.01, andpalatabilities pi take values between 0.01 and 1.Again, the mathematical model for the system isequation (2.1), but in this case with iZ1, 2, ., N.
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For shape parameter bO1, the trade-off curve isconvex (figure 4a) for most settings of the costparameter g and favours extreme types (figure 5a–c).In the limit (as time t/N), the system behaves as atwo-clone system: given p1 is small, and any initialnumber of types arrayed on the trade-off curve, thereare stable EC for the dilution rate dZ0.7 (figure 4a–c).As defence drops ( p1 increases in value), there is first anarrow range of stable coexistence between the twoextreme types, p1 and pN, together with the predator.As with the two-prey system, there is then a substantialrange of defence levels where the SS involves only themost defended type ( p1) and the predator. As thedefence of the most defended type becomes moderate,similar to the two-prey system, there are thenconsumer–resource cycles. The small variation incycle period observed in figure 4b,c for differentnumbers of initial prey types is a transient phenom-enon, the duration of which increases as more preytypes are added to the system and the trade-off curvegets ‘crowded’: each subsequent prey type becomes
pp. 1–14
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Figure 5. Mean clonal frequencies (log scale, note differences in vertical scaling) for surviving prey types after 600 days at adilution rate dZ0.7dK1. (a–c) Assume that there were initially NZ(a) 2, (b) 4 and (c) 32 prey types arrayed on a trade-off curvewith shape parameter bZ2 and cost parameter gZ1. In this case, the surviving clones are the extremes (filled circles), and afterthe transient phase—which increases in length as prey types are added to the trade-off curve—the system behaves approximatelyas a two-clone system: it exhibits stable limit cycles at this dilution rate. (d–f ) Assume that there were initially NZ(d ) 2, (e) 4 and( f ) 32 prey types arrayed on a trade-off curve with shape parameter bZ0.5 and cost parameter gZ1. In this case, there is aninternal equilibrium with the most defended type and one or more very well-defended types (filled circles). The number ofcoexisting types increases with the number of clones and the concavity of the trade-off curve. Clones are indexed of the order ofincreasing palatability.
Rapid evolution in food webs L. E. Jones et al. 7
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more similar to those immediately adjacent to it on the
curve. Figure 5a–c shows surviving prey types for each
of two initial scenarios: NZ2, 4 or 32 prey types, when
bZ2. In each case, it is the extreme prey types (filled
circles) that survive in the presence of the predators,
with the most vulnerable prey type at very low densities
and the best defended at high densities.
For shape parameter b!1, the trade-off curve is
concave (figure 4a), and favours intermediate types.
Again assuming that the most defended type is nearly
invulnerable to predation, p1z0, as the number of prey
clones increases above two types, there is an initial phase
of transient EC followed by equilibrium during which
there is a stable coexistence of two or more of the best-
defended types. With an increase in prey types,
the transient phase becomes shorter and shorter,
and the dynamics are overall more stable with
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well-defended types dominating. In figure 4d–f, we
illustrate what happens as prey clonal diversity is
increased at the experimentally determined ‘cycling’
range of dZ0.7, and for p1z0 and trade-off shape
parameter bZ0.5: given NZ2 prey clones, the system
exhibits stable EC with a period of approximately
30 days and stable cycle amplitudes. As the clones are
increased to NZ4, the cycles rapidly shorten in period
and decline in amplitude with time, as the system goes to
equilibrium. By NZ32, the transient phase comprises
only one complete (evolutionary) cycle, and the system
is otherwise in equilibrium. Predator densities very
slowly increase with the number of initial clones, as the
dominant clone shifts to an intermediate type (e.g. see
figure 5, bZ0.5, NZ32). For further details and analysis
of coexistence equilibria in our experimentally para-
metrized model, please see Jones & Ellner (2004).
–14
8 L. E. Jones et al. Rapid evolution in food webs
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4. RESULTS II: DYNAMIC EFFECTS OF PREY ANDPREDATOR GENETIC VARIABILITYIn §3, we were able to give a rather detailed account ofthe effects of prey genetic diversity on communitydynamics. Of course, there is no a priori reason why thepredator in these systems should not also evolve.Indeed, we have shown that predator evolution doesoccur in our experimental rotifer–algal system and—just as prey evolution—can have strong effects on thestability of the observed predator–prey dynamics(Fussmann et al. 2003). We are only beginning toexplore how contemporary coevolution of predator andprey affects the dynamics. Because both predator andprey in our rotifer–algal system are clonal populations,genetic diversity can easily be introduced at bothtrophic levels simultaneously and the effects oncommunity dynamics can be studied. Given ourexperience with prey-evolution-only systems, weexpect, however, that understanding the resultingeco-evolutionary dynamics will require a detailedmathematical analysis that accounts for the multitudeof possible type-by-type interactions that occur withinand across trophic levels.
We here present a first step in this direction byformulating a predator–prey model that contains up tosix clones/genotypes within predator and prey levelsand allows for the interaction of each predator witheach prey type. So far, we are treating this model as anexploratory tool to understand the dynamical possibi-lities of this complex system, and intend to modelconcrete co-evolutionary predator–prey scenarios (i.e.rotifer and algal clones in the chemostat) in the future.The current model assumes logistic prey growth, amultispecies type-II functional response and is a systemof up to 12 differential equations (MZ6 prey and NZ6predator clones):
_xi Z xi ri 1KXMiZ1
xi =K
!KXNjZ1
aji yj
1CHj
" #; i Z1;.;M
and
_yj Z yj
Qj
1CHj
K dj
� �; j Z 1;.;N ;
ð4:1Þ
where xi and yi are the abundances of thesix prey and predator clones, respectively, and
HjZPM
iZ1bji xi ; QjZPM
iZ1 ajixi are measures of effec-
tive total prey abundance as perceived by predatorclone j. Parameters ri and dj are maximum prey clonegrowth rates and predator mortalities; parameters aji
and bji determine the saturation value and steepness ofthe functional responses for pairwise predator–preyclone interactions. The total abundance of all preyclones is regulated by the carrying capacity K. If noclonal diversity is present (MZNZ1), the systemsimplifies to the Rosenzweig–MacArthur model(Rosenzweig & MacArthur 1963). We parametrizedin agreement with values encountered in planktonpredator–prey systems (Fussmann & Heber 2002)that led to stable limit cycles for a system with a singleprey and a single predator type (figure 6a). Weintroduced clonal diversity by generating aji and bji
matrices with random uniform distribution (G5%)around the base values of aZ7.5 and bZ5.0. To see theeffects of heritable trait variation, we contrasted the
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dynamics of a non-evolving (one-prey–one-predator)system using the base parameters, with the dynamicsof evolving multiple-clone systems with randomlygenerated parameters.
What are the effects on predator–prey dynamicswhen diversity exists at both the predator and preylevels? Numerical simulations of equation (4.1) resultin a wealth of dynamic scenarios but some interesting,repeatable patterns emerge.
(a) Selection processes among types are
important and affect the dynamics at the
species level
In all our simulations, only a subset of the six prey orpredator types persisted in the long run. Selectivesurvival of genotypes—due to natural selection—represents the evolutionary component of the eco-evolutionary dynamics we describe here. A frequentlyobserved outcome in a six-prey–one-predator system isthe selection of a single prey type that coexists with thepredator at stable equilibrium (figure 6b), whereas aone-prey–one-predator system with the prey having thebase parameter values displays limit cycle dynamicswith the predator (figure 6a). Stabilization occursbecause a prey type is selected that provides the highestgrowth rate in the presence of the predator, and at thesame time shifts the predator–prey pair to the stableside of the Hopf bifurcation. Selection of genotypes atboth predator and prey levels is the norm for the fullsix-prey–six-predator system, but very frequentlysystems of multiple prey and predator typesare selected that coexist on compensatory cycles(i.e. predator and prey types alternate regularly inrelative frequency and display oscillatory dynamicscharacterized by pairwise interactions of predator typeswith ‘their’ prey type; figure 6c,e). Figure 6e shows aninteresting example of coexistence of three predatorand three prey types. Each of the three distinguishablepredator–prey pair shows characteristic predator–preydynamics with the typical shift between predator andprey peaks. One predator–prey pair cycles much moreslowly than the other two, whose frequencies areapproximately five times higher. These examplesshow that when prey and predator are evolving intandem, the ‘cryptic cycles’ phenomenon can occur atboth trophic levels, with rapid dynamics at the clone-frequency level resulting in total species abundancesthat remain nearly constant.
(b) High type diversity is rare
Most frequently, systems with two predator and twoprey clones become selected. Complicated systemswith many types appear to be unable to coexist in thehomogeneous environment that this model represents.On the other hand, selection of just one clone of preyand predator each is not the most frequent outcome. Itseems that our six-by-six interaction model is able toreproduce the essential dynamical patterns expected inhomogeneous systems of much higher genetic diversitybecause they all reduce to systems of low to moderatediversity. Clonal genetic diversity in natural commu-nities is often much higher (e.g. De Meester et al.2006). This suggests that complex dynamics incomplex community networks are not a likely
pp. 1–14
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Figure 6. Trajectories of predator–prey systems (equation (4.1)) with multiple prey (green) and predator (red; letter ‘P’)genotypes. (a) Benchmark system with one predator and one prey genotype. (b) Selection of a single prey type in a six-prey–one-predator system. (c) Selection of a two-prey–two-predator system in a six-prey–six-predator system. (d ) Species dynamicsof (c) (summation of predator and prey genotype abundances). (e) Selection of a three-prey–three-predator system in a six-prey–six-predator system. Note the two fast and one slowly cycling predator–prey pairs. ( f ) Species dynamics of (e).(g) Intermittent dynamics alternating between periods of dominance of single and multiple predator–prey pairs. (h) Speciesdynamics of (g). Parameters: riZ2.5, KZ1, djZ1, ajiZ7.5G5%, bjiZ5.0G5%. High-frequency oscillations appear ascontinuously filled areas in (d,f–h).
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mechanism that maintains high levels of geneticdiversity in homogeneous natural systems.
(c) Genotype dynamics are wild, species and
community dynamics are calm
The increased complexity of the multi-predator–preysystem tends to lead to more complex and erratic
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dynamics at the genotype level (figure 6c,e,g),compared with the benchmark one-predator–one-preysystem (figure 6a). However, species dynamics(the sums of the abundances of predator and preytypes, respectively) become stabilized relative to thebenchmark system, as also observed by Vos et al. (2001)for a similar model system. This is partly due to
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10 L. E. Jones et al. Rapid evolution in food webs
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statistical averaging of time series (Cottingham et al.2001), but is primarily caused by the compensatorynature of the dynamics, i.e. the regular succession ofdifferent clones as opposed to their synchronousappearance and disappearance, and may lead toapparently steady-state dynamics at the species level(figure 6d, f ). This is another instance of crypticdynamics in which highly dynamic patterns of cyclicalselection of genotypes are hidden under a calm surfaceof species dynamics. Because this type of crypticdynamics can occur at very moderate levels of traitdiversity (parameters a and b diverging only up to 5%from their mean value), it is likely to play an importantrole in real communities, even when within-speciesdiversity is relatively low.
(d) Species dynamics may appear noisy
or display intermittency
Owing to the complexity of the dynamics, genotypeabundances never add up to smooth steady-state orcyclical species dynamics. Instead, equilibria appear‘noisy’ (figure 6d, f ) or the dynamics show intermittentpatterns. Intermittency occurs because periods domi-nated by multiple genotype interactions alternate withperiods of classical predator–prey oscillations (whenonly one prey and one predator genotype dominate;figure 6g,h). These simulations suggest that the noisyand intermittent patterns so frequently observed innatural communities are potentially due to intrinsic,cryptic genotype dynamics and are not necessarily theresult of changing environmental factors.
The patterns described here emerged from arelatively simple mathematical model in which we—somewhat artificially—generated the potential forevolutionary dynamics by setting initial levels of geneticdiversity of up to 12 genotypes. As such, weinvestigated the interaction between ecologicaldynamics and the dynamical process of naturalselection, but neglected processes that are able torestore genetic diversity. In natural communities,mutation and immigration of genotypes are suchprocesses, and future studies should consider theirimpact on eco-evolutionary dynamics. We suspect thatthe effects of pulsed mutation or immigration eventswill be understandable within the framework that wehave presented here because they just reset geneticdiversity to higher levels at fixed time intervals (as wedid at the start of our simulations). However,continuous rates of mutation or immigration at thetime scale of the ecological dynamics may lead todynamical outcomes not covered by our currentanalysis, and we see the inclusion of these processesas an important continuation of our work.
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5. DISCUSSIONAlthough the fields of ecology and evolutionary biologyare both over a century old, we are only beginning tounderstand how tightly coupled the processes at theheart of these disciplines truly are. Becoming some-body else’s dinner represents very strong naturalselection, and it is hard to imagine the predator–preyinteraction or any other strong interspecific interactionoccurring without direct evolutionary consequences.
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But exactly that thinking is embedded in much of theecological theory underpinning environmental andnatural resource management. By studying somesimple model food webs based directly on experiments,we hope to start developing ecological theory for arapidly evolving biosphere.
We now return to the questions we posed in §1: howrapid contemporary evolution can affect the dynamicsof communities (question (i)), and then comparing thedynamic possibilities when genetic diversity is presentversus absent (question (ii)). Even our simplestexperimental systems (one predator and two preygenotypes) and the models developed to explain themgenerate a range of qualitatively different dynamics(§3). Changing the details of a trade-off between thecost of a defence, and its effectiveness can dramaticallyalter the identity of the surviving prey types, as canenvironmental factors (such as microcosm flow-through rate). Adding realistic, if theoretical, levels ofevolutionary complexity in the form of heritablevariation in ecologically relevant traits of both predatorand prey opens the door to even more possibilities (§4):selection of one prey type under some circumstances,and multiple types under others and dynamics varyingfrom equilibrium to chaos. Conversely, evolutionarydynamics can sometimes make for greater simplicity atthe species or community level, as complex dynamics atthe genotype level may lead to constant or nearlyconstant population abundances, instead of cycles, incoexisting populations (§§3 and 4).
A challenge posed by these findings is to developgeneral theory for linked eco-evolutionary dynamics,so that we can understand which biological conditionsgive rise to different ecological outcomes, and why.One approach that we are currently exploring is thetheory of slow–fast systems. This was used a decadeago (Khibnik & Kondrashov 1997) under the conven-tional assumption of slow evolutionary dynamicsrelative to fast ecological dynamics. To gain insightsinto possible effects of coupled and equally rapidevolutionary and ecological dynamics, we believe thatit will be useful to consider the opposite limit whereevolutionary change is fast relative to ecologicaldynamics (Cortez & Ellner in preparation). This isnot biologically impossible—it could happen if manybirths, balanced by nearly as many deaths, result inslow changes in total population size but allow rapidchange in genotype frequencies. Most importantly, itreduces model dimension and creates real possibilitiesfor mapping out all dynamic possibilities and under-standing when each of them can occur.
Because temporal dynamics provide informationabout underlying processes (e.g. Kendall et al. 2005;Ives et al. 2008), large-scale changes, such as con-sumer–resource cycles, are especially revealing aboutpotential effects of rapid contemporary evolution.Several types of natural large-scale ecological dynamicshave offered opportunities for studying rapid evolutionin the wild, including invasions (e.g. Lavergne &Molofsky 2007; Kinnison et al. 2008), range expansion(Reznick et al. 2008), periodic outbreaks of infectiousdiseases (e.g. Elderd et al. 2008), annual populationcycles driven by seasonality (Duffy & Sivars-Becker2007) and trait cycles (Sinervo & Lively 1996;
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Sinervo et al. 2000). Systems at SS may also be shapedby rapid evolution, e.g. population stability may be anoutcome of the interaction between potentially rapidecological and evolutionary processes (e.g. Doebeli &Koella 1995; Zeineddine & Jansen 2005). But demon-strating what drives this outcome in natural settingsmay require experimental manipulations that arenecessarily high cost and high effort (e.g. Fischeret al. 2001), and whose interpretation has often beenproblematic because of inadvertent confoundingfactors resulting from large-scale interventions(Turchin 2003). Natural dynamic processes may thusoffer the best prospects for confronting theory withdata on consequences of rapid evolution, which iscritically important as the theory begins to develop.
Our most fundamental theoretical prediction is thatthe level of heritable variation in a trait affectingecological interactions is a bifurcation parameter:small gradual quantitative changes in unseen evolution-ary processes can cause large abrupt qualitativechanges at the population and community levels. Forthe practical issues of ecological management andforecasting that we posed in §1, it is already widelyrecognized that we need to consider possible effects ofevolutionary responses that are evoked by humanimpacts and interventions. Our results raise theconverse issue: we may also need to consider the effectsof evolutionary responses that are slowed or con-strained when genetic variation is reduced by humanimpacts, such as habitat loss or fragmentation.
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6. UNCITED REFERENCEHendry et al. (2008).
Our research has been supported primarily by the Andrew W.Mellon Foundation, the James S. McDonnell Foundationand the Natural Sciences and Engineering Research Councilof Canada. We thank Andrew Hendry and two anonymousreferees for their comments on the manuscript, and also themany Cornell undergraduates who assisted with datacollection.
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Author Queries
JOB NUMBER: 20090004
JOURNAL: RSTB
Q1 Reference Duffy et al. (2007) has been cited in text but
not provided in the list. Please supply reference details
or delete the reference citation from the text.
Q2 We have changed ‘figure2e versus figure 2c’ to
‘figure1e versus figure 1c’ in the sentence ‘In addition,
the coefficient. .’ Please check and approve.
Q3 Please give the year during which Becks (unpublished
data) were generated.
Q4 Reference Becks et al. (in preparation) has been cited
in text but not provided in the list. Please supply
reference details or delete the reference citation from
the text.
Q5 Reference Cortez & Ellner (in preparation) has been
cited in text but not provided in the list. Please supply
reference details or delete the reference citation from
the text.
Q6 Reference Elderd et al. (2008) has been cited in text
but not provided in the list. Please supply reference
details or delete the reference citation from the text.
Q7 Reference Hendry et al. (2008) is provided in the list
but not cited in the text. Please supply citation details
or delete the reference from the reference list.
RSTB 20090004—1/3/2009—15:50—JMANOHAR—329484—XML RSB – pp. 1–14
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Phil. Trans. R. Soc. B
