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.
A total of 86 profiles from meat and egg strains of chickens (male and female) were used in this study. Different flexible growth functions were evaluated with regard to their ability to describe the relationship between live weight and age and were compared with the Gompertz and logistic equations, which have a fixed point of inflection. Six growth functions were used: Gompertz, logistic, Lopez, Richards, France, and von Bertalanffy. A comparative analysis was carried out based on model behavior and statistical performance. The results of this study confirmed the initial concern about the limitation of a fixed point of inflection, such as in the Gompertz equation. Therefore, consideration of flexible growth functions as an alternatives to the simpler equations (with a fixed point of inflection) for describing the relationship between live weight and age are recommended for the following reasons: they are easy to fit, they very often give a closer fit to data points because of their flexibility and therefore a smaller RSS value, than the simpler models, and they encompasses simpler models for the addition of an extra parameter, which is especially important when the behavior of a particular data set is not defined previously.
Poultry industries face various decisions in the production cycle that affect the profitability of an operation. Predictions of growth when the birds are ready for sale are important factors that contribute to the economy of poultry operations. Mathematical functions called 'growth functions' have been used to relate body weight (W) to age or cumulative feed intake. These can also be used as response functions to predict daily energy and protein dietary requirements for maintenance and growth (France et al., 1989). When describing growth versus age in poultry, a fixed point of inflexion can be a limitation with equations such as the Gompertz and logistic. Inflexion points vary depending on age, sex, breed and type of animal, so equations such as the Richards and López are generally recommended. For describing retention rate against daily intake, which generally does not exhibit an inflexion point, the monomolecular would appear the function of choice.
Phosphorus is an essential nutrient involved in most metabolic processes. Most of the interest in Ca metabolism relates to eggshell formation. Although the eggshell is composed of Ca carbonate, metabolism of both Ca and P is closely related such that a deficiency in one can interfere with proper utilization of the other. To understand Ca and P metabolism properly, modeling can be of paramount importance. A new dynamic and mechanistic model of P and Ca metabolism in layers has been developed to simulate diurnal changes in Ca and P and the hourly requirement of the layer for those minerals. The model consists of 8 state variables representing Ca and P pools in the crop, stomachs, plasma, and bone. The flow equations are described by Michaelis-Menten or mass action forms. An experiment that measured Ca and P uptake in layers fed different Ca concentrations during shell-forming days was used for model evaluation. The experiment showed that Ca retained in body and egg decreased from 62.5 to 50.5% of Ca intake when the Ca in diet was increased from 25 to 45 mg/g of feed. The model simulations were in agreement with the trend. Predictions of Ca retention in bone and egg were 63.2, 56.1, and 55.3% for low, medium, and high dietary Ca concentrations. The experimental results showed that P retention in body and egg increased significantly from 11.5% of absorbable P intake at the lowest Ca inclusion concentration to 24.1% at the highest. The model also predicted an increase in P retention in bone and egg from 8.4 to 25.4% of absorbable P intake at the lowest and highest concentration of Ca inclusion, respectively. The advantage of the model is that absorption and utilization can be monitored on an hourly basis and that adjustments can be made accordingly. The model successfully showed how the availability of one mineral affects the utilization of the other and is a useful tool to evaluate feeding strategies aimed at reducing P excretion to the environment in poultry manure.
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