Continuous time multi-allelic stepping stone models in population genetics

DOI10.1215/kjm/1250521859zbMath0539.92012OpenAlexW1575656720MaRDI QIDQ794569

Tokuzo Shiga

Publication date: 1982

Published in: Journal of Mathematics of Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/kjm/1250521859

zbMATH Keywords

migrationselectionexistence and uniqueness of solutionsrandom genetic driftmutationsteady-state distributionsmultidimensional Ornstein-Uhlenbeck processinfinite-allelic modelone-locus multiallelic stepping-stone genetic models

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Martingales with continuous parameter (60G44) Diffusion processes (60J60) Genetics and epigenetics (92D10) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70)

Related Items (7)

Elliptic equations with diffusion coefficient vanishing at the boundary: Theoretical and computational aspects ⋮ Stationary states and their stability of the stepping stone model involving mutation and selection ⋮ Neutral evolution in spatially continuous populations. ⋮ Coexistence in locally regulated competing populations and survival of branching annihilating random walk ⋮ The lattice models of neutral multi-alleles in population genetics theory ⋮ Generalized stepping stone model with \(\Xi\)-resampling mechanism ⋮ A measure-valued diffusion process describing the stepping stone model with infinitely many alleles

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