Clines with complete dominance and partial panmixia in an unbounded unidimensional habitat

Thomas Nagylaki and Kai Zeng

Theoretical Population Biology, 2014, vol. 93, issue C, 63-74

Abstract: In spatially structured populations, global panmixia can be viewed as the limiting case of long-distance migration. The effect of incorporating partial panmixia into diallelic single-locus clines maintained by migration and selection with complete dominance in an unbounded unidimensional habitat is investigated. The population density is uniform. Migration and selection are both weak; the former is homogeneous and symmetric; the latter is frequency independent. The spatial factor g̃(x) in the selection term, where x denotes position, is a single step at the origin: g̃(x)=−α<0 if x<0, and g̃(x)=1 if x>0. If α=1, there exists a globally asymptotically stable cline. For α<1, such a cline exists if and only if the scaled panmictic rate β is less than the critical value β∗∗=2α/(1−α). For α>1, a unique, asymptotically stable cline exists if and only if β is less than the critical value β∗; then a smaller, unique, unstable equilibrium also exists whenever β<β∗. Two coupled, nonlinear polynomial equations uniquely determine β∗. Explicit solutions are derived for each of the above equilibria. If β>0 and a cline exists, some polymorphism is maintained even at x=±∞. Both the preceding result and the existence of an unstable equilibrium when α>1 and 0<β<β∗ differ qualitatively from the classical case (β=0).

Keywords: Geographical structure; Spatial structure; Population structure; Migration; Long-distance migration; Selection (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0040580914000045
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:thpobi:v:93:y:2014:i:c:p:63-74

DOI: 10.1016/j.tpb.2014.01.003

Access Statistics for this article

Theoretical Population Biology is currently edited by Jeremy Van Cleve

More articles in Theoretical Population Biology from Elsevier
Bibliographic data for series maintained by Catherine Liu ().