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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)
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)
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)
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 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)