Journal of Dairy Science, Vol 74, Issue 2 557-569, Copyright ©
1991 by American Dairy Science Association
Rapid inversion of dominance relationship matrices for noninbred populations
by including sire by dam subclass effects
I. Hoeschele and P. M. VanRaden
Department
of Dairy Science, Virginia Polytechnic Institute and State University,
Blacksburg 24061-6999.
For estimation of dominance effects and dominance variance, the inverse
of a dominance relationship matrix is required. Dominance effects can
be partitioned into sire x dam or sire x maternal grandsire subclass
effects that are inherited and residuals within subclass that are not
inherited. The subclass effects have immediate use in predicting
performance of offspring from prospective matings. A rapid method for
directly computing the inverse relationship matrix of subclass
effects is presented. The procedure is similar to Henderson's simple
method of computing an inverse additive genetic relationship matrix.
The inverse relationship matrix among subclass effects consists of a
contribution from each subclass of coefficients of a matrix of
maximum size 9 x 9. The algorithm can be modified to compute the
inverse of the relationship matrix among sire x dam or sire x
maternal grandsire subclasses and among individual dominance effects.
Computing cost increases approximately linearly with dimensions of
inverses. Dimensions could be several times the number of subclasses in
the data because subclasses without records but providing
relationship ties must be added. Computation of the inverse
relationship matrix among 136,827 sire x maternal grandsire
subclasses in a population of 765,868 animals required 163 central
processing unit seconds on an IBM 3090 and less than 4 Mbytes of
memory.
