Comparative evaluation of mathematical functions to describe growth and efficiency of phosphorus utilization in growing pigs1

Abstract

Success of pig production depends on maximizing return over feed costs and addressing potential nutrient pollution to the environment. Mathematical modeling has been used to describe many important aspects of inputs and outputs of pork production. This study was undertaken to compare 4 mathematical functions for the best fit in terms of describing specific data sets on pig growth and, in a separate experiment, to compare these 4 functions for describing of P utilization for growth. Two data sets with growth data were used to conduct growth analysis and another data set was used for P efficiency analysis. All data sets were constructed from independent trials that measured BW, age, and intake. Four growth functions representing diminishing returns (monomolecular), sigmoidal with a fixed point of inflection (Gompertz), and sigmoidal with a variable point of inflection (Richards and von Bertalanffy) were used. Meta-analysis of the data was conducted to identify the most appropriate functions for growth and P utilization. Based on Bayesian information criteria, the Richards equation described the BW vs. age data best. The additional parameter of the Richards equation was necessary because the data required a lower point of inflection (138 d) than the Gompertz, with a fixed point of inflexion at 1/e times the final BW (189 d), could accommodate. Lack of flexibility in the Gompertz equation was a limitation to accurate prediction. The monomolecular equation was best at determining efficiencies of P utilization for BW gain compared with the sigmoidal functions. The parameter estimate for the rate constant in all functions decreased as available P intake increased. Average efficiencies during different stages of growth were calculated and offer insight into targeting stages where high feed (nutrient) input is required and when adjustments are needed to accommodate the loss of efficiency and the reduction of potential pollution problems. It is recommended that the Richards and monomolecular equations be included in future growth and nutrient efficiency analyses.

A review of mathematical functions for the analysis of growth in poultry

“…Similar to poultry growth, Kebreab et al (2007) reported for pigs that using a more complex (four parameter) function resulted in lower BIC values (therefore, better) than using three parameter functions and the additional parameter was justified because it gave flexibility to a growth function. The authors argue that although the Gompertz has been used extensively, four parameter growth functions such as the Richards were superior in describing growth over time and are recommended for use in growth data analysis in monogastric animals.…”

A new mathematical model for combining growth and energy intake in animals: The case of the growing pig

“…Population based methods (mixed models) have been more widely applied in analysis of pig growth (Criag and Schinckel, 2001;Kebreab et al, 2007). It is assumed that all animals follow the same functional form with parameters varying according to multivariate normal distribution.…”

Aspects of nitrogen metabolism in sheep-fed mixed diets containing tree and shrub foliages

“…The bilinear relationship between NI and FN was explained by Kebreab et al (7) that microbial FN increased with increasing available energy for the growth of microbial cells, but as the amount of microbial synthesis approached optimum according to the available energy, the contribution to MFN remained constant so the increase in FN was mostly as indigestible N from the protein consumed. In support of the monomolecular model that predicts N excretion better, Kebreab et al (35) noted that the monomolecular equation was best at determining efficiencies of phosphorus utilisation for body weight gain compared with the sigmoidal model. Schulin-Zeuthen et al (23) also showed that the monomolecular model was the best predictor of the relationship between phosphorus retention and available phosphorus intake compared with linear and Gompertz models.…”

“…The sigmoidal curve follows through four phases i.e. lag phase, accelerating phase, deceleration phase and stationary phase (35) . This suggests that NR pattern v. NI may remain lag phase at low NI until basal N requirement is fulfilled, followed by accelerating NR starting from the end of lag phase, then NR goes into the decelerating phase and finally NR does not improve with increasing NI when the optimum live weight gain of animals is reached.…”