The Optimal Clutch Size of Insects When Many Females Oviposit Per Patch Author(S): Anthony R

The Optimal Clutch Size of Insects When Many Females Oviposit Per Patch Author(s): Anthony R. Ives Reviewed work(s): Source: The American Naturalist, Vol. 133, No. 5 (May, 1989), pp. 671-687 Published by: The University of Chicago Press for The American Society of Naturalists Stable URL: http://www.jstor.org/stable/2462074 . Accessed: 15/02/2012 07:21 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. The University of Chicago Press and The American Society of Naturalists are collaborating with JSTOR to digitize, preserve and extend access to The American Naturalist. http://www.jstor.org Vol. 133, No. 5 The American Naturalist May 1989 THE OPTIMAL CLUTCH SIZE OF INSECTS WHEN MANY FEMALES OVIPOSIT PER PATCH ANTHONY R. IVES* Departmentof Biology, PrincetonUniversity, Princeton, New Jersey08544 SubmittedMay 4, 1987; Revised July25, 1988; Accepted August 2, 1988 Manyinsects lay clutcheson discretepatches of larval food. Examples include parasitoidwasps ovipositing on insecthosts, flies on fallenfruit, and butterflies on theleaves of isolatedhost plants. For theseinsects, determining the number of eggsthat a femaleshould lay per patchis akinto an optimal-foragingproblem: how shoulda femaledistribute her eggs among patches to optimizeher lifetime fitness?When more than one femalelays eggson thesame patch, the best clutch size dependson theclutch sizes adoptedby all of theother females in a popula- tion.One way of examiningthis type of group situation is to applythe idea of an evolutionarilystable strategy (ESS). Whenadopted by all individualsin a popula- tion,an ESS cannotbe betteredby an individualemploying a differentstrategy (MaynardSmith and Price 1973; Oster and Wilson1978). Parker and Begon (1986) presenteda modelto analyzethe effectsof differentenvironmental and pheno- typicparameters on theoptimal clutch size and eggsize forinsects whose larvae competeon discreteresource patches. One oftheir results repeats a conclusionof Parkerand Courtney(1984) and Skinner(1985): as theaverage number of females ovipositingper patch increases, the evolutionarily stable clutch size decreases.In derivingthis result, these authors considered only a fewof the possible functions describingcompetition among larvae in a patch.For different,but also realistic, curves describinglarval competition,the evolutionarilystable clutchsize in- creasesas theaverage number of femalesovipositing per patchincreases. Here I discusshow theevolutionarily stable clutch size of insectsdepends on the type of competitionamong larvae withindiscrete patches. This requires examiningdifferent functions that describe larval competition. I first show which typesof larvalcompetition promote increases or decreasesin theevolutionarily stableclutch size withincreasing numbers of females ovipositing per patch. This discussionuses a simplemodel governing female oviposition behavior. Second, I extendthe simple model to ask whetherthe conclusions it generatesare qualita- tivelyaltered by complexitiesthat affect oviposition in nature.Third, I construct larval-competitionfunctions based on assumptionsabout the feeding behavior of * Present address: Departmentof Zoology, NJ-15,University of Washington,Seattle, Washington 98195. Am. Nat. 1989. Vol. 133, pp. 671-687. ? 1989 by The Universityof Chicago. 0003-0147/89/3305-0008$02.00.All rightsreserved. 672 THE AMERICAN NATURALIST Z <,, 25- z 20- - U. '2 15] .0E L) o 5 1 1'5 20 25 Numberof Eggs, N FIG. 1.-The combinedfitness of all larvae, Ns(N), as a functionof the numberof eggs laid on a patch, N. Functionsused fors(N) are givenin equation (1): dottedline, s1(N) withP,u = 4.0 andet = 0.05; dashedline, s2(N) with[L2 = 5.44and r = 0. 1; solidline, s3(N) withp3 = 6.32, a = 1/3o,and b = 4. larvae withinpatches. This analysis shows that small, quantitativedifferences in larval feedingbehavior can produce competitionfunctions that yield opposite predictionsabout how the evolutionarilystable clutch size varies withincreasing numbersof femalesovipositing per patch. This warns againstinferring the behavior of the evolutionarilystable clutch size fromonly qualitative knowledge of larval feedingbehavior. Fourth, I give examples fromthe literatureof insects showing diverse patternsof larval competitionwithin patches. These examples include larval-competitioncurves that promoteeither increases or decreases in the evolutionarilystable clutch size as more females oviposit per patch. A SIMPLE MODEL FOR THE EVOLUTIONARILY STABLE CLUTCH SIZE Parkerand Begon (1986) analyzed manyof the factorsthat influence clutch size in insects. To examinejust one of these factors,I presenta simple,special case of the model given by Parkerand Begon (see also the similarmodels in Parkerand Courtney1984; Skinner1985). Assume thatN eggs are ovipositedby one or more femaleson a discretepatch of larvalfood. Also, assume competitionamong larvae such that the per capita fitness(survival times the adult fecundityof females or timesthe matingsuccess of males) of the larvae, s(N), is a decreasingfunction of N. The formsof s(N) used here are IRI(I - tN) N < 1I/o s1(N) = a>0, RI >0 0O N2 I/otl s2(N) =p2e r > 0, R2 > ( s3(N) = ,u3(1 + aN)-b a > 0, b > 1, R3 > 0. For each of these larval-competitioncurves, figure1 gives a graph of the combined fitnessof all larvae survivingper patch, Ns(N), as a functionof the number OPTIMAL CLUTCH SIZE OF INSECTS 673 of eggs laid. The curve sl(N) is thatused by Parkerand Begon (1986) and implies severe competitionamong larvae. Curves s2(N) and s3(N) are taken fromthe ecological literatureas popular descriptionsof competition(see May 1981). In s3(N), larval fitnessdrops more rapidlywith increasing N whenthe parameterb is large,implying severe competitionat highdensities. As b approaches infinityand a approaches zero, curve s3(N) converges to s2(N) as a limitingcase. For all curves, ,u scales the overall larval fitnessand is set to give each curve the same maximumvalue of Ns(N). To calculate the evolutionarilystable clutchsize forthe simplestpossible case, assume thatthe numberof eggs a female lays on one patch has no effecton the numbershe can lay on otherpatches. Therefore,the evolutionarilystable clutch size fora given female depends only on the costs and benefitsassociated witha single oviposition episode. This is the same assumption used to calculate the "Lack optimalclutch size" when only one femaleoviposits per patch (Charnov and Skinner1984; Godfray1986). Furtherassume thatF femalesoviposit on each patch. If the fates of the eggs and resultinglarvae fromall femalesare identical, thenthe fitnessof a female layingn eggs per clutchwhen all otherfemales lay n' eggs per clutch, w(nIn,),is given by w(n|n,) = ns[n + (F - 1)n]. (2) The evolutionarilystable clutchsize, n*, is the solutionof the equation (Oster and Wilson 1978; Parker and Begon 1986) awl/nln=h = 0 , (3a) providedthat a2W 0n.2n n* ? (3b) For each larval-competitioncurve, the evolutionarilystable clutch sizes are n*= 1/t(F + 1), n*= 1/r, (4) n*= 1/a(b-F) forF<b. As described by Parkerand Begon (1986), n* decreases as morefemales oviposit per patch. However, n* is unaffectedby the numberof females ovipositingper patch. This result was obtained in a slightlydifferent manner by Smith and Lessells (1985) when they applied a larval-competitioncurve like s2(N) to a differentmodel forclutch size. Finally, n* increases withthe numberof females ovipositingper patch, approachinginfinity as F approaches b. When F is equal to or greaterthan b, there is no evolutionarilystable clutch size under the simple assumptionsof this model. However, the next section shows thatmore-realistic assumptionsproduce models forwhich the evolutionarilystable clutch size does not go to infinitywhen larval competitionhas the formof s3(N). The change in the evolutionarilystable clutch size withincreasing numbers of females ovipositingper patch can be explained as follows. The evolutionarily stable clutchsize is determinedby allowingone femaleto optimizethe size of her clutch (n in eq. 2), assuming that the clutch size of all otherfemales is fixedat 674 THE AMERICAN NATURALIST 5 U) U) 4 0. 4 0 5 10 15 20 25 Clutch Size, n FIG. 2.-The combined fitnessof the larvae froma single female when she oviposits a clutch size n on a patch already containing20 eggs laid by two otherfemales. Dashed line, s2(N); solid line, s3(N); parametervalues as in figure1. Survivalfor the thirdfemale is zero forsl(N) and is thereforenot shown. some value n. If the optimalclutch size forthe single,deviating female is the same as the clutchsize assumed forthe otherfemales, then n' is theevolutionarily stable clutch size; any female that deviates fromthe ESS suffersa suboptimalclutch size. To see the effectof the threedifferent larval-competition functions given in figure1, consider the case in which three females oviposit on the same patch. Assume thattwo of thefemales each oviposit 10 eggs; 10 eggs is the optimalclutch size when females oviposit singlyper patch, because n = 10 gives the maximum value of ns(n) for all three larval-competitioncurves. The fitnessof the third female,depending on her clutch

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