DEPARTMENT OF MATHEMATICAL
& STATISTICAL SCIENCES
UNIVERSITY OF ALBERTA
MATHEMATICAL BIOLOGY SEMINAR
MONDAY, March 24, 2003
Dr. Alexei Potapov
Department of Mathematical & Statistical Sciences
University of Alberta
Climate and competition: the effect of moving range boundaries on habitat invasibility
A.B. Potapov and M.A. Lewis
We consider competition model with habitat moving in space due to climate change. This is equivalent to adding an advection term to Fisher equations. We study the influence of advection on the outcome of competition of two species, on the size of critical patch and on the invisibility of habitat.
First we review and get some details about effect of spatial distribution on the outcome of competition. In particular we show that the critical patch size without advection is a fundamental characteristic of species, which controls the outcome of competition in space. For two "incompatible" species, which cannot coexist in a spatially uniform habitat (that is without diffusion terms in a model) we prove sufficient conditions (a) for noninvasibility of the second species and (b) for coexistence of both species within the same patch. We show that in the latter case a layer near the patch edges arises which serves as a retreat for one of the species.
Then we discuss the effects of advection (that is, the climate change). Numerical experiments show that advection makes more typical coexistence of "incompatible" species, and therefore increases the possibility of invasion. Advection makes two patch edges different: the "in-flow" edge becomes more vulnerable to the invasion than the "out-flow" one because of the washing out the dominant species.
Numerical results show that there is another interesting effect - there may be a critical advection speed above which the invading species may not only survive near the boundary, but even completely replace the preexisting one. This effect is related with the propagating front of species replacement. If the advection speed becomes greater than the front speed in stationary environment (there are rigorous estimates for the latter speed), we can observe the reversal of the front and as a result an inversion of the competition outcome.