DEPARTMENT OF MATHEMATICAL
& STATISTICAL SCIENCES

UNIVERSITY OF
ALBERTA

**MATHEMATICAL BIOLOGY SEMINAR**

MONDAY, March 24, 2003

3:00 PM

CAB 657

**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.