"A general fitness wave framework for adaptive evolution"Ged, FrançoisFitness waves in Population Genetics aim at describing the dynamics of adaptation of a population in an abstract trait space. We introduce a framework that allows us to study a population in a general adaptive landscape, such as an inhomogeneous fitness landscape due to epistasis, or adaptation to a moving optimum. To do so, from a population model, we rigorously derive an adaptable free boundary PDE with a travelling wave solution. The speed of the wave's front -- i.e. the rate of adaptation -- can then be related to the genetic diversity of the population at the maximum of the wave. Moreover, the methods of characteristics yields a natural interpretation of the solution of the PDE in terms of the ancestral line of a randomly sampled individual in the population. Our framework is rather flexible and biologically relevant mechanisms can be included, such as infinite variance of the offspring distribution or varying population size. (joint work with Emmanuel Schertzer) |
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