Mutation-Selection Models in Quantitative Genetics

I will give an overview of several mathematical results and applications of a general model for the evolution of a quantitative trait under selection, with mutations drawn from an arbitrary distribution. For stabilizing selection, the properties of the equilibrium distribution are derived, in particular, the problem of the maintenance of genetic variation will be discussed briefly. For a form of directional selection, convergence to an asymptotic distribution that proceeds at a constant rate is proved. Applications to the evolution of recombination will be outlined.