Evolution under the multilocus Levene model without epistasis
Thomas Nagylaki
Theoretical Population Biology, 2009, vol. 76, issue 3, 197-213
Abstract:
Evolution under the multilocus Levene model is investigated. The linkage map is arbitrary, but epistasis is absent. The geometric-mean fitness, w̃(Ï ), depends only on the vector of gene frequencies, Ï ; it is nondecreasing, and the single-generation change is zero only on the set, Λ, of gametic frequencies at gene-frequency equilibrium. The internal gene-frequency equilibria are the stationary points of w̃(Ï ). If the equilibrium points Ï Ë† of Ï (t) (where t denotes time in generations) are isolated, as is generic, then Ï (t) converges as t→∞ to some Ï Ë†. Generically, Ï (t) converges to a local maximum of w̃(Ï ). Write the vector of gametic frequencies, p, as (Ï ,d)T, where d represents the vector of linkage disequilibria. If Ï Ë† is a local maximum of w̃(Ï ), then the equilibrium point (Ï Ë†,0)T is asymptotically stable. If either there are only two loci or there is no dominance, then d(t)→0 globally as t→∞. In the second case, w̃(Ï ) has a unique maximum Ï Ë† and (Ï Ë†,0)T is globally asymptotically stable. If underdominance and overdominance are excluded, and if at each locus, the degree of dominance is deme independent for every pair of alleles, then the following results also hold. There exists exactly one stable gene-frequency equilibrium (point or manifold), and it is globally attracting. If an internal gene-frequency equilibrium exists, it is globally asymptotically stable. On Λ, (i) the number of demes, Γ, is a generic upper bound on the number of alleles present per locus; and (ii) if every locus is diallelic, generically at most Γ−1 loci can segregate. Finally, if migration and selection are completely arbitrary except that the latter is uniform (i.e., deme independent), then every uniform selection equilibrium is a migration-selection equilibrium and generically has the same stability as under pure selection.
Keywords: Geographical structure; Spatial structure; Subdivided populations; Migration; Recombination (search for similar items in EconPapers)
Date: 2009
References: Add references at CitEc
Citations: View citations in EconPapers (4)
Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0040580909000963
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:76:y:2009:i:3:p:197-213
DOI: 10.1016/j.tpb.2009.07.003
Access Statistics for this article
Theoretical Population Biology is currently edited by N. Rosenberg
More articles in Theoretical Population Biology from Elsevier
Bibliographic data for series maintained by Catherine Liu (repec@elsevier.com).