On estimation of genetic variance within families using genome-wide identity-by-descent sharing

Traditionally, heritability and other genetic parameters are estimated from between-family variation. With the advent of dense genotyping, it is now possible to compute the proportion of the genome that is shared by pairs of sibs and thus undertake the estimation within families, thereby avoiding environmental covariances of family members. Formulae for the sampling variance of estimates have been derived previously for families with two sibs, which are relevant for humans, but sampling errors are large. In livestock and plants much larger families can be obtained, and simulation has shown sampling variances are then much smaller.

Based on the assumptions that realised relationship of sibs can be obtained from genomic data and that data are analyzed by restricted maximum likelihood, formulae were derived for the sampling variance of the estimates of genetic variance for arbitrary family sizes. The analysis used statistical differentiation, assuming the variance of relationships is small.

The variance of the estimate of the additive genetic variance was approximately proportional to 1/ (fn2σR2), for f families of size n and variance of relationships σR2.

Because the standard error of the estimate of heritability decreased in proportion to family size, the use of within-family information becomes increasingly efficient as the family size increases. There are however, limitations, such as near complete confounding of additive and dominance variances in full sib families.