Homogenization of a Directed Dispersal Model for Animal Movement in a Heterogeneous Environment

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• 作者：Brian P. Yurk
• 关键词：Spatial heterogeneity ; Advection–diffusion–reaction ; Directed movement ; Homogenization ; Diffusion approximation ; Invasion speed
• 刊名：Bulletin of Mathematical Biology
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：78
• 期：10
• 页码：2034-2056
• 全文大小：818 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematical Biology
  
• 出版者：Springer New York
• ISSN：1522-9602
• 卷排序：78

文摘

The dispersal patterns of animals moving through heterogeneous environments have important ecological and epidemiological consequences. In this work, we apply the method of homogenization to analyze an advection–diffusion (AD) model of directed movement in a one-dimensional environment in which the scale of the heterogeneity is small relative to the spatial scale of interest. We show that the large (slow) scale behavior is described by a constant-coefficient diffusion equation under certain assumptions about the fast-scale advection velocity, and we determine a formula for the slow-scale diffusion coefficient in terms of the fast-scale parameters. We extend the homogenization result to predict invasion speeds for an advection–diffusion–reaction (ADR) model with directed dispersal. For periodic environments, the homogenization approximation of the solution of the AD model compares favorably with numerical simulations. Invasion speed approximations for the ADR model also compare favorably with numerical simulations when the spatial period is sufficiently small.