Japan Journal of Industrial and Applied Mathematics

An Integrodifference Model for Biological Invasions in a Periodically Fragmented Environment

Kohkichi Kawasaki and Nakako Shigesada

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Abstract

An integrodifference model that describes the spread of invading species on a periodically fragmented environment is analyzed to derive an asymptotic speed of range expansion. We consider the case that the redistribution kernel is given by an exponentially damping function and the population growth is subject to a Ricker function in which the intrinsic growth rate is specified by a spatially periodic step-function. We first derive a condition for successful invasion of a small propagule, and then provide a mathematical formula for the rate of spread. Based on the speeds calculated from the formula for various combinations of parameter values, we discuss how the habitat fragmentation influences the invasion speed. The speeds are also compared with the corresponding speeds when the dispersal kernel is replaced by a Gaussian.

Article information

Source
Japan J. Indust. Appl. Math., Volume 24, Number 1 (2007), 3-15.

Dates
First available in Project Euclid: 11 December 2007

Permanent link to this document
https://projecteuclid.org/euclid.jjiam/1197390050

Mathematical Reviews number (MathSciNet)
MR2312291

Zentralblatt MATH identifier
1116.92066

Keywords
integrodifference model periodically fragmented environment traveling periodic wave biological invasion

Citation

Kawasaki, Kohkichi; Shigesada, Nakako. An Integrodifference Model for Biological Invasions in a Periodically Fragmented Environment. Japan J. Indust. Appl. Math. 24 (2007), no. 1, 3--15. https://projecteuclid.org/euclid.jjiam/1197390050


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