# Joint evolution of predator body size and prey-size preference

- 202 Downloads
- 22 Citations

## Abstract

We studied the joint evolution of predator body size and prey-size preference based on dynamic energy budget theory. The predators’ demography and their functional response are based on general eco-physiological principles involving the size of both predator and prey. While our model can account for qualitatively different predator types by adjusting parameter values, we mainly focused on ‘true’ predators that kill their prey. The resulting model explains various empirical observations, such as the triangular distribution of predator–prey size combinations, the island rule, and the difference in predator–prey size ratios between filter feeders and raptorial feeders. The model also reveals key factors for the evolution of predator–prey size ratios. Capture mechanisms turned out to have a large effect on this ratio, while prey-size availability and competition for resources only help explain variation in predator size, not variation in predator–prey size ratio. Predation among predators is identified as an important factor for deviations from the optimal predator–prey size ratio.

## Keywords

Body size Prey-size preference Size-dependency Upper triangularity## Notes

### Acknowledgments

T. A. Troost thanks the International Institute for Applied Systems Analysis (IIASA) in Austria for providing the possibility of a three-month stay during which the basis for this paper was laid out, and the Netherlands Organization for Scientific Research (NWO) for financing this stay. The authors are very grateful for the data kindly provided by J. Cohen, S. Pimm, P. Yodzis, and J. Saldaña, previously published in Cohen et al. (1993), and for their approval to use them in Fig. 2. We also would like to thank M. Boer, O. Diekmann, F. Kelpin, and M. Kirkilionis for helpful discussions on DDEs. Furthermore, we would like to thank two anonymous referees for their comments which have considerably improved the paper. U. Dieckmann gratefully acknowledges financial support by the European Marie Curie Research Training Network FishACE (Fisheries-induced Adaptive Changes in Exploited Stocks), funded by the European Communitys Sixth Framework Programme.

## References

- Aljetlawi AA, Sparrevik E, Leonardsson K (2004) Prey-predator size-dependent functional response: derivation and rescaling to the real world. J Anim Ecol 73(2):239–252CrossRefGoogle Scholar
- Alver MO, Alfredsen JA, Olsen Y (2006) An individual-based population model for rotifer (
*Brachionus plicatilis*) cultures. Hydrobiologia 560:93–208CrossRefGoogle Scholar - Benton MJ (2002) Cope’s rule. In: Pagel M (ed) Encyclopedia of evolution. Oxford University Press, Oxford, pp 185–186Google Scholar
- Bergmann C (1847) Über die Verhältnisse der Wärmeökonomie der Thiere zu ihre Grösse. Gött Stud 3:595–708Google Scholar
- Brown JH, Marquet PA, Taper ML (1993) Evolution of body size: consequences of an energetic definition of fitness. Am Nat 142(4):573–584CrossRefPubMedGoogle Scholar
- Case TJ (1978) Endothermy, and parental care in the terrestrial vertebrates. Am Nat 112(987):861–874CrossRefGoogle Scholar
- Cohen JE (1989) Food webs and community structure. In: Roughgarden J, May RM, Levin SA (eds) Perspectives on ecological theory. Princeton University Press, Princeton, pp 181–202Google Scholar
- Cohen JE, Jonsson T, Carpenter SR (2003) Ecological community description using the food web, species abundance, and body size. Proc Natl Acad Sci USA 100(4):1781–1786Google Scholar
- Cohen JE, Newman CM (1985) A stochastic theory of community food webs 1. Models and aggregated data. Proc R Soc Lond B, Biol Sci 224(1237):448–461Google Scholar
- Cohen JE, Pimm SL, Yodzis P, Saldana J (1993) Body sizes of animal predators and animal prey in food webs. J Anim Ecol 62(1):67–78CrossRefGoogle Scholar
- Combes C (2001) Parasitism; the ecology and evolution of intimate interactions. University of Chicago PressGoogle Scholar
- Cope ED (1896) The primary factors of organic evolution. The Open Court Publishing Company, ChicagoGoogle Scholar
- Dieckmann U (1997) Can adaptive dynamics invade? Trends Ecol Evol 12(4):128–131CrossRefGoogle Scholar
- Dieckmann U, Law R (1996) The dynamical theory of coevolution: a derivation from stochastic processes. J Math Biol 34(5–6):579–612PubMedCrossRefGoogle Scholar
- Diekmann O, van Gils SA, Verduyn Lunel SM, Walther H-O (1995) Delay equations: functional-, complex- and nonlinear analysis, Volume 110 of Applied Mathematical Sciences. Springer-Verlag, New YorkGoogle Scholar
- Driver RD (1977) Ordinary and delay differential equations, Volume 20 of Applied Mathematical Sciences. Springer-Verlag, New YorkGoogle Scholar
- Ellis T, Gibson RN (1997) Predation of 0-group flatfishes by 0-group cod: handling times and size-selection. Mar Ecol Prog Ser 149(1–3):83–90CrossRefGoogle Scholar
- Forsman A (1996) Body size and net energy gain in gape-limited predators: a model. J Herpetol 30(3):307–319CrossRefGoogle Scholar
- Geritz SAH, Gyllenberg M, Jacobs FJA, Parvinen K (2002) Invasion dynamics and attractor inheritance. J Math Biol 44(6):548–560PubMedCrossRefGoogle Scholar
- Geritz SAH, Kisdi É, Meszéna G, Metz JAJ (1998) Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree. Evol Ecol 12(1):35–57CrossRefGoogle Scholar
- Geritz SAH, Metz JAJ, Kisdi É, Meszéna G (1997) Dynamics of adaptation and evolutionary branching. Phys Rev Lett 78(10):2024–2027CrossRefGoogle Scholar
- Gittleman JL (1985) Carnivore body size: ecological and taxonomic correlates. Oecologia 67(4):540–554CrossRefGoogle Scholar
- Hansen B, Bjornsen PK, Hansen PJ (1994) The size ratio between planktonic predators and their prey. Limnol Oceanogr 39(2):395–403CrossRefGoogle Scholar
- Husseman JS, Murray DL, Power G, Mack C, Wenger CR, Quigley H (2003) Assessing differential prey selection patterns between two sympatric large carnivores. Oikos 101(3):591–601CrossRefGoogle Scholar
- Karpouzi V, Stergiou KI (2003) The relationships between mouth size and shape and body length for 18 species of marine fishes and their trophic implications. J Fish Biol 62(6):1353–1365CrossRefGoogle Scholar
- Kooi BW, Kooijman SALM (1997) Population dynamics of rotifers in chemostats. Nonlinear Anal Theory Meth Appl 30(3):1687–1698CrossRefGoogle Scholar
- Kooi BW, Kooijman SALM (1999) Discrete event versus continuous approach to reproduction in structured population dynamics. Theor Popul Biol 56(1):91–105PubMedCrossRefGoogle Scholar
- Kooijman SALM (1986) Energy budgets can explain body size relations. J Theor Biol 121:269–282CrossRefGoogle Scholar
- Kooijman SALM (2000) Dynamic energy and mass budgets in biological systems. Cambridge University PressGoogle Scholar
- Kooijman SALM (2001) Quantitative aspects of metabolic organization; a discussion of concepts. Philos Trans R Soc B, Biol Sci 356(1407):331–349CrossRefGoogle Scholar
- Kristiansen JN, Fox T, Nachman G (2000) Does size matter? Maximising nutrient and biomass intake by shoot size selection amongst herbivorous geese. Ardea 88(2):119–125Google Scholar
- Loeuille N, Loreau M (2005) Evolutionary emergence of size-structured food webs. Proc Natl Acad Sci USA 102(16):5761–5766Google Scholar
- Manatunge J, Asaeda T (1998) Optimal foraging as the criteria of prey selection by two centrarchid fishes. Hydrobiologica 391(1–3):223–240Google Scholar
- Mayr E (1956) Geographical character gradients and climatic adaptation. Evolution 10(1):105–108CrossRefGoogle Scholar
- Mayr E (1963) Animal species and evolution. Harvard University Press, Cambridge, MassGoogle Scholar
- Mehner T, Plewa M, Hulsmann S, Worischka S (1998) Gape-size dependent feeding of age-0 perch (
*Perca fluviatilis*) and age-0 zander (*Stizostedion lucioperca*) on daphnia galeata. Arch Hydrobiol 142(2):191–207Google Scholar - Memmott J, Martinez ND, Cohen JE (2000) Predators, parasitoids and pathogens: species richness, trophic generality and body sizes in a natural food web. J Anim Ecol 69(1):1–15CrossRefGoogle Scholar
- Metz JAJ, Nisbet RM, Geritz SAH (1992) How should we define ‘fitness’ for general ecological scenarios? Trends Ecol Evol 7(6):198–202CrossRefGoogle Scholar
- Metz JAJ, Geritz SAH, Meszéna G, Jacobs FJA, van Heerwaarden JS (1996) Adaptive dynamics: A geometrical study of the consequences of nearly faithful reproduction. In: van Strien SJ, Verduyn Lunel SM (eds) Stochastic and spatial structures of dynamical systems. KNAW Verhandelingen, Amsterdam, pp 183–231Google Scholar
- Neubert MG, Blumenshine SC, Duplisea DE, Jonsson T, Rashleigh B (2000) Body size and food web structure: testing the equiprobability assumption of the cascade model. Oecologia 123(2):241–251CrossRefGoogle Scholar
- Peters RH (1983) The ecological implications of body size. Cambridge University Press, New YorkGoogle Scholar
- Rincon PA, Loboncervia J (1995) Use of an encounter model to predict size-selective predation by a stream-dwelling cyprinid. Freshw Biol 33(2):181–191CrossRefGoogle Scholar
- Rytkonen S, Kuokkanen P, Hukkanen M, Huhtala K (1998). Prey selection by sparrowhawks
*Accipiter nisus*and characteristics of vulnerable prey. Ornis Fenn 75(2):77–87Google Scholar - Svensson JE (1997) Fish predation on
*Eudiaptomus gracilis*in relation to clutch size, body size, and sex: A field experiment. Hydrobiologica 344(1–3):155–161CrossRefGoogle Scholar - Turesson H, Persson A, Bronmark C (2002) Prey size selection in piscivorous pikeperch (
*Stizostedion lucioperca*) includes active prey choice. Ecol Freshwa Fish 11(4):223–233CrossRefGoogle Scholar - Van Valen L (1973). Pattern and the balance of nature. Evol Theory 1:31–49Google Scholar
- Vezina AF (1985) Empirical relationships between predator and prey size among terrestrial vertebrate predators. Oecologia 67(4):555–565CrossRefGoogle Scholar
- Warren PH, Lawton JH (1987) Invertebrate predator-prey body size relationships: an explanation for upper triangular food webs and patterns in food web structure?. Oecologia 74(2):231–235CrossRefGoogle Scholar
- Williams RJ, Martinez ND (2000) Simple rules yield complex food webs. Nature 404(6774):180–183PubMedCrossRefGoogle Scholar
- Yodzis P, Innes S (1992) Body size and consumer-resource dynamics. Am Nat 139(6):1151–1175CrossRefGoogle Scholar