Measurements of milk yield (MY), somatic cell score (SCS), percentage of fat (FP), protein (PP), lactose (LP), casein (CP) and percentage of palmitic (C16:0), stearic (C18:0), oleic (C18:1), total saturated (SFA), unsaturated (UFA), monounsaturated (MUFA) and polyunsaturated (PUFA) fatty acids in milk from 5,224 Holstein cows were evaluated as a function of a temperature and humidity index (THI). Legendre orthogonal polynomials from second to seventh order were tested. The best fit order for MY, PP and C18:0 was the third, whereas the second for all other traits. The heritability estimates decreased for MY (0.31 to 0.14), FP (0.28 to 0.16), LP (0.43 to 0.30), SCS (0.14 to 0.09), SFA (0.33 to 0.22) and C16:0 (0.31 to 0.26), whereas increased for CP (0.32 to 0.42), MUFA (0.08 to 0.13), UFA (0.07 to 0.11) and C18:1 (0.07 to 0.11) as the THI level increased. For PP, heritabilities (0.26 to 0.39) presented larger values in intermediate THI. For PUFA and C18:0, heritabilities were approximately constant (0.13 to 0.14 and 0.15, respectively). However, the greatest variations may have been the result of the limitations of Legendre polynomials at the extreme points of the curve, and the pattern of heritabilities curves was approximately constant for the evaluated traits. Spearman's rank correlations between breeding values in extreme THI levels were greater than 0.80 for all traits considering all animals, only cows and only bulls. When considering the top 1% and the top 50% animals (only cows, only bulls and all), Spearman correlations smaller than 0.70 were found, suggesting reranking of the animals. Although there was little variation in the variance components over THI, it is possible that there is no heat stress in the animals studied, because, on average, there was no great impact of the thermal load on the traits. One possible explanation is the use of herds with little climatic difference among herds, as well as the use of fans and sprinklers into the barns. However, the THI levels may be important factors in the selection process, as reranking of animals was verified.

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