Genealogical constructions of population models

DOI10.1214/18-AOP1266zbMath1466.60147arXiv1402.6724OpenAlexW2964303811MaRDI QIDQ2327935

Thomas G. Kurtz, Alison M. Etheridge

Publication date: 8 October 2019

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

Full work available at URL: https://arxiv.org/abs/1402.6724

zbMATH Keywords

stochastic equationsgeneratorsvoter modelpopulation modelMoran modelstepping stone modelgenealogieslookdown constructionlambda Fleming-Viot process

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Population dynamics (general) (92D25) Ecology (92D40)

Related Items (15)

Markov genealogy processes ⋮ Dynamics of lineages in adaptation to a gradual environmental change ⋮ Spatial birth-and-death processes with a finite number of particles ⋮ Developments in coalescent theory from single loci to chromosomes ⋮ Natural selection in spatially structured populations ⋮ Looking forwards and backwards: dynamics and genealogies of locally regulated populations ⋮ Evolving genealogies for branching populations under selection and competition ⋮ Existence, uniqueness and ergodicity for the centered Fleming-Viot process ⋮ Spine for interacting populations and sampling ⋮ A representation for exchangeable coalescent trees and generalized tree-valued Fleming-Viot processes ⋮ Rescaling limits of the spatial Lambda-Fleming-Viot process with selection ⋮ Stochastic PDEs on graphs as scaling limits of discrete interacting systems ⋮ Fecundity regulation in a spatial birth-and-death process ⋮ Genealogical constructions and asymptotics for continuous-time Markov and continuous-state branching processes ⋮ Stochastic partial differential equations describing neutral genetic diversity under short range and long range dispersal

Cites Work

• A central limit theorem for the spatial \(\Lambda\)-Fleming-Viot process with selection
• Poisson representations of branching Markov and measure-valued branching processes
• Representation theorems for interacting Moran models, interacting Fisher-Wright diffusions and applications
• A new model for evolution in a spatial continuum
• Wandering random measures in the Fleming-Viot model
• Martingale problems for conditional distributions of Markov processes
• Particle representations for measure-valued population models
• Continuum-sites stepping-stone models, coalescing exchangeable partitions and random trees
• Stochastic p.d.e.'s arising from the long range contact and long range voter processes
• The spatial lambda-Fleming-Viot process: an event-based construction and a lookdown representation
• Pathwise uniqueness for stochastic differential equations driven by pure jump processes
• A countable representation of the Fleming-Viot measure-valued diffusion
• Equivalence of Stochastic Equations and Martingale Problems
• Modelling evolution in a spatial continuum
• An Extension of Skorohod's Almost Sure Representation Theorem
• On the unnormalized solution of the filtering problem with counting process observations
• Markov functions
• Stationary solutions and forward equations for controlled and singular martingale problems
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