Analysis of linkage disequilibrium in an island model
type: Item
instance of: scholarly article
title: Analysis of linkage disequilibrium in an island model
zbMATH Open document ID: 0586.92019
DOI: 10.1016/0040-5809(86)90008-0
author: Hidenori Tachida
author: C. Clark Cockerham
published in: Theoretical Population Biology
publication date: 1986-01-01T00:00:00Z
review text: Linkage disequilibria for two loci in a finite island model were parameterized. The total linkage disequilibrium was decomposed into three components, gametic, demic, and population, for which corresponding unbiased estimators were established. Other statistics encountered provided measures of differentiation corresponding to the hierarchical structure of the ecological model. Under the assumption of linkage equilibrium, the variances and covariances of these estimators and statistics were formulated in terms of descent measures, functions of gene frequencies, and the number of individuals, demes, and populations sampled. The functions of gene frequencies fall into two classes, one representing the differentiation of genes at each locus, and the other representing the association of genes between the loci. For a neutral model with extinction, migration, and linkage, transition equations were derived for the descent measures which also take into account deme size and numbers of demes within the population. With the addition of unequal mutation rates for a finite number of alleles at each locus, the transition equations were solved for the descent measures in the equilibrium state. This permitted the exact numerical evaluation of the effects of the sampling and ecological dimensions and of extinction, migration, and mutation rates in any parameter range. Some numerical results were presented for the effects of linkage, extinction, migration, and sampling on the variances of various measures of linkage disequilibrium and genetic differentiation. Also, some results were compared with the approximate numerical results of \textit{T. Ohta} [Proc. Natl. Acad. Sci. USA 79, 1940-1944 (1982; Zbl 0491.92013) and Genetics 101, 139-155 (1982)] which agreed fairly well in the parameter ranges she considered, but not so well in other ranges.
Mathematics Subject Classification ID: 92D40
Mathematics Subject Classification ID: 62P10
Mathematics Subject Classification ID: 92D10
zbMATH DE Number: 3941329
zbMATH Keywords: population genetics
zbMATH Keywords: Linkage disequilibria
zbMATH Keywords: finite island model
zbMATH Keywords: unbiased estimators
zbMATH Keywords: measures of differentiation
zbMATH Keywords: hierarchical structure
zbMATH Keywords: linkage equilibrium
zbMATH Keywords: variances
zbMATH Keywords: covariances
zbMATH Keywords: descent measures
zbMATH Keywords: functions of gene frequencies
zbMATH Keywords: demes
zbMATH Keywords: neutral model
zbMATH Keywords: extinction
zbMATH Keywords: migration
zbMATH Keywords: transition equations
zbMATH Keywords: mutation rates
zbMATH Keywords: numerical results
zbMATH Keywords: genetic differentiation
Wikidata QID: Q52643688
MaRDI profile type: Publication
full work available at URL: 0040-5809(86)90008-0
OpenAlex ID: W2023185254
cites work: Genetic variability and effective population size when local extinction and recolonization of subpopulations are frequent
cites work: Linkage disequilibrium due to random genetic drift in finite subdivided populations
cites work: Linkage and inbreeding coefficients in a finite random mating population
cites work: Q3996232
cites work: Q5803697
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description: scientific article; zbMATH DE number 3941329