In my research I develop mathematical theory of evolution and apply it to real-world problems.
Evolution - a change in heritable characteristics of biological populations over time - is a dynamical process. Much of the theory and modelling evolution is therefore concerned with dynamical systems, optimization and stochastic processes. Computer simulations play an important role in applying the theory to real world. The primary focus of my work is to formalize and understand (A) individual physiological development (B) social interactions between individuals, and (C) the feedback between individual development, social interactions 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 complex population model can be partitioned into smaller sub-models that can be analysed and assembled back together, gaining knowledge on the dynamics of the complex population. Such models are mechanistic and enable population-level explanations and predictions to be made in terms of individual-level observables. For instance, they can be applied to understand how the spread of a disease is influenced by the feedback between within-host pathogen dynamics and the individual-level transmission of the pathogen in a demographically and spatially structured population. My interests and my recent work revolves around developing and applying multiscale methods in evolutionary biology.
Evolution in structured populations - 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 Dr. Piret Avila, we are analyzing function-valued phenotypes such as gene expression and developmental trajectories. To develop the analytical methods we apply various branches of mathematics such as singular perturbation, optimal control and dynamical systems theory.
My work on applications in ecology, epidemiology and evolutionary biology
Supervised Master thesis
See my full publication list here