Ancestral lines under selection for multiple sites: Pruning the Ancestral Selection Graph

Understanding ancestral processes under selection and mutation is among the fundamental challenges in population genetics. An important concept here is the ancestral selection graph (ASG) extracted from the Moran Model. This is, however, difficult to handle, both analytically and computationally, if two or more sites (that is, gene loci or sequence sites) are considered. Here a computational approach to pruning the ASG in the case of M sites is presented. The basic idea explores any incoming selective arrow, putting a hold onto the previously-active line. Should the incoming line be determined to be the ancestral line, it becomes the new active line and the previously-active line is dismissed. The set of types (that is, haplotypes or alleles) can be modelled in terms of sequences s ∈ {0, 1}M or fitness classes w ∈ {0,..,M}. The pruning procedure so far takes advantage of using sequences, but may be adjusted to fitness. Some preliminary results for different mutation and selection parameters and the resulting mutation process on the ancestral line are presented. This is joint work with Ellen Baake.