DEPARTMENT OF MATHEMATICAL AND STATISTICAL SCIENCES
UNIVERSITY OF ALBERTA
PIMS-MITACS MATHEMATICAL BIOLOGY SEMINAR
MONDAY, April 11, 2005
3:00 - 4:00 p.m.
Dr. Steve Cantrell
Department of Mathematics and Computer Science
University of Miami
Reversals of competitive dominance in ecological reserves via external habitat degradation
Habitat degradation is the slow and often subtle deterioration in habitat quality that accompanies human activities through increases in road density, pesticide use, hunting pressure and so forth. Such degradation is of particular concern in fragmented habitats where economic or jurisdictional boundaries rather than ecological ones determine the level of exploitation adjoining habitat patches endure. To examine the consequences habitat degradation might have on species interactions, Chris Cosner, Bill Fagan and I posited a patch of pristine habitat surrounded by "matrix" habitat whose degradation level was variable. The dynamics of 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. Our 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 more recent work Chris Cosner, Yuan Lou and I have addressed 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 showed 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 examined the effects thereof on the number and nature of equilibria through a detailed bifurcation analysis.