Haldane's formula in Cannings models: the case of moderately strong selection.

For a class of Cannings models we prove Haldane's formula, [Formula: see text], for the fixation probability of a single beneficial mutant in the limit of large population size N and in the regime of moderately strong selection, i.e. for [Formula: see text] and [Formula: see text].

Modelling and simulating Lenski's long-term evolution experiment.

We revisit the model by Wiser et al. (2013), which describes how the mean fitness increases over time due to beneficial mutations in Lenski's long-term evolution experiment. We develop the model further both conceptually and mathematically.

Looking down in the ancestral selection graph: A probabilistic approach to the common ancestor type distribution.

In a (two-type) Wright-Fisher diffusion with directional selection and two-way mutation, let x denote today's frequency of the beneficial type, and given x, let h(x) be the probability that, among all individuals of today's population, the individual whose progeny will eventually take over in the population is of the beneficial type. Fearnhead (2002) and Taylor (2007) obtained a series representation for h(x). We develop a construction that contains elements of both the ancestral selection graph and the lookdown construction and includes pruning of certain lines upon mutation.