Random regression models using different functions to model test-day milk yield of Brazilian Holstein cows

Abstract

ABSTRACT. We analyzed 152,145 test-day records from 7317 first lactations of Holstein cows recorded from 1995 to 2003. Our objective was to model variations in test-day milk yield during the first lactation of Holstein cows by random regression model (RRM), using various functions in order to obtain adequate and parsimonious models for the estimation of genetic parameters. Test-day milk yields were grouped into weekly classes of days in milk, ranging from 1 to 44 weeks. The contemporary groups were defined as herd-test-day. The analyses were performed using a single-trait RRM, including the direct additive, permanent environmental and residual random effects. In addition, contemporary group and linear and quadratic effects of the age of cow at calving were included as fixed effects. The mean trend of milk yield was modeled with a fourth-order orthogonal Legendre polynomial. The additive genetic and permanent environmental covariance functions were estimated by random regression on two parametric functions, Ali and Schaeffer and Wilmink, and on B-spline functions of days in milk. The covariance components and the genetic parameters were estimated by the restricted maximum likelihood method. Results from RRM parametric and B-spline functions were compared to RRM on Legendre polynomials and with a multi-trait analysis, using the same data set. Heritability estimates presented similar trends during mid-lactation (13 to 31 weeks) and between week 37 and the end of lactation, for all RRM. Heritabilities obtained by multi-trait analysis were of a lower magnitude than those estimated by RRM. The RRMs with a higher number of parameters were more useful to describe the genetic variation of test-day milk yield throughout the lactation. RRM using B-spline and Legendre polynomials as base functions appears to be the most adequate to describe the covariance structure of the data.

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

“…The LEG.55_ HE4 resulting in the best index value (Table 1). A similar result was observed by BIGNARDI et al (2011) andSANTOS et al (2014) for Holstein and Guzerá breeds, respectively. BROTHERSTONE et al (2000) observed that the non-linear parametric functions were more appropriate for adjusting the lactation curve of primiparous Holstein cows, compared to orthogonal Legendre polynomials with the same number of parameters.…”

“…The additive genetic variance estimated by the four models decreased from the first (@ 31.50) until the 17 th fortnight (@12.15), and increased at the end of lactation, where the WF.33_HE2 and LEG.33_HE2 reached values close to 19.00 and the LEG.55_HE4 reached 14.85 ( Figure 1A). Similar behavior was observed by BIGNARDI et al (2011) andPEREIRA et al (2010) for Holstein and Gir breed cows, respectively.…”

“…The WF.33_HE2 and LEG.33_HE2 presented estimations of genetic and permanent environment correlations, which decreased with an increase in distance among controls; however, negative correlations between the beginning and the end of lactation were verified only by genetic correlations (Figure 3). This behavior is probably associated with the difficulty to model milk production at the beginning of lactation (BIGNARDI et al, 2011), which can be explained by a reduced number of observations and by the proximity to postpartum and pregnancy beginning stress period (BIGNARDI et al, 2009). Negative correlations estimated by random regression models using different functions were shown by COBUCI et al (2005);COSTA et al (2008) andBIGNARDI et al (2011) in Holstein Friesian cows and by PEREIRA et al (2010) in the Gir breed.…”

“…This behavior is probably associated with the difficulty to model milk production at the beginning of lactation (BIGNARDI et al, 2011), which can be explained by a reduced number of observations and by the proximity to postpartum and pregnancy beginning stress period (BIGNARDI et al, 2009). Negative correlations estimated by random regression models using different functions were shown by COBUCI et al (2005);COSTA et al (2008) andBIGNARDI et al (2011) in Holstein Friesian cows and by PEREIRA et al (2010) in the Gir breed. The LEG55_HE4, among the three better models shown by the index, has the highest number of parameters (14 vs 34) and resulted in lower estimations of residual variance at the beginning and at the end of lactation, but overestimated the heritability in the first fortnight and presented a greater difficulty to model genetic and permanent environment correlations among controls.…”

A Comparison of Some Random Regression Models for First Lactation Test Day Milk Yields in Jersey Cows and Estimating of Genetic Parameters

“…TDMs analyzes individual test-day records instead of 305 day milk yields of cows, which are currently used by Ptak and Schaeffer [6] , Swalve [7] , Jamrozik and Schaeffer [8] , Pool and Meuwissen [9] , Schaeffer et al [10] , Takma and Akbas [11] , Takma and Akbas [12] , Bignardi et al [13] , Galic and Kumlu [14] .…”