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Isolation by Distance in a Hierarchically Clustered Population
Stanley Sawyer and Joseph Felsenstein
Journal of Applied Probability
Vol. 20, No. 1 (Mar., 1983), pp. 1-10
Published by: Applied Probability Trust
Stable URL: http://www.jstor.org/stable/3213715
Page Count: 10
You can always find the topics here!Topics: Random walk, Clans, Juveniles, Genetic mutation, Genetics, Population migration, Population density, Population genetics, Multilevel models, Integers
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A biological population with local random mating, migration, and mutation is studied which exhibits clustering at several different levels. The migration is determined by the clustering rather than actual geographic or physical distance. Darwinian selection is assumed to be absent, and population densities are such that nearby individuals have a probability of being related. An expression is found for the equilibrium probability of genetic relatedness between any two individuals as a function of their clustering distance. Asymptotics for a small mutation rate u are discussed for both a finite number of clustering levels (and of total population size), and for an infinite number of levels. A natural example is discussed in which the probability of heterozygosity varies as u to a power times a periodic function of log(1/u).
Journal of Applied Probability © 1983 Applied Probability Trust