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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)

- M Hutzenthaler, 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)

- V Le, E Pardoux, A Wakolbinger, 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)

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

- Steven N Evans, Rudolf Grübel, Anton Wakolbinger
- 2010

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)

- A Greven, A Klenke, A Wakolbinger
- 1999

Consider a countable collection (t) of particles located on a countable group, performing a critical branching random walk where the branching rate of a particle is given by a random medium uctuating both in space and time. Here we study the case where the time{space random medium (t) (called catalyst) is also a critical branching random walk evolving… (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)

- D A Dawson, L G Gorostiza, 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)