DEPARTMENT OF MATHEMATICAL & STATISTICAL SCIENCES

UNIVERSITY OF ALBERTA

**MATHEMATICAL
BIOLOGY SEMINAR**

MONDAY, SEPTEMBER 30, 2002

3:00 PM

CAB
657

**Dr.
Frithjof Lutscher**

**Department of Mathematical and Statistical Sciences**

**University of Alberta**

** **

**Survival in Fragmented Habitats**

Matrix models have been applied successfully in ecology to describe the life cycle of organisms. Recently, spatially explicit models have become increasingly popular. Questions and concerns are how species survive in habitats which become increasingly fragmented or how reserves for endangered species should be designed. In this talk we connect the two modeling approaches and derive stage-structured integrodifference equations by introducing space and dispersal into matrix models. The analysis of such models is concerned with existence and stability of fixed points as well as the bifurcation behavior. Since spatially explicit models are quite complex in that they contain many parameters and require intensive computing power, we show how to approximate these spatially explicit models by modified matrix models, hence, relating the new models back to well-known concepts in ecology. Finally, we show that from these spatially explicit models one can derive metapopulation models and thereby provide a mechanistic underpinning for this spatially implicit approach in ecology