The common ancestor process revisited

Abstract

We consider the Moran model in continuous time with two types, mutation, and selection. We concentrate on the ancestral line and its stationary type distribution. Building on work by Fearnhead (J. Appl. Prob. 39 (2002), 38-54) and Taylor (Electron. J. Probab. 12 (2007), 808-847), we characterise this distribution via the fixation probability of the offspring of all individuals of favourable type (regardless of the offspring's types). We concentrate on a finite population and stay with the resulting discrete setting all the way through. This way, we extend previous results and gain new insight into the underlying particle picture.

25 pages, 4 figures

References in corpus (1)

• Coalescence in a random background

Cited by in corpus (5)

• Looking down in the ancestral selection graph: A probabilistic approach to the common ancestor type distribution
• The common ancestor type distribution of a $\Lambda$-Wright-Fisher process with selection and mutation
• Common ancestor type distribution: a Moran model and its deterministic limit
• On the stationary distribution of the block counting process for population models with mutation and selection
• The mutation process on the ancestral line under selection