Quirino C R, Bergmann J A, Vale Filho V R, Andrade V J, Pereira J C
Escola de Veterinária, Universidade Federal de Minas Gerais, Brazil.
Theriogenology. 1999 Jul 1;52(1):25-34. doi: 10.1016/s0093-691x(99)00107-7.
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.
比较了四种用于表征内洛尔公牛阴囊周长（SC）生长的函数，以确定哪种函数最适合进行生物学解释。本研究使用了1992年9月至1994年12月出生的内洛尔公牛（n = 532）。每年1月、4月、7月和10月的固定日期进行测量。在测量SC时，公牛的年龄范围为200至1300天。用于描述数据的函数为：布罗迪函数，SC = A (1 - B exp -kt)；逻辑斯蒂函数，SC = A/(1 + B exp -kt)；冈珀茨函数，SC = A exp(-B exp -kt)；以及理查兹函数，SC = A (1 + B exp -kt)m，其中SC是t日龄时的阴囊周长，A是成熟时的估计SC，B是由SC和t的初始值确定的积分常数，k是成熟常数，等于最大生长速率与成熟时SC的比值；m是理查兹函数的拐点参数，该参数未收敛。布罗迪函数、冈珀茨函数和逻辑斯蒂函数以类似的方式拟合数据，统计量EMS和R²的值相似，并且它们以相似的计算成本达到收敛。逻辑斯蒂函数呈现出最佳的平均预测误差模式，因此被选用于生物学解释。对于逻辑斯蒂函数，72月龄时成熟时的估计SC（A）为37.95厘米。成熟指数（k）为0.11厘米，在13.09月龄时达到拐点（最大生长时间），平均SC为18.97厘米。
