Convergence to genetically uniform state in stepping stone models of population genetics

DOI10.1007/BF00276987zbMath0463.92011OpenAlexW1984186531WikidataQ52435915 ScholiaQ52435915MaRDI QIDQ1153849

Tokuzo Shiga, Morihiro Notohara

Publication date: 1980

Published in: Journal of Mathematical Biology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00276987

zbMATH Keywords

ergodic propertiesstepping stone modelsgenetically uniform state

Mathematics Subject Classification ID

Sums of independent random variables; random walks (60G50) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Genetics and epigenetics (92D10) Continuous-time Markov processes on discrete state spaces (60J27) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70)

Related Items (5)

Diffusive clustering in an infinite system of hierarchically interacting diffusions ⋮ Finite and infinite systems of interacting diffusions ⋮ Some ergodic theorems for a parabolic Anderson model ⋮ Infinite rate mutually catalytic branching in infinitely many colonies: the longtime behavior ⋮ The lattice models of neutral multi-alleles in population genetics theory

Cites Work

• An interacting system in population genetics
• Infinite dimensional stochastic differential equations and their applications
• Some one-dimensional migration models in population genetics theory
• Results for the stepping stone model, for migration in population genetics
• On convergence to diffusion processes of Markov chains related to population genetics
• The Decay of Genetic Variability in Geographically Structured Populations
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