Some novel growth functions and their application with reference to growth in ostrich

Four novel growth functions, namely, Pareto, extreme value distribution (EVD), Lomolino, and cumulative beta-P distribution (CBP), are derived, and their ability to describe ostrich growth curves is evaluated. The functions were compared with standard growth equations, namely, the monomolecular, Michaelis-Menten (MM), Gompertz, Richards, and generalized MM (gMM). For this purpose, 2 separate comparisons were conducted. In the first, all the functions were fitted to 40 individual growth curves (5 males and 35 females) of ostriches using nonlinear regression. In the second, performance of the functions was assessed when data from 71 individuals were composited (570 data points). This comparison was undertaken using nonlinear mixed models and considering 3 approaches: 1) models with no random effect, 2) random effect incorporated as the intercept, and 3) random effect incorporated into the asymptotic weight parameter (W-f). The results from the first comparison showed that the functions generally gave acceptable values of R-2 and residual variance. On the basis of the Akaike information criterion (AIC), CBP gave the best fit, whereas the Gompertz and Lomolino equations were the preferred functions on the basis of corrected AIC (AIC(c)). Bias, accuracy factor, the Durbin-Watson statistic, and the number of runs of sign were used to analyze the residuals. CBP gave the best distribution of residuals but also produced more residual autocorrelation (significant Durbin-Watson statistic). The functions were applied to sample data for a more conventional farm species (2 breeds of cattle) to verify the results of the comparison of fit among functions and their applicability across species. In the second comparison, analysis of mixed models showed that incorporation of a random effect into W-f gave the best fit, resulting in smaller AIC and AIC(c) values compared with those in the other 2 approaches. On the basis of AIC(c), best fit was achieved with CBP, followed by gMM, Lomolino, and Richards functions, respectively. The exponential, MM, Pareto, and EVD equations produced negative values for initial weight (W-0) if left unconstrained. The Gompertz equation, in spite of having a fixed inflection point and therefore being less flexible, gave accurate estimates of both W-0 and W-f and an acceptable goodness of fit favored by having fewer parameters than the other sigmoidal functions. Nevertheless, all the sigmoidal functions appeared appropriate in describing the growth trajectory of male and female ostriches to a reasonable level of accuracy.