Growth curve for height at withers of Mangalarga Marchador horses with heterocedasticity

ABSTRACT This work aimed to evaluate the fit of models Brody, Gompertz, Logistic and Von Bertalanffy to height at the withers of Mangalarga Marchador horses, weighed by the inverse of variance, in order to select the best model and predict growth and maturity of this breed pf animals. We used data of 230 equines from 06 to 176 months of age who were divided by sex and 16 age classes. The models were compared according to the quality assessors: coefficient of determination (R2); residual standard deviation (RSD) and Akaike information criteria (AIC). The estimation of the parameters from models was performed by the weighted least squares method in Software R. All models evaluated were suitable to describe the growth curve in both sexes. In view of the evaluators used, the logistic model was the most suitable to describe the growth curves in withers height in both sexes for the race Mangalarga Marchador. A strong growth at first age was also observed. The males reached a greater adult height, but females did so sooner, because they presented higher estimates for the maturity index.

摘要 本研究旨在以方差倒数加权的方式，评估Brody模型（Brody）、Gompertz模型（Gompertz）、Logistic模型（Logistic）以及冯·贝塔朗菲模型（Von Bertalanffy）对曼加尔加-马查杜马（Mangalarga Marchador）肩高（height at the withers）的拟合效果，以期筛选最优模型并预测该品种马的生长与成熟规律。
本研究选取230匹月龄介于6至176个月的马属动物，按性别分层并划分为16个年龄组。采用决定系数（coefficient of determination, R²）、剩余标准差（residual standard deviation, RSD）以及赤池信息准则（Akaike information criterion, AIC）作为模型拟合优度评价指标，对上述模型进行比较。模型参数估计采用加权最小二乘法，借助R语言（R）软件完成。
所有供试模型均可准确描述雌雄两性马的生长曲线。基于本次采用的评价指标，Logistic模型最适于描述曼加尔加-马查杜马雌雄两性的肩高生长曲线。研究同时发现，该品种马在幼年阶段生长速率极快。公马的成年体高更高，但母马的成熟更早，这是因为母马的成熟指数估计值更高。