Evolutionarily stable strategies in stable and periodically fluctuating populations: The Rosenzweig–MacArthur predator–prey model
Katrin Grunert, Helge Holden, Espen R. Jakobsen, Nils Chr. Stenseth
Abstract
Significance Many evolutionary studies of ecological systems assume, explicitly or implicitly, ecologically stable population dynamics. Ecological analyses typically assume, on the other hand, no evolution. We study a model (using predator–prey dynamics as an example) combining ecology and evolution within the same framework. For this purpose, we use the evolutionarily stable strategies (ESSs) framework, emphasizing that evolutionary change, in general, will occur as a result of mutant strategies being able to invade a population. The significance of our contribution is to derive mathematical conditions for the existence of an ESS in a periodically limit-cycle ecological system.