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

A solution of the drift paradox

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.