Measure-valued diffusions, general coalescents and population genetic inference

Abstract

We review recent progress in the understanding of the interplay between population models, measure-valued diffusions, general coalescent processes and inference methods for evolutionary parameters in population genetics. Along the way, we will discuss the powerful and intuitive (modified) lookdown construction of Donnelly and Kurtz, Pitman's and Sagitov's $Lambda$-coalescents as well as recursions and Monte Carlo schemes for likelihood-based inference of evolutionary parameters based on observed genetic types.