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

ABSTRACT

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.

DOWNLOAD A FREE, FULL PDF COPY
IF you are connected using the IP of a subscribing institution (library, laboratory, etc.)
or through its VPN.

 

        © 2009 Vlastimil Křivan. All EER articles are copyrighted by their authors. All authors endorse, permit and license Evolutionary Ecology Ltd. to grant its subscribing institutions/libraries the copying privileges specified below without additional consideration or payment to them or to Evolutionary Ecology, Ltd. These endorsements, in writing, are on file in the office of Evolutionary Ecology, Ltd. Consult authors for permission to use any portion of their work in derivative works, compilations or to distribute their work in any commercial manner.

       Subscribing institutions/libraries may grant individuals the privilege of making a single copy of an EER article for non-commercial educational or non-commercial research purposes. Subscribing institutions/libraries may also use articles for non-commercial educational purposes by making any number of copies for course packs or course reserve collections. Subscribing institutions/libraries may also loan single copies of articles to non-commercial libraries for educational purposes.

       All copies of abstracts and articles must preserve their copyright notice without modification.