Journal of Dairy Science, Vol 74, Issue 2 570-579, Copyright ©
1991 by American Dairy Science Association
Rapid inversion of additive by additive relationship matrices by including
sire-dam combination effects
P. M. VanRaden and I. Hoeschele
Animal
Improvement Programs Laboratory, United States Department of Agriculture,
Beltsville, MD 20705-2350.
Inverses of relationship matrices are useful for prediction of
individual additive or nonadditive genetic merits and for estimation
of variance components. An algorithm to form inverses of additive by
additive relationship matrices rapidly from lists of individuals and
their parents was developed. The algorithm uses simple recurrences
among additive by additive and sire-dam combination effects to
construct inverses for noninbred or inbred populations. Dimensions of
matrices produced may be several times the number of individuals in
the population because combination effects for sire-dam subclasses
must be included in matrices. Rules of inheritance of sire-dam
combination effects are the same as for dominance combination
effects. Cost of forming inverses increases linearly with number of
individuals. Each individual contributes 36 or fewer nonzero
coefficients, and each sire-dam subclass contributes an additional 81
or fewer nonzero coefficients to the matrix. Computation of inverse
of the relationship matrix due to 1003 sires and maternal grandsires
of 765,868 cows required forming a matrix of order 137,830 and 4
Mbytes of memory.
