Modelagem das trajetórias médias e funções de covariância do peso vivo e do rendimento de carcaça de Tilápias do Nilo (Oreochromis niloticus) utilizando polinômios B-spline

Abstract

Different statistical models were analyzed to identify the most appropriate to model the mean trajectories and covariance functions for body weight and carcass yield of Nile tilapia (Oreochromis niloticus) using quadratic B-spline polynomials. Data of body weight (8,758) and carcass yield (2,042) of tilapias with ages between 106 and 245 days were obtained from 72 families derived from 36 males and 72 females. The variables sex and tank were considered as classificatory fixed effects. The direct additive genetic, direct permanent environmental and residual were considered as random effects and statistical models were tested with and without the family random effect. The residual variances were modeled with two to five age classes and the coefficients of quadratic polynomials B-spline of two to five equidistant intervals were used as covariables. The mean trajectories of body weight and carcass yield depended on the sex and the tank. The models that considered the effects of sex and tank, the interaction of these factors and the quadratic B-spline polynomials nested within each level of the factors sex x tank were the most appropriate. The inclusion of those effects in the statistical models indicated differences in the mean trajectories of body weight and carcass yield according to sex and tank. Nesting the age effect in the interaction sex x tank is necessary in breeding programs of this species to ensure that the breeding values of the breeding candidates are not under or overestimated. With the increasing number of intervals of B-spline polynomials the number of basis functions is increased, which consequently improves the fit of the polynomials to the data. Most fitted criteria used indicated models with quadratic B-spline polynomial with five equidistant intervals as the best fit for both traits. For body weight, the inclusion of random family effect may have caused confounding between estimates of direct additive genetic and direct permanent environmental variances. For carcass yield, the inclusion of this random effect did not improve the fit. The heritability estimates for body weight ranged from 0.36 to 0.61, and for carcass yield from 0.18 to 0.76, indicating that these traits can be included as selection criteria in breeding programs of this species. The mean genetic correlations between the body weights at different ages were higher than 0.69 and 0.47 for carcass yield, suggesting that selection at early ages can be performed. The fit criteria indicated different models as the most adequate. Considering selection processes conducted based on genetic evaluations using the models identified with the best fitting, the selected individuals would be different. Consequently, there may be differences in responses to selection according to the statistical model considered. In real genetic evaluations, the choice of statistical models should be taken with prudence to optimize the genetic progress.