Use of nonlinear mixed models for describing testicular volume growth curve in Nellore bulls

This study aimed to describe longitudinal testicular volume (TV) data of Nellore bulls by using nonlinear mixed models. Dataset consisted of 2,294 TV measurements from 505 bulls with ages ranging from 563 to 4,307 days. Nine nonlinear models were evaluated: Brody, Gompertz, Hill, Logistic I and II, Meloun, Michaelis-Menten, Mitscherlich and von Bertalanffy. Goodness of fit was evaluated by Akaike's information criterion (AIC), Bayesian information criterion (BIC), adjusted R², percentage of convergence, error sum of squares (ESS), mean absolute deviation (MAD), and average prediction error (APE). These criteria were used to select the best model, then the absolute growth rate (AGR) for TV was estimated by the first derivate of the adjusted model related to time (∂Y/∂t). The values of adjusted R², ESS, MAD and APE were similar among models. Percentage of convergence was higher for the Logistic I (76.8%), Logistic II (75.5%) and Mitscherlich (78.6%) models, but Logistic I and II showed the lowest values of AIC and BIC, indicating a better fit, so the Logistic I model was chosen for subsequent analyses. The TV growth occurred at a high rate until the inflection point, which was estimated at approximately 22 months of age; it stabilized and reached a plateau at approximately 2,500 days of age. This may suggest that TV is more related to sexual maturity than precocity. Additionally, the Logistic I model was used to estimate the growth curve and the AGR of the testicular length and width. As a result, testicular length increased at a higher rate than testicular width until approximately 1,600 days of age, indicating that the testes become longer with increasing age.