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Mathematical modelling in animal nutrition: a centenary review

Published online by Cambridge University Press:  21 February 2008

A. DUMAS*
Affiliation:
Centre for Nutrition Modelling, Department of Animal and Poultry Science, University of Guelph, Guelph, ON N1G 2W1, Canada
J. DIJKSTRA
Affiliation:
Animal Nutrition Group, Wageningen Institute of Animal Sciences, Wageningen University, Marijkeweg 40, 6709 PG Wageningen, The Netherlands
J. FRANCE
Affiliation:
Centre for Nutrition Modelling, Department of Animal and Poultry Science, University of Guelph, Guelph, ON N1G 2W1, Canada
*
*To whom all correspondence should be addressed. Email: adumas@uoguelph.ca

Summary

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.

Type
Modelling Animal Systems Paper
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Agricultural and Food Research Council (AFRC) (1991). Theory of response to nutrients by farm animals. Nutrition Abstracts and Reviews, Series B 61, 683722.Google Scholar
AFRC (1993). Energy and Protein Requirements of Ruminants. Wallingford, Oxfordshire, UK: CAB International.Google Scholar
Agricultural Research Council (1981). The Nutrient Requirements of Pigs. Slough, UK: Commonwealth Agricultural Bureaux.Google Scholar
Almquist, H. J. (1953). Evaluation of vitamin requirement data. Poultry Science 32, 122128.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
Armsby, H. P. (1903). The Principles of Animal Nutrition. New York: John Wiley & Sons.CrossRefGoogle Scholar
Armsby, H. P. (1904). The respiration calorimeter at the Pennsylvania Experiment Station. Experiment Station Records 15, 10371050.Google Scholar
Armsby, H. P. (1917). The Nutrition of Farm Animals. New York: The Macmillan Company.CrossRefGoogle Scholar
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.Google Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
Baldwin, R. L. (1995). Modeling Ruminant Digestion and Metabolism. London: Chapman & Hall.Google Scholar
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.Google Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Baxter, C. F., Kleiber, M. & Black, A. L. (1955). Glucose metabolism in the lactating dairy cow. Biochimica et Biophysica Acta 17, 354361.CrossRefGoogle ScholarPubMed
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.Google Scholar
Bendixen, E. (2005). The use of proteomics in meat science. Meat Science 71, 138149.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Bergman, R. N., Ider, Y. Z., Bowden, C. R. & Cobelli, C. (1979). Quantitative estimation of insulin sensitivity. American Journal of Physiology 236, E667E677.Google ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.Google Scholar
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.Google Scholar
Blaxter, K. L. (1989). Energy Metabolism in Animals and Man. Cambridge, UK: Cambridge University Press.Google Scholar
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.CrossRefGoogle Scholar
Blaxter, K. L. & Ruben, H. (1953). Interim Reports on the Efficiency Project (unpublished). A.R.C. 239/53. Available Online at http://www.uoguelph.ca/cnm/Blaxter&Ruben_1953_Report_1.pdf (verified 4/02/08). 20 pp.Google Scholar
Blaxter, K. L. & Ruben, H. (1954 a). Second Interim Reports on the Efficiency Project (unpublished). A.R.C. 628/54. Available Online at http://www.uoguelph.ca/cnm/Blaxter&Ruben_1954a_Report_2.pdf (verified 4/02/08). 55 pp.Google Scholar
Blaxter, K. L. & Ruben, H. (1954 b). Third Interim Reports on the Efficiency Project (unpublished). A.R.C. 611/54. Available Online at http://www.uoguelph.ca/cnm/Blaxter&Ruben_1954b_Report_3.pdf (verified 4/02/08). 22 pp.Google Scholar
Blaxter, K. L. & Graham, N. McC. (1955). Plane of nutrition and starch equivalents. Journal of Agricultural Science, Cambridge 46, 292306.CrossRefGoogle Scholar
Blaxter, K. L. & Wainman, F. W. (1961). The utilization of food by sheep and cattle. Journal of Agricultural Science, Cambridge 57, 419425.CrossRefGoogle Scholar
Blaxter, K. L. & Clapperton, J. L. (1965). Prediction of the amount of methane produced by ruminants. British Journal of Nutrition 19, 511522.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
Bolie, V. W. (1961). Coefficients of normal blood glucose regulation. Journal of Applied Physiology 16, 783788.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Braude, R. (1967). The effect of changes in feeding patterns on the performance of pigs. Proceedings of the Nutrition Society 26, 163181.CrossRefGoogle ScholarPubMed
Brody, S. (1945). Bioenergetics and Growth with Special Reference to the Efficiency Complex in Domestic Animals. New York: Hafner Publishing Company.Google Scholar
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.CrossRefGoogle ScholarPubMed
Brody, T. (1999). Nutritional Biochemistry, Second Edition. San Diego, USA: Academic Press.Google Scholar
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.Google Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Crabtree, J. R. (1982). Interactive formulation system for cattle diets. Agricultural Systems 8, 291308.CrossRefGoogle Scholar
Curnow, R. N. (1973). A smooth population response curve based on an abrupt threshold and plateau model for individuals. Biometrics 29, 110.Google Scholar
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.CrossRefGoogle Scholar
Davidson, F. A. (1928). Growth and senescence in purebred Jersey cows. University of Illinois Agriculture Experimental Station Bulletin 302, 182235.Google Scholar
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.Google Scholar
Dent, J. B. & Casey, H. (1967). Linear Programming and Animal Nutrition. Philadelphia, PA, USA, and Toronto, ON, Canada: J.B. Lippincott Company.Google Scholar
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.CrossRefGoogle ScholarPubMed
Dijkstra, J. (1994). Simulation of the dynamics of protozoa in the rumen. British Journal of Nutrition 72, 679699.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.Google Scholar
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.CrossRefGoogle Scholar
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.Google Scholar
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.Google ScholarPubMed
Forbes, J. M. (1995). Voluntary Food Intake and Diet Selection in Farm Animals. Wallingford, UK: CAB International.Google Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
France, J., Thornley, J. H. M. & Beever, D. E. (1982). A mathematical model of the rumen. Journal of Agricultural Science, Cambridge 99, 343353.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
François, C. (1999). Systemics and cybernetics in a historical perspective. Systems Research and Behavioural Science 16, 203219.3.0.CO;2-1>CrossRefGoogle Scholar
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.Google Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
Gavora, J. S., Liljedahl, L. E., McMillan, I. & Ahlen, K. (1982). Comparison of three mathematical models of egg production. British Poultry Science 23, 339348.CrossRefGoogle Scholar
Gayon, J. (2000). History of the concept of allometry. American Zoologist 40, 748758.Google Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Glen, J. J. (1980). A parametric programming method for beef cattle ration formulation. Journal of Operational Research Society 31, 689698.CrossRefGoogle Scholar
Glen, J. J. (1987). Mathematical models in farm planning: a survey. Operations Research 35, 641666.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
Halnan, E. T. (1915). The maintenance ration of oxen and the starch equivalent theory. Journal of Agricultural Science, Cambridge 7, 163174.CrossRefGoogle Scholar
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.Google Scholar
Hendricks, W. A. (1931). Fitting the curve of the diminishing increment to feed consumption–live weight growth curves. Science 74, 290291.CrossRefGoogle ScholarPubMed
Henneberg, W. & Stohmann, F. (1864). Beiträge zur Begründung einer rationellen Fütterung der Wiederkäuer II. Braunschweig, Germany: Schwetske.Google Scholar
Hill, A. V. (1910). The combinations of haemoglobin with oxygen and with carbon monoxide I. Journal of Physiology 40, 471480.Google Scholar
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.CrossRefGoogle Scholar
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.Google Scholar
Hungate, R. E. (1966). The Rumen and its Microbes. New York: Academic Press.Google Scholar
Hunt, J. N. & Spurrell, W. R. (1951). The pattern of emptying of the human stomach. Journal of Physiology 113, 157168.CrossRefGoogle ScholarPubMed
Hunt, J. N. & MacDonald, I. (1954). The influence of volume on gastric emptying. Journal of Physiology 126, 459474.CrossRefGoogle ScholarPubMed
Huxley, J. S. (1924). Constant differential growth-ratios and their significance. Nature 114, 895896.CrossRefGoogle Scholar
Huxley, J. S. (1931). Notes on differential growth. American Naturalist 65, 289315.CrossRefGoogle Scholar
Huxley, J. S. & Teissier, G. (1936). Terminology of relative growth. Nature 137, 780781.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.Google Scholar
Jull, M. A. & Titus, H. W. (1928). Growth of chickens in relation to feed consumption. Journal of Agricultural Research 36, 541550.Google Scholar
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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
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).Google Scholar
Kellner, O. & Becker, M. (1966). Grundzüge der Fütterungslehre. Hamburg, Germany: Parey.Google Scholar
Kevles, D. J. (1985). In the Name of Eugenics: Genetics and the Use of Human Heredity. New York: Alfred A. Knopf.Google Scholar
Kleiber, M. (1932). Body size and metabolism. Hilgardia 6, 315353.CrossRefGoogle Scholar
Kleiber, M. (1937). Nutrition (energy metabolism). Annual Reviews of Biochemistry 6, 375394.CrossRefGoogle Scholar
Kleiber, M. (1961). The Fire of Life: An Introduction to Animal Energetics. New York: John Wiley & Sons.Google Scholar
Kleiber, M. (1975). The Fire of Life: An Introduction to Animal Energetics, 2nd edn.New York: Robert E. Krieger Publishing Company.Google Scholar
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.Google Scholar
Kotarbińska, M. (1969). Badania nad przemianą energii u rosnących świń. Instytut Zootechniki, Kraków, Wydawnictwa Własne No. 238.Google Scholar
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.Google Scholar
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.Google Scholar
Kussmann, M., Affolter, M. & Fay, L. B. (2005). Proteomics in nutrition and health. Combinatorial Chemistry and High Throughput Screening 8, 679696.CrossRefGoogle ScholarPubMed
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.Google Scholar
Laplace, J.-P. & Tomassone, R. (1970). Évacuation gastro-duodénale chez le porc. Annales de Zootechnie 19, 303332.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.Google Scholar
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.CrossRefGoogle ScholarPubMed
Lerner, M. I. (1939). Allometric studies of poultry. In Proceedings of the Seventh World Poultry Congress and Exposition, pp. 8588. Cleveland, OH, USA.Google Scholar
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.CrossRefGoogle Scholar
Lotka, A. J. (1925). Elements of Physical Biology. Baltimore, MD: Williams & Wilkins Company.Google Scholar
Lupatsch, I. & Kissil, G. W. (2005). Feed formulations based on energy and protein demands in white grouper (Epinephelus auneus). Aquaculture 248, 8395.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
May, R. M. (1976). Simple mathematical models with very complicated dynamics. Nature 261, 459467.CrossRefGoogle ScholarPubMed
Maynard, L. A. (1937). Animal Nutrition. New York: McGraw-Hill Book Company.Google Scholar
Maynard, L. A. (1953). Total digestible nutrients as a measure of feed energy. Journal of Nutrition 51, 1521.CrossRefGoogle ScholarPubMed
Maynard, L. A. & Loosli, J. K. (1969). Animal Nutrition, 6th edn. New York: McGraw-Hill Book Co.Google Scholar
Mazanov, A. & Nolan, J. V. (1976). Simulation of the dynamics of nitrogen metabolism in sheep. British Journal of Nutrition 35, 149174.CrossRefGoogle Scholar
McCollum, E. V. (1916). The present situation in nutrition. Hoard's Dairyman 51, 989993.Google Scholar
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.Google Scholar
McDonald, I. (1981). A revised model for the estimation of protein degradability in the rumen. Journal of Agricultural Science, Cambridge 96, 251252.CrossRefGoogle Scholar
McMeekan, C. P. (1941). Growth and development in the pig, with special reference to carcass quality characters. Journal of Agricultural Science, Cambridge 31, 117.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Mercer, L. P. (1980). Mathematical models in nutrition. Nutrition Reports International 21, 189198.Google Scholar
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.CrossRefGoogle Scholar
Michaelis, L. & Menten, M. (1913). Die kinetik der invertinwirkung. Biochemische Zeitschrift 49, 333369.Google Scholar
Mignon-Grasteau, S. & Beaumont, C. (2000). Growth curves in birds. Productions Animales (Paris) 13, 337348.Google Scholar
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.CrossRefGoogle ScholarPubMed
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.Google Scholar
Mitchell, H. H. (1924). A method of determining the biological value of protein. Journal of Biological Chemistry 58, 873903.Google Scholar
Mitchell, H. H. (1952). The nutritive evaluation of protein: a half-century of progress. Nutrition Reviews 10, 3337.CrossRefGoogle ScholarPubMed
Mitchell, H. H. (1964). Comparative Nutrition of Man and Domestic Animals, Vol. II. New York: Academic Press.Google Scholar
Mitscherlich-Königsberg, E. I. (1909). Das gesetz des minimums und das gesetz des abnehmenden bodenertrages. Landwirtschaftliche Jahrbücher 38, 537552.Google Scholar
Monod, J. (1942). Recherches sur la Croissance des Cultures Bactériennes, 2nd edn. Paris: Hermann.Google Scholar
Morgan, A. F. (1960). Samuel Brody – a biographical sketch. Journal of Nutrition 70, 39.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
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.Google Scholar
Moulton, C. R. (1918). Availability of the energy of food for growth. International Review of the Science and Practice of Agriculture 9, 472474.Google Scholar
Murray, J. A. (1914). The Chemistry of Cattle Feeding and Dairying. London: Longmans, Green, and Co.CrossRefGoogle Scholar
Murray, J. A. (1915). The starch equivalent theory. Journal of Agricultural Science, Cambridge 7, 154162.CrossRefGoogle Scholar
Murray, J. A. (1921). Normal growth in animals. Journal of Agricultural Science, Cambridge 11, 258274.CrossRefGoogle Scholar
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.Google Scholar
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.CrossRefGoogle ScholarPubMed
Nelson, D. L. & Cox, M. M. (2000). Lehninger Principles of Biochemistry, 3rd edn. New York: Worth Publishers.Google Scholar
Nichols, B. L. (1994). Atwater and USDA nutrition research and service: a prologue of the past century. Journal of Nutrition 124, 1718S1727S.CrossRefGoogle ScholarPubMed
Nolan, J. V. & Leng, R. A. (1972). Dynamic aspects of ammonia and urea metabolism in sheep. British Journal of Nutrition 27, 177194.CrossRefGoogle Scholar
National Research Council (NRC) (1987). Predicting Feed Intake of Food-producing Animals. Washington, DC, USA: National Academy Press.Google Scholar
National Research Council (NRC) (1996). Nutrient Requirements of Beef Cattle, 7th rev. edn.Washington, DC, USA: National Academy Press.Google Scholar
National Research Council (NRC) (1998). Nutrient Requirements of Swine, 10th rev. edn.Washington, DC, USA: National Academy Press.Google Scholar
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.CrossRefGoogle Scholar
Osborne, T. B. & Mendel, L. B. (1912). The role of gliadin in nutrition. Journal of Biological Chemistry 12, 473510.Google Scholar
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.Google Scholar
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.Google Scholar
Parks, J. R. (1982). A Theory of Feeding and Growth of Animals. Berlin: Springer-Verlag.CrossRefGoogle Scholar
Pearl, R. (1925). The Biology of Population Growth. New York: Alfred A. Knopf.Google Scholar
Pearson, K. (1920). Notes on the history of correlation. Biometrika 13, 2545.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
Pirt, J. S. (1975). Principles of Microbe and Cell Cultivation. New York: Blackwell Scientific.Google Scholar
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.CrossRefGoogle Scholar
Poppi, D. P., Gill, M. & France, J. (1994). Integration of theories of intake regulation in growing ruminants. Journal of Theoretical Biology 167, 129145.CrossRefGoogle Scholar
Porter, T. M. (2004). Karl Pearson. Princeton, NJ, USA, and Oxford, UK: Princeton University Press.Google Scholar
Pütter, A. (1920). Studien über physiologische ähnlichkeit. VI. Wachstumsähnlichkeiten. Pflügers Archiv fur die Gesamte Physiologie des Menschen und der Tiere 180, 298340.CrossRefGoogle Scholar
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.Google Scholar
Ratkowski, D. A. (1983). Nonlinear Regression Modeling. New York: Marcel Dekker.Google Scholar
Ratkowski, D. A. (1990). Handbook of Nonlinear Regression Models. New York: Marcel Dekker.Google Scholar
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.Google ScholarPubMed
Richards, F. J. (1959). A flexible growth function for empirical use. Journal of Experimental Botany 10, 290300.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.Google Scholar
Ritzman, E. G. (1917). Nature and rate of growth in lambs during the first year. Journal of Agricultural Research 11, 607623.Google Scholar
Robertson, T. B. (1908). On the normal rate of growth of an individual and its biochemical significance. Archiv fur Entwicklungsmechanik der Organismen 25, 581614.CrossRefGoogle Scholar
Robertson, T. B. (1916). Experimental studies on growth. II. The normal growth of the white mouse. Journal of Biological Chemistry 24, 363383.Google Scholar
Robertson, T. B. (1923). The Chemical Basis of Growth and Senescence. Philadelphia, PA, USA: J.B. Lippincott Company.Google Scholar
Robinson, G. W. & Halnan, E. T. (1912). Probable error in the pig feeding trials. Journal of Agricultural Science, Cambridge 5, 4851.CrossRefGoogle Scholar
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).Google Scholar
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.CrossRefGoogle Scholar
Schiemann, R., Nehring, K., Hoffmann, L., Jentsch, W. & Chudy, A. (1971). Energetische Futterbewertung und Energienormen. Berlin: VEB/Deutscher Landwirtschaftsverlag.Google Scholar
Schinckel, A. P. (1999). Describing the pig. In A Quantitative Biology of the Pig (EdKyriazakis, I.), pp. 938. Wallingford, Oxfordshire, UK: CABI Publishing.Google Scholar
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.Google ScholarPubMed
Seber, G. A. F. & Wild, C. J. (2003). Nonlinear Regression. Hoboken, NJ, USA: John Wiley & Sons.Google Scholar
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.Google ScholarPubMed
Thaer, A. D. (1809). Grundsätze der Rationellen Landwirthschaft. Berlin: Realschulbuchhandlung.Google Scholar
Thomas, C. (2004). Feed into Milk: A New Applied Feeding System for Dairy Cows. Nottingham, UK: Nottingham University Press.Google Scholar
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.Google Scholar
Thornley, J. (1998). Grassland Dynamics – an Ecosystem Simulation Model. Wallingford, Oxfordshire, UK: CAB International.Google Scholar
Thornley, J. & France, J. (2007). Mathematical Models in Agriculture: Quantitative Methods for the Plant, Animal and Ecological Sciences. Wallingford, UK: CAB International.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Tyers, M. & Mann, M. (2003). From genomics to proteomics. Nature 422, 193197.CrossRefGoogle ScholarPubMed
Tyler, C. (1975). Albrecht Thaer's hay equivalents: fact or fiction. Nutrition Abstracts and Reviews 45, 111.Google ScholarPubMed
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.Google Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Van Es, A. J. H. (1975). Feed evaluation for dairy cows. Livestock Production Science 2, 95107.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Verhulst, P.-F. (1838). Notice sur la loi que la population suit dans sa croissance. Correspondance, Mathématiques et Physique 10, 113121.Google Scholar
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.CrossRefGoogle Scholar
von Bertalanffy, L. (1950). An outline of general system theory. British Journal for the Philosophy of Science 1, 134165.CrossRefGoogle Scholar
von Bertalanffy, L. (1957). Quantitative laws in metabolism and growth. Quarterly Review of Biology 32, 217231.CrossRefGoogle Scholar
Waldo, D. R., Smith, L. W. & Cox, E. L. (1972). Model of cellulose disappearance from the rumen. Journal of Dairy Science 55, 125129.CrossRefGoogle ScholarPubMed
Waterlow, J. C. (2006). Protein Turnover. Wallingford, UK: CAB International.CrossRefGoogle Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
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.Google Scholar
Westerfield, W. W. (1956). Biological response curves. Science 123, 10171019.CrossRefGoogle Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
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.CrossRefGoogle ScholarPubMed
Wolff, E. V. (1874). Die Rationelle Fütterung der Landwirtschaftlichen Nutztiere. Berlin: Verlag von Wiegandt, Hempel & Parey.Google Scholar
Wolff, E. V. (1895). Farm Foods: or the Rational Feeding of Farm Animals. London: Gurney & Jackson.Google Scholar
Wood, P. D. P. (1967). Algebraic model of the lactation curve in cattle. Nature 216, 164165.CrossRefGoogle Scholar
Wood, T. B. & Yule, G. U. (1914). Statistics of British feeding trials and the starch equivalent theory. Journal of Agricultural Science, Cambridge 6, 233251.CrossRefGoogle Scholar
Wright, S. (1926). The biology of population growth; the natural increase of mankind – reviews. Journal of the American Statistical Association 21, 493497.CrossRefGoogle Scholar
Yang, N., Wu, C. & McMillan, I. (1989). New mathematical model of poultry egg production. Poultry Science 68, 476481.CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
Zierler, K. (1981). A critique of compartmental analysis. Annual Review of Biophysics and Bioengineering 10, 531562.CrossRefGoogle ScholarPubMed
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