Integrodifference equations (IDEs) are infinite-dimensional discrete dynamical systems. Spatial ecology studies the spatial distribution patterns of populations as they arise from individual growth, interaction, and dispersal processes. In this course, I will present how ecological processes can be modelled using IDEs, how IDEs can be studied analytically and numerically, and how the mathematical insights can be applied to understand ecological scenarios.

IDEs are uniquely suited to model the life cycle of populations with distinct, separate growth and dispersal phases, for example many plants and insect species. In the simplest form, the density $N_t(x)$ of a population is projected forward from one year to the next as

$N_t$$_+$$_1(x)$ = $\int$ $K(x,y)F(N_t (y),y)dy$.

Function $F$ describes the growth phase; dispersal kernel $K$ the probability of moving from location $y$ to location $x$.

I will present results on existence and uniqueness of steady states and their stability, bifurcations, approximations, spreading phenomena, travelling waves and spatial pattern formation. I will relate these to ecological examples and theory, in particular to biological invasions and conservation planning.

Prerequisites:

A solid command of analysis, linear algebra, matrix theory; an interest in ecological questions; as well as knowledge of computer programming and real/functional analysis.

Format:

The course will be taught in person at the University of Ottawa and can be taken via video conferencing elsewhere in Canada. Lectures are Mondays 2:30-4pm and Wednesday 4-5:30pm Eastern Standard/Daylight Time.Students will be evaluated through regular homework assignments and mini-projects. Students outside of the Ottawa-Carleton graduate program will have to inquire with their home departments individually on whether and how they can take this course for credit.

Registration:

Enrollment is limited. Permission of the instructor is required. If you are interested, please send an email to Prof Lutscher (flutsche@uottawa.ca) stating why you are interested and what your background is.