Abstract
In this article we continue an examination of the consequences of habitat degradation on species interactions begun by Cantrell, Cosner and Fagan in Cantrell et al., J. Math. Biol. 37, 491–533 (1998). In Cantrell et al., J. Math. Biol. 37, 491–533 (1998), two competing species were thought to inhabit a pristine patch of habitat surrounded by ‘‘matrix’’ habitat whose level of degradation is variable. The dynamics of the species interactions was modeled by diffusive Lotka–Volterra competition equations in the patch supplemented by Robin boundary conditions on the interface between the pristine patch and the matrix habitat. Habitat degradation was incorporated into the model via a tunable hostility parameter in the boundary conditions. Analysis of the model showed that it is possible for a species to be competitively dominant in the pristine patch when the surrounding environs are only mildly unfavorable but to lose this advantage and be competitively inferior in the patch when matrix hostility is severe. In this article we address the question of just how delicately competitive advantage within the pristine patch depends on the level of degradation in the environs surrounding the pristine patch. We show that it is indeed possible for competitive advantage to reverse more than once as the level of degradation in the matrix habitat increases and also examine the effects thereof on the number and nature of equilibria through a detailed bifurcation analysis.
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References
M. S. Berger (1977) Nonlinearity and Functional Analysis Academic Press New York
R.S. Cantrell C. Cosner (1989) ArticleTitleDiffusive logistic equations with indefinite weights: Population models in disrupted environments. Proc. Royal Soc. Edinburgh 112A. 293–318
R. S. Cantrell C. Cosner W. F. Fagan (2001) ArticleTitleBrucellosis, botflies and brinworms: The impact of edge habitats on pathogen transmission and species extinction J. Math. Biol. 42 95–119
R. S. Cantrell C. Cosner W. F. Fagan (1998) ArticleTitleCompetitive reversals inside ecological preserves: The role of external habitat degradation J. Math Biol. 37 491–533
R. S. Cantrell C. Cosner W. F. Fagan (2002) ArticleTitleHabitat edges and predator-prey interactions: Effects on critical patch size Math. Biosc. 175 31–55
R. S. Cantrell C. Cosner W. F. Fagan (1999) ArticleTitleHow habitat edges change species interactions: A synthesis of data and theory The American Naturalist 153 165–182
R. S. Cantrell C. Cosner W. F. Fagan (2001) ArticleTitleHow predator incursions affect critical patch size: The role of the functional response The American Naturalist 158 368–375
R. S. Cantrell C. Cosner V. Hutson (1993) ArticleTitlePermanence in ecological systems with diffusion Proc. Royal Soc. Edinburgh 123A 533–559
R. S. Cantrell C. Cosner V. Hutson (1993) ArticleTitlePermanence in some diffusive Lotka-Volterra models for three interacting species Dynamic Systems 2 505–530
Guillemin, V. and Pollack, A. (1974). Differential Topology, Prentice-Hall, Englewood Cliffs, N.J.
V. Hutson Y. Lou K. Mischaikow P. Polacik (2002) ArticleTitleCompeting species near a degenerate limit SIAM J. Math. Anal. 35 453–491
T. Kato (1996) Perturbation Theory for Linear Operators Springer-Verlag New York
D. Ludwig D. G. Aronson H. F. Weinberger (1979) ArticleTitleSpatial patterning of the spruce budworm J. Math. Biol. 8 217–258
Schechter, M. (2002). Principles of Functional Analysis, American Mathematical Society, Providence, R.I.
J. Serrin (1971) ArticleTitleA symmetry problem in potential theory Arch. Rational Mech. Anal. 43 304–318
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Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday.
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Cantrell, R.S., Cosner, C. & Lou, Y. Multiple Reversals of Competitive Dominance in Ecological Reserves via External Habitat Degradation. J Dyn Diff Equat 16, 973–1010 (2004). https://doi.org/10.1007/s10884-004-7831-y
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DOI: https://doi.org/10.1007/s10884-004-7831-y