Linkage disequilibrium in finite populations

Abstract

A theoretical investigation has been made of the influence of population size (N) and recombination fraction (c) on linkage disequilibrium (D) between a pair of loci. Two situations were studied: (i) where both loci had no effect on fitness and (ii) where they showed heterozygote superiority, but no epistacy. If the populations are initially in linkage equilibrium, then the mean value of D remains zero with inbreeding, but the mean of D2 increases to a maximum value and decreases until fixation is reached at both loci. The tighter the linkage and the greater the selection, then the later is the maximum in the mean of D2 reached, and the larger its value. The correlation of gene frequencies, r, in the population of gametes within segregating lines was also studied. It was found that, for a range of selection intensities and initial gene frequencies, the mean value of r2 was determined almost entirely by N c and time, measured proportional to N. The implication of these results on observations of linkage disequilibrium in natural populations is discussed. © 1968 Springer-Verlag.