A Comparison of Nonlinear Models for Describing Weight-Age Relationships in Cattle1

Comparison of non-linear growth models to describe the growth curve in West African Dwarf sheep

“…of monthly weight from birth to 180 days of age, the level of significance of fixed effects, the coefficient of determination (R 2 ) and the coefficient of variation (CV) indicated by the proc GLM Fixed effect BW (889) W30 (864) W60 (831) W90 (778) W120 (728) W150 (594) W180 (590) Season of birth ** ** * ** ** ns ns Dry season (2420) 1.71 6 0.02 (390) The goodness of fit was assessed by using the higher R 2 , the lower MSE and AIC values (Brown et al, 1976;Akbas et al, 1999;Topal et al, 2004;Lambe et al, 2006). Even though the selected models provide a view of the predicted weight at fixed age, the parameters A, B and k of the significant effect of season of birth, sex of the lamb, the parity of dam, the type of birth and the year of birth on the observed weight, have been calculated separately (Matlab R , 2006) simulating specific slop of the selected growth curve.…”

“…In previous studies, a broad range of models have been selected, depending on how accurately they fit the data. The Brody model has been similarly selected in cattle (Brown et al, 1976;DeNise and Brinks, 1985;Doren et al, 1989) due to its ability to accommodate missing growth points and converges easily (Kaps et al, 1999). In the Bergamasca sheep in Brazil (McManus et al, 2003), among the fitted growth models (Brody, Richards, and Logistic), the Logistic model showed the goodness of fit.…”

“…However, the advantage of growth models such as Logistic and Gompertz (Renne et al, 2003;Lambe et al, 2006), Von Bertalanffy (Topal et al, 2004) and Brody model (Bathaei and Leroy, 1998), which give an explanation of what is biologically occurring during the growth phase of an animal, and their importance on breeding program (Varona et al, 1997;Lewis and Brotherstone, 2002) were unknown in WAD sheep. Therefore, model selection to predict typical growth in livestock industry, became a daunting task, given the broad range of criteria for goodness of fit, as the Akaike's Information Criteria (AIC) (Akaike, 1974), the coefficient of determination (R 2 ), the mean squares errors (MSE), the loglikelihood (lnL) values, and the least average prediction error (APE) (Brown et al, 1976;Goonewardene et al, 1981;Beltran et al, 1992;Lambe et al, 2006).…”

Critical points on growth curves in autoregressive and mixed models

“…On average, the logistic function presents lower estimates of asymptote, in relation to the other functions (Table 3). It seems to be a characteristic of logistics, underestimate mature weights and overestimate them in the early stages (Brown et al, 1976). This is probably due to the location of the point of infl ection, fi xed at one half of the asymptote.…”

“…Brown et al (1976), with weight-age data for female cattle, attributed the diffi culty of convergence in the Richards function mainly to the high negative value found for the residual correlations between the parameters  and , -0.97. In this study the average value for the residual correlations between the parameters was also -0.97 for the 21 animals in model I and -0.96 for the 22 in model II.…”