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February 2007 An Integrodifference Model for Biological Invasions in a Periodically Fragmented Environment
Kohkichi Kawasaki, Nakako Shigesada
Japan J. Indust. Appl. Math. 24(1): 3-15 (February 2007).

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.

Citation

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Kohkichi Kawasaki. Nakako Shigesada. "An Integrodifference Model for Biological Invasions in a Periodically Fragmented Environment." Japan J. Indust. Appl. Math. 24 (1) 3 - 15, February 2007.

Information

Published: February 2007
First available in Project Euclid: 11 December 2007

zbMATH: 1116.92066
MathSciNet: MR2312291

Rights: Copyright © 2007 The Japan Society for Industrial and Applied Mathematics

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Vol.24 • No. 1 • February 2007
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