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The development and evaluation of multiple regression equations based on four common nutritional analysis packages to predict the metabolisable energy density of diets fed to grower/finisher and adult pigs and their use for rat and mouse diets

Published online by Cambridge University Press:  17 January 2025

Graham Tobin Open the ORCID record for Graham Tobin [Opens in a new window] ,
Annette Schuhmacher ,
Tomasz Górecki  and
Łukasz Smaga
Graham Tobin*
Affiliation:
The Orchard, Weeping Cross, Bodicote OX15 4EE, UK
Annette Schuhmacher
Affiliation:
ssniff Spezialdiaeten, Ferdinand-Gabriel Weg 16, Soest 59494, Germany
Tomasz Górecki
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Uniwersytetu Poznańskiego 4, 61-614 Poznań, Poland
Łukasz Smaga
Affiliation:
Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Uniwersytetu Poznańskiego 4, 61-614 Poznań, Poland
*
Corresponding author: Graham Tobin; Email: gtobin500@gmail.com
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Abstract

We have used multiple regression analyses to develop a series of metabolisable energy prediction equations from chemical analyses of pig diets that can be extended to murine diets. We compiled four datasets from an extensive range of published metabolism studies with grower/finisher and adult pigs. The analytes in the datasets were increasingly complex, comprising (1) the proximate or Weende analysis, (2) the previous analysis but with neutral detergent fibre replacing crude fibre, (3) the neutral detergent fibre package plus starch and (4) the neutral detergent fibre package plus starch and sugars. Diet manufacturers routinely provide most of the analytes for batches of murine diet, or they are easily obtainable. The study uniquely compares the four analytical packages side by side. The number of records in the datasets varies from 367 to 827. With increasing analytical complexity, adjusted R2 values for metabolisable energy prediction improved from 0·751 to 0·869 and the mean absolute error from 0·422 to 0·289 kJ/g. Overall, the models’ prediction interval improved from 1 to 0·7 kJ/g, which is ± 7 to 5 % for a typical dietary metabolisable energy density of 14·8 kJ/g. Although prediction accuracy increases as one extends the range and complexity of the analytes measured, the improvement is slight and may not justify the substantial increase in analytical cost. The equations were validated for use on future datasets by k-fold analysis. Although the equations are developed from pig data, they are suitable for rat and mouse diets, based on comparable digestibility measurements, and substantially improve existing methods.

Keywords

Metabolisable energy density predictionMultiple linear regression analysisPigsRats and mice
Type
Research Article
Information
British Journal of Nutrition , Volume 133 , Issue 4 , 28 February 2025 , pp. 433 - 455
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Nutrition Society

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References

Tobin, G & Schuhmacher, A (2021) Laboratory animal nutrition in routine husbandry, and experimental and regulatory studies. In Handbook of Laboratory Animal Science, 4th ed., pp. 269–311 [Hau, J and Schapiro, S, editors]. Boca Raton, FL: CRC Press.CrossRefGoogle Scholar
Tschop, MH, Speakman, JR, Arch, JR, et al. (2012) A guide to analysis of mouse energy metabolism. Nat Methods 9, 57–63.CrossRefGoogle Scholar
Rozman, J, Klingenspor, M & Hrabě de Angelis, M (2014) A review of standardized metabolic phenotyping of animal models. Mamm Genome 25, 497–507.CrossRefGoogle ScholarPubMed
McLean, JA & Tobin, G (1987) Animal and Human Calorimetry. Cambridge, UK: Cambridge University Press.Google Scholar
Elvert, R, Wille, A, Wandschneider, J, et al. (2013) Energy loss via urine and faeces – a combustive analysis in diabetic rats and the impact of antidiabetic treatment on body weight. Diabetes Obes Metab 15, 324–334.CrossRefGoogle ScholarPubMed
Armitage, G, Hervey, GR, Rolls, BJ, et al. (1983) The effects of supplementation of the diet with highly palatable foods upon energy balance in the rat. J Physiol 342, 229–251.CrossRefGoogle ScholarPubMed
Atwater, W (1900) Discussion of the Terms Digestibility, Availability, and Fuel Value, 12th Annual Report of Storrs Agricultural Experiment Station. Storrs, CT: Storrs Agricultural Experiment Station.Google Scholar
Merrill, AL & Watt, BK (1955) Energy Value of Foods: Basis and Derivation. Washington, DC: US Department of Agriculture.Google Scholar
Sanchez-Pena, MJ, Marquez-Sandoval, F, Ramirez-Anguiano, AC, et al. (2017) Calculating the metabolizable energy of macronutrients: a critical review of Atwater’s results. Nutr Rev 75, 37–48.CrossRefGoogle ScholarPubMed
Maynard, LA (1944) The Atwater system of calculating the caloric value of diets. J Nutr 28, 443–452.CrossRefGoogle Scholar
Bielohuby, M, Bodendorf, K, Brandstetter, H, et al. (2010) Predicting metabolisable energy in commercial rat diets: physiological fuel values may be misleading. Br J Nutr 103, 1525–1533.CrossRefGoogle ScholarPubMed
Schneider, BH (1947) Feeds of the World: Their Digestibility and Composition. Blacksburg, WV: Agricultural Experiment Station, West Virginia University.Google Scholar
Crampton, EW & Harris, LE (1969) Applied Animal Nutrition: The Use of Feedstuffs in the Formulation of Livestock Rations, 2nd ed. San Francisco, CA: Freeman and Company.Google Scholar
Flachowsky, G & Kirchgessner, M (1998) The energetic feed evaluation in Germany. Arch für Tierernährung 51, 111–125.CrossRefGoogle ScholarPubMed
Eeckhout, W & Moermans, R (1981) Prediction of the energy value of commercial pig feeds, according to the various energy systems used in the European Community that are based on simple analytical parameters of the feed. Anim Feed Sci Technol 6, 367–375.CrossRefGoogle Scholar
Schiemann, R, Nehring, K, Hoffmann, L, et al. (1971) Food Energy Evaluation and Energy Standardisation. Berlin, GDR: VEB Deutscher Landwirtschaftsverlag.Google Scholar
Jentsch, W, Beyer, M & Chudy, A (2001) The Rostock research for energetic feed evaluation and energy requirement of farm animals. 2. Further development of the Rostock feed evaluation system. Übers Tierernährg 29, 1–44.Google Scholar
Jentsch, W, Chudy, A & Beyer, M (2000) The Rostock research for energetic feed evaluation and energy requirement of farm animals. 1. Historical retrospect and the experiments on energetic feed evaluation in Rostock. Übers Tierernährg 28, 133–182.Google Scholar
GfE (2006) Recommendations for the energy and nutrient supply of pigs (Energy and Nutrient Requirements of livestock, Volume 10). Committee for Requirement Standards of the German Society of Nutrition Physiology. Frankfurt am Main, DE: DLG-Verlag.Google Scholar
GfE (2008) Prediction of metabolisable energy of compound feeds for pigs. Proc Soc Nutr Physiol 17, 199–204.Google Scholar
Morgan, DJ, Cole, DJA & Lewis, D (1975) Energy values in pig nutrition: II. The prediction of energy values from dietary chemical analysis. J Agric Sci 84, 19–27.CrossRefGoogle Scholar
Just, A, Jørgensen, H & Fernández, JA (1984) Prediction of metabolizable energy for pigs on the basis of crude nutrients in the feeds. Livest Prod Sci 11, 105–128.CrossRefGoogle Scholar
Morgan, CA, Whittemore, CT, Phillips, P, et al. (1987) The prediction of the energy value of compounded pig foods from chemical analysis. Anim Feed Sci Technol 17, 81–107.CrossRefGoogle Scholar
Noblet, J & Perez, JM (1993) Prediction of digestibility of nutrients and energy values of pig diets from chemical analysis. J Anim Sci 71, 3389–3398.CrossRefGoogle ScholarPubMed
Kirchgessner, M & Roth, FX (1983) Equations for prediction of the energy value in mixed feeds for pigs. Z Tierphysiol Tierernahr Futtermittelkd 50, 270–275.CrossRefGoogle Scholar
Furuya, S, Takahashi, S & Kameoka, K (1981) A comparative study of the digestibility by pigs, chickens and rats using identical rations. Jpn J Zootech Sci 52, 459–466.Google Scholar
Nehring, K, Hoffmann, L, Schiemann, R, et al. (1963) The energetic utilization of feed materials. 6. The energetic utilization of feed materials by cattle, sheep, rabbits, pigs and rats. A species comparison. Archiv für Tierernaehrung 13, 193–213.CrossRefGoogle Scholar
Jørgensen, H & Lindberg, JE (2006) Prediction of energy and protein digestibility in pig feeds using growing rats as a model. Anim Feed Sci Technol 127, 55–71.CrossRefGoogle Scholar
Sung, JY & Kim, BG (2021) Prediction equations for digestible and metabolizable energy concentrations in feed ingredients and diets for pigs based on chemical composition. Asian-Australas J Anim Sci 34, 306–311.Google ScholarPubMed
Choi, H, Sung, JY & Kim, BG (2020) Neutral detergent fiber rather than other dietary fiber types as an independent variable increases the accuracy of prediction equation for digestible energy in feeds for growing pigs. Asian-Australas J Anim Sci 33, 615–622.CrossRefGoogle Scholar
R Core Team (2023) A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing.Google Scholar
Altman, DG & Bland, JM (1983) Measurement in medicine: the analysis of method comparison studies. J R Stat Soc Ser D (Statistician) 32, 307–317.Google Scholar
Giavarina, D (2015) Understanding Bland Altman analysis. Biochem Med 25, 141–151.CrossRefGoogle ScholarPubMed
Ludbrook, J (2010) Confidence in Altman-Bland plots: a critical review of the method of differences. Clin Exp Pharmacol Physiol 37, 143–149.CrossRefGoogle ScholarPubMed
Morgan, CA & Whittemore, CT (1982) Energy evaluation of feeds and compounded diets for pigs — a review. Anim Feed Sci Technol 7, 387–400.CrossRefGoogle Scholar
Kromann, RP (1967) A mathematical determination of energy values of ration ingredients. J Anim Sci 26, 1131–1134.CrossRefGoogle ScholarPubMed
Young, LG, Ashton, GC & Smith, GC (1977) Estimating the energy value of some feeds for pigs using regression equations. J Anim Sci 44, 765–771.CrossRefGoogle Scholar
Kim, JW, Koo, B & Nyachoti, CM (2017) Digestible, metabolizable, and net energy of camelina cake fed to growing pigs and additivity of energy in mixed diets. J Anim Sci 95, 4037–4044.CrossRefGoogle ScholarPubMed
Noblet, J, Fortune, H, Dupire, C, et al. (1990) Nutritional value of thirteen feedstuffs in growing pigs. 1. Digestible, metabolizable and net energy contents. Consequences of choice of energy evaluation system. Journées de Recherche Porcine en France 22, 175–184.Google Scholar
Noblet, J & Henry, Y (1993) Energy evaluation systems for pig diets: a review. Livest Prod Sci 36, 121–141.CrossRefGoogle Scholar
Kerr, BJ & Easter, RA (1995) Effect of feeding reduced protein, amino acid-supplemented diets on nitrogen and energy balance in grower pigs. J Anim Sci 73, 3000–3008.CrossRefGoogle ScholarPubMed
Tobin, G & Carpenter, KJ (1978) The nutritional value of dry bean (Phaseolus vulgaris); a literature review. Nutr Abstr Rev Ser A Hum Exp 48, 919–936.Google Scholar
Noblet, J, Wu, S-B & Choct, M (2022) Methodologies for energy evaluation of pig and poultry feeds: a review. Anim Nutr 8, 185–203.CrossRefGoogle ScholarPubMed
Wu, S-B, Choct, M & Pesti, G (2020) Historical flaws in bioassays used to generate metabolizable energy values for poultry feed formulation: a critical review. Poult Sci 99, 385–406.Google ScholarPubMed
Kong, C & Adeola, O (2014) Evaluation of amino acid and energy utilization in feedstuff for swine and poultry diets. Asian-Australas J Anim Sci 27, 917–925.CrossRefGoogle ScholarPubMed
Harrell, FE (2001) Regression Modeling Strategies with Applications to Linear Models, Logistic and Ordinal Regression, and Survival Analysis, Springer Series in Statistics. New York, NY: Springer.Google Scholar
Riley, RD, Ensor, J, Snell, KIE, et al. (2020) Calculating the sample size required for developing a clinical prediction model. BMJ 368, m441.CrossRefGoogle ScholarPubMed
Liu, FT, Ting, K & Zhou, Z-H (2009) Isolation forest. In 2008 Eighth IEEE International Conference on Data Mining. Pisa, Italy: IEEE.CrossRefGoogle Scholar
Belsley, DA, Kuh, E & Welsch, RE (1980) Regression Diagnostics: Identifying Influential Data and Sources of Collinearity. New York: John Wiley & Sons.CrossRefGoogle Scholar
Eisenhauer, JG (2003) Regression through the Origin. Teach Stat 25, 76–80.CrossRefGoogle Scholar
Tay-Zar, A-C, Wongphatcharachai, M, Srichana, P, et al. (2024) Prediction of net energy of feeds for broiler chickens. Anim Nutr 16, 241–250.CrossRefGoogle ScholarPubMed
Noblet, J & Van Milgen, J (2013) Energy and energy metabolism in swine. In Sustainable Swine Nutrition, pp. 23–57 [Chiba, LI, editor]. Ames, IA: Wiley-Blackwell.CrossRefGoogle Scholar
Leach, LF & Henson, RK (2007) The use and impact of adjusted R2 effects in published regression research. MLRV 33, 1–11.Google Scholar
Kozak, A & Kozak, RA (1995) Notes on regression through the origin. For Chron 71, 326–330.CrossRefGoogle Scholar
Anderson-Cook, CM & Borror, CM (2016) The difference between ‘equivalent’ and ‘not different’. Qual Eng 28, 249–262.CrossRefGoogle Scholar
Yarkoni, T & Westfall, J (2017) Choosing prediction over explanation in psychology: lessons from machine learning. Perspect Psychol Sci 12, 1100–1122.CrossRefGoogle ScholarPubMed
Stone, M (1974) Cross-validatory choice and assessment of statistical predictions. J R Stat Soc Ser B (Stat Method) 36, 111–133.CrossRefGoogle Scholar
Geisser, S (1975) The predictive sample reuse method with applications. JASA 70, 320–328.CrossRefGoogle Scholar
Mason, CH & Perreault, WD Jr (1991) Collinearity, power, and interpretation of multiple regression analysis. J Mark Res 28, 268–280.CrossRefGoogle Scholar
Gupta, A, Stead, TS & Ganti, L (2024) Determining a meaningful R-squared value in clinical medicine. Acad Med Surg https://doi.org/10.62186/001c.125154 (accessed November 2024).CrossRefGoogle Scholar
Piñeiro, G, Perelman, S, Guerschman, JP, et al. (2008) How to evaluate models: observed v. predicted or predicted v. observed? Ecol Model 216, 316–322.CrossRefGoogle Scholar
Le Goff, G & Noblet, J (2001) Comparative total tract digestibility of dietary energy and nutrients in growing pigs and adult sows. J Anim Sci 79, 2418–2427.Google ScholarPubMed
Bulang, M & Rodehutscord, M (2009) Development of equations for predicting metabolisable energy concentrations in compound feeds for pigs. Arch Anim Nutr 63, 442–454.CrossRefGoogle ScholarPubMed
Grümpel-Schlüter, A, Berk, A, Schäffler, M, et al. (2021) Evaluation of an equation for predicting metabolisable energy concentration in compound feeds for pigs. Arch Anim Nutr 75, 251–262.CrossRefGoogle ScholarPubMed
Grewal, R, Cote, JA & Baumgartner, H (2004) Multicollinearity and measurement error in structural equation models: implications for theory testing. Mark Sci 23, 519–529.CrossRefGoogle Scholar
Feng, W, Mullen, MR & Sheng, S (2017) Evaluating the impact of multicollinearity on regression. Am J Bus Res 9, 63–73.Google Scholar
O’Brien, RM (2007) A caution regarding rules of thumb for variance inflation factors. Qual Quant 41, 673–690.CrossRefGoogle Scholar
Das, S & Chatterjee, S (2011) Multicollinearity Problem–Root Cause, Diagnostics and Way Outs. Diagnostics and Way Outs (April 29, 2011). http://dx.doi.org/10.2139/ssrn.1830043 (accessed November 2024).CrossRefGoogle Scholar
Selle, PH, Ravindran, V, Cowieson, AJ, et al. (2010) Phytate and Phytase. Wallingford, UK: CABI Publishing.CrossRefGoogle Scholar
Stroebinger, N, Rutherfurd, SM, Henare, SJ, et al. (2021) Fatty acids from different fat sources and dietary calcium concentration differentially affect fecal soap formation in growing pigs. J Nutr 151, 1102–1110.CrossRefGoogle ScholarPubMed
Jørgensen, H, Jakobsen, K & Eggum, BO (1992) The influence of different protein, fat and mineral levels on the digestibility of fat and fatty acids measured at the terminal ileum and in faeces of growing pigs. Acta Agric Scand Sect A 42, 177–184.Google Scholar
Espinosa, CD, Torres, LJ, Velayudhan, DE, et al. (2022) Ileal and total tract digestibility of energy and nutrients in pig diets supplemented with a novel consensus bacterial 6-phytase variant. J Anim Sci 100, skac364.CrossRefGoogle ScholarPubMed
Cowieson, A, Ruckebusch, J-P, Sorbara, J, et al. (2017) A systematic view on the effect of microbial phytase on ileal amino acid digestibility in pigs. Anim Feed Sci Technol 231, 138–149.CrossRefGoogle Scholar
Babyak, MA (2004) What you see may not be what you get: a brief, nontechnical introduction to overfitting in regression-type models. Psychosom Med 66, 411–421.Google Scholar
Voelkl, B, Vogt, L, Sena, ES, et al. (2018) Reproducibility of preclinical animal research improves with heterogeneity of study samples. PLoS Biol 16, e2003693.CrossRefGoogle ScholarPubMed
Hastie, T, Tibshirani, R & Friedman, J (2009) The Elements of Statistical Learning. Data Mining, Inference, and Prediction, Springer Series in Statistics. New York, NY: Springer.Google Scholar
Lowell, JE, Liu, Y & Stein, HH (2015) Comparative digestibility of energy and nutrients in diets fed to sows and growing pigs. Arch Anim Nutr 69, 79–97.CrossRefGoogle ScholarPubMed
Noblet, J & Shi, XS (1993) Comparative digestibility of energy and nutrients in growing pigs fed ad libitum and adults sows fed at maintenance. Livest Prod Sci 34, 137–152.CrossRefGoogle Scholar
Itoh, H, Kaneko, M, Ohshima, S, et al. (2002) Effect of low protein and low energy diet on physiological status and digestibility of F344 rats. Exp Anim 51, 485–491.CrossRefGoogle ScholarPubMed
Mongeau, R & Brassard, R (1982) Determination of neutral detergent fiber in breakfast cereals: pentose, hemicellulose, cellulose and lignin content. J Food Sci 47, 550–555.CrossRefGoogle Scholar
Norman, AG (1935) The composition of crude fibre. J Agric Sci 25, 529–540.CrossRefGoogle Scholar
Stallcup, OT (1958) Composition of crude fiber in certain roughages. J Dairy Sci 41, 963–968.Google Scholar
Hindrichsen, IK, Kreuzer, M, Madsen, J, et al. (2006) Fiber and lignin analysis in concentrate, forage, and feces: detergent v. enzymatic-chemical method. J Dairy Sci 89, 2168–2176.CrossRefGoogle Scholar
Miron, J, Yosef, E & Ben-Ghedalia, D (2001) Composition and in vitro digestibility of monosaccharide constituents of selected byproduct feeds. J Agric Food Chem 49, 2322–2326.CrossRefGoogle ScholarPubMed
Jaworski, NW, Lærke, HN, Bach Knudsen, KE, et al. (2015) Carbohydrate composition and in vitro digestibility of dry matter and nonstarch polysaccharides in corn, sorghum, and wheat and coproducts from these grains. J Anim Sci 93, 1103–1113.CrossRefGoogle ScholarPubMed
Knudsen, KEB (1997) Carbohydrate and lignin contents of plant materials used in animal feeding. Anim Feed Sci Technol 67, 319–338.CrossRefGoogle Scholar
Kaltschmitt, M, Hartmann, H & Hofbauer, H (2009) Energy from biomass. Basics, Techniques and Procedures, 2nd ed. Berlin, DE: Springer.Google Scholar
Demirbaş, A & Demirbaş, AH (2004) Estimating the calorific values of lignocellulosic fuels. Energy Explor Exploit 22, 135–143.CrossRefGoogle Scholar
Demirbaş, A (2003) Relationships between heating value and lignin, fixed carbon, and volatile material contents of shells from biomass products. Energy Sources 25, 629–635.CrossRefGoogle Scholar
Esteves, B, Sen, U & Pereira, H (2023) Influence of chemical composition on heating value of biomass: a review and bibliometric analysis. Energies 16, 4226.CrossRefGoogle Scholar
Kienzle, E, Schrag, I, Butterwick, R, et al. (2001) Calculation of gross energy in pet foods: new data on heat combustion and fibre analysis in a selection of foods for dogs and cats. J Anim Physiol Anim Nutr (Berl) 85, 148–157.CrossRefGoogle Scholar
Agyekum, AK & Nyachoti, CM (2017) Nutritional and metabolic consequences of feeding high-fiber diets to swine: a review. Engineering 3, 716–725.CrossRefGoogle Scholar
Dégen, L, Halas, V & Babinszky, L (2007) Effect of dietary fibre on protein and fat digestibility and its consequences on diet formulation for growing and fattening pigs: a review. Acta Agric Scand A Anim Sci 57, 1–9.Google Scholar
Zhang, S, de Vries, S & Gerrits, WJJ (2024) Quantifying the effects of dietary fibres on protein digestibility in pigs – a review. Anim Feed Sci Technol 308, 115864.CrossRefGoogle Scholar
Wilfart, A, Montagne, L, Simmins, PH, et al. (2007) Sites of nutrient digestion in growing pigs: effect of dietary fiber. J Anim Sci 85, 976–983.CrossRefGoogle ScholarPubMed
Just, A (1982) The influence of ground barley straw on the net energy value of diets for growth in pigs. Livest Prod Sci 9, 717–729.CrossRefGoogle Scholar
Shi, X & Noblet, J (1993) Digestible and metabolizable energy values of ten feed ingredients in growing pigs fed ad libitum and sows fed at maintenance level; comparative contribution of the hindgut. Anim Feed Sci Technol 42, 223–236.CrossRefGoogle Scholar
Steyerberg, EW (2019) Clinical Prediction Models: A Practical Approach to Development, Validation, and Updating, 2nd ed. Cham, CH: Springer.CrossRefGoogle Scholar
Maduro Dias, C, Nunes, H & Borba, A (2024) Near-infrared spectroscopy in animal nutrition: historical insights, technical principles, and practical applications. Analytica 5, 481–498.CrossRefGoogle Scholar
Noel, SJ, Jørgensen, HJH & Knudsen, KEB (2022) The use of near-infrared spectroscopy (NIRS) to determine the energy value of individual feedstuffs and mixed diets for pigs. Anim Feed Sci Technol 283, 115156.CrossRefGoogle Scholar
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