In my research I work on the mathematical theory of population dynamics and evolutionary genetics and apply it to real-world problems. Because evolution is a dynamical process, much of my research is concerned with dynamical systems theory, stochastic processes, optimization and computer simulations.
Below I outline my recent research projects.
Protein adaptation in heterogeneous environments
My current research aims at a finer understanding of the link between evolutionary changes in phenotypic traits and their genetic sequences. As all traits are determined by multitude of interacting proteins, an integrated knowledge of the sequence-protein-organism map can generate new understanding that may otherwise not be accessible. For instance, in certain situations, a genetic sequence associated with a trait may have diverged across populations, and yet its expression has remained non-differentiated. One potential reason is that while the trait expression has been maintained due to stabilizing selection, the underlying proteins and their physico-chemical properties experienced divergent selection: e.g. folding stability of a protein is known to be sensitive to its environment, thus populations experiencing spatially heterogeneous environments may simultaneously facilitate divergence at the molecular level and trait maintenance at the organism level. Without looking at this intermediate molecular scale, such a mechanistic understanding of the evolutionary change may be missed. Research on biophysical and chemical properties of proteins is especially important for understanding adaptation to heterogeneous and changing environments.
Multiscale dynamics in structured populations
A great challenge in understanding and predicting population and evolutionary dynamics is that natural populations consist of multitude of different individuals that change during their lifetime (development). and that are involved in many intertwined and complex social and non-social processes. For instance, the recurrent spread of infectious diseases in an ecological community is affected by the age and spatial structure of the community, the interactions between hosts and other individuals in the community, and by the mutations in the pathogen and the host population altering e.g. the virulence of the pathogen or the immune system of its host.
A powerful method to model and analyze complex processes is to exploit the fact that some of them occur at vastly different timescales. One could compare, for example, the rates at which pathogens and their hosts replicate. If processes operate on different timescales, the complex population model can be partitioned into smaller sub-models that can be first analysed and then assembled back together, gaining knowledge on the dynamics of the complex population. This is called multiscale analysis. It is a mechanistic method that enables population-level explanations and predictions to be made in terms of individual-level observables. For instance, it 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 an age and spatially structured population. My interests and my recent work revolves around developing multiscale methods in structured populations by applying geometric singular perturbation theory, optimal control and dynamical systems theory. See my publications.
Applications in ecology, epidemiology and evolutionary biology
Supervised Master thesis
See my full publication list here