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- Matthias Birkner, Jochen Blath, Marcella Capaldo, Alison Etheridge, Martin Möhle, Jason Schweinsberg +1 other
- 2005

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)

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 dynami-cal system… (More)

- A. WAKOLBINGER
- 2007

For a class of processes modeling the evolution of a spatially struc-tured 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… (More)

We consider an infinite-dimensional system of stochastic differential equations describing the evolution of type frequencies in a large population. The type of an individual is the number of deleterious mutations it carries, where fitness of individuals carrying k mutations is decreased by αk for some α > 0. Along the individual lines of descent, new… (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)

The objective of this paper is the study of the equilibrium behavior of a population on the hierarchical group ΩN consisting of families of individuals undergoing critical branching random walk and in addition these families also develop according to a critical branching process. Strong transience of the random walk guarantees existence of an equilibrium… (More)

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)

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)

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 ge-nealogy evolves: some families will get lost from the population and eventually a new MRCA… (More)

J o u r n a l o f P r o b a b i l i t y Electron. Abstract It is possible to represent each of a number of Markov chains as an evolving sequence of connected subsets of a directed acyclic graph that grow in the following way: initially, all vertices of the graph are unoccupied, particles are fed in one-by-one at a distinguished source vertex, successive… (More)