Effect of Mating Structure on Variation

Measurement of linkage disequilibrium involves two sampling processes. First, there is the sampling of gametes in the population to form successive generations, and this generates disequilibrium dependent on the effective population size ( N , ) and the mating structure. Second, there is sampling of a finite number ( n ) of individuals to estimate the population disequilibrium. ---Two-locus descent measures are used to describe the mating system and are transformed to disequilibrium moments at the final sampling. Approximate eigenvectors for the transition matrix of descent measures are used to obtain formulae for the variance of the observed disequilibria as a function of Ne, mating structure, n, and linkage or recombination parameter.-The variance of disequilibrium is the same for monoecious populations with or without random selfing and for dioecious populations with random pairing for each progeny. With monogamy, the variance is slightly higher, the proportional difference being greater for unlinked loci. HERE is now an extensive theory on the generation of linkage disequilibrium drift in finite populations. Several early studies used haploid models on the assumption that these would be adequate for diploid organisms (e.g., HILL and ROBERTSON 1968). Comparisons of these haploid models with those for monoecious populations with random selfing suggest that there is indeed little difference in the results except for loosely linked loci which, although little disequilibrium OCCLWS between them, account for most pairs of loci in most species. The effects of different mating systems on moments of disequilibrium have not been adequately discussed, however, nor has the mating system been related to moments of the withinand between-gametes disequilibria of COCKERHAM and WEIR (1977). A convenient framework on which to build a theory of linkage disequilibrium is that of two-locus descent measures. For populations initially in linkage equilibrium, only those measures concerned with identity by descent are needed, and a number of transition matrices for these measures in various mating systems have been given by WEIR acd COCKERHAM (1969) and WEIR, AVERY and Paper No 6061 of the Journal Series of the North Carolina Agncultural Research Service, Raleigh, North Carolina. This investiga'ion was supported in part by Public Health Service grant GM 11546 2 Permanent address. Insbtute of Anunal Genencs, West Mans Road, Edinburgh EH9 3JN, Scotland Genetics 95: 477-488 June, 1980 478 B. S. WEIR AND W. G. HILL HILL (1980). Variability in linkage disequilibrium can be obtained from these matrices by suitable transformations. The observed variation in disequilibrium follows from the sampling processes implied in the measurement of the coefficients. First, there is the sampling of gametes to form successive generations. This between-line variation is controlled by the mating system and is dependent on effective size, N e . Second, there is the sampling of individuals to be scored, from which estimates are constructed. This is a within-line variation and is dependent on sample size, n.