Received 7November 2002 Accepted 9January 2003 Publishedonline 31March 2003

Evolutionas a criticalcomponent of dynamics GregorF. Fussmann 1,2* ,Stephen P.Ellner 2 and NelsonG. HairstonJr 2 1Institut fu¨rBiochemieund Biologie,Universita ¨tPotsdam,Maulbeerallee 2, D-14469 Potsdam, Germany 2Departmentof Ecology and EvolutionaryBiology, Corson Hall, Cornell University, Ithaca,NY 14853,USA Microevolutionis typically ignored asa factor directly affecting ongoing population dynamics.We show herethat density-dependentnatural selectionhas a directand measurable effecton aplanktonic predator– prey interaction.We keptpopulations of Brachionuscalyciflorus ,amonogonontrotifer that exhibits cyclical parthenogenesis,in continuousflow-through cultures(chemostats) for more than 900 days.Initially, femalesfrequently produced male offspring,especially at high population densities.We observed rapid evolution,however, towards low propensity toreproduce sexually, andby 750 days,reproduction had becomeentirely asexual. There wasstrong selectionfavouring asexual reproductionbecause, under the turbulentchemostat regime, males wereunable to mate with females,produced no offspring,and so had zerofitness. In replicated chemostatexperiments wefound that this evolutionary processdirectly influ- encedthe population dynamics.We observed very specificbut reproducible plankton dynamicswhich are explained well by amathematical modelthat explicitly includesevolution. This modelaccounts for both asexual andsexual reproductionand treats thepropensity toreproduce sexually asa quantitative trait underselection. We suggest that asimilar amalgam ofecological andevolutionary mechanismsmay drive thedynamics of rapidly reproducing organisms in thewild. Keywords: Brachionuscalyciflorus ;chemostat;clonal selection;cyclical parthenogenesis; evolutionary dynamics;rapid evolution

1. INTRODUCTION The life cyclebegins whendiploid amictic femaleshatch from diploid diapausing eggs.Rapid clonal propagation of Population dynamicsand evolutionary dynamicsare often thesediploid femalescharacterizes theamictic phase.The treatedas separate fieldsthat require differentapproaches sexual phaseis initiated whenamictic (parthenogenetic) andmethodologies both in experimental andtheoretical femalesproduce mictic female offspring.Mictic females studies.In particular, thetwo dynamic processestra- producehaploid eggs that developinto haploid males if ditionally have beenbelieved tooperate ondifferent time- unfertilized.Fertilized mictic eggs,however, develop into scales,that is population dynamicsare rapid while evol- diapausing eggs that canundergo extended periods of dor- ution’s progress is slow(e.g. Khibnik &Kondrashov mancy.Amictic femaleshatching from diapausing eggs 1997). In many cases,however, evolutionary change can initiate another phaseof parthenogenetic reproduction, occurat rates comparable tothe rates at whichthe abun- and so on. dancesof populations andcommunities change anda High population densityof conspecifics has been exper- growing numberof studies have demonstratedrapid evol- imentally establishedas an intrinsic stimulusfor thepro- utionat ecologically relevant time-scales(Thompson ductionof mictic eggs in B.calyciflorus (Gilbert 1963, 1998; Hairston et al. 1999; Hendry et al. 2000; Cousyn et 2002). Gilbert’s (1963) resultssuggest that therate of al. 2001; Reznick& Ghalambor 2001; Stockwell et al. mictic female productionis proportional tothedensity of 2003). In this study,we show how clonal selection femalesand that therotifers obtain information about the operating ona fundamentallife-history trait (thepro- currentpopulation densityvia theconcentration of oneor ductionof amictic versusmictic offspring) affectsthe several chemical substancesthat accumulatewhen dynamicsof plankton populations.We report resultsfrom densityincreases. This is consistentwith observationsof experimental populations ofcyclically parthenogenetic natural populations ofrotifers wherethe onset of mixis is whosedynamics can be accurately describedby a gradual andthe population consistsof mictic andamictic mathematical model(Fussmann et al. 2000). These femalescoexisting in variable fractions(Aparici et al. dynamicswere shaped by evolutionary change,so much 2001). sothat they couldonly becorrectly predictedwhen evol- Sexual reproductionof monogonont rotifers resultsin utionwas explicitly includedin themodel. theproduction of diapausing eggs,an essential adaptation Brachionuscalyciflorus Pallas isa monogonontrotifer that ensuressurvival in thetime-varying environmentsthe speciesthat exhibits cyclical parthenogenesisin thewild; plankton inhabit. Atthe start ofanewseason, genetic vari- apopulation persiststhrough time with phasesof amictic ance—represented by differentclones— is routinely re- (ameiotic) andmictic (sexual) reproductionfollowing one establishedthrough emergencefrom thedormant egg another in aseasonalpattern (e.g.Serra &King 1999). bank (Go´mez &Carvalho 2000). Recently,Gilbert (2002) performed crowdingexperiments with astrain of B.calyciflorus anddetected significant clonal variation in *Authorfor correspondence ([email protected]). thepropensity toproduce mictic femalesin responseto

Proc.R. Soc.Lond. B (2003) 270, 1015–1022 1015 Ó 2003 TheRoyal Society DOI10.1098/ rspb.2003.2335 1016G. F.Fussmann andothers Evolution andplankton dynamics thecrowding stimulus. From theseobservations, and (b) Mictic andamictic rotifers becauseplanktonic rotifers typically undergomany gener- Forour study itwas crucialto beable to distinguishbetween ationsof asexual reproductionduring aseasonalcycle, we micticand amictic B.calyciflorus . While male B.calyciflorus are suspectclonal selectionto have animportant, naturally considerablysmaller and morphologicallydifferent from recurring impact onthe population dynamicsof theseani- females,there are no morphological differences between mictic mals. In ourexperiments, mating ofmale andfemale roti- and amicticfemales. However, females produce any of three ferswas prevented by turbulencein theculture vessels. types of egg that canbe easily distinguished during routine This extreme conditionenabled us to study the effect of microscopicinspection: large, soft-cased subitaneous eggs clonal selectionagainst sexon the rotifer population (amicticeggs that hatch immediately,produced by amictic dynamicswithout any confoundingeffects of recombi- females),small soft-cased ‘male’ eggs (unfertilizedmictic eggs nation. that hatch immediately,produced by micticfemales), or large, Wefoundthat, after ca.2years,the propensity torepro- hard-cased diapausing eggs (fertilizedmictic eggs that go ducesexually had disappeared entirely from therotifer through aperiodof dormancy,produced by micticfemales). population. The rate at which this happenedwas Thus, for allegg-carrying femalesit was straightforward to especially high whenthe chemostat cultures initially determinewhether they weremictic or amictic. For those reachedlarge population size(including male production femalesin asamplethat werenot carryingeggs, we assumedthe by somegenotypes), and then, as the algal resourcewas sameratio of micticto amicticindividuals as found for the egg- depleted,decreased rapidly, thusproducing conditionsfor carryingfemales. The proportion of micticfemales among all strong natural selection.We combined replicated com- females p (‘micticratio ’;table 1)was estimatedas munity experiments andmathematical modelling todem- M 1 N [M /(M 1 A )] onstratethat theobserved dynamics were unlikely toresult pˆ = e e e e e , (2.1) M 1 N 1 A from population interaction alone butthat evolutionof e e e therotifer population towardsasexual reproductionwas a where Me, Ae, and Ne arethe numbersof femaleswith mictic, critical componentof the dynamic process. amictic,and noeggs inasample,respectively.

(c) Quantitativetrait (QT) modelfor mixis 2. METHODS evolution (a) Experiments andextra-experimental The QTmodelwe propose hereis an extensionof amodel observations (F2Kmodel; Fussmann et al. 2000)we have previouslyused to Femalesof the rotifer B.calyciflorus werecollected from Mil- predictsuccessfully the dynamicsof nutrientsand interacting waukee Harbor, Lake Michigan,USA (courtesyof M.Boraas) populations of algae and rotifersin the chemostat system. The and axeniccultures were established using the unicellulargreen F2Kmodel is adoubleMonod model (Nisbet et al. 1983) that alga Chlorellavulgaris Beij.(UTEX no. 26) as food.We cultured doesnot allowfor mixis.It couldthus beexpected to produce these two speciestogether inflow-through culturesystems quantitatively accuratepredictions only for periodswhen rotifer (380ml glass chemostats) at 25 ± 0.3 °C,constant illumination reproductionwas almost exclusivelyamictic. Because our at 120 ± 20 m E m2 2 s2 1 (wide-spectrumfluorescent lamps) and experimentfell into a periodof extensivemictic reproduction useda culturemedium that containednitrogen at aconcen- and becausethere was evidencein the data for selectionagainst tration that limitedalgal growth (80 –514 m mol l2 1), plus non- mixis,we amendedthe F2Kmodel to includemictic females limitingconcentrations of other nutrientsand tracemetals: P, and evolutionof aQTrelatedto mixis(bold type indicates S,B,Ca,K, Na, Mg,Cl, Fe, I, Li,V, Mn,Co, Cu, Zn, Se, these amendments): Rb, Sr,Mo; we addedvitamins B , B ,and biotinto ensure 1 12 dN the long-termsurvival of B.calyciflorus .Sterileair was bubbled = d(N 2 N) 2 F (N)C, dt i C through the chemostat vesselsto preventCO limitationof the 2 dC 1 algae and to enhancemixing. It was this mixingthat prevented = F (N)C 2 F (C)(B 1 M) 2 dC, dt C « B mating of maleand female B.calyciflorus .Formore details on dR the set-up seeFussmann et al. (2000).We culturedthe daughter = (1 2 p)F (C)R 2 (d 1 m1l)R, dt B generationsof the initial B.calyciflorus founderpopulation in dB consecutivechemostats for 901days underconstant conditions, = (1 2 p)F (C)R 2 (d 1 m)B, dt B except that we changed the dilutionrate and nitrogenconcen- dM tration of the culturemedium for the purpose of experimen- = p F (C)R 2 (d 1 m)M, dt B tation, which we have describedelsewhere (Fussmann et al. b N b C 2000).Cultures were sampled daily in duplicate using sterile F (N) = C , F (C) = B . (2.2) C K 1 N B K 1 C syringes.Rotifer density and the occurrenceof micticindividuals C B weredetermined by directcount under a stereodissecting Allstate variablesare modelled in unitsof molesof nitrogen. N microscope.Algal density was establishedusing aCASYIpar- and C denotethe concentrationof nitrogenand Chlorella, ticlecounter. The experimentpertinent to this study was run respectively; B denotesthe densityof amicticfemale Brachionus, from days 0–30,i.e. at the beginningof the culturingperiod, and M isthe densityof micticfemales. R isthe densityof when both micticand amicticrotifers were present. We ran four femalesthat lay subitaneous eggs, asubset of the amicticfrac- simultaneousreplicate trials, which wereinitiated by adding 50 tion.By using two state variablesfor amicticrotifers we incor- B.calyciflorus to eachof the four chemostats that contained porated age structureinto the model: R denotesthe amictic steady-state culturesof C. vulgaris.Weset the dilutionrate of rotiferdensity corrected for the lossof fecunditywith age, with the chemostat culturesto d = 0.44 d2 1 and nitrogenconcen- l beingthe rate at which fecunditydecays. Note that, inthe 2 1 tration inthe inflowmedium to Ni = 514 m mol l . model,mictic females have the sameconsumption rate as amic-

Proc.R. Soc.Lond. B (2003) Evolution andplankton dynamics G.F.Fussmann andothers 1017

Table1. Parameters associated withmixis of Brachionus.

parameter name meaning use

p mixis allocation fraction of subitaneous eggsthat are model (equation (2.2)); unknown for bound to bemictic femaleswhen theyexperimental data mature p mictic ratio proportion of mictic femalesamong all model and data; p(t)isan estimateof p(t), females withan unknown time delay pˆ estimateof mictic asabove data(equation (2.1)); only direct measure ratio of mixis availablefrom experimental data a propensity to mixis constant of proportionality relating p to model (equation (2.4)); shown to bea QT Brachionus density (equation (2.3)) under selection aˆ estimate of asabove, but substituting pˆ for p data; value for QTderived from propensity to mixis experimental data ticfemales but do not reproduce,so we do not needto dis- Table2. Fitted values for model parameters. tinguish betweenolder and younger amicticrotifers. This reflectsthe fact that micticand amicticfemales have the same parameter fitted value size,morphology and feedingbehaviour; however, aerationkept the chemostat contentperpetually turbulent, which effectively « 0.033 033 2 4 2 2 2 preventedrotifer mating and sexualreproduction of offspring n 1.502 ´ 10 ml female 2 1 other than males(we never observed any sexuallyproduced a(0) 0.072 51 mlfemale N content Chlorella 2.054 ´ 102 8 m Mol diapausing eggs inchemostat samples).This meansthat mictic vulgaris rotifershave zerofitness and the biomass and energyinvested N content Brachionus 3.295 ´ 102 4 m Mol intothem and their(male) eggs areeventually washed out of calyciflorus the chemostat vessel.Male rotifers and maleeggs arenot part of the model,as they makeno contributionto growth of the femalepopulation inthe chemostat and donot feed(Serra & table inthe experimentalpart of the study; mixisratio p rep- Snell1998). isthe nitrogenconcentration in the inflow Ni resentsan estimateof p with an unknown timedelay but has to medium; d isthe dilutionrate of the chemostats; ( ) and FC N beestimated in return by pˆ ;equation (2.1)).This method has FB(C)arethe numericalresponse functions of Chlorella and Bra- the advantage of providingan additionalcheck on the model: chionus; bC and bB arethe maximumbirth rates of Chlorella and doesit producepatterns of mixissimilar to the data, eventhough Brachionus; KC and KB arethe half saturation constants of Chlor- itwas not fittedto those data? and ; isthe assimilationefficiency of ; ella Brachionus « Brachionus Wefittedfive parameters (table2): «, n, a(0)and the scaling and is the mortalityrate. m Brachionus factors for Chlorella and Brachionus betweenmodel units (N The parameter p (‘mixisallocation ’;table 1)denotesthe frac- concentration)and data units(individuals per ml). All other tionof subitaneous eggs that aredestined to becomemictic parameters wereheld fixed at the valuesin Fussmann et al. femaleswhen they mature.We assumethat p isalinearfunction (2000).All parameters wereassumed to beconstant across of the currenttotal densityof rotifers, chemostats and constant overtime. In addition, initial con- p = min(a·(B 1 M), 1), (2.3) ditionswere fitted separately for Chlorella (modelvariable C) and Brachionus (modelvariable B)ineachchemostat (i.e.it was not and wish to modelthe dynamicsof a (the ‘propensity for mixis ’; assumedthat initialvalues were measured exactly, because sur- table 1),considered as aQTunderselection. We use the stan- vivorship of the Brachionus inoculum at t0 may have varied dard modelin which the rate of change intrait valueis pro- among chemostats).Other initial conditions were assumed as portionalto the percapita fitnessgradient (Lande1976; follows: Saloniemi1993). For equations (2.2)and (2.3)this gives (with n as the constant of proportionality): (i) R(0) = B(0):experiments initialized with newlymatured da ¶ ¶ p individuals, = v [(1 2 p)F (C)] = 2vF (C) dt ¶ a B B ¶ a (ii) M(0) = 0:initially no mixiswas occurring,based on the mixisindices from the data, 2 vFB(C)(B 1 M) if p , 1 = . (2.4) (iii) N(0) = 50 m mol l2 1 based on measurementsof total sol- H 0 if p = 1 ublenitrogen in the chemostats. The fitnessgradient is always non-positive,reflecting the fact that selectionin the chemostat flow-through environmentnever The fitting criterionwas the sumof absolute errorson our favours mixis. usualplotting scalefor samplecounts ( Chlorella: 106 cells ml2 1; Brachionus: females ml2 1).Fitting was programmedin R (d) Modelparameter estimation (Ihaka &Gentleman1996). We used l soda (in the Odesolve Weestimated parameters by fitting the modelto the four library)to computenumerical solutions of the model,and the experimentalchemostat runs.The modelwas fittedonly to the fitting criterionwas optimizedusing the Nelder –Meadalgorithm Chlorella and Brachionus data, owing to the imprecisionof the (function Optim).To avoid spurious localminima we useda mixisindices based on the data (mixisallocation p itselfis intrac- multistart proceduresimilar to that ofTurchin& Ellner(2000).

Proc.R. Soc.Lond. B (2003) 1018G. F.Fussmann andothers Evolution andplankton dynamics

(a) 15 0.6 0.06 ) e l 0.4 a 10 m

e 0.04 f

r e

p 5 0.2

l m (

ˆ 0.02 a 0 0 (b) 15 0.6 0

0 200400 600 800 10 0.4 o i

days t 1 a _ r l

c m 0.2 i

5 Figure 1. Long-term evolution of theQT a (‘propensity for t s c i mixis’ in Brachionus)in consecutive chemostatcultures over u n m

o r 901 days. Smalldots ( n = 1374) represent estimates( aˆ) of a i h o

c 0 0 1

= 1 _ calculated as aˆ pˆ (B M)from separatechemostat a l r (c) samples(means of two replicate samples),where ( B 1 M) is B 0.6 m 15 e a l l

thetotal density of female Brachionus rotifers (both amictic l a e r m

and mictic) and pˆ is an estimateof theratio between mictic o r l

o 0.4 h and total female Brachionus.Only datafrom sampleswith 10 e C l

2 1

(B 1 M) . 5 Brachionus ml are plotted. Large symbols a 8 0 m 1 indicate theaverage aˆ for eachof four distinct sampling e f 5 0.2 periods. Note thataccumulation of dots at aˆ = 0results in a line-like appearance. 0 0 15 (d) 0.6 That is,randomly generated parameter choices were compared to identifygood contenders,and optimizationwas repeatedfrom multiplegood contendersto confirmthat the same ‘best fit’ was 10 0.4 found repeatedly.We did not attempt to quantify the precision of parameterestimates because our focus is on comparingalter- 5 0.2 nativemodels rather than parameterestimation. Estimates are presentedonly to verifythat the data canbe fitted with para- metervalues that areconsistent with the availableexperi- 0 0 mentalevidence. 0 5 10 15 20 25 days

3. RESULTS Figure 2. Dynamicsof (rotifers) and Chlorella vulgaris (green algae) in four replicate ( a)–(d) Over themore than 900 daysthat wemonitored our chemostattrials (experiment; days0 –26). Open circles with chemostatcultures, the mictic reproductionof B.calyciflorus solid line, B.calyciflorus females; solid line, B.calyciflorus steadily declined(figure 1). The average mictic ratio males; blackcircles withdotted line, mictic ratio; triangles decreasedfrom pˆ = 0.15 during theexperimental period withsolid line, C. vulgaris. (days 0–30) to pˆ = 0.03 for thepost-experimental obser- vation period (days96 –901). Afterday 751 weobserved The concentrationof female Brachionus during the neitherfemale B.calyciflorus carrying mictic eggs normales, experimental period couldbe used to predict howpreva- indicating that reproductionhad becomeentirely amictic in lentsexual reproductionwas in therotifer population. The thechemostat cultures. Accordingly, wefound evidence in mictic ratio pˆ increasedlinearly with Brachionus density thedata for long-term evolutionof the QT a, the ‘propensity (figure 3). The meanvalue ofthe QT a,thepropensity for mixis’. for mixis, canbe estimated as the slope aˆ = 0.0258 ml per Weobservedvery reproducible plankton dynamicsin all female from linear regressionof pˆ versusfemale rotifer fourreplicate chemostattrials (figure 2). The character- density.Our experiments andlong-term observations isticswere: (i) abimodal abundancepattern offemale Bra- revealed,however, that theQT a wassubject to evolution- chionus followedby completeextinction; (ii) amaximum ary change.Selection against mixis in thechemostats was ofmales andmictic ratio falling temporally betweenthe sufficientlystrong tobe detected even during therelatively twomaxima in female Brachionus abundance;and (iii) an shortexperimental period (days0 –30 ofourexperiment): almost steadydecline of the algal population which aˆ ,calculatedfrom amoving regressionof pˆ versusfemale deceleratedbetween the two maxima offemale Brachionus Brachionus concentration,declined in thefirst half ofthe abundance.The timing ofthese characteristic eventsdif- experimental period (figure 4). The reversal ofthis trend feredby afewdays among replicates andthe absolute after day 14 (figure 4) doesnot mark areversal in the values ofabundance and mictic ratio varied slightly. directionof evolution but is due to the fact that pˆ is an

Proc.R. Soc.Lond. B (2003) Evolution andplankton dynamics G.F.Fussmann andothers 1019

0.8 12 (figure 5b),anda local maximum ofthe mictic ratio p ˆ = 0.0258 × (B + M) shortly after thefirst rotifer maximum, followedby equili- r2 = 0.55 brating mictic ratios (figure 5 c).Weobserved a similar plateau ofmictic ratios in twoof the four experimental 0.6 runs(figure 2 b,d and figure 5c)beforetotal rotifer den- sitiesbecame too low for preciseestimates. The model o i

t also predictsthat the ‘propensity for mixis ’ (i.e.the density a

r 0.4 responseparameter a)wasreduced but not eliminated c i t

c over thecourse of theexperiment. Estimatesof aˆ derived i

m from theexperimental data evolve in parallel with the 0.2 value of a predictedby themathematical model during thefirst half ofthe experimental period (figure 4). The differencein absolutevalues between a and aˆ is due to theimperfect estimation of p (model) by pˆ (data).For the 0 secondhalf ofthe experimental period,data andmodel prediction disagree (figure 4), reflecting thefact that the 0 4 8 12 16 20 parameters underlying thecomputation of a,mixis ratio Brachionus: p andmixis allocation p,diverged drastically after the _ (amictic (B) + mictic ( M) females) ml 1 secondmaximum of Brachionus (figure 5c). Mixis andevolution of theQT a are componentsof the Figure 3. Linear regression of mictic ratio versus female model that are essentialto describe correctly thepopu- Brachionus calyciflorus density for thefirst 30 daysof Brachionus culture (experimental period; n = 92). Datafrom lation dynamicsof the rotifers (figure 6). If weremove all sampleswith ( B 1 M) . 0 Brachionus ml2 1 are included. evolutionfrom theQT model(by settingd a/dt = 0 and pˆ = 0.0258 ´ (B 1 M); r 2 = 0.55. a = constant = a(0)) Brachionus nolonger drives thealgal population toextinction andboth speciescoexist at an equilibrium (figure 6 b).Anattempt tofit theexperimental data withoutallowing for thepossibility ofmixis evolution leadsto extinction ofboth rotifers andalgae butthe 0.06 characteristic doublepeak ofrotifer abundancein theorig- ) l e

) inal data isnot recovered (figure 6 c).Similarly, if both d e o l

a evolutionand mixis are removed(the F2K model;see m ( m

e a § 2(c)) themodel predicts again asimple boom-and-crash f

0.04

r r o e

cyclewhere the rotifers rapidly andcompletely exploit ) p

a l t their algal resourcefollowed by their ownextinction a m d ( (

0.02 (figure 6d). ˆ a

4. DISCUSSION 0 The predator –prey dynamicsbetween Brachionus and 0 4 8 12 16 20 Chlorella in ourlaboratory chemostatcultures can be mean day of regression understoodonly by incorporating theevolution of one of Figure 4. Short-term evolution during thefirst 30 daysof thebasic life-history characters ofthe predator, mixis. A Brachionus culture (experimental period). Eachsymbol simple modellacking evolutionenabled us previously to represents theslope aˆ (data) or a (model) ± s.e. of alinear predict key aspectsof the dynamics, including transitions regression, forced through theorigin, for seven consecutive betweenequilibrium coexistenceand stable limit cycles days of pˆ (estimate of mictic ratio; data) or p (mixis (Fussmann et al. 2000). However,this modelproved to allocation; model) versus total female Brachionus density beincomplete when mictic femalesaccounted for acon- 1 (B M).Open symbols, a basedon datagenerated bythe siderable fraction oftherotifer population. Guidedby our mathematicalmodel; blacksymbols, aˆ basedon experimental improved modelwe arrive at thefollowing scenariosfor data; grey symbolsindicate unreliable estimatesof aˆ (see text). Seetable 1 and figure 1for other variable name theexperimental dynamics. definitions. At thebeginning ofour trials, rotifer populations increasedfrom lowinitial numberswhile algal density decreased.Mictic female productionwas density depen- inappropriate estimator ofthe mixis allocation p when dent,and this causedthe mictic ratio andthe numbers of Brachionus femalesno longer reproduce(see § 4 and fig- male rotifers (with adelay) torise together with female ure 5c). density.The mixis ratio reached ca.50%, i.e.about half of Our model(equations (2.2), (2.3) and(2.4); table 2) theavailable resourceswere invested into mictic rotifers,a matchesthe qualitative featuresof the population data non-reproductivedead end in thechemostat setting. The from theexperiment with reasonably goodquantitative rotifer population thenbegan todeclinewhen the amictic agreement (figures 2and5). It capturesthe essentials of rotifer reproductionno longer compensatedfor thecom- theexperimental dynamics:the double peaks of female binedlosses by mortality, decreasedfecundity and chemo- Brachionus at about days5 and12 (figure 5 a),theexploi- statdilution rate. Algal population declinedecelerated tation ofthe algal resource,retarded between days 5 and during this period because,at loweredalgal densities,

Proc.R. Soc.Lond. B (2003) 1020G. F.Fussmann andothers Evolution andplankton dynamics

(a) available resourceswas channelled into the production of 15 mictic, non-successfullymating female andmale rotifers. Ashift towardspredominantly amictic rotifers causedthe 1 12 _ l secondmaximum, after which rotifers diedout because m

s they had overexploited their resource. u 9 n Although themodel performed best on the and

o Chlorella i h

c Brachionus abundancedata towhich it wasfitted (figure

a 6 r 5a,b),it also predictedreasonably well themixis patterns B observedin theexperiments (figure 5 c).Atthebeginning 3 andend of the experiments rotifer abundanceswere very low,which prevented reliable estimatesof the mictic ratio. 0 Mixis indicesbased on sample sizesof less than (b) 5rotifers ml 2 1 may showconsiderable stochastic fluctu- ationsowing tothe presence or absenceof asingle mictic 0.45 1 female in asample, andwere therefore excluded from our _ l interpretation. Also,the use of the observed mictic ratio m

s i pˆ asa surrogate for theunobserved mixis allocation p is r

a 0.30 g only valid prior tothe second rotifer maximum. Beyond l u v

this point rotifers soonstop reproducing, so the ratio of . C

amictic tomictic femalesremains nearly constantdespite 8

0 0.15

1 thedecrease in rotifer abundance(which would lead toa decrease in p if reproductionwere occurring). The result isa spuriousincrease in ourestimates of themixis propen- 0 sity a (grey circlesin figure 4). (c) Serra &King (1999) formulated amathematical model for bisexually reproducing monogonontrotifers that pro- 0.6 duceddynamical patternscomparable tothose we n r o o i

observedin ourexperiments andmodel simulations. Their t o a i c t 0.4 modelis considerably simpler than ourQT modelin that o a l r l

a c it containsneither resourcesas state variables (rotifer

i t s i c

i growth isinstead density dependent) nor age structure, x i

m 0.2 m andmixis allocation (our p)wasincorporated either asa constantintermediate value or asa switchwhere p was either zeroor onedepending on thecurrent rotifer density, 0 X X X X X X X X X X X X X withoutany evolutionof mixis. Despiteits more abstract character, theSerra andKing modelwith constantmixis 0 5 10 15 20 25 days allocation predictedrotifer population sizeto reach an equilibrium after asingle maximum, similar tooursimula- Figure 5. Comparison of model predictions (solid and tionswithout evolution of mixis whererotifer densityand dashed lines) withreal, experimental data(dotted lines) for mixis allocation reacheda constantvalue after damped thechemostat trial shown in figure 2 b. (a) Brachionus oscillations (figure 6 b). When p is switchedbetween zero calyciflorus density, (b) Chlorella vulgaris density, and ( c) andone in responseto a densitythreshold, the Serra and mixis allocation p (solid line), mixis ratio p from model (dashed line), and estimated mixis ratio pˆ from data(dotted King modelpredicts sustained population oscillations line). Xsymbolsabove the x-axisindicate sampling dates driven by theperiodic change betweenamictic andmictic witha female B.calyciflorus density of lessthan 5 ml 2 1. reproduction.The dampedoscillations in ourmodel with- outmixis evolution(figure 6 b)are notdue to density- dependentmixis, butrather are predator –prey oscillations. which resultedin elevatednutrient concentrations (data Our modelincorporates thepopulation dynamicsof the notshown), algal reproductionwas able tocompensate resourcespecies, Chlorella.If weinsteadsupply foodto the for theconsumption by rotifers.As rotifer density rotifers at aconstantrate, wealso observerotifers reaching declined,the fraction ofamictically reproducing rotifers equilibrium after asingle maximum in ourmodel. increasedowing tothe combined effects of reduced Micticfemales accounted for more than 50% oftotal crowdingand continued evolution of areducedpropensity female abundanceshortly after ourcultures were started, for mixis. This allowed therotifer population torise again but after ca.750 daysin continuousculture no signs of andto reach asecondmaximum. Although rotifer density mixis (mictic femalesand males) remained.Boraas (1983) wasthen as high asor higher than at thefirst maximum, andBennett & Boraas (1989) observeda similar lossof both themixis allocation andthe mictic ratio werelower mictic reproductionover time in their B.calyciflorus flow- dueto the evolution against mixis that had occurredup through cultures.Boraas (1983) found ca. 40% mictic tothis point. femalesin newlyestablished Brachionus chemostatcul- Thus,in theexperiment, twovery differentmechanisms tures,but no longer observedmictic femalesand males actedtogether toproduce the bimodal shapeof the rotifer after twoto three months. Boraas (1983) concludedthat dynamics.The first maximum (andthe subsequent selectionagainst sexual reproductionwas responsible for declineof rotifers) occurredwhen a major fraction ofthe his observations,presumably becausethis wasthe most

Proc.R. Soc.Lond. B (2003) Evolution andplankton dynamics G.F.Fussmann andothers 1021

tional selectiontowards the optimum value in this (a) 15 0.6 environment( a = 0becausesexual reproductionyields no offspring).Starting with relatively high values of a at ca. 0.03 ml per female, a approached zeroasymptotically, that 10 0.4 is:very rapidly initially butat adecreasingrate with increasing culturetime. 5 0.2 Wehypothesize that theinitial population of Brachionus collectedfrom LakeMichigan consistedof a widevariety ofgenotypesconstituting the additive geneticvariance, on 0 0 whichdirectional selectioncould act. Gilbert (2002) (b) 15 0.6 experimentally establishedhigh clonal variation in thepro- pensityto produce mictic femalesin B.calyciflorus whereas Go´mez& Carvalho (2000) have usedmicrosatellite analy- 10 0.4

o sisto reveal ‘anunexpectedly high numberof genotypes ’ i t a 1

r ´ _ in afield population of B.plicatilis . Gomez& Carvalho

l c

0.2 i m 5 t (2000) also detecteda reductionof genotypic diversity of

c s i

u this population at theend of its parthenogeneticphase m n

o r i

o revealing theeffects of clonal selection.Similar dynamics

h 0

0 1 c _ l a have beenfound for other cyclical parthenogens(e.g. r (c) m B 15 0.6 Daphnia;Carvalho &Crisp 1987). a e l l l a e Although ourfindings are derivedfrom anartificial and r m o e l

f tightly controlledlaboratory system,they may beof great 10 0.4 h C

relevance for understandingthe dynamics of rotifers and 8 0

1 other cyclical parthenogensin thewild. The factthat only 5 0.2 amictic reproductioncontributes to population growth, a key featureof the chemostat system by design,is also true 0 0 at timesfor natural populations in lakes or temporary bod- iesof water wherefavourable andunfavourable conditions (d) 0.6 40 alternate seasonally.Sexual reproductionof both mono- 30 gonontrotifers andcladocerans is coupledto the pro- 0.4 ductionof diapausing eggs that mustundergo a period of 20 dormancy beforethey may rejointhe active population. 0.2 Dormancy typically lastsat least several months(but may 10 last muchlonger) andthus exceeds by far theaverage gen- eration time ofparthenogenetically reproducing plankton 0 0 populations (usually measuredin days).Therefore, mictic 0 5 10 15 20 femalesin thewild —justlike their counterpartsin the days chemostats—will have zerofitness as participants in the ‘real time’ population dynamics.Selection against clones Figure 6. Dynamicspredicted byfour different versions of exhibiting ahigh propensity for mixis shouldbe strong our model. (a)Full (QT)model withmixis and selection during thegrowing season.With thestart ofanewgrow- againstmixis. ( b and c)Models withmixis but no selection ing season,however, genetic variance becomesreinstated againstmixis. ( b)Simulation withthe same parameter values by theemergence of new,sexually recombinedclones that asin theQT model ( « = 0.033 033; a = 0.072 51 ml per wentinto diapause in previous seasons.As a result,rapid female). (c)Best fit of theexperimental datato themodel without selection ( « = 0.0258; a = 0.075 13 ml per female). natural selectionagainst mixis may act in natural popu- (d)Model (F2K, see text) without mixis (and without lations over short,seasonal periods in muchthe same way selection). Thicksolid lines, Brachionus calyciflorus females; asin thechemostat system. If so,plankton ecologiststry- dashed lines, Chlorella vulgaris ;thin solid lines, mictic ratio p ing tocapture the seasonal community dynamicsin alake (model). or pond,but considering solely demographic parameters andtrophic relationships (asis currently common practice) may notsucceed because they neglectthe evol- parsimonious explanation. Wehave shownthat ourown utionary dimensionof the process. experimental data andmodelling resultsare indeedcon- sistentwith rapid selectionagainst Brachionus clones that M.Boraas and C.Kearns provided advice on chemostatset- are proneto reproduce sexually. Directional selectionof up. R.Babcock, A.Holmes and A.Katholos helped sample aQThasbeen illustrated by ‘climbing upan adaptive hill ’ and maintain thechemostats. Thisstudy wassupported bya grant from theAndrew W.Mellon Foundation to S.P.E. and ofincreasing fitness,gradually approaching atrait value N.G.H. that maximizes fitness(e.g. Futuyma 1998; Orr 2000). The rate ofchange ofthe trait decreasesas the trait approaches its optimal value, andbecomes zero when the REFERENCES optimal value is reachedand selection becomes stabilizing. Aparici, E.,Carmona, M.J.&Serra, M.2001 Variability for The observedlong-term change ofthe mean propensity mixis initiation in . Hydrobiologia 446/447, for mixis in ourcultures (figure 1) isconsistent with direc- 45–50.

Proc.R. Soc.Lond. B (2003) 1022G. F.Fussmann andothers Evolution andplankton dynamics

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