Evol Ecol Res 11: 227-251 (2009)     Full PDF if your library subscribes.

On evolutionary stability in predator–prey models with fast behavioural dynamics

Vlastimil Křivan1 and Ross Cressman2

1Department of Theoretical Ecology, Institute of Entomology, Academy of Sciences of the Czech Republic and Department of Mathematics and Biomathematics, Faculty of Science, University of South Bohemia, České Budějovice, Czech Republic and 2Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada

Correspondence: V. Křivan, Department of Mathematics and Biomathematics, Faculty of Science, University of South Bohemia, Branišovská 31, 370 05 České Budějovice, Czech Republic.
e-mail: vlastimil.krivan@gmail.com


Question: Does optimality in predator–prey models with plastic traits evolving on a fast time-scale imply evolutionary stability?

Mathematical methods: Predator–prey models of population growth described by differential equations with controls and feedback regulation. G-function.

Key assumptions: Plastic responses of organisms to changes in environment are adaptive in the sense that they maximize individual fitness. Population dynamics are deterministic and described by the Lotka-Volterra type dynamics.

Predictions: Adaptive plastic responses do not necessarily lead to evolutionary stability. Mutants with a different strategy can invade a monomorphic resident population, but they cannot replace residents.

Keywords: adaptive foraging, evolutionarily stable strategies, G-function, game theory, ideal free distribution, population dynamics, predator–prey games.

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