Covariance function of Legendre polynomials for the modeling of Polled Nellore cattle growth in northern Brazil

Abstract

This study aimed to compare random regression models fitted by Legendre orthogonal polynomials and determine which best fits changes in Nellore cattle growth parameters. Age polynomial functions of different orders were evaluated using a random-effect modeling associated with a genetic study of cattle growth curves. For this purpose, weight records (15,148) were performed in Polled Nellore bovines (3,115), aged between 1 and 660 days, reared in northern Brazil and born between 1995 and 2010. The fixed effects of analytical models comprised age-matched groups, heifer calving age (linear and quadratic), and fourth-order Legendre age polynomial (cubic), depicting the mean growth curve. Besides, different order functions were considered for random effects, so that (co) variance associated with genetic effects (direct and maternal) and permanent environmental effects (animal and maternal) could be modeled. Residual variance was fitted by six heterogeneous classes throughout the analyzed period. According to AIC and BIC criteria, the model 6333 allowed the fitting of changes in variance and covariance over time (genetic and environmental). Thus, this model can be used to describe age-related changes in Polled Nellore cattle reared in northern Brazil.

Covariance functions under B-spline polynomials to model Polled Nellore cattle growth

“…Cavalcante et al (2019) reported similar behavior in Polled Nellore cattle from birth to 660 days of age. Conversely, maternal genetic variance by the linear model showed increasing values up to the 50th age class (255 to 260 days of age), tending to decline at older ages, and increasing the one that allowed better control of direct additive genetic variance.…”

“…The quadratic and cubic models with more segments had the lowest AIC values, with the lowest value for the model C8888, followed by the models Q7777, C8555, C8855, C7777, L6666, and C6555 models. Higher-order models with more segments are more malleable and best fitted to data, but their higher parametrization increases computational demand and hinders model convergence (Cavalcante et al, 2019). Therefore, the BIC criterion was also considered since it more rigorously penalizes parameterized models.…”

“…again at the end of the growth curve. Most studies that include maternal effects in growth analyses have generally shown reductions after weaning, indicating their low importance (Scalez et al, 2018;Cavalcante et al, 2019;Portes et al, 2020).…”

“…One alternative to traditional Legendre polynomials is segmented polynomials, which have shown promising results for beef cattle growth modeling (Boligon, Mercadante, Forni, Lôbo, & Albuquerque, 2012). A major advantage of segmented polynomials is allowing aggregation of several low-degree polynomial segments from specific positions, known as knots, forming a single continuous curve (Cavalcante et al, 2019).…”