Skip to main content Accessibility help

Mathematical modelling in animal nutrition: a centenary review

  • A. DUMAS (a1), J. DIJKSTRA (a2) and J. FRANCE (a1)


A centenary review presents an opportunity to ponder over the processes of concept development and give thought to future directions. The current review aims to ascertain the ontogeny of current concepts, underline the connection between ideas and people and pay tribute to those pioneers who have contributed significantly to modelling in animal nutrition. Firstly, the paper draws a brief portrait of the use of mathematics in agriculture and animal nutrition prior to 1925. Thereafter, attention turns towards the historical development of growth modelling, feed evaluation systems and animal response models. Introduction of the factorial and compartmental approaches into animal nutrition is noted along with the particular branches of mathematics encountered in various models. Furthermore, certain concepts, especially bioenergetics or the heat doctrine, are challenged and alternatives are reviewed. The current state of knowledge of animal nutrition modelling results mostly from the discernment and unceasing efforts of our predecessors rather than serendipitous discoveries. The current review may stimulate those who wish for greater understanding and appreciation.


Corresponding author

*To whom all correspondence should be addressed. Email:


Hide All
Agricultural and Food Research Council (AFRC) (1991). Theory of response to nutrients by farm animals. Nutrition Abstracts and Reviews, Series B 61, 683722.
AFRC (1993). Energy and Protein Requirements of Ruminants. Wallingford, Oxfordshire, UK: CAB International.
Agricultural Research Council (1981). The Nutrient Requirements of Pigs. Slough, UK: Commonwealth Agricultural Bureaux.
Almquist, H. J. (1953). Evaluation of vitamin requirement data. Poultry Science 32, 122128.
Arab, L. (2004). Individualized nutritional recommendations: do we have the measurements needed to assess risk and make dietary recommendations? Proceedings of the Nutrition Society 63, 167172.
Armsby, H. P. (1903). The Principles of Animal Nutrition. New York: John Wiley & Sons.
Armsby, H. P. (1904). The respiration calorimeter at the Pennsylvania Experiment Station. Experiment Station Records 15, 10371050.
Armsby, H. P. (1917). The Nutrition of Farm Animals. New York: The Macmillan Company.
Atwater, W. O. (1902). Principles of nutrition and nutritive value of food. In Farmers' Bulletin No. 142, pp. 148. Washington, DC, USA: US Department of Agriculture.
Atwater, W. O. & Bryant, A. P. (1900). The Availability and Fuel Value of Food Materials. 12th Annual Report of the Storrs Connecticut Agricultural Experiment Station.
Bajer, P. G., Whitledge, G. W. & Hayward, R. S. (2004). Widespread consumption-dependent systematic error in fish bioenergetics models and its implications. Canadian Journal of Fisheries and Aquatic Sciences 61, 21582167.
Baldwin, R. L. (1995). Modeling Ruminant Digestion and Metabolism. London: Chapman & Hall.
Baldwin, R. L. & Smith, N. E. (1971). Application of a simulation modelling technique in analyses of dynamic aspects of animal energetics. Federation Proceedings 30, 14591465.
Baldwin, R. L., France, J. & Gill, M. (1987 a). Metabolism of the lactating cow I. Animal elements of a mechanistic model. Journal of Dairy Research 54, 77105.
Baldwin, R. L., Thornley, J. H. M. & Beever, D. E. (1987 b). Metabolism of the lactating cow. II. Digestive elements of a mechanistic model. Journal of Dairy Research 54, 107131.
Baldwin, R. L., France, J., Beever, D. E., Gill, M. & Thornley, J. H. M. (1987 c). Metabolism of the lactating cow. III. Properties of mechanistic models suitable for evaluation of energetic relationships and factors involved in the partition of nutrients. Journal of Dairy Research 54, 133145.
Baxter, C. F., Kleiber, M. & Black, A. L. (1955). Glucose metabolism in the lactating dairy cow. Biochimica et Biophysica Acta 17, 354361.
Beever, D. E., France, J. & Alderman, G. (2000). Prediction of response to nutrients by ruminants through mathematical modelling and improved feed characterization. In Feeding Systems and Feed Evaluation Models (Eds Theodorou, M. K. & France, J.), pp. 275297. Wallingford, Oxfordshire: CAB International.
Bendixen, E. (2005). The use of proteomics in meat science. Meat Science 71, 138149.
Bergman, E. N., Reid, R. S., Murray, M. G., Brockway, J. M. & Whitelaw, F. G. (1965). Interconversions and production of volatile fatty acids in the sheep rumen. Biochemical Journal 97, 5358.
Bergman, R. N., Ider, Y. Z., Bowden, C. R. & Cobelli, C. (1979). Quantitative estimation of insulin sensitivity. American Journal of Physiology 236, E667E677.
Black, J. L. & Griffiths, D. A. (1975). Effects of live weight and energy intake on nitrogen balance and total N requirement of lambs. British Journal of Nutrition 33, 399413.
Black, J. L., Campbell, R. G., Williams, I. H., James, K. J. & Davies, G. T. (1986). Simulation of energy and amino acid utilisation in the pig. Research and Development in Agriculture 3, 121145.
Black, J. L., Davies, G. T., Bray, H. J., Giles, L. R. & Chapple, R. P. (1995). Modelling the effects of genotype, environment and health on nutrient utilisation. In Proceeding of the IV International Workshop on Modelling Nutrient Utilisation in Farm Animals (Eds Danfaer, A. & Lescoat, P.), pp. 85105. Foulum, Denmark: National Institute of Animal Science.
Blaxter, K. L. (1989). Energy Metabolism in Animals and Man. Cambridge, UK: Cambridge University Press.
Blaxter, K. L. & Mitchell, H. H. (1948). The factorization of the protein requirements of ruminants and of the protein values of feeds, with particular reference to the significance of the metabolic fecal nitrogen. Journal of Animal Science 7, 351372.
Blaxter, K. L. & Ruben, H. (1953). Interim Reports on the Efficiency Project (unpublished). A.R.C. 239/53. Available Online at (verified 4/02/08). 20 pp.
Blaxter, K. L. & Ruben, H. (1954 a). Second Interim Reports on the Efficiency Project (unpublished). A.R.C. 628/54. Available Online at (verified 4/02/08). 55 pp.
Blaxter, K. L. & Ruben, H. (1954 b). Third Interim Reports on the Efficiency Project (unpublished). A.R.C. 611/54. Available Online at (verified 4/02/08). 22 pp.
Blaxter, K. L. & Graham, N. McC. (1955). Plane of nutrition and starch equivalents. Journal of Agricultural Science, Cambridge 46, 292306.
Blaxter, K. L. & Wainman, F. W. (1961). The utilization of food by sheep and cattle. Journal of Agricultural Science, Cambridge 57, 419425.
Blaxter, K. L. & Clapperton, J. L. (1965). Prediction of the amount of methane produced by ruminants. British Journal of Nutrition 19, 511522.
Blaxter, K. L., Graham, N. McC. & Wainman, F. W. (1956). Some observations on the digestibility of food by sheep, and on related problems. British Journal of Nutrition 10, 6991.
Bolie, V. W. (1961). Coefficients of normal blood glucose regulation. Journal of Applied Physiology 16, 783788.
Boston, R. C. & Weber, K. M. (1984). Modelling with SAAM and its advancement in association with the study of mineral metabolism. Mathematical Biosciences 72, 181198.
Boston, R. C., Greif, P. C. & Berman, M. (1981). Conversational SAAM – an interactive program for kinetic analysis of biological systems. Computer Programs in Biomedicine 13, 111119.
Boston, R. C., Granek, H., Sutton, N., Weber, K., Greif, P. & Zech, L. (1986). The maintenance, distribution and development of biomedical computer software: an exercise in software engineering. Computer Methods and Programs in Biomedicine 22, 305321.
Boussingault, J. B. (1845). Rural Economy in its Relation with Chemistry, Physics, and Meteorology: Or, an Application of the Principles of Chemistry and Physiology to the Details of Practical Farming. London: H. Bailliere.
Boyce, S. J., Murray, A. W. A. & Peck, L. S. (2006). Digestion rate, gut passage, time and absorption efficiency in the Antarctic spiny plunderfish. Journal of Fish Biology 57, 908929.
Braude, R. (1967). The effect of changes in feeding patterns on the performance of pigs. Proceedings of the Nutrition Society 26, 163181.
Brody, S. (1945). Bioenergetics and Growth with Special Reference to the Efficiency Complex in Domestic Animals. New York: Hafner Publishing Company.
Brody, S. & Ragsdale, A. C. (1921). The rate of growth of the dairy cow: extrauterine growth in weight. The Journal of General Physiology 3, 623633.
Brody, T. (1999). Nutritional Biochemistry, Second Edition. San Diego, USA: Academic Press.
Bureau, D. P., Kaushik, S. J. & Cho, C. Y. (2002). Bioenergetics. In Fish Nutrition, 3rd edn (Eds Halver, J. E. & Hardy, R. W.), pp. 159. San Diego, CA, USA: Academic Press.
Buyse, J., Geypens, B., Malheiros, R. D., Moraes, V. M., Swennen, Q. & Decuypere, E. (2004). Assessment of age-related glucose oxidation rates of broiler chickens by using stable isotopes. Life Sciences 75, 22452255.
Cho, Y. C. & Bureau, D. P. (1998). Development of bioenergetic models and the Fish-PrFEQ software to estimate production, feeding ration and waste output in aquaculture. Aquatic Living Resources 11, 199210.
Cobelli, C., Federspil, G., Pacini, G., Salvan, A. & Scandellari, C. (1982). An integrated mathematical model of the dynamics of blood glucose and its hormonal control. Mathematical Biosciences 58, 2760.
Cole, D. J. A., Duckworth, J. E. & Holmes, W. (1967). Factors affecting voluntary feed intake in pigs. I. The effect of digestible energy content of the diet on the intake of castrated male pigs housed in holding pens and in metabolism crates. Animal Production 9, 141148.
Conceição, L. E. C., Verreth, J. A. J., Verstegen, M. W. A. & Huisman, E. A. (1998). A preliminary model for dynamic simulation of growth in fish larvae: application to the African catfish (Clarias gariepinus) and turbot (Scophthalmus maximus). Aquaculture 163, 215235.
Crabtree, J. R. (1982). Interactive formulation system for cattle diets. Agricultural Systems 8, 291308.
Curnow, R. N. (1973). A smooth population response curve based on an abrupt threshold and plateau model for individuals. Biometrics 29, 110.
Darmani Kuhi, H., Kebreab, E., Owen, E. & France, J. (2001). Application of the law of diminishing return to describing the relationship between metabolizable energy intake and growth rate in broilers. Journal of Animal and Feed Sciences 10, 661670.
Davidson, F. A. (1928). Growth and senescence in purebred Jersey cows. University of Illinois Agriculture Experimental Station Bulletin 302, 182235.
de Lange, C. F. M., Morel, P. C. H. & Birkett, S. H. (2003). Modelling chemical and physical body composition of the growing pig. Journal of Animal Science 81 (E. Suppl. 2), E159E165.
Dent, J. B. & Casey, H. (1967). Linear Programming and Animal Nutrition. Philadelphia, PA, USA, and Toronto, ON, Canada: J.B. Lippincott Company.
Dhanoa, M. S., France, J., Siddons, R. C., López, S. & Buchanan-Smith, J. G. (1995). A non-linear compartmental model to describe forage degradation kinetics during incubation in polyester bags in the rumen. British Journal of Nutrition 73, 315.
Dijkstra, J. (1994). Simulation of the dynamics of protozoa in the rumen. British Journal of Nutrition 72, 679699.
Dijkstra, J., Neal, H. D. St. C., Beever, D. E. & France, J. (1992). Simulation of nutrient digestion, absorption and outflow in the rumen: model description. Journal of Nutrition 122, 22392256.
Dijkstra, J., France, J., Dhanoa, M. S., Maas, J. A., Hanigan, M. D., Rook, A. J. & Beever, D. E. (1997). A model to describe growth patterns of the mammary gland during pregnancy and lactation. Journal of Dairy Science 80, 23402354.
Dijkstra, J., Kebreab, E., Bannink, A., France, J. & Lopez, S. (2005). Application of the gas production technique to feed evaluation systems for ruminants. Animal Feed Science and Technology 123–124, 561578.
Dijkstra, J., Kebreab, E., Mills, J. A. N., Pellikaan, W. F., López, S., Bannink, A. & France, J. (2007). Predicting the profile of nutrients available for absorption: from nutrient requirement to animal response and environmental impact. Animal 1, 99111.
Dijkstra, J., Kebreab, E., Bannink, A., Crompton, L. A., López, S., Abrahamse, P. A., Chilibroste, P., Mills, J. A. N. & France, J. (in press). Comparison of energy evaluation systems and a mechanistic model for milk production by dairy cattle offered fresh grass-based diets. Animal Feed Science and Technology doi: 10.1016/j.anifeedsci.2007.05.011.
Emery, R. S., Smith, C. K. & Huffman, C. F. (1956). The amounts of short chain acids formed during rumen fermentation. Journal of Animal Science 15, 854862.
Ewing, P. V. & Smith, F. H. (1917). A study of the rate of passage of food residues through the steer and its influence on digestion coefficients. Journal of Agricultural Research 10, 5563.
Feller, D. D., Strisower, E. H. & Chaikoff, I. L. (1950). Turnover and oxidation of body glucose in normal and alloxan-diabetic rats. Journal of Biological Chemistry 187, 571588.
Forbes, J. M. (1995). Voluntary Food Intake and Diet Selection in Farm Animals. Wallingford, UK: CAB International.
Forbes, J. M. & Blundell, J. E. (1989). Central nervous control of voluntary food intake. In The Voluntary Food Intake of Pigs, Occasional Publication No. 13 (Eds Forbes, J. M., Varley, M. A. & Lawrence, T. L.), pp. 726. Edinburgh, UK: British Society of Animal Production.
Fox, D. G., Tedeschi, L. O., Tylutki, T. P., Russell, J. B., Van Amburgh, M. E., Chase, L. E., Pell, A. N. & Overton, T. R. (2004). The Cornell net carbohydrate and protein system model for evaluating herd nutrition and nutrient excretion. Animal Feed Science and Technology 112, 2978.
France, J., Thornley, J. H. M. & Beever, D. E. (1982). A mathematical model of the rumen. Journal of Agricultural Science, Cambridge 99, 343353.
France, J., Thornley, J. H. M., Dhanoa, M. S. & Siddons, R. C. (1985). On the mathematics of digesta flow kinetics. Journal of Theoretical Biology 113, 743758.
France, J., Gill, M., Dhanoa, M. S. & Siddons, R. C. (1987 a). On solving the fully-interchanging N-compartment model in steady-state tracer kinetic studies with reference to VFA absorption from the rumen. Journal of Theoretical Biology 125, 193211.
France, J., Gill, M., Thornley, J. H. M. & England, P. (1987 b). A model of nutrient utilization and body composition in beef cattle. Animal Production 44, 371385.
France, J., Calvert, C. C., Baldwin, R. L. & Klasing, K. C. (1988). On the application of compartmental models to radioactive tracer kinetic studies of in vivo protein turnover in animals. Journal of Theoretical Biology 133, 447471.
France, J., Dhanoa, M. S., Cammel, S. B., Gill, M., Beever, D. E. & Thornley, J. H. M. (1989). On the use of response functions in energy balance analysis. Journal of Theoretical Biology 140, 8399.
France, J., Siddons, R. C., Dhanoa, M. S. & Thornley, J. H. M. (1991 a). A unifying mathematical analysis of methods to estimate rumen volume using digesta markers and intraruminal sampling. Journal of Theoretical Biology 150, 145155.
France, J., Siddons, R. C. & Dhanoa, M. S. (1991 b). Adaptation of compartmental schemes for interpreting isotope dilution data on volatile fatty acid metabolism in the rumen to the non-steady-state and for single-dose injection. Journal of Theoretical Biology 153, 247254.
France, J., Dhanoa, M. S., Theodorou, M. K., Lister, S. J., Davies, D. R. & Isac, D. (1993). A model to interpret gas accumulation profiles associated with in vitro degradation of ruminant feeds. Journal of Theoretical Biology 163, 99111.
France, J., Bequette, B. J., Lobley, G. E., Metcalf, J. A., Wray-Cahen, D., Dhanoa, M. S., Backwell, F. R. C., Hanigan, M. D., MacRae, J. C. & Beever, D. E. (1995). An isotope dilution model for partitioning leucine uptake by the bovine mammary gland. Journal of Theoretical Biology 172, 369377.
François, C. (1999). Systemics and cybernetics in a historical perspective. Systems Research and Behavioural Science 16, 203219.
Garfinkel, D. (1966). A simulation study of the metabolism and compartmentation in brain of glutamate, aspartate, the Krebs cycle, and related metabolites. Journal of Biological Chemistry 241, 39183929.
Garrett, W. N. (1987). Relationship between energy metabolism and the amounts of protein and fat deposited in growing cattle. In Energy Metabolism of Farm Animals. European Association for Animal Production Publication No. 32 (Eds Moe, P. W., Tyrrell, H. F. & Reynolds, P. J.), pp. 98101. Beltsville, MD, USA: Rowman & Littlefield.
Gavin, W. (1913). Studies in milk records: on the accuracy of estimating a cow's milking capability by her first lactation yield. Journal of Agricultural Science, Cambridge 5, 377390.
Gavora, J. S., Liljedahl, L. E., McMillan, I. & Ahlen, K. (1982). Comparison of three mathematical models of egg production. British Poultry Science 23, 339348.
Gayon, J. (2000). History of the concept of allometry. American Zoologist 40, 748758.
Gerrits, W. J. J., Tolman, G. H., Schrama, J. W., Tamminga, S., Bosch, M. W. & Verstegen, M. W. A. (1996). Effect of protein and protein-free energy intake on protein and fat deposition rates in preruminant calves of 80 to 240 kg live weight. Journal of Animal Science 74, 21292139.
Gerrits, W. J. J., Dijkstra, J. & France, J. (1997). Description of a model integrating protein and energy metabolism in preruminant calves. Journal of Nutrition 127, 12291242.
Gill, M., Thornley, J. H. M., Black, J. L., Oldham, J. D. & Beever, D. E. (1984). Simulation of the metabolism of absorbed energy-yielding nutrients in young sheep. British Journal of Nutrition 52, 621649.
Glen, J. J. (1980). A parametric programming method for beef cattle ration formulation. Journal of Operational Research Society 31, 689698.
Glen, J. J. (1987). Mathematical models in farm planning: a survey. Operations Research 35, 641666.
Go, V. L. W., Nguyen, C. T. H., Harris, D. M. & Lee, W.-N. P. (2005). Nutrient–gene interaction: metabolic genotype–phenotype relationship. Journal of Nutrition 135, 3016S3020S.
Gompertz, B. (1825). On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. Philosophical Transactions of the Royal Society of London 115, 513583.
Gous, R. M., Moran, E. T. Jr., Stilborn, H. R., Bradford, G. D. & Emmans, G. C. (1999). Evaluation of the parameters needed to describe the overall growth, the chemical growth, and the growth of feathers and breast muscles of broilers. Poultry Science 78, 812821.
Gray, F. V., Weller, R. A., Pilgrim, A. F. & Jones, G. B. (1966). The rates of production of volatile fatty acids in the rumen. III. Measurement of production in vivo by two isotope dilution procedures. Australian Journal of Agricultural Research 17, 6980.
Grzesiak, W., Błaszczyk, P. & Lacroix, R. (2006). Methods of predicting milk yield in dairy cows – predictive capabilities of Wood's lactation curve and artificial neural networks (ANNs). Computers and Electronics in Agriculture 54, 6983.
Halas, V., Dijkstra, J., Babinsky, L., Verstegen, M. W. A. & Gerrits, W. J. J. (2004). Modelling of nutrient partitioning in growing pigs to predict their anatomical body composition. 1. Model description. British Journal of Nutrition 92, 707723.
Halnan, E. T. (1915). The maintenance ration of oxen and the starch equivalent theory. Journal of Agricultural Science, Cambridge 7, 163174.
Headley, V. E., Miller, E. R., Ullrey, D. E. & Hoefer, J. A. (1961). Application of the equation of the curve of diminishing increment to swine nutrition. Journal of Animal Science 20, 311315.
Hendricks, W. A. (1931). Fitting the curve of the diminishing increment to feed consumption–live weight growth curves. Science 74, 290291.
Henneberg, W. & Stohmann, F. (1864). Beiträge zur Begründung einer rationellen Fütterung der Wiederkäuer II. Braunschweig, Germany: Schwetske.
Hill, A. V. (1910). The combinations of haemoglobin with oxygen and with carbon monoxide I. Journal of Physiology 40, 471480.
Hocquette, J. F., Ortigues-Marty, I. & Vermorel, M. (2001). Manipulation of tissue energy metabolism in meat-producing ruminants – review. Asian-Australasian Journal of Animal Science 14, 720732.
Hubbell, S. P. (1971). Of sowbugs and systems: the ecological bioenergetics of a terrestrial isopod. In Systems Analysis and Simulation in Ecology, Volume 1 (Ed B. C. Patten), pp. 269–324. New York, USA: Academic Press.
Hungate, R. E. (1966). The Rumen and its Microbes. New York: Academic Press.
Hunt, J. N. & Spurrell, W. R. (1951). The pattern of emptying of the human stomach. Journal of Physiology 113, 157168.
Hunt, J. N. & MacDonald, I. (1954). The influence of volume on gastric emptying. Journal of Physiology 126, 459474.
Huxley, J. S. (1924). Constant differential growth-ratios and their significance. Nature 114, 895896.
Huxley, J. S. (1931). Notes on differential growth. American Naturalist 65, 289315.
Huxley, J. S. & Teissier, G. (1936). Terminology of relative growth. Nature 137, 780781.
Iason, G. R. & Mantecon, A. R. (1991). Seasonal variation in voluntary food intake and post-weaning growth in lambs: a comparison of genotypes. Animal Production 52, 279285.
Imamidoost, R. & Cant, J. P. (2005). Non-steady-state modelling of effects of timing and level of concentrate supplementation on ruminal pH and forage intake in high-producing, grazing ewes. Journal of Animal Science 83, 11021115.
Johnson, D. E., Ferrell, C. L. & Jenkins, T. G. (2003). The history of energetic efficiency research: where have we been and where are we going? Journal of Animal Science 81 (E. Suppl. 1), E27E38.
Jull, M. A. & Titus, H. W. (1928). Growth of chickens in relation to feed consumption. Journal of Agricultural Research 36, 541550.
Kebreab, E., France, J., Agnew, R. E., Yan, T., Dhanoa, M. S., Dijkstra, J., Beever, D. E. & Reynolds, C. K. (2003). Alternatives to linear analysis of energy balance data from lactating dairy cows. Journal of Dairy Science 86, 29042913.
Kebreab, E., Mills, J. A. N., Crompton, L. A., Bannink, A., Dijkstra, J., Gerrits, W. J. J. & France, J. (2004). An integrated mathematical model to evaluate nutrient partition in dairy cattle between the animal and its environment. Animal Feed Science and Technology 112, 131154.
Kellner, O. (1905). Die Ernährung der Landwirtschaftlichen Nutztiere: Lehrbuch auf der Grundlage Physiologischer Forschung und Praktischer Erfahrung. Hamburg, Germany: Parey. Translated by Goodwin, W. (Kellner, O. (1911) The Scientific Feeding of Animals. New York: The Macmillan Company).
Kellner, O. & Becker, M. (1966). Grundzüge der Fütterungslehre. Hamburg, Germany: Parey.
Kevles, D. J. (1985). In the Name of Eugenics: Genetics and the Use of Human Heredity. New York: Alfred A. Knopf.
Kleiber, M. (1932). Body size and metabolism. Hilgardia 6, 315353.
Kleiber, M. (1937). Nutrition (energy metabolism). Annual Reviews of Biochemistry 6, 375394.
Kleiber, M. (1961). The Fire of Life: An Introduction to Animal Energetics. New York: John Wiley & Sons.
Kleiber, M. (1975). The Fire of Life: An Introduction to Animal Energetics, 2nd edn.New York: Robert E. Krieger Publishing Company.
Koehler, R., Pahle, T., Gruhn, K., Zander, R., Jeroch, H. & Gebhardt, G. (1988). Estimation of the rates of protein synthesis for the whole body of growing broilers. Archives of Animal Nutrition 38, 565572.
Kotarbińska, M. (1969). Badania nad przemianą energii u rosnących świń. Instytut Zootechniki, Kraków, Wydawnictwa Własne No. 238.
Kriss, M. (1930). Quantitative relations of the dry matter of the food consumed, the heat production, the gaseous outgo, and the insensible loss in body weight of cattle. Journal of Agricultural Research 40, 283295.
Kronfeld, D. S., Ramberg, C. F. Jr. & Shames, D. M. (1971). Multicompartmental analsysis of glucose kinetics in normal and hypoglycemic cows. American Journal of Physiology 220, 886893.
Kussmann, M., Affolter, M. & Fay, L. B. (2005). Proteomics in nutrition and health. Combinatorial Chemistry and High Throughput Screening 8, 679696.
Kyriazakis, I. (1994). The voluntary feed intake and diet selection of pigs. In Principles of Pig Science (Eds Cole, D. J. A., Wiseman, J. & Varley, M. A.), pp. 85105. Nottingham, UK: Nottingham University Press.
Laplace, J.-P. & Tomassone, R. (1970). Évacuation gastro-duodénale chez le porc. Annales de Zootechnie 19, 303332.
Le Dividich, J., Vermorel, M., Noblet, J., Bouvier, J. C. & Aumaitre, A. (1980). Effects of environmental temperature on heat production, energy retention, protein and fat gain in early weaned piglets. British Journal of Nutrition 44, 313323.
Lehmann, C. (1899). Emil Wolff's rationelle Fütterung der landwirtschaftlichen Nutztiere auf Grundlage der Neueren tierpsychologischen Forschungen Gemeinverständlicher Leitfaden der Fütterungslehre. Berlin: Verlagsbuchhandlung Paul Parey.
Leng, R. A. & Brett, D. J. (1966). Simultaneous measurements of the rates of production of acetic, propionic and butyric acids in the rumen of sheep on different diets and the correlation between production rates and concentrations of these acids in the rumen. British Journal of Nutrition 20, 541552.
Lerner, M. I. (1939). Allometric studies of poultry. In Proceedings of the Seventh World Poultry Congress and Exposition, pp. 8588. Cleveland, OH, USA.
López, S., France, J., Gerrits, W. J. J., Dhanoa, M. S., Humphries, D. J. & Dijkstra, J. (2000). A generalized Michaelis–Menten equation for the analysis of growth. Journal of Animal Science 78, 18161828.
Lotka, A. J. (1925). Elements of Physical Biology. Baltimore, MD: Williams & Wilkins Company.
Lupatsch, I. & Kissil, G. W. (2005). Feed formulations based on energy and protein demands in white grouper (Epinephelus auneus). Aquaculture 248, 8395.
Machiels, M. A. M. & Henken, A. M. (1986). A dynamic simulation model for growth of the African catfish, Clarias gariepinus (Burchell 1822). I. Effect of feeding level on growth and energy metabolism. Aquaculture 56, 2952.
May, R. M. (1976). Simple mathematical models with very complicated dynamics. Nature 261, 459467.
Maynard, L. A. (1937). Animal Nutrition. New York: McGraw-Hill Book Company.
Maynard, L. A. (1953). Total digestible nutrients as a measure of feed energy. Journal of Nutrition 51, 1521.
Maynard, L. A. & Loosli, J. K. (1969). Animal Nutrition, 6th edn. New York: McGraw-Hill Book Co.
Mazanov, A. & Nolan, J. V. (1976). Simulation of the dynamics of nitrogen metabolism in sheep. British Journal of Nutrition 35, 149174.
McCollum, E. V. (1916). The present situation in nutrition. Hoard's Dairyman 51, 989993.
McCollum, E. V., Simmonds, N. & Pitz, W. (1917). Is lysine the limiting amino-acid in the proteins of wheat, maize or oats? Journal of Biological Chemistry 28, 483499.
McDonald, I. (1981). A revised model for the estimation of protein degradability in the rumen. Journal of Agricultural Science, Cambridge 96, 251252.
McMeekan, C. P. (1941). Growth and development in the pig, with special reference to carcass quality characters. Journal of Agricultural Science, Cambridge 31, 117.
Menke, K. H., Raab, L., Salewski, A., Steingass, H., Fritz, D. & Schneider, W. (1979). The estimation of the digestibility and metabolizable energy content or ruminant feedingstuffs from the gas production when they are incubated with rumen liquor in vitro. Journal of Agricultural Science, Cambridge 93, 217222.
Mercer, L. P. (1980). Mathematical models in nutrition. Nutrition Reports International 21, 189198.
Mercer, L. P., Flodin, N. W. & Morgan, P. H. (1978). New methods for comparing the biological efficiency of alternative nutrient sources. Journal of Nutrition 108, 12441249.
Michaelis, L. & Menten, M. (1913). Die kinetik der invertinwirkung. Biochemische Zeitschrift 49, 333369.
Mignon-Grasteau, S. & Beaumont, C. (2000). Growth curves in birds. Productions Animales (Paris) 13, 337348.
Mills, J. A. N., Dijkstra, J., Bannink, A., Cammell, S. B., Kebreab, E. & France, J. (2001). A mechanistic model of whole-tract digestion and methanogenesis in the lactating dairy cow: model development, evaluation, and application. Journal of Animal Science 79, 15841597.
Mitchell, H. H. (1918). Feeding experiments on the substitution of protein by definite mixtures of isolated amino acids. International Review of the Science and Practice of Agriculture 9, 589590.
Mitchell, H. H. (1924). A method of determining the biological value of protein. Journal of Biological Chemistry 58, 873903.
Mitchell, H. H. (1952). The nutritive evaluation of protein: a half-century of progress. Nutrition Reviews 10, 3337.
Mitchell, H. H. (1964). Comparative Nutrition of Man and Domestic Animals, Vol. II. New York: Academic Press.
Mitscherlich-Königsberg, E. I. (1909). Das gesetz des minimums und das gesetz des abnehmenden bodenertrages. Landwirtschaftliche Jahrbücher 38, 537552.
Monod, J. (1942). Recherches sur la Croissance des Cultures Bactériennes, 2nd edn. Paris: Hermann.
Morgan, A. F. (1960). Samuel Brody – a biographical sketch. Journal of Nutrition 70, 39.
Morgan, P. H., Mercer, P. & Flodin, N. W. (1975). General model for nutritional responses of higher organisms. Proceedings of the National Academy of Sciences of the United States of America 72, 43274331.
Morris, J. G., Baldwin, R. L., Maeng, W. J. & Maeda, B. T. (1975). Basic characteristics of a computer-simulated model of nitrogen utilization in the grazing ruminant. In Tracer Studies on Non-protein Nitrogen for Ruminants II (Ed. International Atomic Energy Agency), pp. 6579. Vienna, Austria: International Atomic Energy Agency.
Moulton, C. R. (1918). Availability of the energy of food for growth. International Review of the Science and Practice of Agriculture 9, 472474.
Murray, J. A. (1914). The Chemistry of Cattle Feeding and Dairying. London: Longmans, Green, and Co.
Murray, J. A. (1915). The starch equivalent theory. Journal of Agricultural Science, Cambridge 7, 154162.
Murray, J. A. (1921). Normal growth in animals. Journal of Agricultural Science, Cambridge 11, 258274.
Murray, R. M., Bryant, A. M. & Leng, R. A. (1975). Measurement of methane production in sheep. In Tracer Studies on Non-protein Nitrogen for Ruminants II (Ed. International Atomic Energy Agency), pp. 2127. Vienna, Austria: International Atomic Energy Agency.
Murray, R. M., Bryant, A. M. & Leng, R. A. (1976). Rates of production of methane in the rumen and large intestine of sheep. British Journal of Nutrition 36, 114.
Nelson, D. L. & Cox, M. M. (2000). Lehninger Principles of Biochemistry, 3rd edn. New York: Worth Publishers.
Nichols, B. L. (1994). Atwater and USDA nutrition research and service: a prologue of the past century. Journal of Nutrition 124, 1718S1727S.
Nolan, J. V. & Leng, R. A. (1972). Dynamic aspects of ammonia and urea metabolism in sheep. British Journal of Nutrition 27, 177194.
National Research Council (NRC) (1987). Predicting Feed Intake of Food-producing Animals. Washington, DC, USA: National Academy Press.
National Research Council (NRC) (1996). Nutrient Requirements of Beef Cattle, 7th rev. edn.Washington, DC, USA: National Academy Press.
National Research Council (NRC) (1998). Nutrient Requirements of Swine, 10th rev. edn.Washington, DC, USA: National Academy Press.
Ørskov, E. R. & McDonald, I. (1979). The estimation of protein degradability in the rumen from incubation measurements weighted according to rate of passage. Journal of Agricultural Science, Cambridge 92, 499503.
Osborne, T. B. & Mendel, L. B. (1912). The role of gliadin in nutrition. Journal of Biological Chemistry 12, 473510.
Osborne, T. B., Mendel, L. B. & Ferry, E. L. (1919). A method of expressing numerically the growth-promoting value of proteins. Journal of Biological Chemistry 37, 223229.
Oslage, H. J. & Fliegel, H. (1965). Nitrogen and energy metabolism of growing-fattening pigs with an approximately maximal feed intake. In Energy Metabolism. European Association for Animal Production Publication No. 11 (EdBlaxter, K. L.), pp. 297306. London: Academic Press.
Parks, J. R. (1982). A Theory of Feeding and Growth of Animals. Berlin: Springer-Verlag.
Pearl, R. (1925). The Biology of Population Growth. New York: Alfred A. Knopf.
Pearson, K. (1920). Notes on the history of correlation. Biometrika 13, 2545.
Pettigrew, J. E., Gill, M., France, J. & Close, W. H. (1992). A mathematical integration of energy and amino acid metabolism of lactating sows. Journal of Animal Science 70, 37423761.
Pirt, J. S. (1975). Principles of Microbe and Cell Cultivation. New York: Blackwell Scientific.
Pomar, C., Harris, D. L. & Minvielle, F. (1991). Computer simulation model of swine production systems. I. Modelling the growth of young pigs. Journal of Animal Science 69, 14681488.
Poppi, D. P., Gill, M. & France, J. (1994). Integration of theories of intake regulation in growing ruminants. Journal of Theoretical Biology 167, 129145.
Porter, T. M. (2004). Karl Pearson. Princeton, NJ, USA, and Oxford, UK: Princeton University Press.
Pütter, A. (1920). Studien über physiologische ähnlichkeit. VI. Wachstumsähnlichkeiten. Pflügers Archiv fur die Gesamte Physiologie des Menschen und der Tiere 180, 298340.
Ragsdale, A. C., Elting, E. C. & Brody, S. (1926). Growth and development with special reference to domestic animals. I. Quantitative data: growth and development of dairy cattle. Missouri Agricultural Experiment Station Research Bulletin 96, 740.
Ratkowski, D. A. (1983). Nonlinear Regression Modeling. New York: Marcel Dekker.
Ratkowski, D. A. (1990). Handbook of Nonlinear Regression Models. New York: Marcel Dekker.
Rice, R. W., Morris, J. G., Maeda, B. T. & Baldwin, R. L. (1974). Simulation of animal functions in models of production systems: ruminants on the range. Federation Proceedings 33, 188195.
Richards, F. J. (1959). A flexible growth function for empirical use. Journal of Experimental Botany 10, 290300.
Ricker, W. E. (1979). Growth rates and models. In Fish Physiology Volume VIII: Bioenergetics and Growth (Eds Hoar, W. S., Randall, D. J. & Brett, J. R.), pp. 677743. New York: Academic Press.
Riley, J. E. (1989). Recent trends in pig production: the importance of intake. In The Voluntary Food Intake of Pigs, Occasional Publication No. 13 (Eds Forbes, J. M., Varley, M. A. & Lawrence, T. L.), pp. 15. Edinburgh, UK: British Society of Animal Production.
Ritzman, E. G. (1917). Nature and rate of growth in lambs during the first year. Journal of Agricultural Research 11, 607623.
Robertson, T. B. (1908). On the normal rate of growth of an individual and its biochemical significance. Archiv fur Entwicklungsmechanik der Organismen 25, 581614.
Robertson, T. B. (1916). Experimental studies on growth. II. The normal growth of the white mouse. Journal of Biological Chemistry 24, 363383.
Robertson, T. B. (1923). The Chemical Basis of Growth and Senescence. Philadelphia, PA, USA: J.B. Lippincott Company.
Robinson, G. W. & Halnan, E. T. (1912). Probable error in the pig feeding trials. Journal of Agricultural Science, Cambridge 5, 4851.
Rubner, M. (1902). Die Gesetze des Energieverbrauchs bei der Ernährung. Leipzig: Franz Deuticke. Translated by Markoff, A. & Sandri-White, A. (Rubner, M. (1982). The Laws of Energy Consumption in Nutrition. New York: Academic Press).
Sakomura, N. K., Longo, F. A., Oviedo-Rondon, E. O., Boa-Viagem, C. & Ferraudo, A. (2005). Modelling energy utilization and growth parameter description for broiler chickens. Poultry Science 84, 13631369.
Schiemann, R., Nehring, K., Hoffmann, L., Jentsch, W. & Chudy, A. (1971). Energetische Futterbewertung und Energienormen. Berlin: VEB/Deutscher Landwirtschaftsverlag.
Schinckel, A. P. (1999). Describing the pig. In A Quantitative Biology of the Pig (EdKyriazakis, I.), pp. 938. Wallingford, Oxfordshire, UK: CABI Publishing.
Schneider, K. M., Boston, R. C. & Leaver, D. D. (1987). Quantitation of phosphorus excretion in sheep by compartmental analysis. American Journal of Physiology 252, R720R731.
Seber, G. A. F. & Wild, C. J. (2003). Nonlinear Regression. Hoboken, NJ, USA: John Wiley & Sons.
Steele, R., Wall, J. S., de Bodo, R. C. & Altszuler, N. (1956). Measurement of size and turnover rate of body glucose pool by the isotope dilution method. American Journal of Physiology 187, 1524.
Thaer, A. D. (1809). Grundsätze der Rationellen Landwirthschaft. Berlin: Realschulbuchhandlung.
Thomas, C. (2004). Feed into Milk: A New Applied Feeding System for Dairy Cows. Nottingham, UK: Nottingham University Press.
Thorbek, C. (1969). Studies on the energy metabolism of growing pigs. In Energy Metabolism of Farm Animals: European Association for Animal Production, Publication No. 12 (Eds Blaxter, K. L., Kielanowski, J. & Thorbek, G.), pp. 281289. Newcastle upon Tyne: Oriel Press.
Thornley, J. (1998). Grassland Dynamics – an Ecosystem Simulation Model. Wallingford, Oxfordshire, UK: CAB International.
Thornley, J. & France, J. (2007). Mathematical Models in Agriculture: Quantitative Methods for the Plant, Animal and Ecological Sciences. Wallingford, UK: CAB International.
Tilley, J. M. A. & Terry, R. A. (1963). A two-stage technique for the in vitro digestion of forage crops. Journal of the British Grassland Society 18, 104111.
Tyers, M. & Mann, M. (2003). From genomics to proteomics. Nature 422, 193197.
Tyler, C. (1975). Albrecht Thaer's hay equivalents: fact or fiction. Nutrition Abstracts and Reviews 45, 111.
Vande Wiele, R. L., MacDonald, P. C., Gurpide, E. & Lieberman, S. (1963). Studies on the secretion and interconversion of the androgens. In Recent Progress in Hormone Research, Vol. 19. Proceedings of the 1962 Laurentian Hormone Conference (Ed. Pincus, G.), pp. 275310. New York: Academic Press.
Van der Honing, Y. & Alderman, G. (1988). III. 2. Systems for energy evaluation of feeds and energy requirements for ruminants. Livestock Production Science 19, 217278.
Van der Vaart, H. R. (1977). Biomathematical models: some triumphs and some defeats. In Mathematical Models in Biological Discovery, Lecture Notes in Biomathematics, 13 (Eds Solomon, D. L. & Walter, C.), pp. 217224. Berlin: Springer-Verlag.
Van Es, A. J. H. (1975). Feed evaluation for dairy cows. Livestock Production Science 2, 95107.
Van Es, A. J. H. (1978). Feed evaluation for ruminants. I. The systems in use from May 1977 onwards in the Netherlands. Livestock Production Science 5, 331345.
Verhulst, P.-F. (1838). Notice sur la loi que la population suit dans sa croissance. Correspondance, Mathématiques et Physique 10, 113121.
Verstegen, M. W. A., Brascamp, E. W. & Van der Hel, W. (1978). Growing and fattening of pigs in relation to temperature of housing and feeding level. Canadian Journal of Animal Science 58, 113.
von Bertalanffy, L. (1950). An outline of general system theory. British Journal for the Philosophy of Science 1, 134165.
von Bertalanffy, L. (1957). Quantitative laws in metabolism and growth. Quarterly Review of Biology 32, 217231.
Waldo, D. R., Smith, L. W. & Cox, E. L. (1972). Model of cellulose disappearance from the rumen. Journal of Dairy Science 55, 125129.
Waterlow, J. C. (2006). Protein Turnover. Wallingford, UK: CAB International.
Waters, H. J. (1917). How an animal grows. In Proceedings of 2nd Pan American Scientific Congress 1915, pp. 510517. Washington, DC, USA: Government Printing Office.
Weller, R. A., Gray, F. V., Pilgrim, A. F. & Jones, G. B. (1967). The rates of production of volatile fatty acids in the rumen. IV. Individual and total volatile fatty acids. Australian Journal of Agricultural Research 18, 107118.
Wenk, C. & Schürch, A. (1974). Influence of the level of energy and protein in the feed on the energy metabolism of growing pigs. In Energy Metabolism of Farm Animals. European Association for Animal Production Publication No. 14 (Eds Menke, K. H., Lantzsch, H.-J. & Reichl, J. R.), pp. 173176. Hohenheim, Germany: Universität Hohenheim.
Westerfield, W. W. (1956). Biological response curves. Science 123, 10171019.
Weymouth, F. W., McMillin, H. C. & Rich, W. H. (1931). Latitude and relative growth in the razor clam, Siliqua patula. Journal of Experimental Biology 8, 228249.
Whittemore, C. T. & Fawcett, R. H. (1976). Theoretical aspects of a flexible model to simulate protein and lipid growth in pigs. Animal Production 22, 8796.
Whittemore, C. T., Kerr, J. C. & Cameron, N. D. (1995). An approach to prediction of feed intake in growing pigs using simple body measurements. Agricultural Systems 47, 235244.
Williams, M. B. (1977). Needs for the future: radically different types of mathematical models. In Mathematical Models in Biological Discovery, Lecture Notes in Biomathematics, Vol. 13 (Eds Solomon, D. L. & Walter, C.), pp. 226240. Berlin: Springer-Verlag.
Winsor, C. P. (1932). The Gompertz curve as a growth curve. Proceedings of the National Academy of Sciences of the United States of America 18, 18.
Wolff, E. V. (1874). Die Rationelle Fütterung der Landwirtschaftlichen Nutztiere. Berlin: Verlag von Wiegandt, Hempel & Parey.
Wolff, E. V. (1895). Farm Foods: or the Rational Feeding of Farm Animals. London: Gurney & Jackson.
Wood, P. D. P. (1967). Algebraic model of the lactation curve in cattle. Nature 216, 164165.
Wood, T. B. & Yule, G. U. (1914). Statistics of British feeding trials and the starch equivalent theory. Journal of Agricultural Science, Cambridge 6, 233251.
Wright, S. (1926). The biology of population growth; the natural increase of mankind – reviews. Journal of the American Statistical Association 21, 493497.
Yang, N., Wu, C. & McMillan, I. (1989). New mathematical model of poultry egg production. Poultry Science 68, 476481.
Yearsley, J., Tolkamp, B. J. & Illius, A. W. (2001). Theoretical developments in the study and prediction of food intake. Proceedings of the Nutrition Society 60, 145156.
Zierler, K. (1981). A critique of compartmental analysis. Annual Review of Biophysics and Bioengineering 10, 531562.

Related content

Powered by UNSILO

Mathematical modelling in animal nutrition: a centenary review

  • A. DUMAS (a1), J. DIJKSTRA (a2) and J. FRANCE (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.