Random regression models for the estimation of genetic and environmental covariance functions for growth traits in Santa Ines sheep

Abstract

ABSTRACT. Polynomial functions of different orders were used to model random effects associated with weight of Santa Ines sheep from birth to 196 days. Fixed effects included in the models were contemporary groups, age of ewe at lambing, and fourth-order Legendre polynomials for age to represent the average growth curve. In the random part, functions of different orders were included to model variances associated with direct additive and maternal genetic effects and with permanent environmental effects of the animal and mother. Residual variance was fitted by a sixth-order ordinary polynomial for age. The higher the order of the functions, the better the model fit the data. According to the Akaike information criterion and likelihood ratio test, a continuous function of order, five, five, seven, and three for direct additive genetic, maternal genetic, animal permanent environmental, and maternal permanent environmental effects (k = 5573), respectively, was sufficient to model changes in (co)variances with age. However, a more parsimonious model of order three, three, five, and three (k = 3353) was suggested based on Schwarz's Bayesian information criterion for the same effects. Since it was a more flexible model, model k = 5573 provided inconsistent genetic parameter estimates when compared to the biologically expected result. Predicted breeding values obtained with models k = 3353 and k = 5573 differed, especially at young ages. Model k = 3353 adequately fit changes in variances and covariances with time, and may be used to describe changes in variances with age in the Santa Ines sheep studied.

Growth and performance curve of dairy goats fed with detoxified castor bean cake by different alkaline solutions

“…On the other hand, Saanen goats fed DCC had lower adult weight (46.21 and 43.97 kg for those fed Ca(OH) 2 DCC and NaOH DCC diets, respectively), regardless of the detoxification process. Previous studies showed differences regarding the optimal adult size of an animal, which depends on both the species and the breed after selection practice, as well as the management system adopted and the climatic conditions (Magalhães, Lobo, & Facó, 2013;Sarmento et al, 2016). We verified that there was no difference between the diets on the growth curve of each breed from the contrast established between the curve parameters.…”

“…For the adjustment of non-linear models, we used the iterative procedure in view of which depends on the own estimated parameters, unlike the linear models that can be estimated directly (Sarmento et al, 2016). The criteria used to define the quality of adjustment of the model were: Residual Mean Square (RMS), obtained from the division of the sum of squares of the residue of the model by number of observations, the shorter the better fit of the model.…”

“…The criteria used to define the quality of adjustment of the model were: Residual Mean Square (RMS), obtained from the division of the sum of squares of the residue of the model by number of observations, the shorter the better fit of the model. According to the methodology proposed by Sarmento et al (2016), was calculated as the mean absolute deviation (MAD), asymptotic index (AI) and AIC (Akaike's criterion's Information Criterion). After choosing the model that best adjusted to the data for each breed were performed contrast of the curves of each diet to check the effect on the growth curve of Saanen and Anglo Nubian, it was estimated a curve for each diet and then were compared according to the following hypothesis: Ho:…”

“…The physiological condition of the animal can change markedly ingestion of food. In the growth phase, for example, there is a significant variation, the amending markedly the growth of animals (Sarmento et al, 2016). Through nutrition it is possible to change the curve of growth of animals, and the effects of this amendment will vary depending on the degree and duration of manipulation (Guevara et al, 2018).…”

Adaptability and stability analyses of plants using random regression models

“…One of the most standard ways of adding spatial variations to a statistical model is through structures of spatial variance and covariance, as proposed by Cullis and Gleeson [66] and later refined by Gilmour et al [67]. Furthermore, several studies have incorporated the effects of environmental covariates in their statistical models, through the inclusion of random effects in the incidence matrices [27,28,68,69].…”