A multivariate nonlinear mixed effects method for analyzing energy partitioning in growing pigs

Simultaneous equations have become increasingly popular for describing the effects of nutrition on the utilization of ME for protein (PD) and lipid deposition (LD) in animals. The study developed a multivariate nonlinear mixed effects (MNLME) framework and compared it with an alternative method for estimating parameters in simultaneous equations that described energy metabolism in growing pigs, and then proposed new PD and LD equations. The general statistical framework was implemented in the NLMIXED procedure in SAS. Alternative PD and LD equations were also developed, which assumed that the instantaneous response curve of an animal to varying energy supply followed the law of diminishing returns behavior. The Michaelis-Menten function was adopted to represent a biological relationship in which the affinity constant (k) represented the sensitivity of PD to ME above maintenance. The approach accommodated inclusion of a PD potential ([PD.sub.potential]) concept. This was described by a Gompertz function, which was parameterized in terms of the maximum rate of PD ([PD.sub.Max]) and corresponding BW ([BW.sub.PDMaz]) at that point. Metabolizable energy for LD was equated to the difference between ME intake and the sum of ME used for maintenance and PD. Metabolizable energy designated for PD and LD was used, with efficiencies [k.sub.p] and [k.sub.f], respectively. The new equations were compared with the van Milgen and Noblet (1999) equations using 2 comprehensive data sets on energy metabolism in growing pigs. The 2 equation sets were evaluated using information criteria, which showed that the new equations performed best for data set II, whereas the reverse was true for the first. For the data set I population, estimates for [k.sub.p] and [k.sub.f] were 0.57 (SE = 0.05) and 0.84 (SE = 0.03), respectively. Maintenance was quantified as 1.10 (SE = 0.08) MJ/d x [kg.sup.0.55]. The animal variation in the parameter kp was estimated to be 6% CV. The animal variation in [PD.sub.Max] and [k.sub.f] was estimated to be 9 and 10% of the population estimates, respectively. It was concluded that application of the MNLME framework was superior to the multivariate nonlinear regression model because the MNLME method accounted for correlated errors associated with PD and LD measurements and could also include the random effect of animal. It is recommended that multivariate models used to quantify energy metabolism in growing pigs should account for animal variability and correlated measurement errors. Key words: animal variability, energy metabolism, growth, multivariate nonlinear mixed effects modeling doi: 10.2527/jas.2009-2065