Random regression models using Legendre polynomials or linear splines for test-day milk yield of dairy Gyr (Bos indicus) cattle

Abstract

Studies investigating the use of random regression models for genetic evaluation of milk production in Zebu cattle are scarce. In this study, 59,744 test-day milk yield records from 7,810 first lactations of purebred dairy Gyr (Bos indicus) and crossbred (dairy Gyr × Holstein) cows were used to compare random regression models in which additive genetic and permanent environmental effects were modeled using orthogonal Legendre polynomials or linear spline functions. Residual variances were modeled considering 1, 5, or 10 classes of days in milk. Five classes fitted the changes in residual variances over the lactation adequately and were used for model comparison. The model that fitted linear spline functions with 6 knots provided the lowest sum of residual variances across lactation. On the other hand, according to the deviance information criterion (DIC) and bayesian information criterion (BIC), a model using third-order and fourth-order Legendre polynomials for additive genetic and permanent environmental effects, respectively, provided the best fit. However, the high rank correlation (0.998) between this model and that applying third-order Legendre polynomials for additive genetic and permanent environmental effects, indicates that, in practice, the same bulls would be selected by both models. The last model, which is less parameterized, is a parsimonious option for fitting dairy Gyr breed test-day milk yield records.

Random regression models to estimate genetic parameters for milk production of Guzerat cows using orthogonal Legendre polynomials

“…(Tables 3 and 4). The genetic correlation estimates obtained with the RRMs were high and near the unity for the adjacent records, with the values declining as the interval between the test-day records increased (Tables 3). The same tendency was reported by Bignardi et al (2009) for the Holstein breed, by Kettunen et al (2000) for the Ayrshire breed, by Herrera et al (2008), and Pereira et al (2013b) for the Gyr breed, and Santos et al (2013a) for the Guzerat breed, all of them using parametric function. The three RRMs (Leg.3.5.6, Leg.3.6.6 and Leg.6.6.6) showed negative genetic correlation estimates between milk yield in the first and in the last test-day records, but of small magnitudes.…”

“…Also Pereira et al (2010) observed the similar estimates as the ones of the present study, but in a lager range (0.09 to 0.33). Costa et al (2005), using Legendre polynomials for the Gyr breed, found higher heritability values, which ranged from 0.71, at the start, to 0.21 at the end of lactation, while Pereira et al (2013aPereira et al ( , 2013b found lower estimates, which ranged from 0.12 to 0.24 and from 0.12 to 0.26, respectively. These last authors used Spline function for estimating heritabilities, which ranged from 0.16 to 0.29 .…”

Depressão endogâmica na produção de leite no dia do controle de bovinos Gir leiteiro

“…O pico de produção ocorreu, em média, entre os dias 35 e 79 da lactação, mais tarde do que o relatado por Pereira et al (2013aPereira et al ( , 2013b e a fase da lactação. Nas DIF analisadas dentro de cada fase da lactação (Tabela 2), observaram-se diferenças entre as classes de ∆F i .…”

“…A e p são, respectivamente, as matrizes de covariâncias genético-aditivas e de ambiente permanente entre os coeficientes de regressão; R é a matriz de variâncias residuais, que é uma matriz diagonal com componentes de variância específicos para os intervalos 5-30, 31-60, 61-120, 121-270 e 271-305 dias em lactação, conforme descrito por Pereira et al (2013b). Além disso, assumiu-se que os resíduos para diferentes dias da lactação eram não correlacionados.…”

“…Ferreira et al (1999) comparam modelos com ou sem o efeito fixo de F i , sobre características de crescimento de bovinos da raça Hereford, e concluíram que não houve diferenças entre as estimativas de herdabilidade ao compararem os modelos. As estimativas de herdabilidade variaram entre 0,17 e 0,22 e foram semelhantes às reportadas por Pereira et al (2013aPereira et al ( , 2013b, que trabalharam com parte do conjunto de dados utilizados no presente estudo.…”