I work on the mathematical theory of evolution. My primary interest is to understand (A) individual development (B) interactions between individuals, and (C) the feedback between individuals and ecological and evolutionary phenomena.
A great challenge in explaining and predicting population and evolutionary dynamics is that individuals are involved in many intertwined and complex processes. For instance, the recurrent spread of infectious diseases in an ecological community is affected by the immune response of host individuals to the pathogen, the interactions between hosts and other individuals in the community, and by the mutations in the pathogen and the host population altering these processes e.g. by modifying the virulence of the pathogen or the immune system of its host. A promising avenue to tackle this challenge is to exploit the fact that some of the underlying processes occur at vastly different timescales. Compare, for example, the rates at which pathogens and their hosts replicate. If processes indeed operate on different timescales, the complexity of the problem can be reduced by decomposing the equations to smaller units that can be analysed and then assembled back together, hopefully preserving the information of the original problem. Such multiscale analysis lies at the cross-section of multiple branches of mathematics, in particular dynamical systems and singular perturbation theory. My interests and my recent work revolves around developing and applying multiscale methods in evolutionary biology.
Invasion implies substitution - program
My recent work on the dynamical analysis of populations is centred on individual development and how development affects individual behaviour and interactions with other individuals in the population. These interactions create a so-called environmental feedback loop between an individual and the composition of the population, generally leading to complex non-linear evolutionary dynamics. In a collaboration with Professor Laurent Lehmann, we have outlined a research program that aims at a mathematical formalism of evolutionary dynamics of such structured populations. Of our particular interest is the decomposition of the evolutionary change into model parameters and variables that are interpretable and quantifiable (such as genealogical relationships) consequently allowing explanations and predictions to be made across multiple timescales of natural populations. We have contributed to this program by analysing multispecies ecological communities where individuals are structured into various demographic classes such as different age or size classes. See our new manuscript here. Our current ongoing work deals with spatially structured populations, and together with Piret Avila, we are analyzing function-valued phenotypes such as gene expression and developmental trajectories.
My work on applications in ecology and evolutionary biology
See my full publication list here