Ancestral processes with selection: Branching and Moran models

• Autorzy: Ellen Baake , Robert Bialowons
• Języki publikacji: EN

Abstrakty

EN

We consider two versions of stochastic population models with mutation and selection. The first approach relies on a multitype branching process; here, individuals reproduce and change type (i.e., mutate) independently of each other, without restriction on population size. We analyse the equilibrium behaviour of this model, both in the forward and in the backward direction of time; the backward point of view emerges if the ancestry of individuals chosen randomly from the present population is traced back into the past. The second approach is the Moran model with selection. Here, the population has constant size N. Individuals reproduce (at rates depending on their types), the offspring inherits the parent's type, and replaces a randomly chosen individual (to keep population size constant). Independently of the reproduction process, individuals can change type. As in the branching model, we consider the ancestral lines of single individuals chosen from the equilibrium population. We use analytical results of Fearnhead (2002) to determine the explicit properties, and parameter dependence, of the ancestral distribution of types, and its relationship with the stationary distribution in forward time.

Kategorie tematyczne

• 60J70: Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
• 92D15: Problems related to evolution

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2008
• Tom: 80
• Numer: 1
• Strony: 33-52

Daty

wydano

2008

Twórcy

autor

Ellen Baake

• Technische Fakultät, Universität Bielefeld, Postfach 100131, 33501 Bielefeld, Germany

autor

Robert Bialowons

• Institut für Mathematik und Informatik, Universität Greifswald, Jahnstr. 15a, 17487 Greifswald, Germany

Identyfikatory

DOI

10.4064/bc80-0-2