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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 modeled by a structured coalescent in a random background. For large… (More)

The evolutionary force of recombination is lacking in asexually reproducing populations. As a consequence, the population can suffer an irreversible accumulation of deleterious mutations, a phenomenon known as Muller’s ratchet. We formulate discrete and continuous time versions of Muller’s ratchet. Inspired by Haigh’s (1978) analysis of a dynamical system… (More)

- M. Birkner, J. Blath, +4 authors A. Wakolbinger
- 2004

We determine that the continuous-state branching processes for which the genealogy, suitably time-changed, can be described by an autonomous Markov process are precisely those arising from α-stable branching mechanisms. The random ancestral partition is then a time-changed Λ-coalescent, where Λ is the Beta-distribution with parameters 2− α and α, and the… (More)

- Dirk Metzler, Roland Fleißner, Anton Wakolbinger, Arndt von Haeseler
- Journal of Molecular Evolution
- 2001

When two sequences are aligned with a single set of alignment parameters, or when mutation parameters are estimated on the basis of a single ``optimal'' sequence alignment, the variability of both the alignment and the estimated parameters can be seriously underestimated. To obtain a more realistic impression of the actual uncertainty, we propose sampling… (More)

- A. Wakolbinger
- 2000

We consider particle systems in locally compact Abelian groups with particles moving according to a process with symmetric stationary independent increments and undergoing one and two levels of critical branching. We obtain long time fluctuation limits for the occupation time process of the one– and two–level systems. We give complete results for the case… (More)

- A. WAKOLBINGER
- 2007

For a class of processes modeling the evolution of a spatially structured population with migration and a logistic local regulation of the reproduction dynamics, we show convergence to an upper invariant measure from a suitable class of initial distributions. It follows from recent work of Alison Etheridge that this upper invariant measure is nontrivial for… (More)

- A. Véber, A. Wakolbinger
- 2013

We construct a measure-valued equivalent to the spatial Λ-Fleming-Viot process (SLFV) introduced in [Eth08]. In contrast with the construction carried out in [Eth08], we fix the realization of the sequence of reproduction events and obtain a quenched evolution of the local genetic diversities. To this end, we use a particle representation which highlights… (More)

We study the longtime behaviour of interacting systems in a randomly uctuating (space{ time) medium and focus on models from population genetics. There are two prototypes of spatial models in population genetics: spatial branching processes and interacting Fisher{Wright diiusions. Quite a bit is known on spatial branching processes where the local branching… (More)

- V. Le, A. Wakolbinger
- 2010

We obtain a representation of Feller’s branching diffusion with logistic growth in terms of the local times of a reflected Brownian motion H with a drift that is affine linear in the local time accumulated by H at its current level. As in the classical Ray–Knight representation, the excursions of H are the exploration paths of the trees of descendants of… (More)

Consider a haploid population which has evolved through an exchangeable reproduction dynamics, and in which all individuals alive at time t have a most recent common ancestor (MRCA) who lived at time At, say. As time goes on, not only the population but also its genealogy evolves: some families will get lost from the population and eventually a new MRCA… (More)