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# Mathematical study of the effects of travel costs on optimal dispersal in a two-patch model

• The theoretical dispersal of organisms has been widely studied. It is well known for single species dispersal in a spatially heterogeneous and temporally constant environment that balanced dispersal'' is an evolutionarily stable strategy [36,10]. This assumes that organisms do not pay a cost to move from one part of the environment to another. We begin this paper by proving that the optimal strategy for organisms constrained by perceptual limitations, described by [19], is evolutionarily stable. Then, we extend this idea of optimal dispersal to a situation where constrained organisms pay a cost to move between two patches in a heterogeneous environment. For moderate travel costs, we find a convergent stable strategy that suggests an extension of the balanced dispersal concept. Furthermore, we show for high costs that the best strategy is to ignore information about the environment.
Mathematics Subject Classification: Primary: 34D23; Secondary: 92D25.

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