Lines of descent under selection

Abstract

We review recent progress on ancestral processes related to mutation-selection models, both in the deterministic and the stochastic setting. We mainly rely on two concepts, namely, the killed ancestral selection graph and the pruned lookdown ancestral selection graph. The killed ancestral selection graph gives a representation of the type of a random individual from a stationary population, based upon the individual's potential ancestry back until the mutations that define the individual's type. The pruned lookdown ancestral selection graph allows one to trace the ancestry of individuals from a stationary distribution back into the distant past, thus leading to the stationary distribution of ancestral types. We illustrate the results by applying them to a prototype model for the error threshold phenomenon.

22 pages, 12 figures

References in corpus (5)

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Cited by in corpus (5)

• Moran models and Wright--Fisher diffusions with selection and mutation in a one-sided random environment
• Lines of descent in the deterministic mutation-selection model with pairwise interaction
• Solving the selection-recombination equation: Ancestral lines under selection and recombination
• 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