WIAS Preprint No. 1243, (2007)

Measure-valued diffusions, general coalescents and population genetic inference



Authors

  • Birkner, Matthias
  • Blath, Jochen

2010 Mathematics Subject Classification

  • 92D15 60J70 60G09 60G57

Keywords

  • Generalised Fleming-Viot process, $Lambda$-coalescent, lookdown construction, mathematical population genetics, Monte-Carlo simulation

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

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