Livestock Science 173 (2015) 119–120
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Corrigendum
Corrigendum to “Application of a nonlinear optimization tool to balance diets with constant metabolizability” [Livest. Sci. 158 (1–3) (2013) 106–117] Júlia Gazzoni Jardim a, Ricardo Augusto Mendonça Vieira b,n, Alberto Magno Fernandes b, Raphael Pavesi Araujo a, Leonardo Siqueira Glória a, Nardele Moreno Rohem Júnior b, Norberto Silva Rocha a, Matheus Lima Corrêa Abreu a a Graduate Program in Animal Science, Universidade Estadual do Norte Fluminense Darcy Ribeiro (UENF), Campos dos Goytacazes, RJ, Brazil b Laboratório de Zootecnia e Nutrição Animal, UENF, Av. Alberto Lamego, 2000, Campos dos Goytacazes, RJ CEP 28013-602, Brazil
The authors regret two mistakes in the previously published paper. The new calculations and results are presented here. Despite the biased results presented earlier, the conclusions remain valid. The authors would like to apologise for any inconvenience caused. The basic problem with 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 ¼ ME=M m , M m ¼ ðFHP þ AÞ=km , and km ¼ 0:35ME=GE þ0:503. Nonetheless, the metabolizability of the diet (q ¼ ME=GE) is lower than the metabolizability of the diet at maintenance, namely qm , 8 Lc 4 1 (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 GE ¼ 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 ¼ MEm =GEm . MEm and GEm are the respective metabolizable and gross energy intake rates at maintenance, and MEm meets M m , i.e., MEm =M m ¼ 1. Nonetheless, let us define the dry matter intake measured at maintenance as F m (kg/day), consequently, GEm ¼ 18:8F m . If M m ¼ ME=Lc , M m ¼ ðFHP þ AÞ=km , km ¼ 0:35MEm =GEm þ 0:503, and M m ¼ MEm , 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 : ME ¼ 26:9F m ð 0:503Lc þ ð0:253L2c þ 1:4L2c ðFHP þ AÞ=ð18:8F m ÞÞ1=2 Þ:
ð18Þ
An analytical solution for Eq. (18) exists, but a numerical solution for Eq. (18) can be obtained by using as inputs DE and UE values measured 8 L, as well as ½Dm and F m values measured for L ¼ 1. The Box–Cox transformation (Box and Cox, 1964) is useful for analyzing variables with abnormalities (Sakia, 1992; Peltier et al., 1998), and is less prompt to inference complications than the arcsine transformation (Warton and Hui, 2010). However, the mean (E½Y) and variance (var½Y) of the variable in the original scale are E½Y ¼ expðμþ σ 2 =2Þ, and var½Y ¼ expð2μ þ2σ 2 Þ expð2μ þ σ 2 Þ for lnðYÞ Normalðμ; σ 2 Þ (Mood et al., 1974). Therefore, it is important to retransform adequately means and confidence limits back to the original scale (Gill, 1981). Our published Lc and q0 values were not subjected to this careful quantitative treatment (Jardim et al., 2013), and here we present new Lc and q0 results (Fig. 1, panels DOI of original article: http://dx.doi.org/10.1016/j.livsci.2013.09.012 n Correspondence to: Laboratório de Zootecnia e Nutrição Animal (LZNA), Centro de Ciências e Tecnologias Agropecuárias (CCTA), Universidade Estadual do Norte Fluminense Darcy Ribeiro (UENF), UENF/CCTA/LZNA, Av. Alberto Lamego, 2000, Campos dos Goytacazes, RJ CEP 28013-602, Brazil. Tel.: þ55 22 2748 6397; fax: þ 55 22 2739 7194. E-mail address:
[email protected] (R.A.M. Vieira). http://dx.doi.org/10.1016/j.livsci.2015.01.004 1871-1413/& 2015 Elsevier B.V. All rights reserved.
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0
Fig. 1. Panels (a) and (b) present the metabolizability of the diet (q ) and the corrected or actual plane of nutrition (Lc ) estimated for all planned nutrition levels (L), respectively. Observed values (n¼32) are crosses, solid lines represent estimated values, and dashed lines represent the 99% confidence intervals. 0 The σ 2 estimates for q and Lc equations are 0.005 and 0.011, respectively.
a and b). Fortunately, the same tendencies presented before are observed here and despite the biased results presented earlier, our conclusions remain valid. References Blaxter, K.L., Boyne, A.W., 1978. The estimation of the nutritive value of feeds as energy sources for ruminants and the derivation of feeding systems. J. Agric. Sci. 90, 47–68. Box, G.E.P., Cox, D.R., 1964. An analysis of transformations. J. R. Stat. Soc. Ser. B (Methodol.) 26, 211–252. Gill, J.L., 1981. Evolution of statistical design and analysis of experiments. J. Dairy Sci. 64, 1494–1519. Jardim, J.G., Vieira, R.A.M., Fernandes, A.M., Araujo, R.P., Glória, L.S., Rohem Júnior, N.M., Rocha, N.S., Abreu, M.L.C., 2013. Application of a nonlinear optimization tool to balance diets with constant metabolizability. Livest. Sci. 158, 106–117. Mood, A.M., Graybill, F.A., Boes, D.C., 1974. Intoduction to the Theory of Statistics. McGraw-Hill Kogakusha, LTD., Tokyo. Peltier, M.R., Wilcox, C.J., Sharp, D.C., 1998. Application of the Box–Cox data transformation to animal science experiments. J. Anim. Sci. 76, 847–849. Sakia, R.M., 1992. The Box–Cox transformation technique: a review. J. R. Stat. Soc. Ser. D (Stat.) 41, 169–178. Warton, D.I., Hui, F.K.C., 2010. The arcsine is asinine: the analysis of proportions in ecology. Ecology 92, 3–10.
