The stepping stone model: New formulas expose old myths

DOI10.1214/aoap/1037125866zbMath1016.60089OpenAlexW1977141861MaRDI QIDQ1872358

J. Theodore Cox, Richard T. Durrett

Publication date: 6 May 2003

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

Full work available at URL: https://doi.org/10.1214/aoap/1037125866

zbMATH Keywords

stepping stone modelapproximation formulas for homozygosityhitting time resultsWright's genetic distance \(F_{ST}\)

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Genetics and epigenetics (92D10)

Related Items (17)

How mutation affects evolutionary games on graphs ⋮ The spread of a rumor or infection in a moving population ⋮ Isolation-by-distance-and-time in a stepping-stone model ⋮ Brownian models and coalescent structures ⋮ Rate of coalescence of lineage pairs in the spatial \(\varLambda\)-Fleming-Viot process ⋮ The spatial \(\Lambda\)-Fleming-Viot process on a large torus: genealogies in the presence of recombination ⋮ Global divergence of spatial coalescents ⋮ Exact moment calculations for genetic models with migration, mutation, and drift ⋮ The distribution of \(F_{st}\) and other genetic statistics for a class of population structure models ⋮ The propagation of a cultural or biological trait by neutral genetic drift in a subdivided population ⋮ One-dimensional stepping stone models, sardine genetics and Brownian local time ⋮ The Distribution ofF_stfor the Island Model in the Large Population, Weak Mutation Limit ⋮ The small world effect on the coalescing time of random walks ⋮ The stepping stone model. II: Genealogies and the infinite sites model ⋮ Intermediate range migration in the two-dimensional stepping stone model ⋮ Spatial autocorrelation for subdivided populations with invariant migration schemes ⋮ On spatial coalescents with multiple mergers in two dimensions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A multi-dimensional coalescent process applied to multi-allelic selection models and migration models
• Random shuffles and group representations
• Diffusive clustering in the two dimensional voter model
• Results for the stepping stone model, for migration in population genetics
• Ergodic theorems for weakly interacting infinite systems and the voter model
• Genealogy and subpopulation differentiation under various models of population structure.
• Coalescing random walks and voter model consensus times on the torus in \({\mathbb{Z}}^ d\)
• Effective number of alleles in a subdivided population
• A limit theorem for patch sizes in a selectively-neutral migration model
• The Decay of Genetic Variability in Geographically Structured Populations
• A model for spatial conflict
• Group selection for a polygenic behavioral trait: estimating the degree of population subdivision.
• A mathematical analysis of the stepping stone model of genetic correlation
• Analysis of population structure: II. Two‐dimensional stepping sone models of finite length and other geographically structured populations*
• Chutes and ladders in Markov chains

This page was built for publication: The stepping stone model: New formulas expose old myths