- Reader (Infrastructure and Environment)
Applications of Birth-and-death Processes to Ecology and Population Genetics
The theory of birth-and-death processes forms a natural framework for describing processes that operate on the level of individuals in Ecology and Population Genetics. In collaboration with Todd Parsons from the Mathematics department of the University of Toronto, I have been studying an application of this framework to f ixation in haploid populations experiencing density dependent population dynamics (Parsons and Quince I and II 2007). We approximated the discrete stochastic system with a continuous Fokker-Planck equation and then derived asymptotic analytic solutions to this equation. We then compared these approximate solutions with exact numerical solutions of the original discrete system. This process yielded valuable insights into the fixation of alleles in populations changing deterministically in size and fluctuating about equilibriums due to demographic stochasticity. In future we aim to extend this work to consider the long term interaction of genetics and demographics in haploid populations.
There is a direct mathematical connection between the dynamics of alleles in haploid populations and the clonal population dynamics of microbial organisms. I aim to exploit this connection in my current position using techniques from Population Genetics to develop a mathematical and computational framework for the description of microbial communities.
Optimal Models of Growth in Fish
The other major focus of my research is life history strategies and in particular models of optimal resource allocation between growth and reproduction in seasonally reproducing fish. For this research I focused on lake trout (Salvelinus namaycush), a species which shows substantial life history variation and for which we have good quality growth and maturation data. I derived a growth model based on optimal resource allocation and determined, using Bayesian statistics, the extent to which the model assumptions are supported by hatchery data on individual growth and compared fitted parameters across wild populations.
Coevolution in Communities of Interacting Species
The majority of my published research has focused on food web models of community coevolution. I used simulations of these models to study the structure, resistance to perturbation and relationship between ecological role and evolutionary history in food web communities.
Link to personal webpage