Dynamics of gene differentiation between incompletely isolated populations of unequal sizes

Ranajit Chakraborty, Masatoshi Nei

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Abstract

The progress of gene differentiation between two populations of unequal sizes is studied by taking into account the effects of mutation and migration. Explicit formulae for the eventual rate of approach to equilibrium of the probabilities of identity of genes by descent within and between populations are worked out for the case of small migration. Formulae for the equilibrium values of identity probabilities are also given for some special cases. It is shown that in the case of large migration the Nei-Feldman formulae for the temporal changes and equilibrium values of identity probabilities approximately hold, unless the sizes of the two populations are extremely different. The theories developed are applied to study the evolution of cave fish populations in Astyanax mexicanus. The approximate time after divergence between the cave and river populations of this fish has been estimated to be 525,000-710,000 years, which agrees well with the geological data on cave formation.

Original languageEnglish
Pages (from-to)460-469
Number of pages10
JournalTheoretical Population Biology
Volume5
Issue number3
DOIs
StatePublished - 1 Jan 1974

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