Carbohydrate fractionation scheme

The comparison of carbohydrate fractionation schemes in CNCPS 5.0 and CPM Dairy 3.0 are listed in Table 1. In the CNCPS 5.0 and CPM Dairy 1.0, the carbohydrate fractionation scheme assumed two fractions of non-fibre carbohydrate (NFC): the A fraction that contains organic acids and sugars, and the B1 fraction that contains soluble fibres and starch (Sniffen et al. Reference Sniffen, O'Connor, Van Soest, Fox and Russell1992) as listed in Table 1.

Table 1.

Composition and digestion of carbohydrate fractions in the CNCPS and CPM Dairy models

^a Intestinal digestibility of the rumen escape fraction.

^b Contains plant organic acids and may contain fructans depending on the method used to measure sugars.

During silage fermentation, some of the soluble non-cell wall components are metabolized primarily to lactic and acetic acids (McDonald et al. Reference McDonald, Henderson and Heron1991). These silage acids are useful to the animal as a component of ME but are depleted fermentable sources of ATP for microbial growth under normal rumen conditions (Van Soest Reference Van Soest1994). Thus, ensiling has little effect on feed energy values but can affect supply of protein to the host animal substantially by decreasing bacterial protein production. Therefore, a separation between sugars and organic or silage acids was needed. In the CPM Dairy 3.0, The CHO A fraction has been separated into silage acids (CA1) and sugars (CA2) as shown in Eqns (1)–(4).

(1)

(2)

(3)

(4)

where CHO is g carbohydrate/kg of DM; CP is g crude protein/kg of DM, EE is g ether extract/kg of DM; Ash is g/kg of DM; NFC is g non-fibre carbohydrate/kg of DM, NDF is g neutral detergent fibre/kg of DM; NDICP is g neutral detergent insoluble CP/kg of CP; CA1 is g carbohydrate fraction A1/kg of DM; OA is g organic acids from silage/kg of NFC; CA2 is g carbohydrate fraction A2/kg of DM; Sugar is g simple sugars/kg of NFC; and i is the ith feed.

In the CNCPS 5.0 and CPM Dairy 1.0, the CB1 fraction contained starch, pectin and β-glucans. Grouping these carbohydrates together is not nutritionally correct because they may have different rates of fermentation in the rumen (Engstrom et al. Reference Engstrom, Mathison and Goonewardene1992; Hatfield & Weimer Reference Hatfield and Weimer1995; Hall et al. Reference Hall, Pell and Chase1998), they are not precisely defined or analysed (Van Soest Reference Van Soest1994; Pitt et al. Reference Pitt, Van Kessel, Fox, Pell, Barry and Van Soest1996; Alderman et al. Reference Alderman2001; Offner & Sauvant Reference Offner and Sauvant2004), and it does not account for all the variability observed in NFC digestibility when various processing treatments are applied (Offner & Sauvant Reference Offner and Sauvant2004). Lanzas et al. (Reference Lanzas, Sniffen, Seo, Tedeschi and Fox2007) provided more discussion of fractionation of carbohydrates. As shown in Table 1, some organic acids and fructans might be pooled in CB2 depending on the method used.

In the CPM Dairy 3.0, starch (CB1; Eqn (5)) has been separated from pectin and β-glucans (CB2; Eqn (6)). The composition of fraction CC (Eqn (7)) was not changed. The fraction CC consists of lignin and fibre associated with lignin, representing the material that is not fermented after 200 h (Van Soest et al. Reference Van Soest, Van Amburgh, Robertson and Knaus2005). Carbohydrate fraction C is calculated as lignin×2·4 (Van Soest et al. Reference Van Soest, Van Amburgh, Robertson and Knaus2005). Remaining carbohydrate fraction is the insoluble available fibre (fraction CB3 (Eqn (8)) in the CPM Dairy 3.0), which was fraction CB2 in the CNCPS 5.0 and CPM Dairy 1.0. Several techniques for determining NDF have been developed and used (Hintz et al. Reference Hintz, Mertens and Albrecht1996; Mertens Reference Mertens2002). If sodium sulphite is used in the determination of NDF, a variable amount of NDICP will be removed from the neutral detergent residue, depending on the feed. Therefore with this NDF analysis, the CB3 may be under-estimated when the correction for NDICP is applied. The B fraction carbohydrates are determined as shown in Eqns (5)–(8) below.

(5)

(6)

(7)

(8)

where CB1 is g carbohydrate fraction B1/kg of DM; Starch is g starch complexes/kg of NFC; NFC is g non-fibre carbohydrate/kg of DM; CB2 is g carbohydrate fraction B2/kg of DM; CA1 is g carbohydrate fraction A1/kg of DM; CA2 is g carbohydrate fraction A2/kg of DM; CC is g carbohydrate fraction C/kg of DM; NDF is g neutral detergent fibre/kg of DM; NDICP is g neutral detergent insoluble CP/kg of CP; Lignin is g sulphuric acid or acid detergent lignin/kg of NDF; and i is the ith feed.

Lipid sub-model

Fatty acids and glycerol are lipid compounds of nutritional significance. Crude fat is normally determined by extraction using ether; however, not all ether soluble materials are fatty acids (Van Soest Reference Van Soest1994). As a consequence, the CPM Dairy 3.0 contains a lipid sub-model developed by Moate et al. (Reference Moate, Chalupa, Jenkins and Boston2004) that describes the ruminal digestion and metabolism of long-chain fatty acids (LCFA).

The lipid sub-model was developed to account for (1) intake of fatty acids, (2) ruminal lipolysis of dietary lipids, (3) ruminal biohydrogenation of fatty acids, (4) de novo synthesis of fatty acids in the rumen, (5) effects of fat on rumen digestion and fermentation and (6) intestinal digestion of fatty acids (Moate et al. Reference Moate, Chalupa, Jenkins and Boston2004). The following LCFA were included in this sub-model: n-dodecanoic acid (lauric acid, C12:0), n-tetradecanoic acid (myristic acid, C14:0), n-hexadecanoic acid (palmitic acid, C16:0), hexadecenoic acid (palmitoleic acid, C16:1), n-octadecanoic acid (stearic acid, C18:0), octadecenoic acid (oleic acid, C18:1c, C18:1t); octadecadienoic acid (linoleic acid, C18:2) and octadecatrienoic acid (linolenic acid, C18:3) (Nelson & Cox Reference Nelson and Cox2005).

The lipid sub-model was developed almost entirely with data from published experiments involving lactating dairy cows in which daily dietary intakes, duodenal flows and faecal outputs of individual LCFA were reported (Moate et al. Reference Moate, Chalupa, Jenkins and Boston2004). The initial evaluation included seven experiments utilizing non-lactating cattle (mostly young growing steers) and one experiment utilizing lactating dairy cows. The lipid sub-model explained more than 86% of the variation between predicted and measured absorbed C12:0, C14:0, C16:0, C18:0, C18:1t, C18:1c and C18:2. The predicted mean bias was 12% or less for C12:0, C14:0, C16:0, C18:0 and C18:2. For C18:1t and C18:1c, the correlation was good (r>0·96) but the mean bias was about 20%. This may be a consequence of the small number of comparisons as C18:1t and C18:1c data were only reported for eight diets in two experiments. The absorption of C16:1, C18:3 and other LCFA was poorly predicted by the sub-model. However, only small amounts (2–3 g/d) of C16:1 and C18:3 were absorbed and other LCFA includes LCFA were not always reported in all experiments.

In a more recent evaluation, Moate et al. (Reference Moate, Boston, Lean and Chalupa2006) examined the ability of the lipid sub-model to predict the apparent absorption (intake minus faecal) of total LCFA in lactating dairy cows. There were two types of experiments: abomasal infusion experiments and feeding experiments. The amounts of total LCFA apparently absorbed were regressed against the reported amounts of total LCFA apparently absorbed. For the diets from the infusion experiments, the CCC (r _c; Lin Reference Lin1989) was 0·923 and Pearson correlation coefficient (r) was 0·940. For the diets from the feeding experiments, these values were r _c=0·975 and r=0·977. These evaluations indicated that because the lipid sub-model accurately predicted the apparent absorption of total LCFA infused into the abomasum of dairy cows, appropriate intestinal absorption coefficients were used in the lipid sub-model. Furthermore, the model also accurately predicted the apparent absorption of total LCFA in the feeding experiments, suggesting the model may be correctly describing ruminal processes such as lipolysis, biohydrogenation and the de novo synthesis of LCFA that can influence apparent absorption of total LCFA.

Feed dictionary

The main goal of a feed dictionary or feed library is to provide values for feed chemical analyses needed by the model that are not available for the feeds to be used for the development of rations. The feed dictionary in the CPM Dairy 3.0 represents an evolution from the first dictionary published by Fox et al. (Reference Fox, Sniffen, O'connor, Russell and Van Soest1990) and Sniffen et al. (Reference Sniffen, O'Connor, Van Soest, Fox and Russell1992). More than 10 000 feed analyses were utilized in the development of the feed library for the CPM Dairy 3.0. Degradation rates of available NDF (CB3) were estimated from 30 h in vitro NDF digestion (Van Soest et al. Reference Van Soest, Van Amburgh and Tedeschi2000). For instance, the newly generated degradation rates of CB3 for corn silage were lower and those for alfalfa were higher than the feed dictionary values in the CPM Dairy 1.0.

Despite the effort made to provide correct values in the feed dictionary, actual chemical compositions of the feed carbohydrate and protein fractions used in CPM Dairy 3.0 should be measured in order to determine accurately intake of nutrients and prediction of animal performance. The values reported in a feed dictionary do not represent the mean of the chemical components of randomly selected feed samples because it assumes the chemical components are independent (Tedeschi et al. Reference Tedeschi, Fox, Pell, Lanna and Boin2002). In fact, the chemical components are highly correlated (Tylutki Reference Tylutki2002).

Some feed ingredients (e.g. ground maize) have a low variance in analysis and may not require frequent analysis. Others (e.g. forages, distillers' grains) are quite variable in composition and require frequent analysis. For some components (e.g. lignin, soluble protein, non-protein nitrogen (NPN), amino acids) there is less variance if expressed as a percentage of another component (e.g. NDF, CP, soluble protein, ruminally-undegraded protein (RUP)) than if expressed as a proportion of dry matter (DM). Additionally, some feed components such as lignin, NPN and amino acids may not be analysed and use of the feed dictionary values are facilitated when they are expressed on the basis of a fraction usually analysed or calculated.

Optimization and ration formulation

Ration formulation involves the selection of feed ingredients within a specified DMI so that nutrient supplies meet nutrient requirements at the lowest cost. Nutritional constraints are based upon application of the factorial approach to describe the requirements of cows to perform specific or multiple functions (maintenance, growth, lactation and pregnancy). Linear programming is commonly used for auto-balancing in most nutrition models (Tedeschi et al. Reference Tedeschi, Fox, Chase and Wang2000). In fact, ration formulation was one of the first applications of linear programming. Not only could solutions be found in seconds, but building on contributions of Dantzig (Reference Dantzig and Koopmans1951) to operational research, an array of other very helpful economic properties (shadow prices) relating to the optimal solution could be derived. Nonetheless, the suitability of linear programming for optimization depends on the linearity of the problem. The CPM Dairy 3.0 utilizes a non-linear optimization called the ‘Feasible Sequential Quadratic Programming’ approach (Zhou et al. Reference Zhou, Tits and Lawrence1997). Feed cost is a logical objective for ration formulation; however, other objectives may be desirable for diet formulation in the near future. These include minimization of nutrient excretion by animals and production of specific components of milk that are nutritionally valuable.

Database description

A database containing 228 individually-fed high-producing lactating dairy cows from five studies was utilized to assess the adequacy of the CPM Dairy 3.0 to predict first-limiting ME- or MP-allowable milk production. The database contained adequate information on feed composition and intake, animal description and performance, and environment information necessary to predict milk production with CPM Dairy. Study 1 had 36 primiparous and 40 multiparous Holstein cows fed wet corn gluten feed over 2 years (Kononoff et al. Reference Kononoff, Ivan, Matzke, Grant, Stock and Klopfenstein2006) at the University of Nebraska-Lincoln Dairy Research Unit. Only the post-peak milk production data were utilized in the evaluation. Study 2 consisted of 23 multiparous and 16 primiparous Holstein cows averaging 263 days in milk and 614 kg BW. These cows received three levels of CP (low, medium and high) in a total mixed ration (TMR) for 4 weeks (Ruiz et al. Reference Ruiz, Tedeschi, Marini, Fox, Pell, Jarvis and Russell2002). Study 3 was comprised of 60 multiparous and 21 primiparous Holstein cows (Stone Reference Stone1996). Cows from Study 3 were fed three treatments to evaluate soy hulls as forage or concentrate replacement over a 14 week period. Study 4 consisted of 15 multiparous Holstein cows averaging 126 days in milk and 560 kg BW that were fed fresh-cut orchardgrass (Dactylus glomerata L.) and a concentrate mix with or without Rumensin™ for 3 weeks (Ruiz et al. Reference Ruiz, Albrecht, Tedeschi, Jarvis, Russell and Fox2001). Studies 2, 3 and 4 were conducted at the Cornell University Teaching and Research Centre. Study 5 was conducted at the experimental station of the Brazilian Agricultural Research Corporation (EMBRAPA) at Coronel Pacheco, MG (Brazil) with 14 lactating Holstein cows in a free-stall confinement (Fernando C. F. Lopes, unpublished). Maize silage was offered ad libitum while the concentrate mixture was fed based on the milk production level (4·08–8·16 kg of DM/d). Maize silage and concentrate mixture DMI was measured daily for 5 consecutive days using individual, electronic feeders (Calan gate system). Cows were mechanically milked twice per day (06·00 and 14·00 h) and milk production and milk composition (fat, protein and solids) were determined daily. Dietary ingredients were individually analysed for nutrients necessary to estimate ME and MP using CPM Dairy 3.0. The observed DMI was used to predict ME and MP allowable milk because the use of predicted DMI would cause two uncertainties in predicting milk production: prediction of intake and subsequent milk production.

The LCFA and degradation rates of the feeds used to perform these simulations were set to match comparable feeds listed in the CPM Dairy 3.0 feed dictionary; all other feed compositions were measured as indicated.

Statistical methods

A random coefficients model (Littell et al. Reference Littell, Milliken, Stroup, Wolfinger and Schabenberger2006) was used to combine model predictions of the five studies using PROC MIXED of SAS (Littell et al. Reference Littell, Milliken, Stroup, Wolfinger and Schabenberger2006). Observed milk production was regressed on model-predicted milk production, assuming study as random effects and unstructured variance–(co)variance matrix, as shown in Eqn (9). Adjusted observed milk production was computed as the sum of fixed effects and uncontrolled-random error. Similar analysis was performed for observed and model-predicted DMI for all five studies included in the evaluation data set.

where:

(9)

The variance component analysis of fixed effects (model predictions, R ²_FixedEffects) and study effects (R ²_{RandomEffects}) in explaining the observed milk production was assessed based on coefficients of partial determination (Eqn (10)). The coefficients of partial determination were estimated by regressing observed milk production on fixed effects, study effects and uncontrolled-random error (Neter et al. Reference Neter, Kutner, Nachtsheim and Wasserman1996) using PROC REG of SAS (SAS Inst., Cary, NC) with options PCORR1 (for sequential sum of squares) and PCORR2 (for partial sum of squares).

(10)

where SSR(FixedEffects/RandomEffects) is partial sum of squares of regression of fixed effects when random effects was in the model, SSE(RandomEffects) is sum of squares of error when random effects was the only independent variable in the statistical model, SSR(RandomEffects/FixedEffects) is partial sum of squares of regression of random effects when fixed effects was in the model and SSE(FixedEffects) is sum of squares of error when fixed effects was the only independent variable in the statistical model.