Use of nonlinear models for describing scrotal circumference growth in Guzerat bulls raised under grazing conditions

The objective was to use various nonlinear models to describe scrotal circumference (SC) growth in Guzerat bulls on three farms in the state of Minas Gerais, Brazil. The nonlinear models were: Brody, Logistic, Gompertz, Richards, Von Bertalanffy, and Tanaka, where parameter A is the estimated testis size at maturity, B is the integration constant, k is a maturating index and, for the Richards and Tanaka models, m determines the inflection point. In Tanaka, A is an indefinite size of the testis, and B and k adjust the shape and inclination of the curve. A total of 7410 SC records were obtained every 3 months from 1034 bulls with ages varying between 2 and 69 months (731 days = 3652 SC measurements). Goodness of fit was evaluated by coefficients of determination (R2), error sum of squares, average prediction error (APE), and mean absolute deviation. The Richards model did not reach the convergence criterion. The R2 were similar for all models (0.68–0.69). The error sum of squares was lowest for the Tanaka model. All models fit the SC data poorly in the early and late periods. Logistic was the model which best estimated SC in the early phase (based on APE and mean absolute deviation). The Tanaka and Logistic models had the lowest APE between 300 and 1600 days of age. The Logistic model was chosen for analysis of the environmental influence on parameters A and k. Based on absolute growth rate, SC increased from 0.019 cm/d, peaking at 0.025 cm/d between 318 and 435 days of age. Farm, year, and season of birth significantly affected size of adult SC and SC growth rate. An increase in SC adult size (parameter A) was accompanied by decreased SC growth rate (parameter k). In conclusion, SC growth in Guzerat bulls was characterized by an accelerated growth phase, followed by decreased growth; this was best represented by the Logistic model. The inflection point occurred at approximately 376 days of age (mean SC of 17.9 cm). We inferred that early selection of testicular size might result in smaller testes at maturity.