Additive and testcross genetic variances in crosses among recombinant inbreds

 Breeders desire populations with a high mean performance and a large genetic variance. Theory and methods are lacking for predicting additive variance (V _A ) and testcross variance (V _T ) in biparental populations. Breeders have unsuccessfully attempted to predict V _A based on the coefficient of coancestry ( f ) or molecular-marker similarity between parents. In this paper, we derive the expected values of V _A and V _T in biparental populations, examine the variability of V _A among biparental crosses, and discuss how V _A and V _T may be predicted in applied breeding programs. Suppose i is a recombinant inbred derived from the cross between inbreds P ₁ and P ₂, and inbred j is not a direct descendant of i. Let V _A(i,j) be the additive variance in the F₂ of the (i×j) biparental cross. Let V _T(i, j) be the variance among testcrosses of F₂ individuals with a specific unrelated inbred or population. Assuming linkage equilibrium and the absence of epistasis, V _A(i, j) =λV _A(P1, j) +(1−λ) V _A(P2, j) , where λ= parental contribution of P ₁ to i. Similarly, V _T(i, j) = λV _T(P1, j) +(1−λ) V _T(P2, j) . Additive variance in crosses between recombinant inbreds cannot be modelled as a function of  f if, as indicated in the literature, V _A differs among crosses of founder inbreds. If molecular-marker similarity between parents is used as an estimate of f, then a strong linear relationship is likewise not expected between V _A and marker similarity. Differences between the actual and expected λ led to variation in V _A . In applied breeding programs, modelling V _A or V _T in biparental crosses may be feasible with estimates of V _A or V _T in prior crosses and information on λ obtained from molecular-marker data. Received: 23 September 1997 / Accepted: 30 December 1997