Waves in Population Genetics

The main purpose of population genetics is to understand the complex genetic diversity observed around us and to identify the evolutionary processes which produced this diversity. With the advance of molecular biology, the past decades have produced an enormous amount of observations and a major challenge ahead of us consists in identifying the relative importance of key evolutionary forces (mutation, genetic drift, natural selection, demography, recombination etc.) by making use of those detailed observations. In this back- casting approach to evolution, one needs to understand how the latter key processes operate in a mathematical framework whose outcomes may be compared to data. The common feature of the models investigated in this proposal is that they describe the stochastic propagation of some biological characteristics in space. Space will bear different interpretations depending on the model at hands; sometimes referring to the actual spatial position of individuals, but also to an abstract fitness value (fitness waves). In such large populations, the density of individuals can often be described in terms of a travelling front and my first objective is to produce rigorous predictions on the observed genetic diversity. Beyond addressing technical challenges, our goal is to leverage our mathematical approach to investigate some of the fundamental Biological implications of our findings. Understanding genetic diversity is critical in the current context since new mutations may enable populations to adapt to a rapidly changing environment. A key aim of the current project is to go beyond the conventional models of population genetics and propose a comprehensive framework capable of addressing some of the questions arising from the ongoing crisis.