DEPARTMENT OF MATHEMATICAL
& STATISTICAL SCIENCES

UNIVERSITY
OF ALBERTA

**MATHEMATICAL BIOLOGY SEMINAR**

**MONDAY OCTOBER 27,
2003.**

**3:00-4:00 p.m.**

**CAB 657**

**Dr. Elizaveta
Pachepsky**

**Department of Ecology, Evolution and Marine Biology
University of California, Santa Barbara**

** **

Abstract:

We explore the effect of discrete population numbers on population dynamics using two models of a waterflea Daphnia. The first model is a partial differential equation model, and the second is a simulation model that tracks individual Daphnia. Under limiting conditions without a spatial component both models exhibit the same cyclical dynamics (which agrees with experimental results). However, when the spatial component is added, the models differ in their predictions. While the partial differential equation model exhibits the same behavior with or without space, introduction of space into the simulation model changes the magnitude of the population cycles. We examine reasons for the discrepancy between the predictions of the two models, and discuss further dynamical implications of discreteness in population numbers.