Additive by additive variance with inbreeding and linkage.

Two-locus coancestries, which provide the coefficients of the additive by additive component in the variance and covariance of relatives for a quantitative trait, were formulated generally in terms of two-locus probabilities of identity by descent for combinations of parental and recombinant gametes. Explicit expressions, with linkage, were developed for all relatives of self-fertilization, for selfed and outbred relatives and for full and half sibs from unrelated inbred parents. The relative effect of linkage on the two-locus coancestry decreases rapidly as inbreeding and relatedness of the relatives increase. It was concluded that the error caused by ignoring linkage would probably be small in the estimation of genetic variances or in the projection of selection response with self-fertilization.