PMID: 3611978Jan 1, 1987Paper

The sampling theory of neutral alleles and an urn model in population genetics

Journal of Mathematical Biology
Fred M Hoppe

Abstract

The behaviour of a Pólya-like urn which generates Ewens' sampling formula in population genetics is investigated. Connections are made with work of Watterson and Kingman and to the Poisson-Dirichlet distribution. The order in which novel types occur in the urn is shown to parallel the age distribution of the infinitely many alleles diffusion model and consequences of this property are explored. Finally the urn process is related to Kingman's coalescent with mutation to provide a rigorous basis for this parallel.

References

Apr 1, 1977·Theoretical Population Biology·G A Watterson, H A Guess
Apr 1, 1977·Theoretical Population Biology·J F Kingman
Oct 1, 1974·Theoretical Population Biology·G A Watterson
Mar 1, 1972·Theoretical Population Biology·S Karlin, J McGregor
Mar 1, 1972·Theoretical Population Biology·W J Ewens
Sep 1, 1973·Theoretical Population Biology·W J Ewens
Feb 1, 1980·Theoretical Population Biology·R C Griffiths

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Citations

Jan 1, 1989·Journal of Mathematical Biology·R C Griffiths
Dec 1, 1992·Genetical Research·G A Watterson, P Donnelly
Jul 17, 2004·Genome Research·Shin LinDavid J Cutler
Nov 28, 2007·PLoS Computational Biology·Hailiang HuangJoel S Bader
Nov 4, 2008·Statistical Applications in Genetics and Molecular Biology·Asger HobolthCarsten Wiuf
Jul 21, 2007·Journal of Theoretical Biology·Rampal S EtienneAlan J McKane
Feb 9, 2006·American Journal of Human Genetics·Jonathan MarchiniUNKNOWN International HapMap Consortium
Sep 13, 2007·PloS One·Amro ZayedLaurence Packer
Oct 25, 2007·Journal of Evolutionary Biology·E G Leigh
Dec 17, 2004·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A J McKane, T J Newman
Aug 10, 2017·Royal Society Open Science·Bernardo MonechiVittorio Loreto
Sep 27, 2018·Physical Review. E·Avinash Chand Yadav
Dec 9, 2020·Entropy·Francesca TriaVito D P Servedio
Mar 8, 2020·Theoretical Population Biology·John Wakeley
Oct 1, 2019·Theoretical Population Biology·Olivier François

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