Lines of descent in a Moran model with frequency-dependent selection and mutation

Ellen Baake, Luigi Esercito, Sebastian Hummel

Published 2020-11-17Version 1

We consider the two-type Moran model with frequency-dependent selection and two-way mutation, where selection follows either the nonlinear dominance or the fittest-type-wins scheme, which will turn out as two sides of the same coin. The ancestral selection graph (ASG) of the fittest-type-wins model contains multiple branching events in addition to the binary branching and coalescence events of the classical ASG. We establish both the \emph{killed ASG} and the \emph{pruned lookdown ASG} in this setting by using the information contained in the mutation events to reduce the ASG to those parts that are informative with respect to the types of an individual from the present population, or the type of the ancestor of such an individual, respectively. The killed ASG and the pruned lookdown ASG are in factorial moment duality with the Moran model and a relative thereof, respectively.