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- Alison Etheridge, Peter Pfaffelhuber, Anton Wakolbinger
- 2005

For a genetic locus carrying a strongly beneficial allele which has just fixed in a large population we study the ancestry at a linked neutral locus. During this " selective sweep " the linkage between the two loci is broken up by recombination, and the ancestry at the neutral locus is modelled by a structured coalescent in a random background. For large… (More)

- Ute Lenz, Sandra Kluth, Ellen Baake, Anton Wakolbinger
- Theoretical population biology
- 2015

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… (More)

- Ellen Baake, Ute Lenz, Anton Wakolbinger
- 2016

Using graphical methods based on a 'lookdown' and pruned version of the ancestral selection graph, we obtain a representation of the type distribution of the ancestor in a two-type Wright-Fisher population with mutation and selection, conditional on the overall type frequency in the old population. This extends results from [15], now including the case of… (More)

- Ellen Baake, Ute Lenz, Anton Wakolbinger
- 2016

Using graphical methods based on a 'lookdown' and pruned version of the ancestral selection graph, we obtain a representation of the type distribution of the ancestor in a two-type Wright-Fisher population with mutation and selection, conditional on the overall type frequency in the old population. This extends results from [17], now including the case of… (More)

- Ellen Baake, Anton Wakolbinger
- 2015

This is a review of William Feller's important contributions to mathematical biology. The seminal paper [Feller 1951] Diffusion processes in genetics was particularly influential on the development of stochastic processes at the interface to evolutionary biology, and interesting ideas in this direction (including a first characterization of what is nowadays… (More)

- Adrián González Casanova, Noemi Kurt, Anton Wakolbinger, Linglong Yuan
- 2015

The Lenski experiment investigates the long-term evolution of bacterial populations. In this paper we present an individual-based probabilistic model that captures essential features of the experimental design, and whose mechanism does not include epistasis in the continuous-time (intraday) part of the model, but leads to an epistatic effect in the… (More)

- Andreas Greven, Peter Pfaffelhuber, Cornelia Pokalyuk, Anton Wakolbinger, Greven, Introduction
- 2014

For a beneficial allele which enters a large unstructured population and eventually goes to fixation, it is known that the time to fixation is approximately 2 log(α)/α for a large selection coefficient α. For a population that is distributed over finitely many colonies, with migration between these colonies, we detect various regimes of the migration rate µ… (More)

J o u r n a l o f P r o b a b i l i t y Electron. Abstract In mathematical population genetics, it is well known that one can represent the genealogy of a population by a tree, which indicates how the ancestral lines of individuals in the population coalesce as they are traced back in time. As the population evolves over time, the tree that represents the… (More)

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