J. Dairy Sci. 88:282-295
© American Dairy Science Association, 2005.
Development of a System to Predict Feed Protein Flow to the Small Intestine of Cattle*
H. G. Bateman, II1,
J. H. Clark2 and
M. R. Murphy2
1 Department of Dairy Science, Louisiana State University Agricultural Center, Baton Rouge 70803
2 Department of Animal Sciences, University of Illinois, Urbana 61801
Corresponding author: H. G. Bateman, II; e-mail: hbateman{at}agcenter.lsu.edu.
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ABSTRACT
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A data set constructed from research trials published between 1979 and 1998 was used to derive equations to adjust published tabular values for the rumen-undegradable protein (RUP) content of feeds to better predict the passage of nonammonia nonmicrobial N (NANMN) to the small intestine of lactating dairy cows. Both linear and nonlinear forms of equations were considered for making adjustments. Iterative processes were used to estimate equation parameters. A logistic equation was developed and considered to be the most optimal for adjustment of published tabular RUP contents of feeds. The equation is a function of dietary dry matter intake (DMI) and includes terms for tabular RUP and nonprotein N contents of individual feeds. The equation has a standard error of prediction of 69.29 g of NANMN/ d per cow and a root mean square prediction error of 104.63 g of NANMN/d per cow. Independent evaluation of the equation indicated that the concept of variable RUP content for feeds based on DMI is correct. Further refinements may be needed as other data become available to quantify the effects of additional factors on the RUP value of feeds.
Key Words: protein • degradability • model • dairy cow
Abbreviation key: MCPI = maintenance CP intake, MEI = maintenance energy intake, MPIAF = MCPI adjustment factor, MSPE = mean square prediction error, NANMN = nonammonia nonmicrobial N, RDTP = ruminally degradable true protein, RMSPE = root mean square prediction error, SEY = standard error of prediction
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INTRODUCTION
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Numerous factors have been suggested to affect passage of microbial and feed protein to the small intestine of ruminants including feed intake; forage-to-concentrate ratio in the diet; source, quality, and amount of carbohydrate and CP in the diet; ruminal pH; associative effects of feeds; frequency of feeding; forage and grain processing; forage conservation methods; micro-nutrient supply; feeding buffers, salts, and ionophores; and environmental conditions (Clark and Davis, 1983; NRC, 1985; Sniffen and Robinson, 1987; Clark et al., 1992). Because many variables affect degradability of protein in the rumen, RUP content of a given feed is not constant in all feeding situations. The many factors that affect degradation of feed protein in the rumen currently make it impossible to predict passage of feed protein to the small intestine with sufficient accuracy.
Santos et al. (1998) reviewed published literature where protein sources considered high in RUP content replaced soybean meal and concluded that increasing the RUP content of diets fed to lactating cows does not consistently improve lactational performance. Santos et al. (1998) also indicated that this may have resulted from 1) decreased microbial CP synthesis in the rumen, 2) poor AA profile of RUP, 3) low intestinal digestibility of RUP, or 4) the RUP content of control diets being adequate to maximize lactational performance. Bateman et al. (2001a) reported that prediction models underestimated the mean passage of feed CP to the small intestine of dairy cows. The underestimation of feed protein passage to the small intestine of dairy cows eating large amounts of feed was attributed to an overestimation of degradability of individual feed proteins.
Clark et al. (1992) reported a linear relationship between OM intake and passage of nonammonia nonmicrobial N (NANMN) to the small intestine of dairy cows. Santos et al. (1998) reported that there were no differences in DM or N intakes when soybean meal was replaced by protein sources reported to be high in RUP content. Therefore, it is likely that the RUP content of feeds increases as DMI increases.
The objectives of this work were 1) to evaluate some tabular values for the RUP content of feeds (NRC, 1985, 1989, 1996) for their ability to predict feed protein flow to the small intestine of lactating dairy cows and 2) to develop an equation that could be used to modify tabulated RUP values to better predict feed protein flow to the small intestine of lactating dairy cows.
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MATERIALS AND METHODS
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Model Development
A data set was constructed from research trials published between 1979 and 1998 (Appendix Table 1
). The data set consisted of 150 treatment means from 35 research papers. The data set was supplemented with 8 treatment means from 2 unpublished trials from the University of Illinois. All were Latin square designs that measured passage of total, microbial, and NANMN to the small intestine of cattle. All trials were conducted using duodenally cannulated cattle. All treatment means were assumed to have been measured without bias, which might or might not have been correct.
Dry matter intake was reported in all studies. Diet composition was either reported or could be calculated for all studies. When CP content of individual feeds was reported, those values were used to calculate CP intake; otherwise, values in Table 1 were used to calculate CP intake. The CP compositions of feeds in Table 1 are those reported by NRC (2001). The NPN values (Table 1) were supplied by W. Weiss (personal communication, 1998) and represent a compilation of data from commercial laboratories, literature data, Nutrient Requirements of Beef Cattle (NRC, 1996), and unpublished data provided by university researchers. Tabulated values for RUP were from published sources (NRC, 1985, 1989, 1996). When published values conflicted for feeds, the more recent value was used for further analysis. Published RUP values were supplemented with data compiled from literature when feeds were encountered that had no published values. Tabulated values for forages were grouped in ways similar to those in the dairy NRC (2001). The RUP intake was calculated by multiplying CP intake from each N-containing feed in the diet by the RUP percentage of that feed and then summing intakes of RUP from all feeds in a diet. The calculated RUP intake was assumed to be equal to passage of RUP to the small intestine and was compared with passage of NANMN to the small intestine after dividing estimated passage of RUP by 6.25.
Two forms of equations (linear and nonlinear) were developed to adjust RUP values of individual feeds as a function of DMI. To develop these equations, maintenance energy intake (MEI) for lactating cows was set equal to 6 kg of DM/d, and maintenance CP intake (MCPI) was set equal to 2.5 kg of DM/d when the DMI contained 1.72 Mcal of NEL/kg and 17% CP. These quantities of DM were adequate to supply the energy and protein for maintenance of a 650-kg cow (NRC, 1989).
Equations were developed that adjusted published RUP values (Table 1
) to maximize the coefficient of multiple determination when the observed passage of NANMN was regressed against the predicted passage of NANMN. Equations were parameratized by an iterative process using the solver in Microsoft Excel 2002. After providing initial estimates for coefficients in all equations based on a visual estimation from plots of measured and predicted passage of RUP, iterations were conducted to maximize the coefficient of multiple determination (R2). Iterations were constrained by forcing the slope to equal unity while the intercept equaled zero for the prediction line. Equations were considered to adequately adjust RUP values when the slope of the regression of predicted and measured values did not differ from unity, and the intercept of this regression did not differ from zero (Graybill and Iyer, 1994). All regression lines were considered significant when a Student’s t-test indicated that their slope differed from zero with a probability of P < 0.05. Bias in prediction was determined when the slope of the regression line between the prediction residuals (measured – predicted values) and the predicted values differed from zero with a probability of P < 0.05.
Model Evaluation
A second data set was constructed from research trials published between 1998 and 2003 (Appendix Table 2). These data represented 52 treatment means from 12 research papers that were from trials similar to those used for model development. The data set was supplemented with 4 treatment means from one unpublished trial from the University of Illinois. Again, all treatment means were assumed to have been measured without bias, which might or might not have been correct.
Dry matter intake and diet composition were either available for all trials or could be calculated. When CP contents of feeds were reported, those values were used to calculate CP intake; otherwise, values in Table 1 were used to calculate CP intake. The NPN values were from Table 1. Tabulated values for RUP contents of feeds were from Table 1. The calculations used for estimating flow of RUP were similar to those used in model development. The calculated RUP intake was assumed to equal the passage of RUP to the duodenum and was compared with passage of NANMN to the duodenum after dividing estimated passage of RUP by 6.25.
A 2-tailed Student’s t-test was used to compare mean predicted and measured passage of NANMN to the duodenum (Snedecor and Cochran, 1989). Subtracting the predicted passage of NANMN from the measured passage of NANMN generated residuals of prediction for the individual observations. 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 be subdivided into proportions of 1) error of predicting the mean (mean bias); 2) systematic errors in the prediction function, which can be corrected through a linear adjustment (slope bias); and 3) error in prediction because of random variance around the line of perfect prediction (dispersion). Mean bias was calculated as (mean predicted – mean observed)2. Slope bias was calculated as R2 for regression of predicted and observed values x (MSPE – mean bias). Dispersion was calculated as MSPE – mean bias – slope bias.
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RESULTS AND DISCUSSION
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A summary of the univariate statistics for the data set used to develop the equations is shown in Table 2. A wide range of diets and DMI were included in the data set (see references in Appendix Table 1).
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Table 2. Mean, maximum, minimum, and standard error of the mean for DMI, N intake, and measured flow of nonammonia nonmicrobial N (NANMN) to the small intestine from published data.1
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The relationship between predicted passage of NANMN using tabulated values for the RUP contents of feeds and measured passage of NANMN to the duodenum from the data set is presented in Figure 1. There was a positive linear relationship between measured and predicted passage of NANMN to the duodenum. Furthermore, a linear bias was indicated by the regression of residuals (measured – predicted) for NANMN and predicted passage of NANMN to the duodenum. Using tabular values to predict flow of NANMN at the small intestine produced a root mean square prediction error (RMSPE) of 89.34 g of NANMN/d (Theil, 1966) and a standard error of prediction (SEY) of 43.07 g of NANMN/d. Distribution of the errors contained in the MSPE analysis is presented in Table 3. These data indicate that tabulated values for the RUP contents of feeds did not accurately predict the measured passage of RUP to the duodenum of cattle and are in agreement with previous evaluations from our laboratory (Bateman et al., 2001a,b).
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Figure 1. Relationship between measured ( ) or residual (•) (measured – predicted) passage of nonammonia nonmicrobial N (NANMN) and predicted NANMN at the duodenum of dairy cows using tabular values for the RUP content of feeds to predict the passage of NANMN. Measured NANMN = 1.29 ± 0.074 x predicted NANMN + 6.78 ± 13.36 (P < 0.01); R2 = 0.6605; root mean square prediction error = 89.34 g of NANMN/d. Residual NANMN = 0.287 ± 0.074 x predicted NANMN + 6.93 ± 13.36 (P < 0.01); R2 = 0.0879.
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Table 3. Precision of predictions for flow of nonammonia nonmicrobial N (NANMN) to the small intestine of cattle by various models as measured by the mean square prediction error (MSPE) criterion.
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Tyrrell and Moe (1975) reported that the digestibility of a specific feed is not constant but changes with intake. An approximate 4 percentage unit decrease in total digestible nutrient content of a diet has been reported for each multiple that energy intake increases above that required for maintenance (Moe and Tyrrell, 1976). This reduction in total digestible nutrient content of a diet is a result of the depression in the digestibility of the diet as energy intake (and presumably DMI) increases. It is unlikely that the entire depression of digestibility occurs postruminally without any depression of ruminal fermentation. If ruminal fermentation was depressed, a larger percentage of the CP from the feed would pass intact to the small intestine. Therefore, an equation (not shown) was developed to apply a 4 percentage unit decrease in ruminal degradability of protein for each multiple increase in MEI above maintenance to all feeds, and the relationship between predicted and measured passage of NANMN to the duodenum of cows in the data set were compared. Dry matter intake for maintenance was set to 6 kg/d for this analysis and was based on a dietary energy content of 1.72 Mcal of NEL/kg of DM, which supplied 10.32 Mcal of NEL/d and is equal to the maintenance energy requirement of a 650-kg mature lactating cow (NRC, 1989). Under practical feeding situations, it is unlikely that diets with energy content similar to this would be fed at the low levels needed for maintenance. However, an energy content of 1.72 Mcal of NEL/kg of DM also was used when calculating the DMI requirements for cows producing >40 kg of milk/d (NRC, 1989) and was similar to the energy concentration of most of the diets represented in the model development database (Appendix Table 1).
The relationship between observed or residual passage of NANMN to the duodenum and predicted passage of NANMN to the duodenum after increasing RUP values by 4 percentage units for each multiple increase in MEI above maintenance is shown in Figure 2. Decreasing the RUP content of feeds by 4 percentage units per multiple of maintenance energy intake resulted in a RMSPE of 70.00 g of NANMN/d (Table 3) and a SEY of 57.01 g of NANMN/d. The decrease in the slope of the regression between predicted and measured passage of NANMN compared with that of Figure 1, along with the decrease in the RMSPE, indicates that increasing the RUP content of feeds by 4 percentage units for each multiple increase in MEI above maintenance improved the accuracy of prediction of passage of NANMN to the duodenum compared with the tabular values. This adjustment removed most of the mean bias, but a significant slope bias remained. Because increasing RUP as a function of MEI improved the accuracy of prediction of NANMN passage to the duodenum, but did not eliminate all bias of prediction, additional adjustment equations were required.
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Figure 2. Relationship between measured () or residual (•) (measured – predicted) passage of nonammonia nonmicrobial N (NANMN) and predicted NANMN at the duodenum of dairy cows after increasing tabular values for the RUP content of feeds by 4 percentage units per multiple increase in maintenance energy intake to predict the passage of NANMN. Measured NANMN = 0.976 ± 0.056 x predicted NANMN + 20.74 ± 12.73 (P < 0.01); R2 = 0.6567; root mean square prediction error = 70.00 g of NANMN/d. Residual NANMN = – 0.025 ± 0.056 x predicted NANMN + 20.71 ± 12.73 (P > 0.6); R2 = 0.0012.
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When the ruminal availabilities of N and energy are not adequately balanced in the rumen, an uncoupling of fermentation may occur (Hespell and Bryant, 1979; Stern and Hoover, 1979). For diets containing 17% CP, only 2.5 kg of DM are needed to supply the CP requirement for maintenance of mature cows. As with the situation for energy, it is unlikely that a small amount of feed would be offered with a high content of CP. However, the level of CP chosen was similar to that of the diets represented in the model development data set (Appendix Table 1). Because a smaller amount of DM can be used to supply the maintenance requirement for protein than the maintenance requirement for energy, the potential must exist for the change in RUP to be different per unit of MEI than per unit of MCPI. Therefore, a 4 percentage unit increase in RUP values for each multiple increase in MCPI above maintenance was used to estimate NANMN passage to the duodenum. Changing the adjustment to the equation from an energy basis to a CP basis improved the accuracy of predicting the mean passage of NANMN to the duodenum but had no effect on bias of prediction (data not shown).
To correct the linear bias, an adjustment factor based on MCPI was developed. Iteration was used to determine the optimal unit change per multiple of MCPI and the MCPI that equates to tabulated RUP values. Iterations were evaluated by comparing the resulting variation around the regression of predicted and measured passage of NANMN to the duodenum. Also, NPN content of the diet was not included in measurements of passage of feed CP (NANMN) to the duodenum because it is degraded to NH3 in the rumen. Therefore, an adjustment was made to the equation to correct for NPN content of the feed. The following equation was developed for adjusting the RUP contents of feeds, expressed as a percentage of CP, per multiple of MCPI above maintenance.
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where RUPadj1 is the adjusted percentage of RUP in CP of a feed used to predict passage of CP to the duodenum, RDTP is the percentage of ruminally degradable true protein in a feed, MPIAF is an adjustment factor for MCPI of cows, and NPN is expressed as a percentage of CP and is considered to be ruminally degradable. Ruminally degradable true protein was calculated as
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where RUPtab is the percentage of RUP for an individual feed reported in Table 1. The adjustment factor for MCPI was calculated as
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where DMI is the measured or expected DMI for the cows and is expressed in kg/d, the 2.5 represents the kg of DM needed to meet the CP requirement for maintenance of a 650-kg mature cow when the diet contains 17% CP, and the 0.13 and 9.56 are constants determined using an iterative process to adjust the unit change per multiple increase in MCPI to correct the linear bias.
An evaluation of predicted and measured passage of NANMN to the duodenum of dairy cows based on adjustments using eq. 1 previously presented is presented in Figure 3. When applying the adjustment of eq. 1 to individual feeds, both slope and mean bias were lowered (Table 3). Equation 1 has a SEY of 52.01 g of NANMN/d and a RMSPE of 99.35 g of NANMN/d. However, at low DMI, eq. 1 will predict negative RUP values for some feeds, and at high DMI, eq. 1 will predict RUP values for some feeds in excess of 100% of CP. Also, the multiple coefficient of determination (R2) between measured values and values predicted using eq. 1 was only 0.27. This suggests that a linear adjustment based on maintenance protein intake was inadequate for adjusting tabulated RUP values of feeds and that the actual relationship between the RUP content of feeds and feed intake may be nonlinear.
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Figure 3. Relationship between measured () or residual (•) (measured – predicted) passage of nonammonia nonmicrobial N (NANMN) and predicted NANMN at the duodenum of dairy cows after increasing tabular values for the RUP content of feeds using a linear function of maintenance protein intake to predict the passage of NANMN. Measured NANMN = 1.00 ± 0.131 x predicted NANMN – 0.01 ± 29.88 (P < 0.01); R2 = 0.2711; root mean square prediction error = 99.35 g of NANMN/d. Residual NANMN = 0.00 ± 0.13 x predicted NANMN + 0.009 ± 29.88 (P > 0.9); R2 = 0.0000.
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A nonlinear adjustment equation was considered to prevent adjusted RUP values from going outside the biologically possible range of 0 to 100% of CP. A sigmoidal (logistic) curve was chosen to represent the RUP content of a feed as DMI was increased. At low DMI, fractional passage rate from the rumen is relatively low, and the majority of protein in feed is degraded in the rumen. As DMI increases, fractional passage rate increases so that both the quantity and proportion of feed protein escaping degradation and reaching the duodenum increases. At high DMI, there is only a small increase in the proportion of CP that escapes ruminal degradation, and a plateau is reached in measured RUP values.
The specific form of the sigmoidal curve chosen to describe the change in RUP values was
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where y is the apparent percentage of RUP in a feed adjusted to a given DMI, a represents the upper asymptote or highest possible RUP value for a feed, DMI is the observed (or expected) DMI in kilograms, b is a constant used to describe the range in DMI over which the majority of change in RUP values occurs, and c is a constant equal to the DMI at the inflection point of the RUP curve (Koops and Grossman, 1991).
Tabular values (Table 1) for the percentage of RUP in feeds were largely determined in vitro or in animals consuming between 1 and 3x their maintenance energy requirement (6 to 18 kg of DMI). Therefore, a series of c values was generated that resulted in RUP values equal to tabular values. For this process, a was set to 100, b to 7, and DMI to 12. The upper asymptote of the equation (a) was set to 100 because that would represent complete passage of CP in a feed, b was set to 7 to represent approximately 4x the standard deviation for DMI (Koops and Grossman, 1991), and DMI was set to 12 to represent 2x the maintenance energy requirement of lactating cows. While holding these parameters constant, c was estimated for various values of y. This process was then repeated after changing DMI to 15, which represented the DMI needed to supply approximately 2.5x the maintenance energy requirement for lactating cows. Linear relationships were observed between the values for c and y, which had identical slopes but differed in the intercept by the same amount as the change in DMI. Therefore, c was described as a linear function of RUPtab with the intercept of this function being an indicator of the inflection point of the RUP adjustment curve.
Iteration was used to determine values for the intercept of the linear relationship between c and RUPtab, and b in the nonlinear curve that maximized the R2 for the regression of predicted and measured NANMN to the duodenum under the condition that the slope of this regression did not differ from unity, whereas the intercept did not differ from zero. The parameters estimated from the iterations were part of the nonlinear equation. However, the constraints used in generating them were based on the linear regression between measured and predicted data. Because NPN in feeds must be excluded from the predictions for them to be comparable with observed flows of NANMN, the upper asymptote of the nonlinear function (a) was set to 100 minus the NPN for each feed, where NPN was expressed as a percentage of CP. This process resulted in the following equation being accepted for predicting an adjusted RUP as a percentage of the CP in a feed at a specific DMI:
 | ([5]) |
where c = 27.36 – 0.1253 x RUPtab.
Equation 5 eliminated both linear and mean bias from the prediction of NANMN passage to the duodenum (Figure 4) and maintained the RUPadj2 values in the biologically allowable range of 0 to 100% of the CP. Equation 5 had a SEY of 69.29 g of NANMN/d and a RMSPE of 104.63 g of NANMN/d (Table 3). Therefore, adjustments to the RUP content of feeds using eq. 5 were only slightly superior to those using eq. 1 and were slightly inferior to adjusting the RUP content of feeds by 4 percentage units for each multiple increase in maintenance energy intake in their ability to predict flow of NANMN at the small intestine. However, use of eq. 5 was concluded to be most optimal because its predictive ability was similar to the other approaches considered and it maintained predicted RUP values in the biologically valid range of 0 to 100% of CP.
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Figure 4. Relationship between measured () or residual (•) (measured – predicted) passage of nonammonia nonmicrobial N (NANMN) and predicted NANMN at the duodenum of dairy cows after increasing tabular values for the RUP content of feeds using a nonlinear function of maintenance protein intake to predict the passage of NANMN. Measured NANMN = 1.01 ± 0.060 x predicted NANMN + 76.91 ± 10.03 (P < 0.01); R2 = 0.6496; root mean square prediction error = 104.63 g of NANMN/d. Residual NANMN = 0.01 ± 0.060 x predicted NANMN + 76.89 ± 10.03 (P > 0.8); R2 = 0.0003.
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The relationship between measured and predicted passage of NANMN to the duodenum for the data set used for evaluation of eq. 5 (Appendix Table 2) is presented in Figure 5. Use of eq. 5 to predict passage of NANMN to the duodenum in these experiments did not eliminate the bias of prediction. However, failure of the equation to remove all bias of prediction should not necessarily be considered evidence that the equation is incorrect. The data set used for evaluation purposes was somewhat limited in number and range of the observations (Appendix Table 2). The data set used for evaluation also contained data from steers consuming diets that were somewhat different than those represented in the data set used for model development. Additional observations should increase the power associated with the regression while simultaneously decreasing the impact of any one individual observation to skew the regression (Graybill and Iyer, 1994). Also, additional observations from lactating cows should lessen the impact of the steer data. The mean predicted flow of NANMN to the duodenum differed from the mean measured flow (P < 0.01), indicating that eq. 5 was not making satisfactory adjustments to tabulated RUP values for the evaluation data set. The evaluation data set produced a SEY of 56.30 g/d with a RMSPE of 82.71 g/d. The MSPE analysis (Theil, 1966) of the residuals from the evaluation of eq. 5 (Table 3) indicated that 47.32% of the error was attributable to inaccurate prediction of the mean passage of NANMN to the duodenum, 28.38% of the error was correctable through a linear function of the measured and predicted passages of NANMN at the duodenum, and the final 24.30% of the error was random variation. St Pierre (2003) suggested that any perceived bias should be evaluated in relation to reported measurement errors to determine its potential impact on the predictive ability of the model. It is likely that differences in the type of diets represented in the model evaluation and model development data sets were negatively impacting the apparent predictive ability of the model. As more data become available, it will be possible to determine whether there are true errors or if the problems uncovered in this exercise are an artifact of the analysis related to abnormalities in the evaluation data set (Mayer and Butler, 1993; Carroll and Galindo, 1998; Oreskes, 1998; Carroll et al., 1999).
Figures 6, 7, 8, 9, 10, and 11 present apparent predicted RUP content of selected feeds at different levels of DMI. Apparent predicted RUP contents of cereal grains as intake increases from 0.5 to 5x maintenance energy intake (3 to 30 kg DMI) are presented in Figure 6. Similar information for oil seed meals is presented in Figure 7. Apparent predicted RUP contents of oil seeds at differing multiples of maintenance energy intake are presented in Figure 8, and similar data for forages are presented in Figure 9. Figure 10 presents the apparent predicted RUP content as estimated by eq. 5 for byproduct feeds, and Figure 11 is a similar representation for animal protein meals. All of the example feeds exhibited the expected sigmoidal shape to their apparent predicted RUP content curve. At low DMI, the majority of the CP in most feed is degraded, resulting in a low apparent RUP content of that feed. However, at high DMI, the majority of the CP in most feed is not degraded in the rumen but passes to the small intestine, resulting in a high apparent RUP content of that feed. At high DMI, a large amount of degradable CP is supplied from feeds that have large quantities of NPN, such as corn silage or legume forages, and smaller amounts of degradable CP are supplied from other feeds. The amount of RDP and RUP that is supplied from these feeds when diets with a typical forage content are fed to lactating dairy cows at high DMI appears adequate to support microbial protein synthesis and the predicted passage of RUP to the small intestine.
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CONCLUSIONS
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Current tabular values for the RUP content of feeds do not allow accurate prediction of NANMN passage to the duodenum of lactating dairy cows. Tabular values for RUP can be adjusted using either a linear or nonlinear function of DMI to better predict passage of NANMN. A nonlinear function relating RUP to DMI agreed better with the underlying biology of lactating dairy cows than did a linear function because estimated RUP values for individual feeds remained within the biologically possible range of 0 to 100% of CP. Both of the equations developed for adjusting tabular RUP values of feeds better predicted the passage of NANMN to the small intestine than did tabular values. The nonlinear equation was able to eliminate the bias in predicting flow of NANMN to the small intestine, but it was not able to completely remove the variation around the line of prediction. This is an indication that, although the concept of adjusting tabulated RUP values based on DMI is correct, other factors are also influencing the apparent RUP content of feeds. When more data for cows consuming larger amounts of DM become available, this equation should be reevaluated for its ability to properly adjust RUP values of feeds reported by NRC. Furthermore, as other data become available that quantify the effects of factors other than DMI on the apparent RUP values of feeds, they should also be incorporated into an adjustment equation to better predict passage of NANMN to the duodenum.
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APPENDIX
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FOOTNOTES
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* Approved by the director of the Louisiana Agricultural Experiment Station as publication No. 04-24-0121. 
Received for publication March 12, 2004.
Accepted for publication September 9, 2004.
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ABSTRACT
INTRODUCTION
. Measured NANMN = 0.719 ± 0.091 x predicted NANMN + 82.89 ± 11.25 (P < 0.01); R2 = 0.5387; root mean square prediction error = 47.32 g of NANMN/d. Residual NANMN = 0.28 ± 0.091 x predicted NANMN – 82.89 ± 11.25 (P < 0.01); R2 = 0.1518.
), corn grain (
), solvent-extracted soybean meal (
