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

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## 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.

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