Inbreeding coefficients for 9.3million registered Holsteins were computed by constructing a small relationship matrix for each animal and its ancestors instead of one large matrix for the whole population. Recent cows averaged 2.0% inbreeding if each pedigree path was extended to the most recent ancestor born before 1960. Inbreeding was underestimated because some pedigrees included unknown ancestors more recent than the defined base year. Alternative estimates of inbreeding can be derived by assigning mean relationship and inbreeding of known ancestors to unknown ancestors of the same period. Animals of different breeds are less related than animals of the same breed. Relationships and inbreeding within and across populations can be measured back to the common base population from which the breeds arose by treating earliest known ancestors within each breed as related and inbred. Increased heterozygosity and heterosis of crossbred animals are then predicted from their lower inbreeding coefficients. Relationship matrices that include related and inbred unknown-parent groups treated as random or fixed effects can be constructed and inverted quickly.
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