Mathematical representations of correlations among yield traits and somatic cell score on test day.

Prediction of lactation yields and accuracies of yields for use in genetic evaluation can be improved by including information from test day correlations, especially for milk recording plans that vary in the numbers of milk weights recorded and component samples taken. Daily milk weights for 658 lactations of Canadian cows and monthly test records of milk, fat, and protein yields and somatic cell scores for 500,000 lactations of US cows were used to estimate phenotypic correlations between test days within herd-year. Correlations between daily yields for a designated interval between test days generally were highest for midlactation and were lowest for early and late lactation. Regression (two linear, two quadratic, and interaction effects) on mean DIM and interval between test days predicted correlations with a squared correlation of 0.94 for daily milk yields. Similar relationships were found for US monthly data. Variation in sampling was reduced, computer memory was minimized, and positive definiteness was guaranteed by fitting regressions on simply defined sources of correlation. An autoregressive matrix represented the within-trait correlations very well. The equations developed could be used to derive covariances and, subsequently, to estimate lactation yields and accuracies from combinations of individual daily milk, fat, and protein yields and somatic cell score.