J. Dairy Sci. 84:649–664 American Dairy Science Association, 2001.
Accuracy and Precision of Computer Models to Predict Passage of Crude Protein and Amino Acids to the Duodenum of Lactating Cows H. G. Bateman, II,*,1 J. H. Clark,* R. A. Patton,† C. J. Peel,‡ and C. G. Schwab§ *Department of Animal Sciences University of Illinois, Urbana 61801 †Nittany Dairy Nutrition, Mifflinburg, PA 17844 ‡Degussa Corporation Ridgefield Park, NJ 07660 §Department of Animal and Nutritional Sciences University of New Hampshire, Durham 03824
ABSTRACT To evaluate the ability of several models to accurately and precisely predict the passage of crude protein (CP) and amino acids to the duodenum of lactating cows, we simulated data from six published studies using the 1989 National Research Council equations, the Mepron Dairy Ration Evaluator (version 1.1), the University of Pennsylvania release of the Net Carbohydrate and Protein System (version 2.12p), the Cornell Net Carbohydrate and Protein System (version 3), and CPM Dairy (version 1.0). Models overestimated the passage of CP from microbes by an average of 323 g/d, and underestimated the passage of CP from feed by an average of 874 g/d. These two errors were partially canceled when CP from microbes and feed were summed to estimate passage of total CP to the duodenum. Many dietary composition variables appeared to bias the predictions; however, the influence of any one variable was small. The efficiency of modeling was high for most predictions but was variable for predicting passage of specific individual amino acids to the small intestine depending on the model selected. These simulations indicated no obvious advantage for any model over the others tested. The models responded to changes in diets by altering the amount of protein from microbes and feed that reached the duodenum, resulting in improved accuracy of predictions of duodenal CP passage compared with simply assuming a constant value for passage of CP to the duodenum. (Key words: modeling, protein, amino acid, dairy cows) Abbreviation key: CNCPS = Cornell Net Carbohydrate and Protein System, CPM = CPM Dairy, ME-
Received December 3, 1999. Accepted September 20, 2000. Corresponding author: J. H. Clark; e-mail:
[email protected]. 1 Current address: LSU Agricultural Center, Department of Dairy Science, Baton Rouge, LA 70803.
PRON = Mepron Dairy Ration Evaluator, MSPE = mean squared prediction error, NAN = nonammonia nitrogen, NANMN = nonammonia nonmicrobial nitrogen, PENN = University of Pennsylvania release of the Net Carbohydrate and Protein System, RMSPE = root mean square prediction error. INTRODUCTION An accurate prediction of the supply of nutrients to the small intestine of cows is required to accurately predict the lactation response to a particular diet. Mathematical models have been developed that simulate ruminal fermentation and predict nutrient requirements and passage to the duodenum (Agricultural and Food Research Council, 1993; Baldwin et al., 1977; 1987; Dijkstra et al., 1992; France et al., 1982; Institut National de la Recherche Agronomique, 1989; NRC, 1989; 1996; Russell et al., 1992). The most notable of these models are the Cornell Net Carbohydrate and Protein System (CNCPS; Russell et al., 1992), the equations presented in the Nutrient Requirements for Dairy Cattle (NRC, 1989), the model of Baldwin et al. (1977, 1987), the Danish model of Dijkstra et al. (1992), the French system for determining feeding requirements (Institut National de la Recherche Agronomique, 1989), and the British system for estimating nutrient requirements (Agricultural and Food Research Council, 1993). Additionally, several feed companies possess proprietary models. The CNCPS and its derivatives were designed for field application as an aid to on- farm decision making and as an aid in ration planning. Many of the proprietary models were designed as an aid in the ration formulation process. The mechanistic models of Baldwin et al. (1977, 1987) and Dijkstra et al. (1992) were designed for research planning and evaluation. The empirical models of NRC (1989, 1996) were designed for ration planning across a variety of management situations and may lack sensitivity to di-
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etary and animal variation. The French and British models have limitations for use in North America because inputs to these models are often not available in North American production settings to mechanistically predict supply of net energy and AA from feeds (NRC, 1996). The ability of any model to accurately and precisely predict nutrient passage to the duodenum must be compared with results obtained experimentally (Firkins et al., 1998), and results of those comparisons must be evaluated against the intended applications of the models (Firkins et al., 1998). Even when these comparisons are completed, one cannot be absolutely positive that the variation observed is because of the model. Some of the variation observed can be because of the extreme technical limitations in measurement of nutrients being evaluated in the dynamic and complex microbial, biochemical, and physiological systems of the lactating dairy cow. The objective of this study was to evaluate models designed for field application as decision-making aids for accuracy and precision of predicting passage of CP and AA to the duodenum. Predictions by models for CP and AA that pass to the duodenum were compared with results from trials in which lactating dairy cows were used to measure CP and AA passage to the duodenum. For this analysis, it was assumed that data from trials with lactating cows were measured without error. MATERIALS AND METHODS Trials Simulated Individual cow data from research trials that were summarized in six papers (Klusmeyer et al., 1991a, 1991b; McCarthy et al., 1989; Overton et al., 1995; Putnam et al., 1997; Schwab et al., 1992) published between 1989 and 1997 were used to evaluate the accuracy and precision of models to predict passage of N fractions to the small intestine of lactating dairy cows. All data were from digestibility trials that used surgically modified, lactating Holstein cows in Latin square designs. Multiparous cows were used in all trials, except for the trial of Putnam et al. (1997), in which primiparous cows were used. These trials were chosen because of the relative completeness of data, including diet composition and animal characteristics, and because of the availability of data from individual cows at two different laboratories. The trials used represent four trials conducted at the University of Illinois (Klusmeyer et al., 1991a, 1991b; McCarthy et al., 1989; Overton et al., 1995) and two trials conducted at the University of New Hampshire (Putnam et al., 1997; Schwab et al., 1992). Chromic oxide was used as the digesta flow marker in all of the trials. Purines were used as the microbial marker in all trials except for that of Schwab et al. (1992), who used diamiJournal of Dairy Science Vol. 84, No. 3, 2001
nopimelic acid. This data set represented 164 individual observations from cows. Measured data from these trials were used as inputs to models to describe the cows being simulated. Data available to describe the cow being simulated included DIM, DMI, milk yield, and milk composition measured during the trials. When available, measured BW was used as an input to the models, otherwise, a constant BW of 600 kg was assigned to multiparous cows and a constant BW of 550 kg was assigned to primiparous cows. Lactation number (parity) was changed to 3 for consistency for cows from publications by Klusmeyer et al., 1991a, 1991b; McCarthy et al., 1989; Schwab et al., 1992; and Overton et al., 1995 and equal to 1 for cows from the publication by Putnam et al. (1997). Models and Constants Used for Simulation Data were used to evaluate predictions of passage to the duodenum of CP and AA by the following models: NRC (1989), the Mepron Dairy Ration Evaluator (MEPRON) version 1.1 from the Degussa Corporation (Ridgefield Park, NJ), the University of Pennsylvania release of the Net Carbohydrate and Protein System (PENN) version 2.12p, the CNCPS (Russell et al., 1992) version 3, and the CPM Dairy version 1.0. For the PENN, CNCPS, and CPM models, environmental factors and frame scores were estimated using constants from the model being evaluated. For the NRC model, cows were assumed to be neither gaining nor losing BW, and DMI was assumed to provide 100% of NEL requirements because BW gain within periods was not recorded in the trials used for this paper. For all models, days pregnant were assumed to be DIM minus 60 when DIM were greater than 60 and 0 when DIM were less than or equal to 60. The nutrient composition of dietary ingredients remained at program defaults unless nutrient composition was available in published papers or from principal investigators. When nutrient composition for a feedstuff was available, the feed library of each model was adjusted so that nutrient composition as analyzed was used in the model. Nutrient composition values associated with the proximate analysis were available for all forages and for some concentrate ingredients. Amino acid composition of feeds (% of DM) was available for all feeds from the trials conducted in New Hampshire. Because the PENN, CNCPS, and CPM models use AA as a percentage of buffer insoluble protein, these data were not used to modify the feed tables in these models. The AA composition of feeds in the MEPRON model is specified as a percentage of the DM; therefore, the analyzed AA composition of feeds from the New Hampshire data was used with this model. The MEPRON model has a function
PREDICTING NITROGEN PASSAGE TO THE DUODENUM
that modifies the AA composition for a feed based on the CP content of the feed. Because the AA composition of some feeds was available and because this function modifies the default feed tables, it was not used with these data. The disappearance rate constants and fractions of protein and carbohydrate in feeds were not available; therefore, program default values for disappearance rate constants and fractions of CP and carbohydrates in individual feeds were used throughout these evaluations as is usual in on-farm situations. Adjustments to Model Equations The MEPRON, PENN, CNCPS, and CPM models do not produce direct estimates of CP passage to the duodenum that can be subdivided into passage of CP from bacteria and feed that can be compared with measured passage of CP. Predictions of metabolizable protein passage by the PENN, CNCPS, and CPM models were equated to CP passage to the duodenum after scaling outputs in these models as described below. To convert metabolizable protein to CP in the PENN and CPM models, we made the following adjustments. Bacterial true protein was increased from 60 to 100% of the bacterial CP. Therefore, estimates reported as metabolizable protein from bacteria were converted to CP and included cell wall associated (25% of bacterial CP) and nucleic acid (15% of bacterial CP) CP. Intestinal digestibility of the slowly degradable feed protein (fraction B3) was increased from 80 to 100%, and intestinal digestibility of bound feed protein (fraction C) was increased from 0 to 100% to convert metabolizable feed protein to feed CP. The CP from feed and microbes were summed to provide estimates of total CP passage to the duodenum. In the CNCPS model, intestinal digestibilities of protein fractions B3 and C were increased from 80 and 0%, respectively, to 100% for both feed and microbial protein to include all protein passing to the duodenum in the final estimates of metabolizable protein produced by the model. The estimates of CP from feed and microbes were summed to provide an estimate of passage of total CP to the duodenum. The MEPRON model estimates absorbable protein. This estimate for absorbable protein was used with program defaults for intestinal digestibility to estimate passage to the duodenum of CP. The MEPRON model gives a direct estimate of passage to the small intestine of CP from ruminal microbes. The estimate of microbial CP was used with the estimate of absorbable protein and the default percentage of microbial CP which is true protein (60%) to calculate an estimated passage of CP from feed as follows: Feed CP passage = absorbable protein – (microbial CP passage × 0.6). Passage to the duode-
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num of total CP was calculated as the sum of CP from feed and microbes. The estimated passages of AA from the PENN, CNCPS, and CPM models were used without modification of any equations. The MEPRON model estimates AA passage to the small intestine in units of absorbed AA. Program defaults for AA digestibilities were used to convert estimated absorbed AA to estimated AA that passed to the duodenum; therefore, passages to the duodenum of all individual AA were estimated (absorbed AA ÷ 0.8). The NRC model estimates total absorbed protein required at the small intestine to meet the animals requirements for maintenance and production. The model also estimates microbial CP produced in the rumen that passes to the small intestine. Requirements for digestible CP in feed are calculated as the requirement for absorbed protein minus the digestible true protein in the microbial CP where: Digestible true protein in microbial protein = (microbial CP × 0.8) × 0.8. The passage of feed CP required at the small intestine is calculated as digestible feed CP ÷ 0.8. Total passage of CP to the duodenum is calculated as the sum of CP from feed and microbes. Comparisons of Simulated and Measured Data The MEPRON, PENN, CNCPS, and CPM models estimate passage to the duodenum of CP and AA in addition to estimating nutrient requirements of cows. The NRC model (1989) estimates the CP requirement of cows and does not estimate the amount of protein supplied by the diet. Therefore, any comparisons of predictions from the NRC model (1989) to data measured in the trials are actually comparisons of how well the estimated requirements compared with actual nutrient intakes for these cows. Comparisons of predictions from the MEPRON, PENN, CNCPS, and CPM models in this paper are estimates of how well these models predicted measured CP and AA passage to the duodenum. This is independent of how well the diet that was consumed met the requirements of the cows. Within each model, estimated passage of total CP to the duodenum was compared with nonammonia nitrogen (NAN) × 6.25 measured in the trials, estimated passage to the duodenum of CP from feed was compared with measured nonammonia- nonmicrobial nitrogen (NANMN) × 6.25, and estimated passage to the duodenum of microbial CP was compared with measured microbial N × 6.25. The estimated passages of AA from the MEPRON, PENN, CNCPS, and CPM models were compared with measured passage of AA. Schwab et al. (1992) reported partitioning of the passage of N to the small intestine in two ways. One calculation assumed that all dietary diaminopimelic acid was Journal of Dairy Science Vol. 84, No. 3, 2001
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degraded in the rumen and that diaminopimelic acid measured at the duodenum measured only microbial protein synthesis. The second calculation assumed that all dietary diaminopimelic acid passed the rumen undegraded and that diaminopimelic acid from microbial protein synthesis was calculated as total diaminopimelic acid arriving at the duodenum minus diaminopimelic acid in feed. We compared both sets of calculated N passage to the duodenum with other data sets and determined that passage calculated assuming that all dietary diaminopimelic acid was degraded in the rumen provided abnormally high estimates of microbial N and low estimates of NANMN passage. If it was assumed that all dietary diaminopimelic acid was degraded in the rumen, zero or negative passage of NANMN to the duodenum was observed, which probably cannot occur. Therefore, the passage of N that was calculated assuming that dietary diaminopimelic acid was undegraded in the rumen and passed to the small intestine was used in this analysis. Rahnema and Theurer (1986) reported similar observations when diaminopimelic acid was used without correcting for the diaminopimelic acid content of the diet to partition duodenal N flow into proportions from microbes and feed. To compare mean passage of N fractions among models, least squares means of estimated passage of total CP, CP fractions, and AA were generated for modelsimulated data by ANOVA (SAS, 1985). Simulated data from all trials (except for the simulation of data from Schwab et al., 1992) were analyzed using the same statistical model as was used in the individual trials with lactating cows. Treatments in the trial of Schwab et al. (1992) were duodenal infusions superimposed on a single diet, which varied according to stage of lactation. Because of this, data from the trial of Schwab et al. (1992) along with all model simulations of these data were analyzed using a statistical model different from that reported with the measured data. In our study, we used a model that included terms for cow, lactation period (early, peak, mid, and late), and period within the experiment. With all studies, least squares means from measured and simulated data were combined into one data set and analyzed by ANOVA (Table 1). The model used for this analysis included only a term for the source of the treatment mean (NRC, MEPRON, PENN, CNCPS, CPM, and data from animal trials) as the source of variation (SAS, 1985). Residuals of prediction for the individual observations were generated by subtracting the measured passage in the animal trial from the predicted passage for each simulation of each cow within each model. These residuals were statistically analyzed using the mean square prediction error (MSPE) according to procedures outlined by Theil (1966). This analysis allows the MSPE to Journal of Dairy Science Vol. 84, No. 3, 2001
be subdivided into proportions of 1) error of predicting the mean (central tendency), 2) systematic errors in the prediction function which can be corrected through a linear adjustment (linear regression), and 3) error in prediction because of random variance around the line of perfect prediction (random disturbance). Additionally, residuals were regressed (Graybill and Iyer, 1994) against dietary composition (percentages of DM, OM, starch, ADF, NDF, and CP) and cow variables (measured DMI, CP, microbial CP, feed CP, and their predicted passage to the duodenum) expected to bias the predictions. Variables were considered to contribute to bias when the slope of the regression line between prediction residuals and the variable being evaluated differed from zero. Differences in predictions by models were compared using efficiency of modeling as described by Mayer and Butler (1993). Modeling efficiency was calculated as: 1 − (sum of squares of the difference between prediction and measured values)/(sum of squares of the measured values) and has direct analogy to the coefficient of determination in linear regression analysis (Mayer and Butler, 1993). RESULTS AND DISCUSSION The passages of protein and AA to the duodenum of cows were assumed to be measured without error. Measurement errors, including sampling and analytical biases, may be present in the measured data. In particular, measured duodenal protein of feed origin is calculated as the difference between the total protein flow and that estimated to be of microbial origin. Thus any error in measurement of microbial protein is present in the measurement of feed protein. These types of errors have diverse consequences and are likely to introduce errors into the values predicted from a model without regard to the form of the model (Marcus and Elias, 1998). Therefore, differences between measured and predicted values are likely to include errors due to variation in both the measured and predicted values. This added variation will add to both the systematic and random bias of the predictions by models. When evaluating models by regression of predicted values against measured values with the hypothesis Ho: y = α + βx + error, β = 1, α = 0, errors in measured values tend to decrease the slope estimate from unity while simultaneously increasing the intercept from zero (Carroll and Galindo, 1998; Marcus and Elias, 1998), suggesting that correction terms should be applied. However, Carroll and Galindo (1998) report that it is not acceptable to use correction factors for measurement errors from one data set to correct other data sets. More importantly, any function used to correct for measurement errors must be based on a priori knowl-
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PREDICTING NITROGEN PASSAGE TO THE DUODENUM Table 1. Least squares means for CP and AA passage to the duodenum predicted from NRC, MEPRON, PENN, CNCPS, and CPM models compared with measured means from research trials.1
Item
Measured in trial
Total CP Microbial CP Feed CP Met Arg His Ile Leu Lys Phe Thr Val
3754a 1802c 1952a 56.3b 146.9b 74.2 154.3a 293.2a 200.2a 160.3a 151.9a 185.2a
Predicted from model NRC
MEPRON
PENN
3163c 2064ab 1099c
3364bc 2220a 1144c 58.9b
3233bc 2222a 1011c 66.2a 172.1a 72.0 146.3ab 216.4bc 195.4a 143.5b 150.3a 163.2b
CNCPS
CPM
SEM
3414b 2092ab 1322b 66.5a 171.5a 70.6 147.7ab 227.2bc 196.7a 144.4b 135.5bc 159.6b
2840d 2027b 812d 55.9b 158.3b 70.8 137.2b 212.9c 177.2b 135.6b 124.4c 154.0b
81.4 56.8 54.7 1.97 4.12 3.04 3.98 8.80 5.42 3.17 4.64 4.37
(g/d)
150.6a 241.0b 197.0a 139.8ab 161.9b
Means within a row lacking a common superscript differ (P < 0.05). Analysis of variance performed on predicted and measured treatment means using the source of observations as the source of variation. NRC = National Research Council, MEPRON = Mepron Dairy Ration Evaluator, PENN = University of Pennsylvania release of the Net Carbohydrate and Protein System, CNCPS = Cornell Net Carbohydrate and Protein System, CPM = CPM Dairy. a,b,c,d 1
edge of the distribution of those errors (Marcus and Elias, 1998) that the modeler may not possess. When models are evaluated by comparing simulated data with measured data, it may not be possible to correct for errors in the measured data. Oreskes (1998) indicated that validation of models should be replaced by an evaluation of models because the uncertainties around predictions from models will never be completely eliminated. The limited methods available to correct these errors rely on knowledge of the size and distribution of these errors (Carroll and Galinda, 1998; Marcus and Elias, 1998). When evaluating predictions of passage of N fractions to the duodenum by models, these errors would include both the cow and trial variation. These sources of variation are usually assumed to be random and unknown for purposes of ANOVA (Snedecor and Cochran, 1989), and therefore, estimates of these effects are not reported. Furthermore, because these effects may vary among data sets (Carroll and Galindo, 1998), the application of any one estimate to the model validation procedure would not necessarily validate the model for other situations. We attempted to minimize the impact of measurement errors by using data from multiple trials that used multiple cows and trials conducted at various sites. If cow and trial effects are truly random and unknown, they will have a mean of zero for the entire population of dairy cattle and research trials (Snedecor and Cochran, 1989). Therefore, by using data from multiple cows in multiple trials conducted at multiple sites, the average influence of any one data point is minimized. Figure 1 compares the measured passage to the duodenum of CP in microbes from lactating Holstein cows used
in the six trials with the passage predicted by NRC (1989). Although the data of Schwab et al. (1992) were calculated assuming that diaminopimelic acid in dietary ingredients was not degraded in the rumen and was passed to the duodenum, the passage of microbial N was greater than that measured in the other five trials in which purines were used as the marker to measure passage to the duodenum of microbial CP. Data from this trial were included in the data set because there was no valid scientific reason for their removal. There were large discrepancies between the measured quantities of microbial, feed, and total CP that passed to the small intestine and the quantities predicted to pass by the models (Table 1). The models, on average, overpredicted the passage of microbial CP by 323 g/d and under predicted passage of CP in feed by 874 g/d, resulting in passage of total CP being underestimated by 551 g/d. Compared with measured passage to the small intestine, the NRC, MEPRON, PENN, CNCPS, and CPM models overestimated passage of microbial CP by 262, 418, 420, 290, and 225 g/d, respectively, and underestimated passage of protein in feed by 853, 808, 941, 630, and 1140 g/d, respectively, resulting in total CP passage to the small intestine being underestimated by 591, 390, 521, 340, and 914 g/d, respectively. The differences between measured and predicted passage to the small intestine for CP in microbes and feed indicate potential errors in prediction equations used in the models. The NRC and MEPRON models base their estimates of microbial protein production on energy intake. The NRC model uses the required NEL intake, and the MEPRON model uses an estimated NEL intake modified for Journal of Dairy Science Vol. 84, No. 3, 2001
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Figure 1. Predicted passage to the small intestine of CP from microbes by the NRC model compared with measured passage of CP from microbes of lactating Holstein cows in research trials. Data from: Klusmeyer et al. (1991a, 䊏), McCarthy et al. (1989, ♦), Klusmeyer et al. (1991b, 䊐), Overton et al. (1995, ▲), Putnam et al. (1997, 䊉), and Schwab et al. (1992, 䊊).
intake of dietary fat and fermentable feeds. For these comparisons, DMI from the research trials and NEL concentrations from the feed libraries in the model were used to calculate NEL intake for the MEPRON model. Energy intake, as expressed in the NRC and MEPRON models, might not fully discount the availability of substrate for microbial growth, and therefore, the models overestimated microbial protein synthesis. The PENN, CNCPS, and CPM models base microbial protein synthesis on rate of carbohydrate fermentation in the rumen, ruminal carbohydrate availability, and the passage rate from the rumen. Errors in the models for estimating the ruminal digestibility of feedstuffs or their passage rates from the rumen would result in errors in estimating microbial protein synthesis and also errors in estimating passage to the small intestine of CP in feed. Because default values from the feed libraries of these models were used to estimate digestibility coefficients and passage rates from the rumen, some of the feeds may not have been characterized adequately, which resulted in biased estimates of CP in microbes and feed that passed to the small intestine. Errors in predicting passage of CP in microbes and feeds were partially canceled when total CP passage to the small intestine was calculated by summing passage of CP in microbes and feed. Differences between some least squares means for AA passage to the duodenum predicted from the models and Journal of Dairy Science Vol. 84, No. 3, 2001
measured in vivo were significant (Table 1). The PENN and CNCPS models predicted that a greater amount of Met and Arg would pass to the duodenum than was measured in vivo. The PENN, CNCPS, and CPM models predicted a smaller passage of Leu, Phe, and Val, and the CNCPS and CPM models predicted a smaller passage of Thr than was measured in vivo. The PENN model predicted similar amounts of Thr as measured in vivo. The CPM model predicted a smaller passage of Ile and Lys than was measured in vivo, but similar quantities of Met and Arg. Predicted passage of His, Ile, and Lys by the PENN and CNCPS models did not differ from measured passage to the duodenum of these AA. Measured passages of Met, Ile, Lys, and Thr were similar to predicted passage of these AA by the MEPRON model, but measured passages for Leu and Val were greater than predicted. Differences among some predicted least squares means for AA passage to the duodenum from the four models were significant (Table 1). The PENN, CNCPS, and CPM models predicted similar quantities of His, Ile, Leu, Phe, and Val would pass to the duodenum. However, least squares means for passage of Met, Arg, and Lys predicted by the PENN and CNCPS were greater than predictions by the CPM model. The MEPRON and CPM models predicted similar quantities of Met would pass to the duodenum, which was a smaller
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quantity than predicted by the PENN and CNCPS models. There was no difference between the MEPRON, CNCPS, and PENN models for the quantity of Ile, Leu, and Lys predicted to pass to the duodenum. The CPM model predicted that smaller quantities of Ile, Leu, Lys, and Thr would pass to the small intestine than did the MEPRON model. Differences in assumed AA composition of microbial protein and undegradable protein in feed in addition to differences in the calculated amount of feed and microbial protein, probably contributed to differences in measured and predicted passage to the small intestine of AA among models. Clark et al. (1992) reported that coefficients of variation for the AA composition of microbial protein ranged from 4.8 for Asp to 25.6 for Met. These data indicate that some differences between measured and predicted passage to the small intestine of AA may have occurred because of the variability between AA composition of microbial protein that passed and the AA composition that was used in the models. It is unlikely that this discrepancy can be corrected until there is a much greater understanding of the factors that determine the relative populations of the different microbial species that inhabit the rumen. Errors in either measuring or predicting the total passage to the duodenum of CP or in predicting the proportion of the total CP that is microbial and feed CP also would contribute to differences in the measured and predicted passage of individual AA. The MSPE criterion of Theil (1966) is the variance of the errors of prediction. It can be used to separate the prediction error into three proportions. They are the errors that result from the inability of models to predict the mean response (central tendency), errors in prediction that can be accounted for by a linear correction factor (regression), and random error of prediction (disturbance). Errors associated with central tendency can be corrected by the addition of a constant to the final prediction by a model. Errors associated with linear regression indicate errors in equations used to make predictions by a model. Errors associated with random disturbance are those errors of prediction that cannot be accounted for by central tendency or linear regression. Linear regression and disturbance offer the most information for evaluation and future correction of models (Theil, 1966). For predictions by models to be useful, a small percentage of the prediction error should be attributed to a central tendency or be correctable by a linear function. For all models except CPM, the passage to the duodenum of feed CP had a greater percentage of error attributed to central tendency than did passage of total CP (Tables 2, 3, 4, 5, and 6). For all models, error associated with central tendency was smaller for passage to the
Table 2. Precision of predictions from NRC model for crude protein passage to the small intestine as measured by the mean squared prediction error (MSPE) criterion. Percentage of MSPE attributable to errors in: Item
Central tendency
Linear regression
Total CP Microbial CP Feed CP
51.47 13.63 55.84
1.95 5.89 0.71
Random disturbance
RMSPE1
46.58 80.48 43.46
g/d 747 542 985
(%)
1
Root mean square prediction error.
duodenum of microbial CP than for total CP or for feed CP. Similar observations can be made from data in Table 1, where the mean predicted passage to the duodenum of microbial CP was closer to the measured passage than was total CP or CP in feed. Predictions of all models for passage to the duodenum of total CP, except for the PENN model, had more than 50% of the MSPE associated with errors in central tendency. The PENN model had about 47% of the MSPE associated with errors in central tendency. This indicated that the mean prediction of CP passage to the duodenum is different than the mean measured values from cows used in these trials. The only predictions of AA passage to the duodenum that had more than 10% of the MSPE associated with errors in the central tendency were predictions for Met and Arg by the PENN and CNCPS models, and Leu and Arg prediction by the CPM model. Less than 6% of the MSPE could be corrected by linear functions for passage to the duodenum of total CP, microbial CP, and feed CP by the NRC and PENN models (Tables 2 and 4). For the MEPRON, CNCPS, and CPM models, linear functions accounted for 13.08, 17.50, and
Table 3. Precision of predictions from MEPRON model for CP and AA passage to the small intestine as measured by the mean squared prediction error (MSPE) criterion. Percentage of MSPE attributable to errors in: Item
Central tendency
Linear regression
Random disturbance
RMSPE1
Total CP Microbial CP Feed CP Met Lys Leu Ile Val Thr
51.39 12.68 56.28 6.24 1.25 3.52 0.95 0.31 0.48
(%) 13.08 47.01 8.17 47.05 40.29 30.07 27.21 26.87 22.75
35.53 40.32 35.55 46.71 58.46 66.41 71.84 72.82 76.76
g/d 815 819 1168 29 88 129 64 77 62
1
Root mean square prediction error. Journal of Dairy Science Vol. 84, No. 3, 2001
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Table 4. Precision of predictions from PENN model for CP and AA passage to the small intestine as measured by the mean squared prediction error (MSPE) criterion.
Table 6. Precision of predictions from CPM model for CP and AA passage to the small intestine as measured by the mean squared prediction error (MSPE) criterion.
Percentage of MSPE attributable to errors in:
Percentage of MSPE attributable to errors in:
Item
Central tendency
Linear regression
Random disturbance
RMSPE1
Item
Central tendency
Linear regression
Random disturbance
RMSPE1
Total CP Microbial CP Feed CP Met Lys Leu Ile Val Thr Arg His Phe
46.86 36.46 67.82 30.34 4.16 1.94 1.52 0.15 1.53 34.81 0.00 0.00
(%) 1.69 2.93 2.54 19.43 26.76 69.77 20.45 23.10 42.44 0.54 0.64 19.41
51.44 60.61 29.64 50.23 69.08 28.29 78.03 76.75 56.03 64.64 99.36 80.19
g/d 708 584 1012 28 80 198 61 74 70 58 63 60
Total CP Microbial CP Feed CP Met Lys Leu Ile Val Thr Arg His Phe
77.76 1.64 53.20 5.38 0.13 13.12 0.35 1.56 5.34 11.09 0.17 2.75
(%) 0.00 34.07 11.00 49.29 47.46 25.96 36.82 37.68 32.95 8.35 37.48 34.26
22.24 64.28 35.80 45.34 52.41 60.91 62.83 60.77 61.72 80.52 62.35 63.00
g/d 1028 599 1145 27 87 134 65 80 66 56 79 66
1
1
Root mean square prediction error.
Root mean square prediction error.
0.00% of the MSPE associated with prediction of total CP passage to the duodenum; 8.17, 1.08, and 11.00% for feed CP; and 47.01, 47.07, and 34.07% for microbial CP. The large error associated with linear functions for predicting microbial CP passage to the duodenum suggests that either equations used by these models for prediction of microbial protein are inadequate or that there is error associated with the measurement of microbial protein. Theil (1966) indicated that if large proportions of the MSPE are correctable by linear transformations of the data, systematic errors of prediction are occurring. Several predictions for individual AA passage to the duode-
Table 5. Precision of predictions from CNCPS1 model for crude protein and amino acid passage to the small intestine as measured by the mean squared prediction error (MSPE) criterion. Percentage of MSPE attributable to errors in: Item
Central tendency
Linear regression
Random disturbance
RMSPE2
Total CP Microbial CP Feed CP Met Lys Leu Ile Val Thr Arg His Phe
53.13 0.19 62.67 29.99 4.45 2.17 2.44 0.02 0.18 34.94 0.01 0.03
(%) 17.50 47.07 1.08 21.52 57.76 46.31 27.09 30.63 15.96 0.66 0.68 19.16
29.38 52.74 36.25 48.49 37.80 51.51 70.47 39.35 83.86 64.40 99.31 80.80
g/d 972 711 855 29 110 146 64 78 59 59 63 60
1
Cornell Net Carbohydrate and Protein System. Root mean square prediction error.
2
Journal of Dairy Science Vol. 84, No. 3, 2001
num had relatively large proportions of MSPE that were correctable by linear transformations (Tables 3, 4, 5, and 6) and include predictions from all models for Met, Lys, Leu, Ile, Val, Thr, and Phe (range from 15.96 to 69.77%). Similar values for Arg and His from the PENN and CNCPS models were much lower averaging less than 1%. The proportion of MSPE associated with linear regression from the CPM model for Arg and His was 8.35 and 37.48%, respectively. Errors in predicting the passage of individual AA to the duodenum may result from errors of estimating AA composition of the feed or microbes or from errors of predicting the amount of feed or microbial protein that passed to the duodenum or both. With the exception of the above cases in which MSPE associated with central tendency and linear regression were large, the random disturbance proportion of MSPE was large for prediction of passage to the duodenum of all CP fractions and AA by all models (Tables 2, 3, 4, 5, and 6). Random disturbance of these models ranged from 22.24 to 99.36% of MSPE for passage of CP fractions and AA to the duodenum. Ideally, the major proportion of the MSPE should be associated with random disturbance, and this was observed for many of the predicted passages to the duodenum of CP and AA. Data in Table 1 and statistical analyses shown in Tables 2, 3, 4, 5, and 6 indicated that differences between measured and predicted passage to the duodenum of CP fractions and AA are because of both systematic errors in prediction (central tendency and linear regression) and random error (disturbance). The distribution of the MSPE for total passage to the duodenum of CP in microbes, feed, or a combination of both by the models is variable. All models except PENN had relatively low proportions of the MSPE for prediction
PREDICTING NITROGEN PASSAGE TO THE DUODENUM
657
Figure 2. Scatter plots and lines of best fit of residuals for prediction (predicted – observed values) of passage to the duodenum of microbial CP by the NRC model versus measured (A) or predicted (B) passage of microbial CP. Equations for lines of best fit are as follows: (A) Y = –0.668X + 1395 and (B) Y = 0.406X – 770.
of microbial protein passage to the duodenum attributable to errors in central tendency (
