[en] Under projected climate changes, considerations for heat stress tolerance but also for genotype by environment interactions should enter breeding decisions, both for importing, but also exporting countries. Most studies concerning the breeding strategies on heat stress tolerance used the temperature humidity index (THI) to assess the thermal stress in a given environment and assumed a specific threshold to each studied population with the same response to each individual above this threshold. Recently new comprehensive thermal indices (TI) integrating radiation solar, wind speed, in addition to temperature and relative humidity were developed. Therefore, the aim of this study is advanced modelling of milk yield trait to evaluate the genetic variation in heat stress tolerance of Holsteins in a temperate environment using random regressions models and six new comprehensive TI. A total of 107,350 test day milk records were available for 12,099 primiparous Holsteins calving from 2000 to 2010. Test-day milk records were merged with meteorological data from 14 public weather stations across Luxembourg. Daily values of 6 new comprehensive TI (3 THI and 3 apparent temperature indices) were calculated by averaging hourly TI over 24 hours. The average distance between herds and their meteorological reference station was of 16 km. Sensitivity of cows to the climate environmental conditions was modelled by applying a reaction norm for each animal, representing its EBV for milk yield on values of the TI on the day in milk (DIM). Six separate random regression models were applied using time-dependent (DIM) and specific TI-dependent covariates. Random effects were additive genetic, permanent environmental, and herd year modelled with Legendre polynomials of order 2 for both DIM and TI. Genetic variances of the different TI evaluated in this study represent 27 to 30% of their correspondent variances for DIM effect. Permanent environmental and genetic variances of TI effect were in the same range. Additive genetic variances and heritabilities for daily milk yield slightly decreased with increasing degrees of the different THI and apparent temperature indices. The average daily milk heritability overall the lactation at the mean of each of the six TI was of 0.28. Genetic correlations between adjacent points across the lactation were > 0.90. Correlations between extreme distant DIM (e.g. early and late lactation stage) were reduced at 0.38 to 0.52. The overall genetic correlations between the different values of each TI remain high (> 0.85). EBV’s summing regular additive effect (DIM effect) and tolerance to heat stress (TI effect) were computed for several combinations of DIM and TI values. Ranking for sires and cows did not change among the 6 heat stress indicators. The correlations between EBVs estimated with the six models were greater than 0.90. In conclusion, the different models depicted genetic variation of milk yield among combinations of DIM and TI levels without defining thresholds in advance. Genetic variation was slightly lower when TI values exceed the thermoneutral zone. Breeding for reduced thermal sensitivity using any of the six indicators of heat stress evaluated in this study is possible. The indicator TI2 representing the adjusted THI for radiation solar and wind speed is favoured because it was the indicator that did identify the highest yearly milk losses under this continental temperate environment.
