1	Predicting Genetic Interactions Within and Across Breeds
2	Modeling Genetic Interactions Crossbreeding and heterosis in an all-breed animal model Estimate breed differences routinely Recommend mating strategies Inbreeding depression adjustments in genetic evaluations Within-breed interactions predicted using dominance relationships
3	All-Breed Analyses Crossbred animals Will have EBVs, most did not before Reliable EBVs from both parents Purebred animals Information from crossbred relatives More contemporaries Routinely used in other populations New Zealand (1994), Netherlands (1997) USA goats (1989)
4	Purebred and Crossbred Data USA milk yield records
5	Across-Breed Methods All-breed animal model Purebreds and crossbreds together Age adjust to 36 months, not mature Variance adjustments by breed Unknown parents grouped by breed Westell groups instead of regressing on breed fractions General heterosis subtracted
6	Unknown Parent Groups Groups formed based on Birth year Breed Path (dams of cows, sires of cows, parents of bulls) Origin (domestic vs other countries) Paths have >1000 in last 15 years Groups each have >500 animals
7	All- vs Within-Breed Evaluations Correlations of PTA Milk
8	Display of PTAs Genetic base Compute on all-breed base Convert back to within-breed-of-sire bases for ease of comparing to previous PTA Heterosis and inbreeding Both effects removed in the animal model Heterosis added to crossbred animal PTA Expected Future Inbreeding (EFI) and genetic merit differ with mate breed
9	Within-Breed Methods Adjust for inbreeding depression Remove past F, include future F Expected future F (EFI) = .5 mean A_ij EBV₀ vs EBV_EFI vs unadjusted EBV Optimal selection theory Maximize w’ EBV₀ + b_y.F w’ A w Use of EBV₀ avoids double-counting
10	Effect of Inbreeding Adjustments Used in USA since 2005 Protein genetic trend estimates 3% more for EBV₀ than EBV 6% less for EBV_EFI than EBV Correlations of EBVs within breed .993 corr(EBV_EFI, EBV) for cows .998 corr(EBV_EFI, EBV) for bulls Select on EBV₀ for crossbreeding?
11	Within-Breed Interactions Dominance relationship matrix 5.5 million Holstein cows with data 1.6 million interactions among 4263 sires and maternal grandsires 30 minutes for D^-1, 16 hours to solve Dominance variance Assumed 5% of phenotypic variance Estimate from Van Tassell et al, 2000
12	Predicted Sire-MGS Interactions 305-d milk kg (heterosis = 318 kg)
13	Conclusions Can predict genetic interactions Inbreeding adjustments since 2005 All-breed animal model expected 2007 Sire-MGS dominance effects within breed mostly smaller than heterosis Future research on interactions Specific heterosis and epistasis Delivery of information to breeders