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 organismal level, and then derive and analyze population-level phenomena across various timescales of natural populations. My work consists of three interacting layers. 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 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 biological quantities, such as genealogical relationships, vital rates and population densities. Such analytic predictive measures are useful in understanding the (i) population dynamics of the ecological community, as well as (ii) the evolutionary dynamics of quantitative phenotypes. 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 structured populations. This requires research on invariant manifolds in Banach spaces, geometric singular perturbation methods and on stochastic processes such as coalescence. |
