Modeling the efficiency of phosphorus utilization in growing pigs. 
Microbial phytase has been used to reduce P excretion from swine to mitigate environmental pollution.  The objective of the study was to quantify the effect of feeding a low-P phytase-supplemented diet on growth and P utilization in growing pigs using mathematical models.  A total of 20 weaned piglets (BW = 6.5 kg) housed in metabolism cages were randomly assigned to a standard diet (STD) or P-amended diet containing reduced P content and supplemented with phytase (AMN) with 10 pigs/diet.  Body weight and feed consumption were recorded weekly so complete growth and cumulative P intake (cPI) curves could be modeled.  A function with fixed point of inflexion (Gompertz) and a variable point of inflexion (generalized Michaelis-Menten) were considered in determining bioequivalence by analyzing BW vs. age relationships, whereas the monomolecular function was used to describe BW vs. cPI.  All functions were incorporated into a nonlinear mixed effects model, and a first-order autoregressive correlation structure was implemented to take into account repeated measures.  There was no difference between the 2 groups in final BW when the Gompertz equation was fitted (176 vs. 178 kg with SE of 7 kg for the STD and AMN, respectively) or the rate parameter (0.0140 vs. 0.0139 with SE of 0.0004 for the STD and AMN, respectively).  The generalized Michaelis-Menten equation also showed a similar trend.  When BW was expressed as a function of cPI the derivative with respect to cPI represented P efficiency, so it was possible to analyze the expected difference of the 2 diets in using P for BW gain and express it as a continuous function of cPI.  The analysis showed through the entire growth period the difference in P efficiency was different from zero.  On average, 56 g of supplemented inorganic P was consumed by a pig fed the AMN to reach market weight.  In contrast, 309 g of supplemented inorganic P was consumed by the group fed the STD to reach similar BW.  It would depend on other factors, but feeding pigs the AMN can result in economic benefit.  Pigs fed the AMN excreted 19% less P compared with those fed the STD.  In conclusion, nonlinear mixed model analysis (with repeated measures) was suitable for growth and efficiency analysis and showed that pigs fed the AMN consumed less than 20% of the inorganic P and performed as well as those fed the traditional inorganic P supplemented diet.  The implications for mitigating P pollution, especially in areas where P loading is already problematic, are substantial.