Comparação de Alguns Modelos Matemáticos para Ajuste à Curva de Lactação Média de um Rebanho da Raça Caracu

Abstract

The present study was carried out to estimate the average lactation curve of 7239 lactations of Caracu cows based on 299,949 weekly records. The functions fitted to the mean data of the lactation curve were: Linear Hyperbolic and Logarithmic Quadratic as linear and Incomplete Gamma and Inverse Polynomial function as non-linear. The parameters were estimated by iterative methods, Gauss-Newton method. The adjusted Coefficient of Determination (R2A), the Durbin-Watson test (DW) and the deviations (%) from actual and predicted total milk yield were used as measurement of goodness of fit. The estimated residues, even though small, presented a positive serially correlation because the DW test was significant for the four studied functions, indicating violation of the assumption of the independence among the residues. The R2A were higher than 97%, and the deviations between actual and predicted milk yields were small, indicating that, in accordance with this criterion, any function could be used to fit the average lactation curve of the herd. Regarding to the components of the lactation curve the best approach was obtained by the Inverse Polynomial function for initial production, time and production on peak. The Incomplete Gamma and Logarithmic Quadratic functions presented similar adjustment, however, the first one presented better definition of parameters and components of the lactation curve.