Linkage Disequilibrium with the Island Model

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Linkage disequilibrium between two linked loci was studied for a finite population with a subdivided population structure. Wright's island model was used; extinction and replacement of colonies were also incorporated. Two alleles (A1 and A2 at the first locus, and B1 and B2 at the second locus) with symmetric mutation rates were assumed, and equilibrium properties of linkage disequilibrium coefficients were analyzed. In terms of analogy with the subdivision of inbreeding coefficient, the variance of linkage disequilibrium is divided into several components: D2IS (variance of within-colony disequilibrium), D2ST (variance of correlation of A1 and B1 of different gametes of one colony relative to that of the total population), and D2IT (total variance of disequilibrium). Other subdivisions are D'2IS (variance of correlation of A1 and B1 of one gamete of a colony relative to that of the average gamete of the population) and D'2ST (variance of the ordinary disequilibrium of the whole population). When migration is limited, the variance becomes large if the correlation of A1 and B1 of one colony is taken relative to that of the whole population (D2ST and D'2IS). Also, when the rate of extinction-replacement of colonies is high, the whole-population disequilibrium coefficient (D'2ST) can become fairly large. Observed linkage disequilibria, such as those among markers in the major histocompatibility complex of man and mouse, may well be explained by limited migration, without assuming epistatic natural selection.

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