Nonlinear spatio-temporal dynamics in biological invasions
Currently, my research is concerned with mathematical models of biological invasions.
The ever-increasing global trade in plants and animals, and accidental transportation by sea and air,
poses a threat to our agriculture, wildlife and natural ecosystems. Invaders compete with native species
for resources, produce an increased predatory effect and bring with them novel diseases. For example, rusty crayfish has been spread outside
its historical range by human vectors. Applying mathematics to biological invasions has the potential
to quantify management and control strategies, provide solutions to general questions in ecological
theory and also generate interesting and difficult mathematical problems that require novel solutions
I focus on aquatic invaders in the freshwater ecosystem of the Great Lakes, where non-indigenous species are creating changes in the resident species abundance and diversity.
Rusty crayfish, which is an aggressive invader, is changing the population dynamics of many lakes by interfering with fish reproduction, overgrazing on lake vegetation and causing the local extirpation of resident crayfish species. These lakes are highly valued for recreational
purposes, and one proposed management method is the use of smallmouth bass
(a prized angling fish)
as a biological control agent.
I have started to investigate conditions for perturbing the lake population dynamics that will lead to
control, using a system of coupled reaction-diffusion equations to model the crayfish and bass densities.
The interactions between the invading and resident crayfish are another area of research interest.
Research on the dynamics and economics of invading aquatic species is the focus of an international
collaborative research team (ISIS) with mathematical team members at Alberta (Centre for Mathematical Biology),
biological team members at the University of Notre Dame (David Lodge and Gary Lamberti), and economic team
members at the University of Wyoming (David Finnoff and Jason Shogren).
Butterfly dynamics in southern Alberta
This project is concerned with finding mechanisms that give rise to two-cycles observed in the population dynamics of Parnassius smintheus. This is part of an ongoing collaboration with Jens Roland (Biological Sciences), Mark Lewis (Centre for Mathematical Biology).
Ungulate control and management
In Elk Island National Park, where hunting is not permitted, ungulate biomass has increased to such levels
that resources are suppressed. We implemented a model to find the optimal density and configuration of species given a desired
level of resource use. This tool will be used by Parks Canada to determine the number of animals to be removed. This is a collaborative project with Gerry Kuzyk and Robert Hudson (Renewable Resources), Norm Cool (Parks Canada), Edward Bork (Agricultural, Food and Nutritional Science) and Evelyn Merrill (Biological Sciences).