CALCULATION OF BREED DIRECT AND MATERNAL GENETIC FRACTIONS AND BREED SPECIFIC DIRECT AND MATERNAL HETEROZYGOSITY FOR CROSSBREEDING DATA

Teaching, research, and herd breeding applications may require calcula tion of breed additive contributions for direct and maternal genetic e ffects and fractions of heterozygosity associated with breed specific direct and maternal heterosis effects. These coefficients can be obtai ned from the first NE rows of a pseudo numerator relationship matrix w here the first NE rows represent fractional contributions by breed to each animal or group representing a specific breed cross. The table be gins with an NE x NE identity matrix representing pure breeds. Initial animals or representative crosses must be purebreds or two-breed cros ses. Parents of initial purebreds are represented by the corresponding column and initial two-breed cross progeny by the two corresponding c olumns of the identity matrix. Af ter that, usual rules are used to ca lculate the NE column entries corresponding to breeds for each animal. The NE entries are fractions of genes expected to be contributed by e ach of the pure breeds and correspond to the breed additive direct fra ctions. Entries in the column corresponding to the dam represent breed additive maternal fractions. Breed specific direct heterozygosity coe fficients are entries of an NE x NE matrix formed by the outer product of the two NE by 1 columns associated with sire and dam of the animal . One minus sum of the diagonals represents total direct heterozygosit y. Similarly, the NE x NE matrix formed by the outer product of column s associated with sire of dam and dam of dam contains breed specific m aternal heterozygosity coefficients. These steps can be programmed to create covariates to merge with data. If X represents these coefficien ts for all unique breed crosses, then the reduced row echelon form fun ction of MATLAB or SAS can be used on X to determine estimable functio ns of additive breed direct and maternal effects and breed specific di rect and maternal heterosis effects.