Classical nonlinear models to describe the growth curve for Murrah buffalo breed

With the objective of to adjust nonlinear models for the growth curves for a buffaloes herd raised in floodable lands in Rio Grande do Sul state, monthly records measured from birth to two years-old of 64 males and 63 females born between 1982 and 1989 were used. The models used were: Von Bertalanffy, Brody, Gompertz and Logistic. The parameters were estimated by NLIN procedure and the criteria used to evaluate the adjustment given by the models were: asymptotic standard deviation; coefficient of determination; average absolute deviation of residues and asymptotic index. Von Bertalanffy and Brody models overestimated the male asymptotic weight (A) in 15.9 and 171.3kg, respectively, and the Gompertz and Logistic models underestimated it in 4.5 and 13.4kg, respectively. For females, the Logistic model underestimated the asymptotic weight (-2.09kg), and Gompertz, Von Bertalanffy and Brody overestimated this parameter in 8.04, 17.7, and 280.33kg, respectively. The biggest average deviation was estimated by Brody model for both sexes, characterizing the biggest index. Considering the criteria, it is recommended the Gompertz and Logistic models for adjust females and males Murrah buffaloes breed growth curves.Com o objetivo de ajustar modelos não-lineares ao crescimento ponderal para búfalos criados em terras baixas no Estado do Rio Grande do Sul, foram utilizados registros mensais mensurados do nascimento aos dois anos de idade de 64 machos e 63 fêmeas, nascidos no período de 1982 a 1989. Utilizaram-se os modelos: Von Bertalanffy, Brody, Gompertz e Logístico. Os parâmetros foram estimados usando o procedimento NLIN e os critérios utilizados para verificar o ajuste dos modelos foram: desvio padrão assintótico; coeficiente de determinação; desvio médio absoluto dos resíduos e o índice assintótico. Os modelos Von Bertalanffy e Brody superestimaram o peso assintótico (A) para os machos em 15,9 e 171,3kg, respectivamente, e os modelos Gompertz e Logístico, subestimaram em 4,5 e 13,4kg, respectivamente. Para as fêmeas, o modelo Logístico subestimou o peso assintótico (-2,09kg) e os modelos Gompertz, Von Bertalanffy e Brody superestimaram esse parâmetro em: 8,04; 17,7 e 280,33kg, respectivamente. O maior desvio médio absoluto foi estimado pelo modelo Brody para ambos os sexos, caracterizando o melhor índice. Considerando os critérios, recomenda-se o modelo Gompertz e o modelo Logístico para ajustar a curva de crescimento de fêmeas e machos da raça Murrah

Critical points on growth curves in autoregressive and mixed models

Adjusting autoregressive and mixed models to growth data fits discontinuous functions, which makes it difficult to determine critical points. In this study we propose a new approach to determine the critical stability point of cattle growth using a first-order autoregressive model and a mixed model with random asymptote, using the deterministic portion of the models. Three functions were compared: logistic, Gompertz, and Richards. The Richards autoregressive model yielded the best fit, but the critical growth values were adjusted very early, and for this purpose the Gompertz model was more appropriate