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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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