Random regression models using different functions to estimate genetic parameters for milk production in Holstein Friesians

The objective of this study was to compare the functions of Wilmink and Ali and Schaeffer with Legendre polynomials in random regression models using heterogeneous residual variances for modeling genetic parameters during the first lactation in the Holstein Friesian breed. Five thousand eight hundred and eighty biweekly records of test-day milk production were used. The models included the fixed effects of group of contemporaries and cow age at calving as covariable. Statistical criteria indicated that the WF.33_HE2, LEG.33_HE2, and LEG.55_HE4 functions best described the changes in the variances that occur throughout lactation. Heritability estimates using WF.33_HE2 and LEG.33_HE2 models were similar, ranging from 0.31 to 0.50. The LEG.55_HE4 model diverged from these models, with higher estimates at the beginning of lactation and lower estimates after the 16th fortnight. The LEG55_HE4, among the three better models indicated by the index, is the one with highest number of parameters (14 vs 34) and resulted in lower estimation of residual variance at the beginning and at the end of lactation, but overestimated heritability in the first fortnight and presented a greater difficulty to model genetic and permanent environment correlations among controls. Random regression models that used the Wilmink and Legendre polynomials functions with two residual variance classes appropriately described the genetic variation during lactation of Holstein Friesians reared in Rio Grande do Sul. RESUMO: Objetivou-se comparar as funções de Wilmink e Ali e Schaeffer com polinômios de Legendre em modelos de regressão aleatória, utilizando variâncias residuais heterogêneas, para modelar parâmetros genéticos ao longo da primeira lactação na raça Holandesa. Foram utilizados cinco mil oitocentos e oitenta registros quinzenais de produção de leite no dia do controle. Os modelos incluíram os efeitos fixos de grupo de contemporâneos e a idade da vaca ao parto como covariável. Os critérios estatísticos apontaram as funções WF.33_HE2, LEG.33_HE2 e a LEG.55_HE4 como as melhores em descrever as mudanças nas variâncias que ocorrem ao longo da lactação. As herdabilidades estimadas pelos modelos WF.33_HE2 e LEG.33_HE2 foram semelhantes, variando de 0,31 a 0,50. O LEG.55_HE4 divergiu destes, no início da lactação, com estimativas superiores e, a partir da 16ª quinzena, com estimativas inferiores. O LEG55_HE4, entre os três melhores modelos indicados pelo índice, é o mais parametrizado (14 vs