Brucellosis, botflies, and brainworms: the impact of edge habitats on pathogen transmission and species extinction |
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Authors: | Robert Stephen Cantrell Chris Cosner William F Faganantrell |
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Institution: | (1) Department of Mathematics and Computer Science, University of Miami, Coral Gables, FL 33124, USA. e-mail: rsc@math.miami.edu, US;(2) Department of Biology, Arizona State University, P.O. Box 871501, Tempe, AZ 85287-1501, USA. e-mail: bfagan@asu.edu, US |
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Abstract: | Ecological interactions between species that prefer different habitat types but come into contact in edge regions at the
interfaces between habitat types are modeled via reaction-diffusion systems. The primary sort of interaction described by
the models is competition mediated by pathogen transmission. The models are somewhat novel because the spatial domains for
the variables describing the population densities of the interacting species overlap but do not coincide. Conditions implying
coexistence of the two species or the extinction of one species are derived. The conditions involve the principal eigenvalues
of elliptic operators arising from linearizations of the model system around equilibria with only one species present. The
conditions for persistence or extinction are made explicit in terms of the parameters of the system and the geometry of the
underlying spatial domains via estimates of the principal eigenvalues. The implications of the models with respect to conservation
and refuge design are discussed.
Received: 10 June 1999 / Revised version: 7 July 2000 / Published online: 20 December 2000 |
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Keywords: | : Reaction-diffusion – Lotka-Votterra – Habitat edges – Principal eigenvalues – Pathogen mediated competition – Persistence – Permanence – Extinction |
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