Genetic (Co)Variances for Milk, Fat, and Protein Yield in Holsteins Using an Animal Model

First lactation milk, fat, and protein yields for first lactations of 8044 Holstein cows in New York from 24 herds were used to estimate genetic and phenotypic covariances with an animal model by restricted maximum likelihood. Numerator relationships within herd, including those from sires, were utilized, although relationships across herds were ignored. Each analysis was terminated after 300 rounds of iteration. Average milk production (twice daily milking, 305-d lactation, mature equivalent) was 8630 kg. Estimates were obtained for each individual herd and groups of 3, 6, and 12 herds. Average estimates from separate analyses of the 24 herds were nearly identical to those from combined analysis. Heritability estimates from combined analysis were .36, .35, and .33 for milk, fat, and protein yield with standard errors of approximately .03. Genetic correlations were .72 for milk and fat, .88 for milk and protein, and .77 for fat and protein. Phenotypic correlations were .81, .91, and .82. Heritabili ty estimates for individual herds were quite variable with standard errors of about .15. The largest environmental standard deviation for a herd was about twice the smallest. Estimates from only one analysis failed to converge-a group of three herds. All single herd analyses reached convergence as did the other 7 trios of herds and all sets of 6 and 12 herds. Received March 10, 1988. Accepted June 9, 1988. L. D. V A N VLECK and M. G. DONG Department of Animal Science Cornell University Ithaca, NY 14853 I N T R O D U C T I O N When inexpensive protein testing was introduced in the early 1980's, reports of heritabili ty for protein yield and correlations with milk and fat yield were rare and based on relatively small and difficult to obtain data sets (4, 16, 27). Review papers (1, 10, 14, 23) outl ined potential benefits and cost effectiveness of protein testing and selection. When multiple-trait (milk, fat, and protein) sire evaluation was introduced (9) in the Northeast, estimates of required genetic and phenotypic covariances were needed. Estimates obtained from small data sets available from paid testing for protein (15, 17) were marked by unrealistic estimates of the correlation between milk and fat and relatively small or inconsistent heritabil i ty estimates for milk, fat and protein. In fact, the genetic covariance matrix reported by Manfredi et al. (17) was negative definite. Lawlor's (15) estimates obtained from records based on the first 15 mo of widescale protein testing (July 1981 to September 1982) with a relatively large data set (37,233 first lactation records of daughters of 702 sires) using REML procedures, but not relationships among the sires, also featured very small estimates of heritabili ty (.20, .20, and .15 for milk, fat, and protein) and a relatively small estimate of the genetic correlation between milk and fat yield (.51). Because the data resulted mostly from daughters of proved bulls, heritability estimates might have been reduced because of selection. Hargrove et al. (11). using differences from modified contemporary averages and method 1 of Henderson (12), reported estimates similar to those of Lawlor (15). Cue et al. (5), also using a sire model and REML with relationships among sires considered to be zero and a Canadian Holstein data set smaller than that of Lawlor, reported estimates remarkably similar to those that are reported in this paper except for a smaller estimate of heritabili ty for protein yield. 1988 J Dairy Sci 71 : 3040-3046 3 040 GENETIC VARIANCES FOR MILK, FAT, AND PROTEIN 3041 Swalve and Van Vleck (21) used REML with a multiple-trait animal model to estimate the covariance structure among first three milk lactation records. The animal model for simultaneous bull and cow evaluation (20, 25, 26) will require estimates of variances appropriate to an animal model. The purposes of this study were 1) to obtain estimates of covariances needed for genetic evaluations for protein, fat, and milk with an animal model, 2) to examine groups of data sets to obtain some idea of the sampling variances of covariance matrices estimated from relatively small samples with an animal model, and 3) to determine the range of estimates obtained from individual herds, which is one possible approach to evaluation with heterogeneous genetic and environmental variances. M A T E R I A L S A N D M E T H O D S