Maciel et al (2019) Evolutionarily stable movement strategies in
reaction–diffusion models with edge behavior. J Math Biol DOI 10.1007/s00285-019-01339-2
Many types of organisms disperse through heterogeneous environments as
part of their life histories. For various models of dispersal, including
reaction-advection-diffusion models in continuously varying environments, it has been shown by pairwise invasibility analysis that dispersal strategies which generate an ideal free distribution are evolutionarily steady strategies (ESS, also known as evolutionarily stable strategies) and are neighborhood invader strategies (NIS). That is, populations using such strategies can both invade and resist invasion by populations using strategies that do not produce an ideal free distribution. (The ideal free distribution arises from the assumption that organisms inhabiting heterogeneous environments should move to maximize their fitness, which allows a mathematical characterization in terms of fitness equalization.) Classical reaction diffusion models assume that landscapes vary continuously. Landscape ecologists consider landscapes as mosaics of
patches where individuals can make movement decisions at sharp interfaces between patches of different quality. We use a recent formulation of reaction-diffusion systems in patchy landscapes to study dispersal strategies by using methods inspired by evolutionary game theory and adaptive dynamics. Specifically, we use a version of pairwise
invasibility analysis to show that in patchy environments, the behavioral
strategy for movement at boundaries between different patch types that
generates an ideal free distribution is both globally evolutionarily
steady (ESS) and is a global neighborhood invader strategy (NIS).