A Mathematical Model for Invasion Range of Population Dispersion Through a Patchy Environment
 Hiromi Seno,
 Shinko Koshiba
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We focus on the question of how the dispersion of an invading population is affected by the spatial distribution of patches that have resource available for the population’s settlement and reproduction. We have developed and analyzed a mathematical model with a simple stochastic process. The patches are grouped into three classes – free, occupied and abandoned – depending on the state of the patch used by the population. We especially consider the range expanded by invaded patches, the invaded range R, assuming a certain generalized relation between R and the total number of invaded patches k, making use of an index, a sort of fractal dimension, to characterize the spatial distribution of invaded patches. We show that the expected velocity is significantly affected by the nature of spatial distribution of resource patches, and is temporally variable. When the invading population finally becomes extinct at a certain moment, the terminal size of the invaded range at that the moment is closely related to the nature of the spatial distribution of resource patches, which is explicitly demonstrated by our analysis.
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 Title
 A Mathematical Model for Invasion Range of Population Dispersion Through a Patchy Environment
 Journal

Biological Invasions
Volume 7, Issue 5 , pp 757770
 Cover Date
 20050901
 DOI
 10.1007/s1053000552110
 Print ISSN
 13873547
 Online ISSN
 15731464
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 fractal dimension
 invasion
 metapopulation
 patch
 stochastic process
 velocity
 Authors

 Hiromi Seno ^{(1)}
 Shinko Koshiba ^{(2)}
 Author Affiliations

 1. Department of Mathematical and Life Sciences, Graduate School of Science, Hiroshima University, 7398526, Higashihiroshima, Japan
 2. Department of Information and Computer Sciences, Faculty of Science, Nara Women’s University, Nara, 6308506, Japan