Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

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

Pages: 1625 - 1638, Volume 20, Issue 6, August 2015      doi:10.3934/dcdsb.2015.20.1625

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Theodore E. Galanthay - 212A Williams Hall, 953 Danby Road, Ithaca, NY 14850, United States (email)

Abstract: 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.

Keywords:  Dispersal, optimal dispersal strategy, cost of dispersal, global stability, evolutionarily stable strategy.
Mathematics Subject Classification:  Primary: 34D23; Secondary: 92D25.

Received: November 2013;      Revised: April 2014;      Available Online: June 2015.