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

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.

Meta-analysis of phosphorus balance data from growing pigs.

Many studies have highlighted concerns over current methods of determining endogenous P losses and P requirements in growing pigs. Therefore, a database containing observations on 350 pigs was assembled from various studies. Four functions for analyzing P balance data were considered: 1) a straight line, 2) a diminishing returns function (monomolecular), 3) a sigmoidal function with a fixed point of inflection (Gompertz), and 4) a sigmoidal function with a flexible point of inflection (Richards). The nonlinear functions were specifically reparameterized to assign biological meaning to the parameters. Meta-analysis of the data was conducted to estimate endogenous P excretion, maintenance requirement, and efficiency of utilization. Phosphorus retention was regressed against either available P intake or total P intake [all variables scaled by metabolic BW (BW(0.75))]. There was evidence of non-linearity in the data, and the monomolecular function provided the best fit to the data. The Richards equation did not fit the data well and appeared overparameterized. Estimates of endogenous P excretion of 14 and 17 mg/kg of BW(0.75) x d based on available and total P analysis, respectively, were predicted by the monomolecular equation, which were within the range reported in the literature. Maintenance requirement values of 15 mg of available P/kg of BW(0.75) x d and 37 mg of total P/kg of BW(0.75) x d were obtained, based on the monomolecular equation. Average efficiencies of conversion of dietary P to retained P were 65 and 36% for available and total P, respectively, with greater efficiency values calculated for low P intakes. Although the monomolecular equation fitted the data best, more observations at high P intakes/kg of BW(0.75) are required to determine conclusively whether P retention scaled by metabolic BW is linearly related to available or total P intake.

Effects of phosphorus intake on phosphorus flow in growing pigs: application and comparison of two models.

A comparison of the models of Vitti et al. (2000, J. Anim. Sci. 78, 2706-2712) and Fernández (1995c, Livest. Prod. Sci. 41, 255-261) was carried out using two data sets on growing pigs as input. The two models compared were based on similar basic principles, although their aims and calculations differed. The Vitti model employs the rate:state formalism and describes phosphorus (P) flow between four pools representing P content in gut, blood, bone and soft tissue in growing goats. The Fernández model describes flow and fractional recirculation between P pools in gut, blood and bone in growing pigs. The results from both models showed similar trends for P absorption from gut to blood and net retention in bone with increasing P intake, with the exception of the 65 kg results from Date Set 2 calculated using the Fernández model. Endogenous loss from blood back to gut increased faster with increasing P intake in the Fernández than in the Vitti model for Data Set 1. However, for Data Set 2, endogenous loss increased with increasing P intake using the Vitti model, but decreased when calculated using the Fernández model. Incorporation of P into bone was not influenced by intake in the Fernández model, while in the Vitti model there was an increasing trend. The Fernández model produced a pattern of decreasing resorption in bone with increasing P intake, with one of the data sets, which was not observed when using the Vitti model. The pigs maintained their P homeostasis in blood by regulation of P excretion in urine.