Recombination and ancestral recombination trees

Date

May 16, 2012

Time

5:00 PM - 6:00 PM

Speaker

Prof. Dr. Ellen Baake

Affiliation

Universität Bielefeld, Technische Fakultät

Series

TUD Dresdner Mathematisches Seminar

Language

de

Main Topic

Mathematik

Other Topics

Mathematik

Host

Prof. Dr. A. Voigt

Description

Recombination is the genetic mechanism by which two parent individuals create the mixed type of their offspring during sexual reproduction; it is one of the major sources of genetic variability in populations. We consider both stochastic and deterministic models for the evolution of populations under recombination. Starting from the stochastic version (the Wright-Fisher model with recombination for a population of $N$ individuals), we trace back the ancestry of single individuals from the present population. In the $N \to \infty$ limit, this ancestral process is described by a random tree. With the help of a decomposition of the trees into subtrees and an inclusion-exclusion principle, we find a losed-form expression for the probabilities of the topologies of these ancestral trees. At the same time, these probabilities lead to an explicit solution of the deterministic recombination equation. The latter is a discrete-time dynamical system that emerges from the Wright-Fisher model via a law of large numbers as $N \to \infty$, and has been waiting for a solution for many decades. This is joint work with Ute von Wangenheim.

Links

• Prof. Dr. Ellen Baake

Last modified: May 4, 2012, 12:23:08 PM