title: Clines with partial panmixia in an environmental pocket.
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.
authors.affiliation: Department of Ecology and Evolution, The University of Chicago, 1101 East 57th Street, Chicago, IL 60637, USA. Electronic address: nagylaki@uchicago.edu.
authors.forename: Thomas
authors.initials: T
authors.lastname: Nagylaki
authors.affiliation: Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria. Electronic address: linlin.su@univie.ac.at.
authors.forename: Linlin
authors.initials: L
authors.lastname: Su
authors.affiliation: Department of Applied Mathematics, Brown University, Providence, RI 02912, USA. Electronic address: ianalevy@gmail.com.
authors.forename: Ian
authors.initials: I
authors.lastname: Alevy
authors.affiliation: Departments of Computer Science and Mathematics, The University of Chicago, Chicago, IL 60637, USA. Electronic address: dupont@cs.uchicago.edu.
authors.forename: Todd F
authors.initials: TF
authors.lastname: Dupont
mesh_terms: D000483:Alleles; D017753:Ecosystem; D004641:Emigration and Immigration; D012641:Selection, Genetic
keywords: Geographical structure; Long-distance migration; Migration; Population structure; Selection; Spatial structure