Mathematical population genetics and evolutionary games

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This research is directed towards a variety of population genetics and population dynamics models and the concomitant evolutionary and ecological perspectives. The long-term objectives are: a) to describe and explain the observed biodiversity; b) to develop mathematical, statistical and computational methods to analyse population structures and make inferences about related parameters or assumptions; c) to deduce evolutionary principles that may result from selection, migration, random drift, mutation and recombination; and d) to incorporate the effects of complex interactions between individuals and between populations. In the next five years, the focus will be put on the following projects:****1. Evolution of recombination. A recent stunning application of coalescent theory is the identification of hotspots of recombination, where chromosomes are more likely to break during meiosis. Theoretical studies are needed to address the question of their evolution and their effect on genetic variability. **2. Ancestral processes of phylogenetic trees. Reconstructing the history of migration in humans and the phylogeny of different species, not to mention the recombination maps of ancient species, from whole-genome data is the most important challenge in statistical genetics today. This requires a better understanding of the multispecies coalescent and new ancestral-type approaches of birth-and-death processes. ****3. Cooperation in public goods games. Evolutionary game theory has recently gained a lot of interest with experiments of public goods games and the introduction of conditions that favor the evolution of cooperation in structured populations. The roles of reproductive values, mate choice and intergenerational relationships have been mostly ignored up to now. They are expected to enlighten key evolutionary issues related to reciprocity. **4. Inclusive fitness theory in game dynamics. The right definition of fitness and reproductive value in age-structured populations is a controversial subject. With interactions between kin, the validity of an inclusive fitness approach has to be addressed in this context in order to settle the debate.****The project on recombination is connected to a central question in biology, namely the evolution of sex, which is still puzzling. As for the multispecies coalescent, "the field of phylogenetics is entering a new era in which trees of historical relationships between species are increasingly inferred from multilocus and genomic data" (Degnan and Rosenberg 2009). On the other hand, the evolution of cooperation through individual or species interactions in common goods games is of prime interest in view of contemporary environmental issues. Finally, inclusive fitness theory is widely used in behavioral ecology. It is related to Fisher's Fundamental Theorem of Natural Selection whose meaning is still passionately discussed in population genetics.******************