MaBS

Theoretical models in population genetics usually make simplifying assumptions about the underlying ecology. However, the ecological characteristics of an environment often have a strong influence on the genetical evolution of a population. I am interested in relaxing some of these assumptions so that we may situate our population genetic models in more realistic ecological settings. As a mathematician, I am interested in stochastic modeling.

On the fixation process of beneficial mutations in variable environments

For adaptive evolution to proceed, beneficial mutations, while rare, must survive genetic drift. Ecological changes that affect the total population size or the selective advantage of a particular mutation can often occur on the same time scale as the fixation of that allele and can, therefore, have a dramatic effect on its ultimate probability of fixation. To address this, we have used the theory of inhomogeneous branching processes to derive analytical expressions for the fixation probability and the distribution of passage times when the total population size and the selection coefficient vary over time.

Evolutionary rescue in a deterioating environment

Changes in an environment, such as those induced by global warming, the appearance of a new predator, or the onset of drug therapy, might cause a well-adapted population to become maladapted. This new selection pressure - if severe - can potentially drive the population extinct, unless a "rescue mutation" arises. We are interested in the probability of evolutionary rescue in a gradually deterioating spatial environment.