Genetic analysis of Holstein cattle populations in Brazil and the United States.

Genetic relationships between Brazilian and US Holstein cattle populations were studied using first-lactation records of 305-d mature equivalent (ME) yields of milk and fat of daughters of 705 sires in Brazil and 701 sires in the United States, 358 of which had progeny in both countries. Components of(co)variance and genetic parameters were estimated from all data and from within herd-year standard deviation for milk (HYSD) data files using bivariate and multivariate sire models and DFREML procedures distinguishing the two countries. Sire (residual) variances from all data for milk yield were 51 to 59% (58 to 101%) as large in Brazil as those obtained from half-sisters in the average US herd. Corresponding proportions of the US variance in fat yield that were found in Brazil were 30 to 41% for the sire component of variance and 48 to 80% for the residual. Heritabilities for milk and fat yields from multivariate analysis of all the data were 0.25 and 0.22 in Brazil, and 0.34 and 0.35 in the United States. Genetic correlations between milk and fat were 0.79 in Brazil and 0.62 in the United States. Genetic correlations between countries were 0.85 for milk, 0.88 for fat, 0.55 for milk in Brazil and fat in the US, and 0.67 for fat in Brazil and milk in the United States. Correlated responses in Brazil from sire selection based on the US information increased with average HYSD in Brazil. Largest daughter yield response was predicted from information from half-sisters in low HYSD US herds (0.75 kg/kg for milk; 0.63 kg/kg for fat), which was 14% to 17% greater than estimates from all US herds because the scaling effects were less severe from heterogeneous variances. Unequal daughter response from unequal genetic (co)variances under restrictive Brazilian conditions is evidence for the interaction of genotype and environment. The smaller and variable yield expectations of daughters of US sires in Brazilian environments suggest the need for specific genetic improvement strategies in Brazilian Holstein herds. A US data file restricting daughter information to low HYSD US environments would be a wise choice for across-country evaluation. Procedures to incorporate such foreign evaluations should be explored to improve the accuracy of genetic evaluations for the Brazilian Holstein population.

C. R. Henderson, the statistician; and his contributions to variance components estimation.

C. R. Henderson's 1953 Biometrics paper "Estimation of Variance and Covariance Components" is an outstanding landmark in the discipline of statistics. It sets out the very first ideas of how to estimate variance components from unbalanced (unequal subclass numbers) data in situations more complicated than the one-way classification (completely randomized design). As such it had three important, long-lasting impacts. First, it provided methods for actually using unbalanced data, even in large quantity, for estimating variance components. And this has played a tremendous role in population genetics and in animal breeding where the use of estimated variance components is vital to the application of selection theory and selection index techniques. Second, that 1953 paper stimulated numerous statisticians to become interested in random effects, mixed models, and variance components estimation, with such statistical greats as H. O. Hartley and C. R. Rao making contributions in the late 1960s and early 1970s. By then, improved methods of estimating variance components from unbalanced data had been developed, namely maximum likelihood (ML) and restricted maximum likelihood (REML). Once computing power had expanded to the point where these methods became feasible, Henderson made notable contributions to these methods, allied to his two great interests: animal breeding and feasible computing procedures. For both of these, his mixed model equations were a salient feature. Third, these methods reached a wide audience of geneticists and statisticians.

Phenotypic and genetic statistics of components of milk and two measures of somatic cell concentration.

Heritabilities, genotypic and phenotypic correlations for milk, fat, and protein yields, and two traits related to somatic cell concentration (cumulative lactation score and lactational somatic cell concentration) were estimated. A total of 18,416 first lactations of Holstein cows were analyzed by a new procedure for estimating variance components. Heritabilities were .21, .23, .19, .17, and .61 for milk, fat, and protein yields, cumulative lactation score, and lactational somatic cell concentration. Addition of protein yields to the current selection for two traits with nil economic value for protein would improve genetic gains for fat and milk yields in the northeastern United States. If cumulative lactation score and lactational somatic cell concentration were incorporated in current selection for two traits, restricted selection indexes should be used to avoid reduction in genetic gains for milk and fat yields.

The value of indirect selection : II. Progeny testing.

Conditions are developed under which progeny-testing using indirect selection can give more rapid genetic improvement than using direct selection. Analogous conditions for mass selection are given in Searle [1954].