A Comparison of Dispersal Strategies for Survival of Spatially Heterogeneous Populations

Authors:
  • DHDouglas P. Hardin
    Douglas P. Hardin
  • PTPeter Takáč
    Peter Takáč
  • GWG. F. Webb
    G. F. Webb
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Abstract
This paper analyzes a discrete-time model of populations that grow and disperse in separate phases. The growth phase is a nonlinear process that allows for the effects of local crowding. The dispersion phase is a linear process that distributes the population throughout its spatial habitat. This study quantifies the issues of survival and extinction, the existence and stability of nontrivial steady states, and the comparison of various dispersion strategies. The results show that all of these issues are tied to the global nature of various model parameters. The extreme strategies of staying-in-place and going-everywhere-uniformly are compared numerically to diffusion strategies in various contexts. The mathematical analysis of our model is approached from a functional analysis and an operator theory point of view. Recent results from the theory of positive operators in Banach lattices are used.

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