Clines with partial panmixia in an unbounded unidimensional habitat

Thomas Nagylaki

Theoretical Population Biology, 2012, vol. 82, issue 1, 22-28

Abstract: In geographically structured populations, global panmixia can be regarded as the limiting case of long-distance migration. The effect of incorporating partial panmixia into diallelic single-locus clines maintained by migration and selection in an unbounded unidimensional habitat is investigated. Migration and selection are both weak. The former is homogenous and isotropic; the latter has no dominance. The population density is uniform. A simple, explicit formula is derived for the maximum value β0 of the scaled panmictic rate β for which a cline exists. The former depends only on the asymptotic values of the scaled selection coefficient. If the two alleles have the same average selection coefficient, there exists a unique, globally asymptotically stable cline for every β≥0. Otherwise, if β≥β0, the allele with the greater average selection coefficient is ultimately fixed. If β<β0, there exists a unique, globally asymptotically stable cline, and some polymorphism is retained even infinitely far from its center. The gene frequencies at infinity are determined by a continuous-time, two-deme migration-selection model. An explicit expression is deduced for the monotone cline in a step-environment. These results differ fundamentally from those for the classical cline without panmixia.

Keywords: Geographical structure; Spatial structure; Population structure; Subdivided populations; Migration; Long-distance migration (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:82:y:2012:i:1:p:22-28

DOI: 10.1016/j.tpb.2012.02.008

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