Pergamon J. Frank/in Inst. Vol. 33SB, No. 2, pp. 241-258, 1998 0 1997 ThC Franklin Institute PII: s0016-0032(97)00010-0 Published by Elsevier Science Ltd Prmted III Great Britam 0016-0032/98 $19.00+0.00 Biomathematical Applications in Ruminant Nutrition by J.FRANCE Department of Agriculture, University of Reading, U.K. J.DIJKSTRA Department of Animal Nutrition, Wageningen Agricultural University, Marijkeweg 40,6709 PG, Wageningen, The Netherlands M.S.DHANOA IGER, Plus Gogerddan, Aberystwyth, Dyfed SY23 3EB, U.K. and R. L.BALDWIN Department of Animal Science, University of California, Davis, CA 95616-8521, U.S.A. (Received inJinalform 4 December 1996; accepted 1.5 January 1997) ABSTRACT : Applications of the rate : state formalism are illustrated using examples drawn fLom our own work. The examples selected demonstrate the use of mechanistic mathematical modelling at the level of’ the component process, the whole organ and the whole organism, and the interplql that exists between modelling at these different levels of organisation and between modelling and experimental research. 0 1997 The Franklin Institute. Published by Elsevier Science Ltd The products of animal agriculture contribute significantly to the world food supply. Food-producing animals, particularly ruminants, play a key role in converting plant material humans cannot or choose not to consume into desirable, high-quality human food. Plant resources utilized in ruminant animal production include forage and silage crops, pasture and range forage, cereal grains, crop residues, and a wide range of by- products from food processing. A basic goal of scientists studying ruminants is to advance animal production, and thereby reduce excretion of waste, through a greater understanding of ruminant digestion and metabolism. This necessitates elucidating the mechanisms governing the kinetics and energetics of nutrient utilisation by the animal. The methods of applied mathematics, which have evolved over centuries for the study of kinetics and energetics in physical systems, and based on the differential and integral calculus, are now recog- nised as a useful and legitimate tool in the study of ruminant nutrition. Evidence of this is provided by recent books on mechanistic modelling (1,2). 241