 Clines with partial panmixia in an environmental pocketThomas Nagylaki, Linlin Su, Ian Alevy and Todd F. Dupont Theoretical Population Biology, 2014, vol. 95, issue C, 24-32 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 (i.e., asymptotically stable equilibria) maintained by migration and selection in an isotropic environmental pocket in n dimensions is investigated. The population density is uniform. Migration and selection are both weak; the former is homogeneous and isotropic; the latter is directional. If the scaled panmictic rate β≥1, then the allele favored in the pocket is ultimately lost. For β<1, a cline is maintained if and only if the scaled radius a of the pocket exceeds a critical value an. For a step-environment without dominance, simple, explicit formulas are derived for a1 and a3; an equation with a unique solution and simple, explicit approximations are deduced for a2. The ratio of the selection coefficients outside and inside the pocket is −α. As expected intuitively, the cline becomes more difficult to maintain; i.e., the critical radius an increases for n=1,2,3,… as α, β, or n increases. Keywords: Geographical structure; Spatial structure; Population structure; Migration; Long-distance migration; Selection (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:95:y:2014:i:c:p:24-32 DOI: 10.1016/j.tpb.2014.05.003 Access Statistics for this article Theoretical Population Biology is currently edited by Jeremy Van Cleve More articles in Theoretical Population Biology from Elsevier |
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