Flexible alternatives to the Gompertz equation for describing growth with age in turkey hens

Abstract

A total of 49 profiles of growing turkey hens from commercial flocks were used in this study. Three flexible growth functions (von Bertalanffy, Richards, and Morgan) were evaluated with regard to their ability to describe the relationship between BW and age and were compared with the Gompertz equation with its fixed point of inflection, which might result in its overestimation. For each function, 4 ways of analysis were implemented. A basic model was fitted first, followed by implementation of a first-order autoregressive correlation structure. A model that considered only mature BW varied with year and another that considered only the rate coefficient varied with different years were applied. The results showed that the fixed point of inflection of the Gompertz equation can be a limitation and that the relationship between BW and age in turkeys was best described using flexible growth functions. However, the Richards equation failed to converge when fitted to the turkey growth data; therefore, it was not considered further. Inclusion of an autoregressive process of the first order rendered a substantially improved fit to data for the 3 growth functions. The Morgan equation provided the best fit to the data set and was used for characterizing mean growth curves for the 7 yr of production. It was estimated that the maximum growth rate occurred at 3.74, 3.65, 3.99, 4.18, 4.05, 4.01, and 3.77 kg BW for production years from 1997 to 2003, respectively. It is recommended that flexible growth functions should be considered as an alternative to the simpler functions (with a fixed point of inflection) for describing the relationship between BW and age in turkeys because they were easier to fit and very often gave a closer fit to data points because of their flexibility, and therefore a smaller residual MS value, than simpler models. It can also be recommended that studies should consider adding a first-order autoregressive process when analyzing repeated measures data with nonlinear models.

Critical points on growth curves in autoregressive and mixed models

“…In model II, however, the value is very early, the ratio y pi /a is only 0.080. This anticipation in the occurrence of the infl ection point of functions with fl exibility in its location is reported by Porter et al (2010). The asymptotic deceleration points, pda, were nearly the same for the three functions and models I and III ( 41 months, three races in average).…”

“…However, caution must be taken in adjusting these functions, since measurements in the same individual over time cannot be considered independent, since errors are serially correlated, and this information should be added to the model (Draper and Smith, 1998). Porter et al, 2010), Mendes et al (2009), Mazzini et al (2005), Bergamasco et al (2001) and Calegario et al (2005) have demonstrated the superiority of models with correlation structure in the errors compared to models that do not consider this correlation including. In all comparisons, autoregressive models were superior to models without autocorrelation.…”

Non-Linear Model to Describe Growth Curves of Commercial Turkey in the Tropics of Mexico

“…The estimated NLM growth curves and the curve of observed body weights for females and males are shown in Figures 1 and 2, and therefore, the results of the Brody and Richards' curves are not shown, because those models fail to converge, and they were dropped from further analysis. Porter et al (2010) also found that the Richards model fail to converge in Hybrid turkey females.…”

“…Growth is the result of an animal gaining weight with time until it reaches maturity (Porter et al, 2010). The knowledge of the growth curve of turkeys is important to develop management practices that could help increase their productivity.…”

Comparative Study on Growth Patterns of 25 Commercial Strains of Korean Native Chicken

“…Since it is not appropriate to use linear mathematical functions for describing growth trajectory, a number of nonlinear function has been investigated as alternatives (Sengül and Kiraz, 2005). Thereby, several nonlinear models (NLM) to describe the chicken growth pattern have been proposed (Gompertz, 1825;Grossman et al, 1982;Porter et al, 2010;Tompić et al, 2011).…”