Evaluation of four mathematical functions to describe scrotal circumference maturation in Nellore bulls

Four functions to characterize scrotal circumference (SC) growth in Nellore bulls were compared to identify which was the most suitable for biological interpretation. Nellore bulls (n = 532), born between September and December of 1992 to 1994 were used in the study. Measurements were made on fixed dates in January, April, July and October of each year. At the time of SC measurements, the ages of the bulls ranged from 200 to 1300 d. The functions used to describe the data were: Brody, SC = A (1 - B exp -kt); Logistic, SC = A/(1 + B exp -kt); Gompertz, SC = A exp(-B exp -kt) and Richards SC = A (1 + B exp -kt)m, where SC is the scrotal circumference at t days of age, A is the estimated SC at maturity, B is the integration constant established by the initial values of SC and t, k is the maturity constant, which equals the ratio between the maximum rate of growth and SC at maturity; m is the inflection point parameter for Richards function, which did not converge. The Brody, Gompertz and Logistic functions fitted the data in a similar fashion, with similar values for the statistics EMS and R2, and they reached convergence with similar computational costs. The Logistic function presented the best pattern of average prediction error, and therefore, it was selected for biological interpretation. For the Logistic function, estimated SC at maturity (A) was 37.95 cm at 72 mo of age. The maturity index (k) was .11 cm, and the inflection point (time of maximum growth) was reached at 13.09 mo of age at an average SC of 18.97 cm.