Coalescent lineage distributions

DOI10.1239/aap/1151337077zbMath1092.92035OpenAlexW2072513129MaRDI QIDQ5480005

Robert C. Griffiths

Publication date: 25 July 2006

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1239/aap/1151337077

zbMATH Keywords

hypergeometric functionprobability generating functionscoalescent processage of mutationJacobi polynomialinfinitely-many-alleles modeldeath processesline of descentcoalescent lineage distribution

Mathematics Subject Classification ID

Problems related to evolution (92D15) Applications of branching processes (60J85) Applications of hypergeometric functions (33C90) Distribution theory (60E99) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70)

Related Items (7)

A coalescent dual process in a Moran model with genic selection ⋮ Orthogonal polynomial kernels and canonical correlations for Dirichlet measures ⋮ Optimal filtering and the dual process ⋮ Single and simultaneous binary mergers in Wright-Fisher genealogies ⋮ Ancestral inference from haplotypes and mutations ⋮ Theory and applications of a deterministic approximation to the coalescent model ⋮ Exact simulation of coupled Wright–Fisher diffusions

Cites Work

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• Motoo Kimura's use of diffusion theory in population genetics
• The frequency spectrum of a mutation, and its age, in a general diffusion model
• Ewens' sampling formula and related formulae: combinatorial proofs, extensions to variable population size and applications to ages of alleles
• The sampling theory of selectively neutral alleles
• On the genealogy of nested subsamples from a haploid population
• The age of a mutation in a general coalescent tree

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