Forni S, Piles M, Blasco A, Varona L, Oliveira H N, Lôbo R B, Albuquerque L G
Faculdade de Ciências Agrárias e Veterinárias, Universidade Estadual Paulista Julio de Mesquita Filho, Jaboticabal, São Paulo, 14884900, Brazil.
J Anim Sci. 2009 Feb;87(2):496-506. doi: 10.2527/jas.2008-0845. Epub 2008 Aug 15.
This work aims to compare different nonlinear functions for describing the growth curves of Nelore females. The growth curve parameters, their (co)variance components, and environmental and genetic effects were estimated jointly through a Bayesian hierarchical model. In the first stage of the hierarchy, 4 nonlinear functions were compared: Brody, Von Bertalanffy, Gompertz, and logistic. The analyses were carried out using 3 different data sets to check goodness of fit while having animals with few records. Three different assumptions about SD of fitting errors were considered: constancy throughout the trajectory, linear increasing until 3 yr of age and constancy thereafter, and variation following the nonlinear function applied in the first stage of the hierarchy. Comparisons of the overall goodness of fit were based on Akaike information criterion, the Bayesian information criterion, and the deviance information criterion. Goodness of fit at different points of the growth curve was compared applying the Gelfand's check function. The posterior means of adult BW ranged from 531.78 to 586.89 kg. Greater estimates of adult BW were observed when the fitting error variance was considered constant along the trajectory. The models were not suitable to describe the SD of fitting errors at the beginning of the growth curve. All functions provided less accurate predictions at the beginning of growth, and predictions were more accurate after 48 mo of age. The prediction of adult BW using nonlinear functions can be accurate when growth curve parameters and their (co)variance components are estimated jointly. The hierarchical model used in the present study can be applied to the prediction of mature BW in herds in which a portion of the animals are culled before adult age. Gompertz, Von Bertalanffy, and Brody functions were adequate to establish mean growth patterns and to predict the adult BW of Nelore females. The Brody model was more accurate in predicting the birth weight of these animals and presented the best overall goodness of fit.
本研究旨在比较用于描述内罗尔母牛生长曲线的不同非线性函数。通过贝叶斯层次模型联合估计生长曲线参数、它们的（协）方差分量以及环境和遗传效应。在层次结构的第一阶段，比较了4种非线性函数：布罗迪函数、冯·贝塔朗菲函数、冈珀茨函数和逻辑斯蒂函数。使用3个不同的数据集进行分析，以检验拟合优度，同时考虑记录较少的动物。考虑了关于拟合误差标准差的3种不同假设：整个轨迹上恒定、直到3岁线性增加然后恒定、以及遵循层次结构第一阶段应用的非线性函数变化。基于赤池信息准则、贝叶斯信息准则和偏差信息准则对整体拟合优度进行比较。应用格尔范德检验函数比较生长曲线不同点的拟合优度。成年体重的后验均值范围为531.78至586.89千克。当认为拟合误差方差沿轨迹恒定时，观察到成年体重的估计值更大。这些模型不适用于描述生长曲线开始时的拟合误差标准差。所有函数在生长开始时提供的预测不太准确，而在48月龄后预测更准确。当联合估计生长曲线参数及其（协）方差分量时，使用非线性函数预测成年体重可以是准确的。本研究中使用的层次模型可应用于部分动物在成年前被淘汰的牛群中成年体重的预测。冈珀茨函数、冯·贝塔朗菲函数和布罗迪函数足以建立平均生长模式并预测内罗尔母牛的成年体重。布罗迪模型在预测这些动物的出生体重方面更准确，并且总体拟合优度最佳。
