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Isolation by distance in a hierarchically clustered population

  • Stanley Sawyer (a1) and Joseph Felsenstein (a2)

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(l/u).

Corresponding author
Postal address: Department of Mathematics, Purdue University, W. Lafayette, IN 47907, U.S.A.
∗∗ Postal address: Department of Genetics SK-50, University of Washington, Seattle, WA 98105, U.S.A.
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Partially supported by NSF Grant MCS79-03472.

Partially supported by Task Agreement No. DE-AT06-76EV71005 under Contract No. DE-AM06-76RL02225 between the U.S. Department of Energy and the University of Washington.

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Journal of Applied Probability
  • ISSN: 0021-9002
  • EISSN: 1475-6072
  • URL: /core/journals/journal-of-applied-probability
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