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

Theodore E.  Galanthay

doi:10.3934/dcdsb.2015.20.1625

Article Contents

2015, Volume 20, Issue 6: 1625-1638. Doi: 10.3934/dcdsb.2015.20.1625

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

Theodore E. Galanthay^1,

1.
212A Williams Hall, 953 Danby Road, Ithaca, NY 14850

Received: November 2013

Revised: April 2014

Published: August 2015

Abstract / Introduction Related Papers Cited by

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.

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Mathematics Subject Classification: Primary: 34D23; Secondary: 92D25.

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