Research.I am an applied mathematician working on theory and applications in ecology and evolutionary biology. The underlying principle of my research is to identify and model processes on the molecular and/or individual level, taking explicitly into account the social environment of the individual, and then derive and analyze the population-level population dynamical and evolutionary behaviour. My work consists of three interacting layers (see Figure at the bottom). The top layer represents the various questions and hypothesis in ecology and evolutionary biology that I am fascinated by. I am in particular interested in (i) local adaptation and speciation, (ii) the evolution of cooperation, and (iii) the evolution of genomic architecture in self-incompatibility haplotypes in plants. The middle layer consists of the development of theoretical frameworks that enable the modelling and analysis of the biological questions posed in the top layer. Special attention is given to deriving "analytic predictive measures" in terms of well-known and easily obtainable biological quantities, such as genealogical relationships, vital rates and population densities. Such analytic predictive measures can then be used to better understand the (i) population dynamical properties of the ecological community, as well as (ii) the evolutionary trajectory of quantitative traits. The bottom layer lays out the mathematical foundation necessary in tackling the questions in the above two layers. The focus is on developing multiple scaling methods that allow the coupling of ecological and evolutionary processes in generally structured population models. This requires research on invariant manifolds in Banach spaces, geometric singular perturbation methods and on stochastic processes such as coalescence. |
