Volume 20, Number 1, Spring 2012
EVOLUTIONARY STABILITY OF IDEAL FREE
Dedicated to Herb Freedman on the occasion of his 70th birthday
DISPERSAL STRATEGIES: A NONLOCAL
ROBERT STEPHEN CANTRELL, CHRIS COSNER,
YUAN LOU AND DANIEL RYAN
Abstract. An important question in the study of the evolution of dispersal is what kind of dispersal strategies are evolutionary stable. This work is motivated by recent work of Cosner et al. , in which they introduced a class of ideal free dispersal kernels and found conditions suggesting that they determine evolutionarily stable dispersal strategies. The goals of this paper are to introduce a more general class of ideal free dispersal kernels and further to show that such ideal free dispersal strategies are indeed evolutionary stable. Our work also extends some recent work on the evolutionary stability of ideal free dispersal for reaction-diffusion equations and patch models to nonlocal dispersal models.