Random regression analyses using B-spline functions to model growth of Nellore cattle

Abstract

The objective of this study was to estimate (co)variance components using random regression on B-spline functions to weight records obtained from birth to adulthood. A total of 82 064 weight records of 8145 females obtained from the data bank of the Nellore Breeding Program (PMGRN/Nellore Brazil) which started in 1987, were used. The models included direct additive and maternal genetic effects and animal and maternal permanent environmental effects as random. Contemporary group and dam age at calving (linear and quadratic effect) were included as fixed effects, and orthogonal Legendre polynomials of age (cubic regression) were considered as random covariate. The random effects were modeled using B-spline functions considering linear, quadratic and cubic polynomials for each individual segment. Residual variances were grouped in five age classes. Direct additive genetic and animal permanent environmental effects were modeled using up to seven knots (six segments). A single segment with two knots at the end points of the curve was used for the estimation of maternal genetic and maternal permanent environmental effects. A total of 15 models were studied, with the number of parameters ranging from 17 to 81. The models that used B-splines were compared with multi-trait analyses with nine weight traits and to a random regression model that used orthogonal Legendre polynomials. A model fitting quadratic B-splines, with four knots or three segments for direct additive genetic effect and animal permanent environmental effect and two knots for maternal additive genetic effect and maternal permanent environmental effect, was the most appropriate and parsimonious model to describe the covariance structure of the data. Selection for higher weight, such as at young ages, should be performed taking into account an increase in mature cow weight. Particularly, this is important in most of Nellore beef cattle production systems, where the cow herd is maintained on range conditions. There is limited modification of the growth curve of Nellore cattle with respect to the aim of selecting them for rapid growth at young ages while maintaining constant adult weight.Keywords: growth curve, covariance functions, segmented polynomials, Nellore cattle Implications Random regression models (RRMs) applying spline functions could be an option to model weights until mature age, as these functions are less susceptible to the problems frequently observed with orthogonal Legendre polynomials. However, to date there are no studies that have applied RRM on B-spline functions to estimate genetic parameters for weights in Nellore cattle. The results of this research showed that RRMs using Bspline functions revealed similar description of the trajectory of the variances and heritability estimates. Moreover, random regression on B-spline functions required lower computational requirement and faster convergence in relation to Legendre polynomials or multi-trait analysis. In genetic evaluation programs, with large data set, the application of RRMs using ...

Polynomials to model the growth of young bulls in performance tests

“…According to Meyer (2005), some effects of joints between pieces of polynomials may have contributed to the oscillations. In general, the results of the present study corroborate those of Albuquerque and Meyer (2001) and Boligon et al (2012), thereby suggesting that selection for body weight at any age changes the weight at any other age in the same direction. The estimates of correlations among weights were lower in the quadratic B-spline model using four regular intervals than in the quintic Legendre polynomial model.…”

“…The age intervals and distribution of records over the range of ages can also be important aspects of data fitting, and thus these factors may affect the type of polynomial that should be used. In addition to the wider range of ages, the distribution of weight records in the data set of Baldi et al (2010b) and Boligon et al (2012) was less stable than the distributions of records in the data sets of Meyer (2005) and the present data sets. These distributions might be an additional factor to consider before choosing the type of polynomial to be used in genetic evaluations.…”

“…These results are in agreement with those presented by Meyer (2005) for the weight of Angus cattle from birth to 820 days. However, Baldi et al (2010b) and Boligon et al (2012) found that Legendre polynomials performed better than linear, quadratic and cubic B-splines to fit Canchim and Nellore weight data from birth to adult age. According to Meyer (2005), the lower degrees of B-splines in the individual segments and the local rather than global influence of individual observations partially explain the better fit of B-splines.…”

“…The modelling of the fixed average growth trajectory and random additive genetic and permanent environmental effects by quadratic B-splines with three to four regular intervals (QBS5 and QBS6) provided a better fit with the weight data of Nellore and MA bulls submitted to performance tests than other models. Normally, a better fit can be achieved by increasing the number of intervals (Meyer, 2005;Baldi et al, 2010b;Boligon et al, 2012) because each quadratic B-spline function will be responsible for fitting a smaller interval. However, the minimum and mean individual numbers of the records may limit the slicing of an age interval.…”

“…Polynomials have frequently been used in studies conducted using beef cattle growth data, and the general functions that describe the average growth trajectory and the direct additive genetic and permanent environmental effects have been modelled using orthogonal polynomials, such as Legendre polynomials (Bohmanova et al, 2005;Boligon et al, 2010;Baldi et al, 2010a), or by B-spline polynomials (Meyer, 2005;Baldi et al, 2010b;Boligon et al, 2012).…”