Although crossbreeding is widely used in beef, sheep and swine industries, genetic evaluations are usually restricted to purebreds. The super-breed approach was suggested for genetic evaluation in multibreed populations, but has not been implemented to date. Theory of super-breed population parameters under one locus models was derived. An algorithm for setting up the inverse of a multibreed numerator relationship matrix needed in best linear unbiased prediction (BLUP) was given. The multiple trait (crossbred model) and super-breed approaches were investigated for genetic evaluation of purebreds and crossbreds. Data for two purebred swine lines A (n = 6,022), B (n = 24,170) and their reciprocal cross C (n = 6,135) was used. The traits in the study were lifetime daily gain (LDG) and backfat. The super-breed approach was not used due to difficulty in estimating relative inbreeding. Heritability (h2) estimates from within line and crossbred model analyses were similar. For LDG, h 2 estimates were .23, .28 and .27 for lines A, B and C, respectively. Corresponding heritability estimates for backfat were .53, 38 and .30. The genetic correlations between purebreds and crossbreds (rpc) were .45 (A-C), .64 (B-C) for LDG, .32 (A-C) and .70 (B-C) for backfat. To assess usefulness of crossbred information, mean accuracy was computed with the genetic covariance between purebreds and crossbreds present or ignored in the crossbred model. Increase in mean accuracy of predicted purebred breeding values was 2 to 9% with inclusion of crossbred data. Increase in mean accuracy of predicted crossbred breeding values with use of crossbred data was 21 to 72%. Rank correlations of breeding values from within line and crossbred models were high (>.99) for purebreds, but lower (≤.85) for crossbreds. Rank correlations of purebred breeding values from approximate and crossbred models were high (≥.96). It is concluded that gains in accuracy of predicted purebred breeding values with the crossbred model will be small with limited crossbred data, but may be substantial for crossbred breeding values. When variances are similar across lines, an approximate model can be used for joint evaluation of purebreds and crossbreds with negligible loss in selection accuracy.
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