Abstract
•We find a dispersal strategy that will produce an ideal free distribution in a logistic reaction-diffusion-advection model for population dynamics with dispersal in an environment that is variable in space and periodic in time, where the total amount of a resource in the environment is fixed but the location of the resource can move periodically.•We show that in the class of strategies we consider the one that can produce an ideal free distribution is both evolutionarily stable and is a neighborhood invader strategy with respect to strategies that do not produce an ideal free distribution.•In temporally periodic and spatially varying environments, achieving an ideal free distribution requires the use of nonlocal information. This is in contrast with the case of environments that are variable in space but constant in time, where an ideal free distribution can be achieved by using purely local information.
Roughly speaking, a population is said to have an ideal free distribution on a spatial region if all of its members can and do locate themselves in a way that optimizes their fitness, allowing for the effects of crowding. Dispersal strategies that can lead to ideal free distributions of populations using them have been shown to exist and to be evolutionarily stable in a number of modeling contexts in the case of habitats that vary in space but not in time. Those modeling contexts include reaction-diffusion-advection models and the analogous models using discrete diffusion or nonlocal dispersal described by integro-differential equations. Furthermore, in the case of reaction-diffusion-advection models and their nonlocal analogues, there are strategies that allow populations to achieve an ideal free distribution by using only local information about environmental quality and/or gradients. We show that in the context of reaction-diffusion-advection models for time-periodic environments with spatially varying resource levels, where the total level of resources in an environment remains fixed but its location varies seasonally, there are strategies that allow populations to achieve an ideal free distribution. We also show that those strategies are evolutionarily stable. However, achieving an ideal free distribution in a time-periodic environment requires the use of nonlocal information about the environment such as might be derived from experience and memory, social learning, or genetic programming.
