MODELING MILK COMPOSITION J.P. Cant Department of Animal and Poultry Science University of Guelph, Canada INTRODUCTION "Modeling" has taken on the status of a buzz word in the past few years but animal nutritionists have been using models since the inception of scientific ration formulation in 1858 (1). For this discussion, a model can be defined as a set of mathematical equations that attempt to truthfully represent nutrient utilization in a dairy cow in a simpler manner than actually occurs so that the important aspects of her nutrition can be concentrated upon. The division of nutrient use into maintenance and productive functions is a model representation of the cow (Figure 1) for which the maintenance component has been expressed mathematically as a function of body weight since its first appearance. This simple model stayed in place for a long time; the 1971 NRC committee still used it (2). Equations in the model essentially served as scaling mechanisms so that protein levels, for example, deemed adequate in feeding experiments could be applied to animals of different body weights or milk protein yields. The current NRC (3) model (Figure 2) differs from its predecessors in two respects: 1) that protein requirements are calculated as a summation of losses into feces, urine, scurf and lactation; and 2) that rumen-degradable and -undegradable protein in the diet provide absorbed protein in different ways. Essentially, though, the calculation of a balance between the amount of nutrient consumed and the amount Figure 1. Information flow in a maintenance/production model of nutrient utilization. Arrows carry information, circles represent a calculation, and inputs are ovalled (from 2, 4). Figure 2. Information flow in the NRC (3) absorbed protein model of nutrient utilization.
Arrows carry information, circles represent a calculation, and inputs are ovalled. predicted to be required from a set of performance inputs remains the same. This approach will not work to formulate rations for a desired protein and fat composition of milk because of the backwards nature of the animal component calculations and the lumping of milk precursors together according to their combustible energy content. As the illustrious energeticist Kleiber remarked in 1961 (5), "the study of milk formation [is] essentially a problem of chemistry rather than of energetics." And even in 1902, Henry (6) pointed out that "while it is important from a scientific standpoint to study the fuel values of rations, such use in compounding them for practical purposes is hardly warranted, since a statement of the several nutrients themselves is more explicit and satisfactory." In requirement model equations, NE requirements would be a function of milk composition, which is an unequivocally contestable position, but milk composition in a dairy cow is not a unique function of NE supply. So the NE requirement that one might calculate would be unlikely to result in the composition of milk desired. DePeters et al. (7) fed isocaloric and isonitrogenous high-forage, high-fat or low-forage, low-fat diets to cows and observed marked differences in milk fat and lactose yields and fat and protein percentages in milk. The results were not unexpected because of the difference in milk precursor supply from the different diets. Fat feeding would provide long-chain fatty acids for milk fat synthesis and forage:concentrate ratios would affect acetate, propionate and microbial amino acid supplies. The fact that milk composition is, in experiments, a function of milk precursor supply, and not NEL supply, must be taken into account in milk composition models. This can be accomplished if the model is forward-driven, calculating dairy cow performance from dietary inputs, and considers the precursors of milk fat, protein and lactose explicitly. I will review three models published in the scientific literature that have these characteristics. A MULTIPLE LINEAR REGRESSION MODEL Rook et al. (8) compiled milk component yield, feed intake and liveweight data from 8 experiments in which grass silage was fed ad lib and concentrate given at a constant daily rate. Weekly measures on 251 cows between weeks 4 and 13 of lactation were available. The regression equations that gave the best prediction are given in Table 1. All
component yields were related to DM intake which, incidentally, was a better predictor than DE intake. Fat yields were a function of fibre characteristics of the diet, probably through rumen VFA effects. Nitrogen intake was not important for milk protein prediction but digestible organic matter content of the silage was significant. Liveweight only entered into the lactose yield equation. It was concluded that predictive accuracy was poor and might be improved with more mechanistic descriptions of milk precursor supply (8). Table 1. Coefficients in linear regression models to predict milk component yields from measured variables (from 8). variable fat yield protein yield lactose yield constant -0.04-0.02 0.80 silage DMI (kg/d) 0.0652 0.0569 concentrate DMI (kg/d) 0.0329 0.0407 total DMI (kg/d) 0.047 liveweight (kg) -0.00043 parity 0.0248 0.0318 silage N (g/kg) -0.0041 0.0088 silage NDF (g/kg) 0.00042-0.00044 silage digestible OM (g/kg) 0.00041-0.00077 silage ph 0.066 0.032 silage DM (g/kg as-fed) 0.00087 concentrate NDF (g/kg) -0.00079-0.00076 R 2 0.383 0.520 0.345 AN ADAPTIVE-PREDICTIVE MODEL Johnson and Tran (9) proposed a model of lactation in which ME intake, milk energy yield and maintenance/bodyweight change requirements were state variables governed by differential equations. In an application of this model to predicting milk component yields (10), milk energy was partitioned into fat, protein and lactose with time-dependent parameters γi: milk energy(t) = γ1fat(t) + γ2protein(t) + γ3lactose(t) A Kalman filter algorithm was used to correct predictions of milk composition for each week of lactation based on observations from the previous week. Results (Figure 3) show that the predictions tended to lag behind observed values so that as long as week-to-week changes were small, predictions were satisfactory. Although no consideration was given to the distinct mechanisms of milk fat, protein and lactose synthesis, the Kalman filter algorithm did provide an approach to correct predictions of performance as a cow's lactation progresses. Figure 3. Observations (solid lines) and predictions (dashed lines) of milk fat, protein and lactose from the adaptive-predictive model of Tran and Johnson (10).
A DYNAMIC, MECHANISTIC MODEL Forward-driven mechanistic elements have already been incorporated into the traditional requirement-type models. The CNCPS calculates metabolizable protein and energy supply from a simulation of rumen degradation and microbial synthesis (Figure 4). The value of this type of modeling derives not from the accuracy of animal requirement equations but from the ability to predict consequences of feeding a certain diet. If the absorption of nutrients in the gastrointestinal tract of a cow can be predicted from a chemical description of the feed, it is not much of a philosophical leap to say the production of milk and its components can also be predicted from diet inputs. And the dairy cow model of Baldwin et al., (11, 12) updated in 13 Figure 4. Information flow in the Cornell Net Carbohydrate and Protein System. Arrows carry information, circles represent a calculation, and inputs are ovalled (from 14, 15, 16).
does just that (Figure 5). One of the unique structural features of this type of model is that it includes an added dimension of time. There are many loops in the flow of information each box in the diagram represents a state variable that, as Figure 6 shows, contains such a loop. Additionally, the growth of rumen microbes, for instance, must be known to calculate soluble carbohydrate fermentation, which must be known to calculate growth of rumen microbes. Likewise, concentrations of glucose in the cow's body regulate catabolic and anabolic hormones which influence, among other things, the conversion of amino acids to glucose and, hence, glucose concentrations. This is not a level of complexity added for confusion but simply states exactly how we understand homeostasis the tendency for blood glucose concentration to remain constant, for example. Because of the circular flow of information, the entire model must be recalculated after all the equations have already been solved. After each iteration through the model, time is incremented slightly so that after many such iterations, a week of simulated time may have passed, or a month, or a full lactation. USING MATHEMATICAL MODELS IN FEEDING FOR MILK COMPOSITION To illustrate the use of a predictive model in making decisions related to feeding dairy cows in a multiple component pricing system, a ration was formulated according to NRC (3) "requirements" for a 650-kg cow of constant body weight producing 38 kg/d milk containing 4.0% fat. Then this ration was evaluated in the CNCPS which indicated a deficit in ME, rumen peptides and effective NDF. Dietary Figure 5. Information flow in the Baldwin (13) dairy cow model. Arrows carry information, circles represent a calculation, rectangles enclose state variables (see Figure 6) and inputs are ovalled.
Figure 6. Information flow in a state variable. fat sources were added, corn and alfalfa silage proportions adjusted, and protein supplements modified to balance ME, metabolizable protein, rumen nitrogenous compounds and effective NDF supplies against requirements (Table 2). The two rations are slightly different in chemical composition, most notably in energy supply from fat, so it is reasonable to expect a difference in milk production and composition as a result of choosing one diet over the other for feeding. Which is better? The requirement-type modelling does not assist but the forward-driven model of Baldwin (13), christened MOLLY, predicts that after 21 days on each of the two rations, cows will produce 33.1 and 32.8 kg/d milk. The second diet is more expensive to purchase so the expected return over feed cost is less. The modelling analysis indicates that the cheaper ration, although perhaps not meeting some of the arbitrary requirements for ME and rumen peptides, causes milk components to be produced in a more economical fashion. Table 2. Prediction with MOLLY (Baldwin, 13) of milk and milk component yield responses to diets formulated for 38 or 22 kg/d milk with NRC (3) or CNCPS models. 38 kg/d @ 4.0% fat 22 kg/d @ 4.0% fat NRC CNCPS NRC CNCPS
ingredient composition of diets (% of DM) corn silage 21.67 27.36 timothy silage 63.20 56.36 alfalfa silage 21.67 18.24 barley 27.02 20.00 corn, high moisture 31.19 25.54 fish meal 7.00 0 soybean meal 9.79 10.03 soybean meal 2.79 8.18 brewers grains, wet 14.15 9.12 corn, cracked 0 15.45 soybeans, roasted 0 6.38 tallow 0 1.82 vit/min premix 1.53 1.51 chemical composition of diets (% of DM) NEL (Mcal/kg) 1.71 1.80 NEL (Mcal/kg) 1.57 1.62 CP (% of DM) 18.3 18.2 CP (% of DM) 15.6 13.8 ADF (% of DM) 19.4 19.3 ADF (% of DM) 24.8 22.6 EE (% of DM) 3.6 6.1 EE (% of DM) 2.8 2.6 UIP (% of CP) 37.0 43.4 UIP (% of CP) 44.5 38.8 MOLLY yield (kg/d) milk 33.1 32.8 milk 21.7 22.2 fat 1.251 1.265 fat 1.174 1.206 protein 1.052 1.068 protein 0.796 0.769 lactose 1.588 1.573 lactose 1.042 1.067 milk price ($/d) 17.53 17.72 milk price ($/d) 14.26 14.24 feed cost ($/d) 4.60 5.14 feed cost ($/d) 2.67 2.74 income over feed ($/d) 12.93 12.58 income over feed ($/d) 11.60 11.50 The same cow, MOLLY, was fed two rations formulated for 22 kg/d milk with the NRC and CNCPS models (Table 2). Again, the NRC-constrained ration was deficient in ME and only marginally sufficient in rumen N according to the CNCPS. Metabolizable protein availability was also calculated to be 20% greater than necessary. MOLLY produced more milk and milk fat on the CNCPS ration but protein yields were less. Other economic indicators were not affected substantially by the diet change. Interestingly enough, the highforage, low-energy diets formulated for 22 kg/d resulted in about $1.20 less returned over feed cost than the more expensive rations that sustained a higher level of milk production. In a call for a change in livestock feeding systems in 1962, Blaxter (17) wrote that "what is needed is a method whereby the productive performance of an individual animal can be predicted with some precision from a knowledge of the quantities of the different foods which make up its ration, and of the conditions under which it is kept." Today, the power of computers and the knowledge of the physiological chemist have advanced to the point that the attempt to predict or calculate requirements can be abandoned in favour of a much more useful prediction of milk production response to diet, as Blaxter envisioned. REFERENCES 1. Wolff, E. v. 1874. Farm Foods or, The Rational Feeding of Livestock. Translated by H. H. Cousins. Gurney & Jackson, London, UK. 2. NRC. 1971. Nutrient Requirements of Domestic Animals. Number III. Nutrient Requirements of Dairy Cattle (4th Ed.). National Academy of Sciences, Washington, D.C.
3. NRC. 1988. Nutrient Requirements of Dairy Cattle (6th Ed.). National Academy Press, Washington, D.C. 4. Armsby, H. P. 1917. The Nutrition of Farm Animals. The MacMillan Co., New York, NY. 5. Kleiber, M. 1961. The Fire of Life: An Introduction to Animal Energetics. John Wiley & Sons, New York, NY. 6. Henry, W. A. 1902. Feeds and Feeding. 4th ed. W. A. Henry, Madison, WI. 7. DePeters, E.J., S.J. Taylor, and R.L. Baldwin. 1989. Effect of dietary fat in isocaloric rations on the nitrogen content of milk from Holstein cows. J. Dairy Sci. 72:2949. 8. Rook, A.J., J.D. Sutton, and J. France. 1992. Prediction of the yields of milk constituents in dairy cows offered silage ad libitum and concentrates at a flat rate. Anim. Prod. 54:313. 9. Johnson, C.L., and C.L. Tran. 1990. Rationale of feeding systems for lactating dairy cows. J. Dairy Res. 57:151. 10. Tran, C.L., and C.L. Johnson. 1991. Prediction of responses in milk constituents to changes in the nutrition of dairy cows. J. Dairy Res. 58:373. 11. Baldwin, R.L., J. France, and M. Gill. 1987. Metabolism of the lactating cow. I. Animal elements of a mechanistic model. J. Dairy Res. 54:77. 12. Baldwin, R.L., J.H.M. Thornley, and D.E. Beever. 1987. Metabolism of the lactating cow II. Digestive elements of a mechanistic model. J. Dairy Res. 54:107. 13. Baldwin, R. L. 1995. Modeling Ruminant Digestion and Metabolism. Chapman & Hall, London, UK. 14. Fox, D.G., C.J. Sniffen, J.D. O'Connor, J.B. Russell, and P.J. Van Soest. 1992. A net carbohydrate and protein system for evaluating cattle diets: III. Cattle requirements and diet adequacy. J. Anim. Sci. 70:3578. 15. Russell, J.B., J.D. O'Connor, D.G. Fox, P.J. Van Soest, and C.J. Sniffen. 1992. A net carbohydrate and protein system for evaluating cattle diets: I. Ruminal fermentation. J. Anim. Sci. 70:3551. 16. Sniffen, C.J., J.D. O'Connor, P.J. Van Soest, D.G. Fox, and J.B. Russell. 1992. A net carbohydrate and protein system for evaluating cattle diets: II. Carbohydrate and protein availability. J. Anim. Sci. 70:3562. 17. Blaxter, K. L. 1962. The Energy Metabolism of Ruminants. Hutchinson & Co., London, UK.