Talk abstract:

Biological Invasions into Fragmented Environments: Reaction-diffusion Models

Nanako Shigesada
Department of Information and Computer Sciences
Nara Women's University
Kita-Uoya Nishi-machi
630-8506, Nara
Japan
sigesada@ics.nara-wu.ac.jp

Range expansions of invading species in homogeneous environments have been extensively studied, since the pioneer works by Fisher and Skellam. Here, I focus on range expansion in heterogeneous environments that are generated by segmenting an original favorable habitat into a regularly striped or crisscrossed pattern. When the invading species enters an unfavorable habitat, it will be able to expand its range only if it successfully survives in that habitat and reaches a favorable one lying ahead. If unfavorable habitats dominate, the population may become extinct without expanding the range. To deal with range expansion in such fragmented environments, we modify Fisher's model by assuming that the intrinsic growth rate and diffusion coefficient vary depending on habitat properties. The model is analyzed to examine how the spread of organisms is influenced by the patterns of habitat fragmentation, and which type of fragmentation is more favorable for species survival.

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1998-1999 Mathematics in Biology