Research
My research interests are quite broad, but in general I apply mathematical modelling approaches to understand ecological processes in population and evolutionary ecology. I am particularly interested in host-parasite and host-pathogen systems and how environmental heterogeneity can shape these systems. I am an active member of the interdisciplinary 'Boyd Orr Centre for Population and Ecosystem Health'. I use a range of mathematical tools and I am particularly interested in dynamical systems, integrodifference equations, bifurcation theory, state dependent-delay differential equations and more recently homogenisation.
This page is continually under construction. Please also see my publications page for recent projects.
Under construction. Information about trypanosome antigenic variation to follow soon. In the mean time please go here for more information.
In many ecosystems timing can be crucial: the synchronisation of insect emergence with leaf budding; the timing of predator and prey life cycles; the timing of adult mosquito biting season and disease transmission. Being 'at the right place at the right time' can be important in determining the survival of many populations. This is particularly the case for insects, but more generally many consumer-resource systems. In the face of constantly changing environments it becomes not only important to be 'on time', but also to be able to adapt the timing of develop in accordance with the environment. We are using a range of tools to study these questions, including state-dependent delay differential equations, adaptive dynamics and quantitative genetics. (Collaborators: Steven White (CEH Wallingford).
Landscape and habitat features can have a large impact on population survival and interactions. Developing mathematical tools to study the effect of habitat fragmentation on population dynamics and peristence is another important focus of my research. The spatial models I have been working with recently consist of systems of integrodifference equations. This has lead to a number of challenging mathematical problems that require novel approaches. (Collaborators: Frithjof Lutsher (Ottawa) and members of the NIMBioS working group on Forest insects.)
