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Fitness minimization and dynamic instability as a consequence of predator-prey coevolution

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Summary

We analyse dynamic models of the coevolution of continuous traits that determine the capture rate of a prey species by a predator. The goal of the analysis is to determine conditions when the coevolutionary dynamics will be unstable and will generate population cycles. We use a simplified model of the evolutionary dynamics of quantitative traits in which the rate of change of the mean trait value is proportional to the rate of increase of individual fitness with trait value. Traits that increase ability in the predatory interaction are assumed to have negative effects on another component of fitness. We concentrate on the role of equilibrial fitness minima in producing cycles. In this case, the mean trait of a rapidly evolving species minimizes its fitness and it is ‘chased’ around this equilibrium by adaptive evolution in the other species. Such cases appear to be most likely if the capture rate of prey by predators is maximal when predator and prey phenotypes match each other. They are possible, but less likely when traits in each species determine a one-dimensional axis of ability related to the interaction. Population dynamics often increase the range of parameter values for which cycles occur, relative to purely evolutionary models, although strong prey self-regulation may stabilize an evolutionarily unstable subsystem.

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Author notes

  1. Peter A. Abrams

    Present address: Department of Zoology, University of Maryland, 20742, College Park, MD, USA

Authors and Affiliations

  1. Department of Ecology, Evolution and Behavior, University of Minnesota, 1987 Upper Buford Circle, 55108, St Paul, MN, USA

    Peter A. Abrams

  2. Department of Biology, Faculty of Science, Kyushu University, Higashi-ku, 812-81, Fukuoka, Japan

    Hiroyuki Matsuda

Authors
  1. Peter A. Abrams
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  2. Hiroyuki Matsuda
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Abrams, P.A., Matsuda, H. Fitness minimization and dynamic instability as a consequence of predator-prey coevolution. Evol Ecol 10, 167–186 (1996). https://doi.org/10.1007/BF01241783

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