Tree-valued Fleming-Viot dynamics with mutation and selection

DOI10.1214/11-AAP831zbMath1316.92048arXiv1101.0759MaRDI QIDQ1931328

Andrej Depperschmidt, Peter Pfaffelhuber, Andreas Greven

Publication date: 25 January 2013

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1101.0759

zbMATH Keywords

resamplingdualityFleming-Viot processcoalescentmetric measure spaceancestral selection graphgenealogical treemeasure-valued diffusiongirsanov theoremtree-valued Fleming-Viot dynamics

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Genetics and epigenetics (92D10)

Related Items (21)

The distribution of the spine of a Fleming-Viot type process ⋮ The fixation probability and time for a doubly beneficial mutant ⋮ Branching Processes -- A General Concept ⋮ Convergence of metric two-level measure spaces ⋮ Branching trees I: concatenation and infinite divisibility ⋮ Quantitative approximation of the discrete Moran process by a Wright-Fisher diffusion ⋮ Multilevel mutation-selection systems and set-valued duals ⋮ Evolving genealogies for branching populations under selection and competition ⋮ Slow-fast stochastic diffusion dynamics and quasi-stationarity for diploid populations with varying size ⋮ Tree-valued resampling dynamics martingale problems and applications ⋮ The Aldous chain on cladograms in the diffusion limit ⋮ Modifiers of mutation rate in selectively fluctuating environments ⋮ A representation for exchangeable coalescent trees and generalized tree-valued Fleming-Viot processes ⋮ Pathwise construction of tree-valued Fleming-Viot processes ⋮ The total external length of the evolving Kingman coalescent ⋮ Evolving phylogenies of trait-dependent branching with mutation and competition. I: existence ⋮ Genealogical distances under low levels of selection ⋮ The ancestral selection graph under strong directional selection ⋮ On the Simpson index for the Wright–Fisher process with random selection and immigration ⋮ Spaces of algebraic measure trees and triangulations of the circle ⋮ The evolving Moran genealogy

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