Application of a nonlinear optimization tool to balance diets with constant metabolizability

The goals of this study were to evaluate the ability of a nonlinear optimization tool to provide solutions for maintaining consistent qualities of diets irrespective of the plane of nutrition (L) and to evaluate the effect of the plane of nutrition on intake and digestibility of dry matter (DM), organic matter (OM), crude protein (CP), crude fat (CF), non fibrous carbohydrates (NFC), neutral detergent fiber (NDF), and metabolizability (qm) of diets using sheep as a generalized experimental model. Eight wethers were randomly assigned to two balanced four-treatment Latin squares conducted simultaneously with four diets providing nutritional levels that were multiples of maintenance levels (ME=Mm; 1.5Mm; 2Mm; and 2.5Mm, where ME is the metabolizable energy intake, and Mm is the metabolizable energy intake for maintenance). The ME, Mm, metabolizable protein (MP) and NDF of the diet were subjected to nonlinear constraints; the model was considered a general nonlinear programming problem and solved using Microsoft Excel Solver® with Newton's method of resolution. The intake of nutrients, digestible nutrients, digestible energy (DE) and the amounts of feces and urine produced daily were measured and analyzed statistically by fitting a linear mixed model. The corrected metabolizability (qm') and plane of nutrition (Lc) were obtained on the basis of the digestible, urinary, and simulated methane losses. The trends of some variables were reanalyzed by regressing observed values against Lc. All measured variables were affected by L. The intakes of DM and OM increased in an asymptotic fashion as Lc increased, whereas the intake of NDF increased linearly as Lc increased. At levels immediately below maintenance, observed values were approximately constant. Digestible amounts of OM, DE, CF, and CP consumed increased linearly at levels above maintenance, whereas the digestible amounts of total carbohydrates, neutral detergent solubles, and ashes increased in an asymptotic fashion. Under conditions of controlled feeding, the nonlinear optimization tool yielded dietary solutions with a nearly constant metabolizability in which the rate of increase in crude protein, digestible crude protein, and digestible energy intakes remained constant as the plane of nutrition increased.