DEPARTMENT OF MATHEMATICAL
& STATISTICAL SCIENCES

UNIVERSITY
OF ALBERTA

**MATHEMATICAL BIOLOGY SEMINAR**

MONDAY SEPTEMBER 8, 2003.

3:00-4:00 p.m.

CAB 657

**Dr. Frithjof Lutscher**

**Department of Mathematics and Statistical Sciences
University of Alberta**

Abstract: The term "drift paradox" arose in the
ecology of populations in rivers and streams. It describes the surprising observation
that individuals such as aquatic insects, which are subject to downstream
advection, can persist in upper reaches of the stream.

In this talk, we present a general model for populations
subject to unidirectional flow. The model has the form of an
integrodifferential equation, i.e., movement of individuals is modeled by
integration with respect to a dispersal kernel. We derive an appropriate
dispersal kernel from a mechanistic movement model. We explore how the critical
domain size depends on the advection velocity and find two possible
explanations of the drift paradox. Then we determine the spread speed of the
population in the direction with and against the advection. We show that the
two ecologically relevant quantities "critical domain size" and
"spread speed", which have been studied separately so far, are
closely related in systems which unidirectional flow.