Integrodifference models for persistence in fragmented habitats
type: Item
instance of: scholarly article
title: Integrodifference models for persistence in fragmented habitats
zbMATH Open document ID: 0923.92031
DOI: 10.1007/BF02459473
author: R. W. Van Kirk
author: M. A. Lewis
published in: Bulletin of Mathematical Biology
publication date: 1999-05-05T00:00:00Z
review text: The authors study a nonlinear, discrete time, integro-difference equation as a model of population dynamics in which population growth and dispersal phases are separated in time. The model is assumed to have a dispersal kernel of compact support since the authors are particularly interested in patch fragmentation and boundary effects. Mathematically, they study the existence, uniqueness and stability of equilibrium solutions and relate their results to conclusions concerning how population ``persistence'' (i.e., survivability in an equilibrium sense) depends on spatial scales of dispersal distances and habitat sizes. A bifurcation result is proved for a general model equation using the classical theory of integral operators. Selected examples are further studied using computer explorations. They conclude that ``when organisms tend to disperse only a short distance, population persistence is dominated by local conditions in high quality patches, but when dispersal distance is relatively large, poor quality habitat exerts a greater influence''.
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 45P05
Mathematics Subject Classification ID: 45M99
zbMATH DE Number: 1038953
reviewed by: J. M. Cushing
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02459473
OpenAlex ID: W4234353633
description: scientific article; zbMATH DE number 1038953