The critical domain size of stochastic population models

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• 作者：Jody R. Reimer ; Michael B. Bonsall ; Philip K. Maini
• 关键词：Critical domain size ; Stochasticity ; Individual ; based model ; Integrodifference equation ; Branching processes
• 刊名：Journal of Mathematical Biology
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：74
• 期：3
• 页码：755-782
• 全文大小：824KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematical and Computational Biology; Applications of Mathematics;
• 出版者：Springer Berlin Heidelberg
• ISSN：1432-1416
• 卷排序：74

文摘

Identifying the critical domain size necessary for a population to persist is an important question in ecology. Both demographic and environmental stochasticity impact a population’s ability to persist. Here we explore ways of including this variability. We study populations with distinct dispersal and sedentary stages, which have traditionally been modelled using a deterministic integrodifference equation (IDE) framework. Individual-based models (IBMs) are the most intuitive stochastic analogues to IDEs but yield few analytic insights. We explore two alternate approaches; one is a scaling up to the population level using the Central Limit Theorem, and the other a variation on both Galton–Watson branching processes and branching processes in random environments. These branching process models closely approximate the IBM and yield insight into the factors determining the critical domain size for a given population subject to stochasticity.