Demographic noise (together with Arne Traulsen and Chaitanya Gokhale)
We studied a system with two traits with intra- and interspecific competition (stochastic competitive Lotka-Volterra) under fluctuations in population size. We were mostly interested in the impact of the four competition parameters which we interpreted in terms of an evolutionary game. We found that in order to disentangle the ecological (population size fluctuations) from the evolutionary (trait frequency dynamics) scale in this system the two traits need to be very similar, i.e. we are in the context of nearly neutral mutations.
Fixation probabilities in populations under demographic fluctuations, Journal of Mathematical Biology, 77(4), 1233-1277 (view online)
Disentangling eco-evolutionary effects on trait fixation (accepted in Theoretical Population Biology) (pre-print) (TPB link)
Mating type dynamics (together with Dave Rogers)
Self-incompatible mating types are (more or less) the norm in the fungal world and also observed in various other species (e.g. Tetrahymena thermophila or Dictyostelium discoideum). Often there do not only exist 2 mating types but there can be up to hundreds or thousands. Therefore, the question is simple: given a finite population of N individuals, each carrying a certain self-incompatible mating type, how many mating types are we expect to see in the population on average? Quantifying genetic drift and balancing selection we found a rough estimate for this value when emergence of new mating types is rare.
Publication: Evolution of mating types in finite populations: the precarious advantage of being rare (submitted) (pre-print)
Spatial models (together with Peter Pfaffelhuber)
We studied the impact of space on a typical cooperator-defector interaction, i.e. defectors have a larger basal birth rate than cooperators and cooperators boost the birth rate (e.g. through providing a public good) of their neighbor. We found phase transitions in all dimensions and an explicit boundary in one dimension, thus showing that nearest neighbor interactions support the emergence and maintenance of cooperation.
Publication: A spatial model for selection and cooperation, Journal of Applied Probability 54 (2), 522-539. (view online)
See also my Dissertation: Phenotypic heterogeneity in bacterial populations – a mathematical study (view online)