Variance of effects of lactation stage within herd by herd yield

First-lactation test-day yields from New York, Wisconsin, and California herds with low (<7257 kg), medium (9072 to 9525 kg), and high (>11,340 kg) annual milk yields were adjusted additively for age and lactation stage. Two random regression models with third-order Legendre polynomials for permanent environmental and genetic effects were used. The second model also included a random effect with the same polynomial regressions for 2-yr intervals within herd (herd-stage effect). Mean adjusted test-day milk yields were 35.4 kg (75,838 test days in 9108 lactations) for high-yield herds, 28.8 kg (74,845 test days in 8887 lactations) for medium-yield herds, and 25.6 kg (71,996 test days in 8490 lactations) for low-yield herds. Although estimated phenotypic variances also declined with herd yield, those variances were surprisingly similar for medium- and low-yield herds. Herd-stage effect on phenotypic variance was negligible. Heritabilities for high- and medium-yield herds initially decreased and then gradually increased across lactation stages. Maximum heritability (0.33, high-yield herds; 0.30, mediumyield herds) was reached from 200 to 300 d in milk. Heritabilities were lower for low-yield herds but increased rapidly (maximum of 0.22 at lactation end). Introduction of a herd-stage effect eliminated the heritability decrease in early lactation for high- and medium-yield herds and reduced the increase in late lactation for low-yield herds. Heritabilities generally were lower with inclusion of a herd-stage effect, which indicated that variances for this effect were partly considered genetic in the less complete model. Herd-stage variances relative to phenotypic variance were highest at the beginning (12%) and end of lactation (7%) for medium-yield herds. Herd yield and stage had a large effect on variance size and change across lactation stages during first lactation and should be considered when accounting for heterogeneous variances in genetic evaluations.