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HIGGS ET AL.

values in which equation [16] summed to 100% DM. The optimization step was completed last in the calculation process to fit the components within each feed together within the described constraints. The process was dy- namic in that the values calculated in the optimization fed back into the matrix and regression calculations described above. Typically, the optimizer had to be run numerous times before it would converge and stabilize. If insufficient data were available to perform any of the calculation steps described above, current CNCPS library values were retained. The approach was not ac- ceptable for proprietary feeds due to a lack of robust data of chemical components or the functional nature of some ingredients beyond the nutrient content. For example, products such as Met analogs are partially ab- sorbed through the rumen wall and do not completely flow to the small intestine, yet the supply of Met to the animal or the conservation of the AA due to the supplementation of the analog is documented (Chen et al., 2011). Conventional chemical analysis does not adequately estimate the true nutrient supply for these types of feeds. Current library values were retained in these circumstances. Approximately 75% of the feeds in the feed library were updated and 25% remained unchanged. Those remaining unchanged were primar- ily commercial products, minerals, and vitamins, along with unusual feeds with little information within the databases. AA In addition to the chemical components described above, each feed in the CNCPS feed library includes a profile of the 10 essential AA. Amino acid profiles were updated using data sets provided by Evonik Industries AG (Hanau, Germany), Adisseo (Commentry, France), and taken from the NRC (2001). Data provided were mean values from analyses completed in the respec- tive companies’ laboratories or published in the NRC (2001). In all cases, AA analyses were completed on the whole feed and are expressed in the CNCPS on a percent CP basis. This differs from previous versions of the CNCPS, where AA were expressed as a percent of the buffer-insoluble residue (O’Connor et al., 1993). The most appropriate profile was assigned based on data availability and was used as received by the source without alteration. If profiles for specific feeds were not available in the data sets provided, current CNCPS val- ues were retained. Proprietary feeds were not changed. Model Sensitivity The sensitivity of model outputs to variation in feed library inputs was also evaluated. The analysis was

split into 2 parts. Part 1 looked at the likely range in 6 major chemical components in the diet: (1) CP, (2) starch, (3) NDF, (4) lignin, (5) ash, and (6) EE; and 4 model outputs: (1) ME-allowable milk, (2) MP- allowable milk, (3) MP from RUP, and (4) MP from bacteria. To complete this part of the analysis, a refer- ence diet was constructed in a spreadsheet version of the CNCPS (Van Amburgh et al., 2013). The diet was formulated using ingredients typically found in North American dairy cattle rations and was balanced to provide enough ME and MP for a mature, nonpreg- nant, 600-kg cow in steady state (0 energy balance) to produce 35 kg of milk containing 3.1% true protein and 3.5% fat (Table 7). Probability density functions were fit to chemical components within each feed in the reference diet (Table 4) and correlated to each other with Spearman rank order correlations (Table 5) using @Risk version 5.7 (as previously described). Frequency distributions for model outputs were then generated us- ing a Monte Carlo simulation with 10,000 iterations to describe the range of possible outcomes for each output and the relative likelihood of occurrence. Part 2 of the analysis investigated which feed library inputs for the feeds in the reference diet had the most influence on selected model outputs: (1) ME-allowable milk, (2) MP-allowable milk, (3) MP from RUP, and (4) MP from bacteria. The feed library inputs investi- gated were those described in part 1 of the analysis, as Table 7. Diet ingredients, chemical composition, and model predicted ME and MP for the reference diet used to analyze model sensitivity Item 1 Unit Diet ingredient (kg of DM) Corn silage 4.76 Alfalfa silage 3.14 Grass hay 4.03 Corn grain ground fine 6.48 Soybean meal solvent extracted 2.58 Blood meal 0.20 Minerals and vitamins 0.50 Total DMI 21.69 Diet composition (% of DM unless stated) CP 16.7 SP (% of CP) 35.3 ADICP (% of CP) 6.4 NDICP (% of CP) 15.6 WSC 3.5 Starch 29.0 NDF 31.8 Lignin (% of NDF) 11.5 EE 3.0 Ash 7.7 2,385 1 WSC = water-soluble carbohydrates; SP = soluble protein; ADICP = acid detergent-insoluble CP; NDICP = neutral detergent-insoluble CP; EE = ether extract. Model outputs ME (Mcal/d) 53.7 MP (g/d)

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Journal of Dairy Science Vol. 98 No. 9, 2015