Corrigendum to 'Application of a nonlinear optimization tool to balance diets with constant metabolizability' [Livest. Sci. 158 (1–3) (2013) 106–117]

The basic problemwith the approach we adopted in the paper of Jardim et al. (2013) is that we found the denominator of the reported ratio Eq. (17)/Eq. (18) by assuming Lc 1⁄4ME=Mm, Mm 1⁄4 ðFHPþAÞ=km, and km 1⁄4 0:35ME=GEþ0:503. Nonetheless, the metabolizability of the diet (q1⁄4ME=GE) is lower than the metabolizability of the diet at maintenance, namely qm, 8 Lc41 (Blaxter and Boyne, 1978). We maintained terms and units here accordingly. In the paper of Jardim et al. (2013), we assumed the gross energy intake as GE1⁄4 18:8F (MJ/day). Therefore, our km values were biased because our qm values were also biased to some extent. By definition, qm is measured at maintenance (Blaxter and Boyne, 1978): qm 1⁄4MEm=GEm. MEm and GEm are the respective metabolizable and gross energy intake rates at maintenance, and MEm meets Mm, i.e., MEm=Mm 1⁄4 1. Nonetheless, let us define the dry matter intake measured at maintenance as Fm (kg/day), consequently, GEm 1⁄4 18:8Fm. If Mm 1⁄4ME=Lc, Mm 1⁄4 ðFHPþAÞ=km, km 1⁄4 0:35MEm=GEmþ0:503, and Mm 1⁄4MEm, then after algebraically isolating ME and taking only its positive root and simplifying constants, we have a new Eq. (18) based on the correct definition of qm: ME1⁄4 26:9Fmð 0:503Lcþð0:253Lc þ1:4Lc ðFHPþAÞ=ð18:8FmÞÞÞ: ð18Þ