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An integrodifference model for biological invasions in a periodically fragmented environment

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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.

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Authors and Affiliations

  1. Faculty of Culture and Information Science, Doshisha University, 610-0321, Kyotanabe, Japan

    Kohkichi Kawasaki & Nakako Shigesada

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  1. Kohkichi Kawasaki
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  2. Nakako Shigesada
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Correspondence to Kohkichi Kawasaki.

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Kawasaki, K., Shigesada, N. An integrodifference model for biological invasions in a periodically fragmented environment. Japan J. Indust. Appl. Math. 24, 3–15 (2007). https://doi.org/10.1007/BF03167504

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  • DOI: https://doi.org/10.1007/BF03167504

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