Common ancestor type distribution: a Moran model and its deterministic limit

Abstract

We study the common ancestor type distribution in a $2$-type Moran model with population size $N$, mutation and selection, and in the deterministic limit regime arising in the former when $N$ tends to infinity, without any rescaling of parameters or time. In the finite case, we express the common ancestor type distribution as a weighted sum of combinatorial terms, and we show that the latter converges to an explicit function. Next, we recover the previous results through pruning of the ancestral selection graph (ASG). The notions of relevant ASG, finite and asymptotic pruned lookdown ASG permit to achieve this task.

30 pages, 11 figures

References in corpus (4)

• Mutation, selection, and ancestry in branching models: a variational approach
• Looking down in the ancestral selection graph: A probabilistic approach to the common ancestor type distribution
• The deterministic limit of the Moran model: a uniform central limit theorem
• The common ancestor process revisited

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• 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
• On the stationary distribution of the block counting process for population models with mutation and selection
• Solving the selection-recombination equation: Ancestral lines under selection and recombination
• The mutation process on the ancestral line under selection