A Holistic Approach to Evaluating Linear and Non-Linear Mixed Models to Predict Phosphorus Retention in Growing and Finishing Pigs

SIMPLE SUMMARY: Phosphorus (P) is an essential mineral in the diets of pigs. The degree to which P is utilized has both economic and environmental consequences to the swine industry. Mathematical models can be used to describe the relationship between P intake and P retention. These models provide information regarding P utilization that can be used to formulate diets aimed at reducing P overfeeding, and therefore decrease P wastage. The objective of this study was to assess the ability of four non-linear models (monomolecular, Michaelis-Menten, Richards, and Morgan) and one simple linear model to describe the relationship between P intake and P retention in growing and finishing pigs. Through fitting these models to data from P balance studies, non-linear models which describe diminishing returns type behaviour, the monomolecular and the Michaelis-Menten models, were found to best describe the relationship between P intake and P retention in these categories of pig. The parameter of these models allows estimates of endogenous P losses, P requirement for maintenance and theoretical maximum P retention enabling the more efficient use of P in the swine industry. ABSTRACT: The ability of four non-linear mixed models and one linear mixed model to describe phosphorus (P) retention as a function of dietary P intake, expressed on an available P (avP) basis, was assessed in growing and finishing pigs. Of the four non-linear models, the monomolecular and Michaelis-Menten describe diminishing returns behaviour, while the Richards and Morgan describe sigmoidal behaviour with the ability to also describe diminishing returns. Using a meta-analysis approach, models were fitted to avP intake vs. P retention data from P balance studies. Pig bodyweights (BW) ranged from 43.5 to 133 kg, P intake ranged from 0.055 to 0.468 g kg(−1) BW(0.75) d(−1) for avP, and 0.151 to 0.806 g kg(−1) BW(0.75) d(−1) for total P, with P retention ranging from 0.026 to 0.329 g kg(−1) BW(0.75) d(−1). Models were evaluated using statistical measures of goodness-of-fit and inspection of residuals. The monomolecular and Michaelis-Menten best described the relationship between P retention and P intake. Endogenous P losses and P requirement for maintenance were found to be higher in finishing pigs compared to growing pigs as BW increased.