Academic journal article Genetics

Linkage Disequilibrium under Skewed Offspring Distribution among Individuals in a Population

Academic journal article Genetics

Linkage Disequilibrium under Skewed Offspring Distribution among Individuals in a Population

Article excerpt


Correlations in coalescence times between two loci are derived under selectively neutral population models in which the offspring of an individual can number on the order of the population size. The correlations depend on the rates of recombination and random drift and are shown to be functions of the parameters controlling the size and frequency of these large reproduction events. Since a prediction of linkage disequilibrium can be written in terms of correlations in coalescence times, it follows that the prediction of linkage disequilibrium is a function not only of the rate of recombination but also of the reproduction parameters. Low linkage disequilibrium is predicted if the offspring of a single individual frequently replace almost the entire population. However, high linkage disequilibrium can be predicted if the offspring of a single individual replace an intermediate fraction of the population. In some cases the model reproduces the standard Wright-Fisher predictions. Contrary to common intuition, high linkage disequilibrium can be predicted despite frequent recombination, and low linkage disequilibrium under infrequent recombination. Simulations support the analytical results but show that the variance of linkage disequilibrium is very large.

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LINKAGE disequilibrium (LD) refers to the nonrandom association of alleles at different loci (Lewontin and Kojima 1960). Changes in population size, natural selection, population structure, and random drift can all lead to LD. Recombination, or the reciprocal exchange of material between homologous chromosomes, breaks down associations between alleles at different loci. Estimating LD can thus give insight into the forces that have shaped extant genetic diversity. The potential utility of LD for fine-scale mapping of human disease loci has also raised interest in estimating levels of linkage disequilibrium in human populations ( Jorde 1995; Lander 1996; Risch and Merikangas 1996). The evolutionary history of many organisms is marked by growth and decline of populations as well as various kinds ofsubdivision(withor withoutmigrationandadmixture). As an example, the Icelandic human population has undergoneseverebottlenecks, accompaniedbyrecentpopulation growth, in its ~1100-year history (Thorarinsson 1961; Thorsteinsson and Jónsson 1991; Jónsson and Magnússon 1997). Bataillon et al. (2006) report extensive linkage disequilibrium in the Icelandic human population and estimate the effective population size N^sub e^ to be ~5000, much less than the current census size of ~300,000 (Gardarsdóttir and Sigurjónsson 2006).

Linkage disequilibrium is a function of the frequencies of alleles in the population and LD can be quantified as a function of allele frequencies in a number of ways (cf. Hedrick 2000). One commonly used measure of LD is the coefficient D of linkage disequilibrium and is defined as the difference between the observed frequency of a gametic type (haplotype) and the frequency expected on the basis of random association of alleles in gametes (Lewontin and Kojima 1960). The coefficient D can be written as D = P^sub AB^P^sub ab^ - P^sub aB^PP^sub Ab^ in which P^sub xy^ is the frequency of haplotype xy. High absolute values of D correspond to high linkage disequilibrium in the population.

Following Slatkin (1994) we can understand the effects of population history on LDbetween two diallelic loci by considering the shape of the gene genealogy of a sample without recombination. In this case the alleles at both loci have the same gene genealogy. As an example, consider a population that has recently grown in size. Figure 1a shows a gene genealogy of a sample from a population that has experienced recent expansion. A single neutral mutation has arisen at each locus. The location of the mutations on the gene genealogy determines the level of linkage disequilibrium. Since neutral mutations arise randomly on the genealogy, the shape of the gene genealogy becomes a deciding factor. …

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