Stochastic true digestible amino acid values

The concept of using amino acid digestibility coefficients has been reported to be valuable in formulating diets to meet the requirements of livestock. Digestibility coefficients of nutrients reflect the amounts of components of a feedstuff that become available to meet livestock requirements. Most biological factors, including feed ingredient amino acid means and their digestibility values, have variabilities associated with them. Chance constrained (stochastic) programming for feed formulation has been suggested as a method that accounts for variability. The ingredient matrix for stochastic formulation requires means and standard deviations (S.D.s) for all nutrients involved in the formulation. l references were used to provide ingredient amino acid means and S.D.s, and true digestibility coefficient means and S.D.s. When there is variability associated with two or more variables in a calculation (e.g. nutrient mean and S.D., coefficient of true digestibility mean and S.D.), it is a nonlinear problem involving the application of the principles of probability theory for a solution. It is a mathematical oversimplification to multiply an amino acid S.D. by the coefficient of true digestibility for the calculation of the digestibility S.D. This technique would result in an under-estimation of the S.D. associated with the digestibility of the amino acid. A Microsoft Excel© 2000 Spreadsheet was used to input data from references and to develop formulae based on probability theory. Values derived from these formulae were summarized in reference tables. A Monte Carlo simulation verified the analytical results of the multiplication of the means and S.D.s of the amino acid value and its coefficient of true digestibility.