Genotype by Environment Interaction for Production Traits While Accounting for Heteroscedasticity

Grazing (G) provides an alternative management system for dairy production. Heteroscedasticity (HV) of the data may bias estimates of genetic correlations of yield traits between environments, an indicator of genotype-by-environment interaction (G×E). The objective of this study was to investigate the effect of HV on estimates of heritabilities and genetic correlations for mature-equivalent milk, protein, and fat yield, and lactation-average somatic cell scores of daughters, and to determine if HV affects the ability of sire's predicted transmitting ability (PTA) to predict daughter production in G and confinement (C) herds. Data consisted of 72,489 records from 35,674 cows in 366G herds from 11 states, and 117,629 records from 50,963 cows in 373C herds from the same 11 states plus 1 geographically contiguous state. Herds were divided into variance quartiles (QV1–QV4) based on milk yield. A transformation was used to reduce HV by standardizing the within-herd standard deviation to the average across-herd standard deviation of a base year for each parity, and was similar to the method used in current USDA-DHIA genetic evaluations. Regression of daughter yield on sire PTA showed that PTA overestimated production of all traits in QV1–QV3 and of milk in QV4 of G herds. For C herds, yields of milk in QV1 and QV2, and of protein and fat in QV1 were overestimated, and protein was underestimated in QV4. Reducing HV had little effect on G herds, but for C herds, regression did not differ from unity for milk and protein in QV1 and QV2. For milk, protein, and fat in G, heritabilities were approximately 0.17, 0.17, and 0.19, respectively. The heritabilities for milk, protein, and fat in C herds were approximately 0.16, 0.17, and 0.21, respectively. Genetic correlations between C and G did not suggest a G×E in 3 upper quartiles, but a possible G×E (correlation = 0.21, estimated standard error = 0.22) for the lowest quartile. Reducing HV did not affect estimates of heritabilities or genetic correlations. Results indicated that modest evidence for existence of G×E did not arise solely from HV.