Ability of three dairy feed evaluation systems to predict postruminal outflows of amino acids in dairy cows: A meta-analysis

Adequate prediction of postruminal outflows of essential AA ( EAA ) is the starting point of balancing rations for EAA in dairy cows. The objective of this meta-analysis was to compare the performance of 3 dairy feed evaluation systems (National Research Council [ NRC ], Cornell Net Protein and Carbohydrate System version 6.5.5 [ CNCPS ], and National Academies of Sciences, Engineering and Medicine [ NASEM ]) to predict EAA outflows (Trp was not tested). The data set included a total of 354 treatment means from 70 duodenal and 24 omasal studies. To avoid Type I error, mean and linear biases were considered of concern if statistically significant and representing > 5.0% of the observed mean. Analyses were conducted on raw observed values and on observations adjusted for the random effect of study. The analysis on raw data indicates the ability of the feed evaluation system to predict absolute values whereas the analysis on adjusted values indicates its ability to predict responses of EAA outflows to dietary changes. For the prediction of absolute values (based on raw data), NRC underpredicted outflows of all EAA, from 5.3 to 8.6% of the observed mean ( % obs.mean ) except for Leu, Lys, and Val; NASEM overpredicted Lys (10.8% obs.mean ); and CNCPS overpredicted Arg, His, Lys, Met, and Val (5.2 to 26.0% obs.mean ). No EAA had a linear bias of concern with NASEM, followed by NRC for His (6.8% obs.mean ), and CNCPS for all EAA (5.6 to 12.2% obs.mean ) except Leu, Phe, and Thr. On the other hand, for the prediction of responses to dietary changes (based on adjusted data), NRC had 2 EAA presenting a linear bias of concern, followed by NASEM and CNCPS


INTRODUCTION
A few decades ago, to improve precision feeding, dairy feed evaluation systems began to add predictions of the digestible flow of EAA and related recommendations to their models (e.g., O'Connor et al., 1993;Rulquin and Vérité, 1993;NRC, 2001).These feed evaluation systems are regularly upgraded to incorporate recent knowledge.For example, in North America, the Cornell Net Carbohydrate and Protein System (CNCPS) has been in constant evolution (Sniffen et al., 1992;Fox et al., 2004;Tylutki et al., 2008;Higgs et al., 2015;Van Amburgh et al., 2015).The CNCPS v6.5.5 predicts postruminal outflows (hereafter termed outflows) of EAA based on a factorial method, assuming that CP outflow is the sum of RUP and bacterial protein, with no contribution from endogenous protein (ECP).The outflows of RUP and microbial protein predicted with CNCPS were compared with observations from 20 omasal studies in Van Amburgh et al. (2015).A revised, dynamic version of the CNCPS (v7) predicts rumen protozoa and endogenous N secretions along the entire gastrointestinal tract (Higgs et al., 2023), but this version was not available for the current analysis.
The 7th version of the Nutrient Requirements of Dairy Cattle from the National Research Council (NRC, 2001) predicts the outflows of microbial protein (MCP), RUP, and ECP based on 390 treatment means from 99 duodenal studies (including 27 on growing cattle).In the 8th revision of NRC from the National Academies of Sciences, Engineering, and Medicine (NASEM, 2021), equations were based on 82% duodenal studies and 18% omasal studies, all in dairy cows (582 treatment means).For the EAA outflows, NRC developed predictions based on a data set of 199 treatment means from 57 duodenal studies (including 11 on growing cattle) using a semi-mechanistic approach.In contrast, NASEM developed EAA predictions downstream from the estimations of RUP, MCP, or ECP outflows using a factorial approach.In the 3 feed evaluation systems, EAA included 8 essential AA (His, Ile, Leu, Lys, Met, Phe, Thr, Val) plus Trp in NASEM and CNCPS, and the semi-essential Arg.
Because the flows of digestible EAA derived from estimates of EAA outflows are the starting point of balancing rations for EAA, it is important that EAA outflows be predicted with sufficient precision and accuracy.Despite this importance, there are limited comparisons between observed EAA outflows versus predictions by different North American feed evaluation systems (Bateman et al., 2001;Pacheco et al., 2012).Furthermore, these comparisons do not include the latest revisions made to CNCPS (v6.5.5) and, obviously, the newly-released NASEM.Therefore, the main objective of the current study was to compare the fit statistics of NRC, NASEM, and CNCPS to predict EAA outflows.Our hypothesis was that the 2 most recent feed evaluation systems would have better fit statistics than NRC.A second objective was to investigate the influence of sampling site and some dietary characteristics on residual errors of prediction to identify factors that may be useful to improve predictions by feed evaluation systems.

MATERIALS AND METHODS
The project was submitted to and approved by the Institutional Committee for Animal Care of the Sherbrooke Research Centre (Quebec, Canada), although no animals were required for this study.All data handling and statistical analyses was completed using R (v. 4.1.3;R Core Team, 2020) within R Studio (v. 1.2.5042).

Data Collection
A comprehensive search of the literature was conducted to identify studies that reported outflows of DM, OM, nitrogenous compounds [NAN, microbial N (MiN), and nonammonia nonmicrobial N (NANMN)], NDF, ADF, starch, ether extract (EE), fatty acids, and EAA in dairy cows.The literature search was conducted between December 2019 and November 2022, and included 2 search engines: the Scopus database (https: / / www .scopus.com)and Google Scholar (https: / / scholar .google.com/).The sets of key words used in the search query are reported in the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) flowchart (Supplemental Figure S1; https: / / doi .org/ 10 .17632/xxxxx, Martineau et al., 2024).References listed in every article recovered, including reviews and meta-analyses, were screened for additional articles on the subject.If data from the same study were reported in multiple or companion manuscripts, the study received a single entry in the data set to avoid artificial duplication.The data were collated in an Excel workbook (Microsoft Corp.) which included 1,842 treatment means (421 studies).The performance of NRC, NASEM, and CNCPS to predict outflows of N fractions was reported in Martineau et al. (2023a).
For the current meta-analysis, the data set was limited to studies reporting DMI, CP intake, feed ingredients and their inclusion rates, and outflows of 1 or more EAA.In line with Martineau et al. (2023a), the site of sampling was categorized as duodenal (sampling from the abomasum or the duodenum) or omasal (sampling from the reticulum or the omasum).Digesta was sampled from the abomasum in Mabjeesh et al. (1997) and Shabi et al. (2000), and was sampled from the reticulum in Naadland et al. (2016).Overall, the data set included 279 treatment means from 71 duodenal studies and 82 treatment means from 24 omasal studies before screening for outlying treatments.the predictions of outflows were calculated using NRC, NASEM,and CNCPS (v6.5.5).Briefly, when available, the nutrient composition of feed ingredients reported in each study was used to create the diet.When these composition data were not available, they were populated from the feed tables of each feed evaluation system by selecting the feed matching the description in the original text.Therefore, unless the chemical composition of all feed ingredients was reported, diet characteristics differed between feed evaluation systems due to small discrepancies between feed ingredient composition.For example, default CP concentrations of corn gluten meal are, respectively, 65.0, 68.5, and 65.5% of DM in NRC, NASEM, and CNCPS.
Data Filtering To avoid selection of feed ingredients with a wrong CP concentration, if the ratio of reported on predicted CP intake was greater than 3.0 SD from the mean across treatments, the treatment mean was removed from the data set as outlined in Martineau et al. (2023a).Therefore, the 4 treatments from Lynch et al. (1991) and 3 (out of 4) treatments from Erasmus et al. (1994) were not included in the final data set which included 354 treatments from 94 studies referenced in Supplemental Table S1 (https: / / doi .org/ 10 .17632/xxxxx, Martineau et al., 2024).
Prediction of EAA Outflows.As mentioned above, different approaches are used to predict RUP, MCP, ECP, and EAA outflows between feed evaluation systems.A semi-mechanistic approach to predict EAA outflows is used in NRC: (1) the total EAA flow in duodenal protein is determined by regression from EAA supplied by RUP and MCP; and (2) the % of each EAA in the total EAA flow is determined by regression based on 2 variables: (a) the % EAA supplied by RUP (for all EAA), and (b) the duodenal RUP flow as a % of total duodenal protein flow (for all EAA except Arg and Val).
In NASEM, EAA outflows are calculated using a factorial method based on estimations of RUP, MCP, and ECP outflows, and their respective EAA profile (Tables 6-2 and 19-2 in NASEM, 2021).The EAA profile of RUP is assumed to be similar to that of their respective feed ingredients.The EAA profile in MCP is a composite concentration of liquid-and particle-associated bacteria, and protozoa (Sok et al., 2017).In NASEM, the EAA composition of RUP, MCP, and ECP are corrected to account for the incomplete recovery of EAA with 24-h acid hydrolysis (Lapierre et al., 2019).However, NASEM also reports EAA outflows uncorrected for this incomplete recovery, and these are used in the current study so predictions from the 3 feed evaluation systems are on the same uncorrected basis.
The CNCPS v6.5.5 was used to estimate EAA outflows and will be referred to as CNCPS.In CNCPS, the EAA outflows are also calculated using a factorial method based on EAA composition of RUP and bacterial CP, but ECP is not acknowledged to contribute to NAN outflow.As in NASEM, the EAA profile of RUP is assumed to be similar to that of their respective feed ingredients.Bacterial CP is a composite of EAA from cell and non-cell wall rumen bacteria (Fox et al., 2004).Protozoa do not contribute to microbial protein production in CNCPS v6.5.5 (and older versions) but have been accommodated for by reducing the theoretical maximum growth yield of bacteria from 0.5 to 0.4 g cells per g of carbohydrate fermented in the rumen (Higgs, 2016).
Data Weighting.Weighting factors were based on the standardized SEM (w 2 ) centered around unity computed separately in studies using fixed-and mixed-effects model as w w w 2 1

=
, where w 1 and w are, respectively, 1/SEM and its average across studies (St-Pierre, 2001;Roman-Garcia et al., 2016).In the calculation of w 2 , mixed effects models with SEM computed from SED (e.g., Brito et al., 2006) were treated as fixed effects models.In fixed-and mixed-effect models, SEM was trimmed to one-half of the mean SEM across studies using either a fixed-or mixed-effects model (Firkins et al., 2001;Roman-Garcia et al., 2016).On average, the percentage of trimmed SEM was ≤ 19% among EAA outflows.

Evaluation of Feed Evaluation Systems.
Outliers An inner StudentResid function in R was used to identify outliers before conducting the analyses (Anonymous, 2015).Observed values were regressed on predicted values in models adjusted for the random study effects, with observations weighted by the standardized SEM.Observations with an absolute studentized residual value greater than 3 were vetted for possible data entry error; if not, they were considered outliers and removed from all fit statistics and metaregressions as outlined in Martineau et al. (2023a).To improve the robustness of relationships, influential observations based on the Cook's distance were removed from regression models if the statistical significance of variables changed (Martineau et al., 2013).

Descriptive and Fit Statistics
The overall agreement between the observed and the predicted values was computed as reported in Martineau et al. (2023a).Briefly, the concordance correlation coefficient (CCC; Lin, 1989) was extracted from the epi.ccc function of the epiR package in R version 2.0.52.The mean square prediction error (MSPE) was calculated as: where n = number of experimental units per treatment, O i = ith observed value, and P i = ith corresponding predicted value.The square root of MSPE (RMSPE) and the relative prediction error (RPE; RMSPE as a % of the average of observed values) were used to assess the goodness-of-fit of predictions from each feed evaluation system.The MSPE was decomposed into error in central tendency (ECT), error due to deviation of the regression slope from unity (ER), and error due to disturbances (ED; not reported) (Theil, 1966;Bibby and Toutenburg, 1978).The ratio between the RMSPE and the SD of observed values was also computed (RSR; the smaller the better the model performance; Moriasi et al., 2007).

Mean and Linear Biases
The mean bias and its significance were, respectively, the mean and the Student's t-test P-value of residual errors (observed minus predicted values).The coefficient and standard error (SE) of the slope between observed and predicted values were determined using the lm function in R. The probability of the slope being different from unity was assessed by regressing residual errors on predicted values using the lm function in R. The level of agreement between observed values and predicted values was assessed in plots created using the ggplot2 package (version 3.3.6;Wickham, 2009).New plots were also created to explore the relationships between observed values and residual errors versus predicted values.Milk protein was assumed to be CP for publications earlier than 1990 and true protein thereafter; milk true protein = CP × 0.951 (DePeters and Cant, 1992). 4RDP = (CP intake -RUP intake)/DMI × 100. 5 Refer to Martineau et al. (2023) for more details about the small Rum_dcNDF value.
The mean biases and the slopes were compared among feed evaluation systems through a pairwise comparison approach (Tukey's test) performed using the emmeans and emtrends functions from the package emmeans v.1.8.2 (Martineau et al., 2023b).The magnitude of the linear biases was computed for first and third quantiles of predicted values to exclude extreme values (adapted from St-Pierre, 2003;Martineau et al., 2023a), and the absolute difference between both biases was calculated and hereafter termed the linear bias.
Biological Relevance of Biases To avoid Type I error related to the large amount of data used in the analyses, which could result in statistically significant but biologically meaningless relationships, we set a threshold at > 5.0% of the observed mean for the mean and linear biases (Pacheco et al., 2012;Martineau et al., 2023a).Below that threshold, the biases were considered to fall within acceptable limits even if statistically significant.Above the 5.0% threshold, the biases were considered large enough to be of concern both in statistical and biological terms; therefore, these biases of concern will hereafter be referred to as biologically relevant.
Raw and Adjusted Data St-Pierre (2001) argued that the results from a mixed regression model cannot be graphed simplistically in the form of a Y versus X plot because the observed values come from a multidimensional space, i.e., as many as the number of studies in the data set plus 2. However, the regression will be unbiased if the observed or Y values are adjusted for the lost dimensions when collapsing data from the multi-into a 2-dimensional space.The statistical procedure and R codes used to adjust the observed values for the lost dimensions are reported in Martineau et al. (2023a,b).Briefly, (1) the observed values are regressed on the predicted values in a model adjusted for the random study effects (generating a single intercept for each study) with observations weighted by the standardized SEM; (2) the fitted Y values are calculated for each prediction: intercept + (slope × predicted value); (3) the conditional residuals from the regression model are extracted; and (4) the adjusted Y values are computed as the summation of the conditional residuals and their corresponding fitted Y values.The analysis of feed evaluation systems was conducted on raw and adjusted data, both having their own interpretation.
Interpretation of Raw Data As previously discussed in Daniel et al. (2020) and Martineau et al. (2023a), statistical analyses performed on raw data evaluate the ability of feed evaluation systems to predict outflows on an absolute basis, based on ration composition and ingestion and cow characteristics.Each treatment mean is treated as an independent observation (i.e., not part of an experiment); therefore, the prediction errors include the uncontrolled variation related to the study (e.g., animals: measurement error in DMI, diet specifications, and production; sampling error; analytical methods; management and environmental conditions; and random undefined errors; see Ch.Twenty in NASEM, 2021).The analysis conducted on raw data should represent the feed evaluation system's performance to generate absolute values of EAA outflows (absolute values and relative responses to input changes) on a given farm with normal sampling and measurement error and no prior knowledge of the other sources of variation.Therefore, it is relevant to know how feed evaluation systems perform in this context.

Interpretation of Adjusted Data
The adjustment of observations for study effects captures the uncontrolled variation among studies mentioned above in the form of a random mean adjustment of the intercept unique to each study (refer to Figure 1 in Hanigan et al., 2013).Therefore, the analysis on adjusted data reflects only the feed evaluation system's ability to predict the direction and amplitude of responses in EAA outflows to dietary changes.This is a useful tool for optimizing an existing ration if the model is calibrated to current conditions on the farm.Because both approaches have their own significance, both are presented and discussed.
Influence of Moderators We explored the relationships between residual errors (observed raw values minus predictions) and factors associated with diets, either inputted in the feed evaluation system or available but not used to generate predictions of EAA outflows (e.g., EE is not used to predict EAA outflows).Patterns correlated with inputs indicate a feed evaluation system structure or parameter problem, whereas those correlated with ignored factors suggest a missing component in the feed evaluation system.On that basis, the site of sampling and ration factors were evaluated.
Categorical Moderator The effect of the site of sampling (duodenum vs. omasum) on residual errors was evaluated in regression models that included the interaction between the predicted values centered around their mean and the site of sampling.Regression models were adjusted for random study effects, with observations weighted by the standardized SEM.This test has a limitation that must be acknowledged because no study reported EAA outflows from the 2 sampling sites; therefore, the effect of the site of sampling on residual errors is compared across studies.
Continuous Moderators For the outflow of each EAA in each feed evaluation system, separate linear regression analyses were conducted between the residual errors and each moderator in univariate models adjusted for the random effect of study, with observations weighted by the standardized SEM.The continuous moderators included DMI (kg/d), the dietary concentrations (% DM) of NDF, CP, starch, and EE, and RDP (% CP), as well as the apparent rumen degradabilities of NDF (Rum_dcNDF, %NDF) and starch (Rum_dcSt, %starch).Except for DMI, all moderators were computed by each feed evaluation system; because starch, Rum_dcNDF, and Rum_dcSt were not available in NRC, their effect on residual errors could not be assessed.The correlation matrix among moderators was computed using the rcorr function from the Hmisc package in R (version 4.7-1).
The multiple regression analyses were conducted on the full model which included all moderators with P ≤ 0.10 from the univariate models, the random study effects, and the standardized SEM.A backward elimination procedure with a significance level of P ≤ 0.10 was used to reduce iteratively the full model.

Statistical Methodology
All models were computed using the rma.mv and robust functions of the metafor package in R (version 3.8-1; REML method; Viechtbauer, 2010Viechtbauer, , 2018) ) to obtain unbiased estimates of fixed effects.Valid estimates of P-values are obtained using the robust function (Viechtbauer, 2021).Observations were weighted by the standardized SEM.The corrected Akaike's information criterion (AICc) was computed using the fitstats function of the metafor package.The statistical model is fully described in Martineau et al. (2023a).

Features of the Data Set
Composition of Feed Ingredients.Data were reported for 329 forages in 33 studies, 149 proteinaceous feeds in 16 studies, and 79 grains in 12 studies.The CP of the ration was reported in 75% (267/354) of treatments (Table 1).However, CP (% DM) and EAA (% CP) were reported for 1 or more feed ingredients of the ration only in 36% of studies.Overall, dietary protein was fully defined from ingredient observations for 55 (of 354) treatment means, and the remainder were created from a combination of observed ingredient composition supplemented with tabular information from the feed tables of each feed evaluation system.It should be noted that the dietary intake of individual EAA was reported for 60% of treatment means (Table 1); however no attempts were made to select feed ingredients for this information.Therefore, to improve predictions and potentially feed evaluation systems, researchers are reminded to analyze main feed ingredients for appropriate nutrients and others (e.g., starch, NDF digestibility, EE, fatty acids), otherwise feed evaluation systems are reliant on static values from feed libraries.As such, the reliance on static values may skew the predicted outflows of EAA, particularly when these values are applied to predicted NANMN values which are derived differently in the 3 feed evaluation systems.
Representativeness of the Parent Data Set.The 354 treatment means included in the current data set were a subset of 1,294 treatment means with outflows of N fractions (Martineau et al., 2023a).For comparison purposes with the parent data set, fit statistics for the outflows NAN, MiN, and NANMN are reported in Supplemental Table S2 (https: / / doi .org/ 10 .17632/xxxxx, Martineau et al., 2024).In the current subset, the RPE for the raw data of NAN, MiN, and NANMN across feed evaluation systems averaged, respectively, 95, 90, and 101% those in the parent data set; and, respectively, 112, 102, and 94% for the adjusted data of NAN, MiN, and NANMN.Therefore, even with a smaller number of observations, it can be concluded that the current data set reporting EAA outflows was representative of the parent data set based on similar fit statistics.
Summary Statistics.The summary statistics on intakes, outflows, and cow characteristics reported in publications are detailed in Table 1, and the diet characteristics predicted with the 3 feed evaluation systems are reported in Table 2. Outflows of Trp were reported in only 27 studies and were therefore not included in the current study.The actual data set encompassed 354 EAA outflows, i.e., 59% more outflows than reported in Hanigan et al. (2021) and NASEM (2021); however, the average outflows were similar between both data sets.In Table 2, dietary concentrations of CP, NDF, starch, and EE, as well as predicted EAA intakes were markedly similar among the 3 feed evaluation systems.It is worth noting that the EAA profile of feed ingredients in the NASEM and CNCPS feed libraries are from the same source, i.e., Evonik Operations GmbH (Hanau, Germany).Feed evaluation systems use different methodologies to compute RDP, Rum_dcNDF, and Rum_ dcSt (Martineau et al., 2023a).In the current data set, CCC of RDP was 91% between NRC and NASEM, and 55% between NASEM and CNCPS because NRC and NASEM use a similar methodology to compute RDP in contrast to CNCPS.The CCC of Rum_dcNDF and Rum_dcSt were ≤ 2% between NASEM and CNCPS (data not shown).
Biases in Raw and Adjusted Data.The adjustment for the random effects of study has a very small effect on the average of observed adjusted values but it reduces their range (Tables 3 to 8).Therefore, the mean biases (observed minus predicted values) were similar in raw and adjusted data.In addition, the mean bias is not a concept that applies to adjusted data (Daniel et al., 2020).Therefore, the discussion on mean biases will be carried out only for the raw data.In contrast, the slopes between observed and predicted outflows differed in the analyses on the raw versus adjusted data.For the 9 EAA of the 3 feed evaluation systems, the slopes averaged, respectively, 0.90 g/g (SD = 0.100; range 0.68 to 1.07) and 0.84 g/g (SD = 0.074; range 0.66 to 0.96) in the analyses on the raw and adjusted data (Tables 3  to 8).Using digestion data and the Molly cow model, Hanigan et al. (2013; Figure 1) reported a reduction of slope when data were analyzed on a within-versus between-study which led to the investigation of factors influencing digestive processes.In the current study, the adjustment of observed values for random study effects captured the variability associated with the improved efficiency of EAA analyses, and the greater DM and CP intakes of cows over time.Therefore, the discussion for the linear biases (based on the slopes) will be performed separately for the raw and the adjusted data.
Outflows of Raw Data.The tables and figures herein report data per set of 3 AA based on general interest and biology.The AA are grouped as follows: His, Lys, and Met; the branched-chain AA (BCAA; Ile, Leu, and Val); and the 3 remaining AA: Arg, Phe, and Thr.
Fit Statistics for the Raw Data.The relationships between observed EAA outflows and predictions with each feed evaluation system are depicted in Figures 1,  2, and 3, and the statistical fits are detailed in Tables 3, 4, and 5. Overall, RPE was, on average, 13% higher (26.1 vs. 23.2%obs.mean ) for EAA outflows predicted with CNCPS versus those from NRC and NASEM; RPE of Arg (+51%), Met (+21%), and His (+19%) were the major contributors to the 13% difference observed between CNCPS and the other 2 feed evaluation systems.The CCC of His and Met averaged 54% and were lowest among the EAA across the 3 feed evaluation systems; that of Leu, Phe, and Thr averaged 73% and were the highest.A large proportion of MSPE was attributed to ECT for predictions of EAA outflows with CNCPS, followed by NRC and NASEM; the highest ECT being observed for Arg, His, and Met predicted with CNCPS (≥24% MSPE ).A smaller proportion of MSPE was attributed to ER which averaged 4.1, 0.9, and 0.4% MSPE for predictions of EAA outflows with CNCPS, NRC, and NASEM, respectively.The ER of EAA outflows   2 n = number of treatment means; minimum (Min) and maximum (Max).CCC = concordance correlation coefficient (Lin, 1989); RMSPE = root mean squared prediction error (Theil, 1966); RPE = relative prediction error (RMSPE as a % of mean observed); ECT = error in central tendency; ER = error due to the regression (Bibby and Toutenburg, 1978); RSR = ratio of RMSPE and SD of observed values (the smaller, the better; Moriasi et al., 2007). 3The coefficient and SE of the slope are from the simple linear regression of observed versus predicted values; P-value of the slope being different from 1.0 is reported. 4The linear bias is the absolute difference between biases computed for first and third quantiles of predicted values (adapted from St-Pierre, 2003), and is used to assess the biological relevance of the slope.Mean and linear biases in bold character have biological relevance (>5.0% of observed mean; refer to the text). 5Outliers were identified based on an absolute studentized residual value > 3 using an inner StudentResid function in R (refer to the text).
predicted with CNCPS were ≥ 3.7% MSPE for all EAA except Leu and Thr.
Albeit the fact that CNCPS had the best fit statistics of the 3 feed systems for NAN predictions, it slightly overpredicted MiN (4% obs.mean ) and underpredicted NANMN (8% obs.mean ) (Supplemental Table S2).For Arg and His, CNCPS uses a microbial composition higher for these 2 AA compared with NASEM (Arg: 6.04 vs. 5.47; His: 2.41 vs. 2.21 g/100 g true protein, respectively).If the microbial AA composition used by NASEM was applied in the calculations of CNCPS, that would reduce, on average, Arg and His outflows by 11 and 5 g/d, respectively.This correction would represent, respectively, 35 and 57% of the average overprediction of Arg and His outflows by CNCPS.For Met, however, CNCPS and NASEM adopt a similar microbial composition (2.60 vs. 2.63 g/100 g true protein, respectively).For this specific EAA, the non-inclusion of the endogenous fraction in the protein outflow, which has a low Met concentration (NASEM, 2021), might be responsible of the overprediction of Met with CNCPS.
Linear Biases for the Raw Data.The slopes of observed versus predicted outflows were not different  2 n = number of treatment means; minimum (Min) and maximum (Max).CCC = concordance correlation coefficient (Lin, 1989); RMSPE = root mean squared prediction error (Theil, 1966); RPE = relative prediction error (RMSPE as a % of mean observed); ECT = error in central tendency; ER = error due to the regression (Bibby and Toutenburg, 1978); RSR = ratio of RMSPE and SD of observed values (the smaller, the better; Moriasi et al., 2007). 3 The coefficient and SE of the slope are from the simple linear regression of observed versus predicted values; P-value of the slope being different from 1.0 is reported.
(P ≥ 0.06) from unity for 17 out of 27 EAA outflows (Tables 3, 4, and 5).The NRC-generated slopes were not different (P ≥ 0.06) from unity except for 3 EAA (His, Ile, and Phe) which were lower (P ≤ 0.04) than unity.However, of these 3 EAA, only His had a linear bias of concern (7% obs.mean ; Table 3; Figure 1).The NASEM-generated slopes were not different (P ≥ 0.07) from unity for all EAA and presented no linear bias of concern.The CNCPS-generated slopes were lower (P < 0.001) than unity for all EAA except for Leu and Thr (Tables 4 and 5; Figures 2 and 3).This induced a linear bias of concern (6 to 12% obs.mean ) for Arg, His, Ile, Lys, Met, and Val, whereas that of Phe did not reach the 5.0% obs.mean threshold.
Overall, these results on raw data indicate that NASEM would best predict EAA outflows on an absolute basis when formulating a dairy ration, because the mean, except for Lys, and linear biases were not of concern.The NRC feed system would also offer good predictions: a linear bias was of concern only for His but 6 of the 9 EAA outflows were overpredicted.Of the 3 feed systems, CNCPS would offer the poorest predictions of the 3 feed evaluation systems with important mean and linear biases for many EAA outflows.
To clarify if a misspecification of feed ingredients and their EAA composition might be involved in those biases, the analysis was repeated on a subset of studies where the composition of EAA was reported in 1 or more feed ingredients of the diet (n = 127 treatment means).This analysis decreased, on average, by 49% the mean biases (% obs.mean ) of Arg, His and Met with CNCPS, although they still remained above the 5.0% threshold (data not shown).For NRC, the mean biases of all EAA were of concern and were 2-fold higher than those in the complete data set (data not shown).For NASEM, the mean bias of His was 5.0% obs.mean and above that threshold for Arg, Leu, Lys, and Met (data not shown).

Fit Statistics of Adjusted Data
The relationships for the adjusted data are depicted in Figures 4, 5, and  6, and the statistical fits are detailed in Tables 6, 7, and 8. Overall, RPE were, on average, 59% higher (13.6 vs. 8.6% obs.mean ) for EAA outflows predicted with CNCPS versus those from NRC and NASEM; again, RPE of Arg (+297%), Met (+234%), and His (+183%) were major contributors to the 59% difference observed between CNCPS and the other 2 feed evaluation systems.The CCC were all improved with the adjustment of observed values but they remained ≤ 80% for Arg, His, and Met outflows predicted with CNCPS.The proportion of MSPE attributed to ER was, on average, 67% higher for the EAA outflows predicted with CNCPS versus the other 2 feed evaluation systems; the difference was mainly attributed to higher ER for Ile, Phe, Thr, and Val outflows predicted with CNCPS.
Compared with Figures 3, 4, and 5, the adjusted observed values in the corresponding Figures 6, 7, and 8 are much closer to the regression line after the capture of the differences related to the study by the adjustment function.This resulted in all slopes being different (P ≤ 0.004) from unity averaging 0.84 g/g (SD = 0.074; range = 0.66 to 0.96).Compared with CNCPS, the slopes of adjusted data were closer to unity for NRC and NASEM (0.87 g/g for both) and were, on average, 10% lower (P ≤ 0.02) with CNCPS.The adjustment for the random effects of study decreased all slopes except His (NRC and CNCPS) and Phe (CNCPS), and the effect was relatively more important (17%) for the slopes of Leu and Met predicted with NASEM.This is an indication that there is some structure in the random effects across studies that is correlated with the independent variable (Hanigan et al., 2013).
Linear Biases for the Adjusted Data The decrease observed on the slopes with the adjustment for the effect of study increased the number of EAA having a linear bias of concern in NRC (Leu) and NASEM (Arg, His, Lys, and Met), and no change in CNCPS.The linear bias of His was of concern for all 3 feed evaluation systems (Table 6) whereas those of Arg, Lys, and Met were of concern with NASEM and CNCPS (Tables 6 and 9).It should be noted that the linear biases were ≤ 7% obs.mean among the EAA outflows of the 3 feed evaluation systems, except for those of Arg, His, and Met with CNCPS ranging from 9 to 12% obs.mean which were also associated with large negative mean biases indicating that the overprediction increased with the EAA outflow.Measured chemistry of CP and EAA on feed ingredients (36% of the studies) decreased, on average, the linear biases by 12% across the 3 feed evaluation systems (data not shown).
Overall, these results on adjusted data indicate that if dietary changes are planned in a situation with a known background, the responses in EAA outflows would be better predicted by NRC, closely followed by NASEM, whereas CNCPS would overpredict the response for 7 EAA.

Comparison with Results from Previous Studies
Only limited literature is available on comparison of observed EAA outflows with predictions by the feed evaluation systems compared in the current metaanalysis, and no study has yet reported on predictions of NASEM (2021).Of the comparisons that have been published, Bateman et al. (2001) compared EAA outflows with predictions from an early version of CNCPS (v.3.0; Russell et al., 1992).A feature of Bateman's  2012) are from duodenal studies and are included in the current analysis; therefore, the results from the 2 studies will not be discussed further.
Over 220 treatment means from duodenal and omasal studies (ratio 80:20, respectively) were included in the preliminary works of Fleming et al. (2019) 2019), were overpredicted.The mean biases were 20% obs.mean for Lys versus 11% obs.mean , on average, for the EAA other than Leu and Lys.In the current study, the fit for the EAA outflows predicted with NASEM was better and only Lys was overpredicted by 11% obs.mean (Table 3).The large overprediction for Lys was not discussed specifically but Fleming et al. (2019) reported that prediction errors of EAA could be driven by missing dietary nutrient interactions, incorrectly specified feed composition, systematic bias in the EAA composition of 1 or more protein fractions, or poorer 24-h acid hydrolysis recovery in practice than reflected in the adjustment factors used in their study.  n = number of treatment means; minimum (Min) and maximum (Max).CCC = concordance correlation coefficient (Lin, 1989); RMSPE = root mean squared prediction error (Theil, 1966); RPE = relative prediction error (RMSPE as a % of mean observed); ECT = error in central tendency; ER = error due to the regression (Bibby and Toutenburg, 1978); RSR = ratio of RMSPE and SD of observed values (the smaller, the better; Moriasi et al., 2007). 3The coefficient and SE of the slope are from the simple linear regression of observed versus predicted values; P-value of the slope being different from 1.0 is reported. 4The linear bias is the absolute difference between biases computed for first and third quantiles of predicted values (adapted from St-Pierre, 2003), and is used to assess the biological relevance of the slope.Mean and linear biases in bold character have biological relevance (>5.0% of observed mean; refer to the text). 5Outliers were identified based on an absolute studentized residual value > 3 using an inner StudentResid function in R (refer to the text).
If the factorial approach used in NASEM is adequate for all EAA except for Lys which is overpredicted, this would indicate a specific problem with Lys, not a systematic one.The NASEM is using a composite composition of EAA for MCP, assuming a fixed proportion of fluid-(33.4%)and particle-associated bacteria (50.1%), and protozoa (16.5%).Because Lys concentration in protozoa is approximately 50% higher than bacteria (Sok et al., 2017), the weighed composition of MCP averaged 8.1 g of Lys per 100 g of microbial AA, very close to the weighed value of 8.0 recently reported (Gresner et al., 2022), compared with an average value of 7.54 if only bacteria would be considered.Using this latter value would decrease, on average, the Lys outflow by 10 g/d, slightly more than half of the overprediction.The impact of including protozoa for the EAA composition is smaller or negligeable for the other EAA, because the composition of bacteria and protozoa is similar (Sok et al., 2017;Gresner et al., 2022).An ideal microbial marker should account for both the bacteria and protozoa (Broderick and Merchen, 1992).Although it is acknowledged that no microbial marker (e.g., 2,6-diaminopimelic acid, labeled 15 N, purine bases or nucleic acids) labels to the same extent bacteria and protozoa (Rahnema and Theurer, 1986;Zinn and Owens, 1986;Firkins et al., 1987), protozoa are nonetheless labeled to some degree.Otherwise, we could not think of other reasons for this discrepancy observed only for Lys with NASEM.
To further study the goodness-of-fit of the data, Hanigan et al. ( 2021) reported the slope of residual errors versus predicted values, which can be converted as the slope between observed and predicted values (1 minus slope).These slopes of all EAA were smaller than unity and the slope of His was 0.72 g/g.On average, the slopes were 4 to 18% lower compared with those in the current study.It is possible that the addition of 130 treatment means in the current study or the use of NASEM ( 2021) to predict the EAA outflows resulted in better statistical fits compared with the preliminary work reported by Fleming et al. (2019) and Hanigan et al. (2021).was well demonstrated in White et al. (2016), Hanigan et al. (2021), andMartineau et al. (2023a).The effect was also present in the current study (Supplemental Table S3; https: / / doi .org/ 10 .17632/xxxxx, Martineau et al., 2024).Therefore, it was considered important to test the influence of sampling site on EAA outflows to verify if differences in MiN outflows between sampling sites lead to differences in EAA outflows predicted with the 3 feed evaluation systems.The influence of sampling site was evaluated 2-ways: (1) by regressing residual errors against the interaction of predicted values centered around their mean and the sampling site (Table 9), and (2) by computing the fit statistics on the observed values adjusted for the random study effects which were calculated separately in the subsets of duodenal and omasal studies (Table 10).Only the EAA presenting a difference of P ≤ 0.10 between sampling sites for mean biases or slopes are shown in Tables 9 and 10.

Duodenal versus Omasal Sampling Studies. The effect of sampling site on predictions of MiN outflows
Relationships for the Effect of Sampling Site.In Table 9 (Figure 7), the difference in mean biases between sampling sites was P ≤ 0.05 for the outflows of Arg (NASEM), Met (all 3 feed evaluation systems), Phe (NRC and NASEM), and Thr (NRC and NAS-EM), and it was a tendency (0.05 > P ≥ 0.10) for the outflows of Arg (NRC), Phe (CNCPS), and Thr (CNCPS).The effect of sampling site on the mean bias was nonsignificant for the other EAA.For Met and the 3 feed evaluation systems, the difference in mean biases between omasal versus duodenal studies was similar, averaging 15 g/d (P < 0.001; Table 9), i.e., 33% of the observed Met outflows in duodenal studies (45 g/d; Table 10).Based on similar comparisons, the differences in mean biases between omasal versus duodenal studies were ≤ 12% greater in omasal versus duodenal studies for Arg (NASEM), Phe (NRC and NASEM) and Thr (NRC and NASEM).Therefore, the impact of the site of sampling was proportionally far greater for Met than Arg, Phe or Thr (Table 9; Figure 7).A difference in slopes between sampling site was only present (P = 0.04) for Leu with NASEM.  2 n = number of treatment means; minimum (Min) and maximum (Max).CCC = concordance correlation coefficient (Lin, 1989); RMSPE = root mean squared prediction error (Theil, 1966); RPE = relative prediction error (RMSPE as a % of mean observed); ECT = error in central tendency; ER = error due to the regression (Bibby and Toutenburg, 1978); RSR = ratio of RMSPE and SD of observed values (the smaller, the better; Moriasi et al., 2007). 3 The coefficient and SE of the slope are from the simple linear regression of observed versus predicted values; P-value of the slope being different from 1.0 is reported.
Outliers were identified based on an absolute studentized residual value > 3 using an inner StudentResid function in R (refer to the text).
The same analysis was also conducted in the studies reporting the composition of EAA in 1 or more feed ingredients of the diet (n = 84 and 43 treatment means in duodenal and omasal studies, respectively).Of the EAA identified above, only Met retained a significant difference in mean biases between sampling sites (data not shown).The difference in mean biases of Met between omasal versus duodenal studies was 9.1 g/d (or 19% higher relative to the average of Met outflows in duodenal studies).
Fit Statistics for the Effect of Sampling Site.The fit statistics for the EAA presenting a difference in the mean or slope biases between sampling site in Table 9 are reported in Table 10 and discussed below.Although there was a difference in mean biases between sampling site for Arg with NASEM, the mean biases were not of concern in duodenal and omasal studies (Table 10).The mean biases of Met were different between sampling site for the 3 feed systems (Table 9) and were all of concern (5.1 to 27.5% obs.mean ) except for that in duodenal studies with NRC (Table 10).For Met specifically, NRC and CNCPS performed the best with the type of studies used to develop or test their respective model.The NRC predictions of Met outflows had a nearly 3-fold higher CCC in duodenal compared with omasal studies; in contrast, CCC for Met predictions with CNCPS was 84% in omasal versus 55% in duodenal studies (Table 10).The NASEM which used data from both sites of sampling to develop its model had CCC of 80 and 68% for predictions of Met outflows in duodenal and omasal studies, respectively.Interestingly, the difference in mean biases between the 2 sampling sites was of similar magnitude in the 3 feed evaluation systems (Tables 9 and 10).
The mean biases of Phe and Thr differed between sampling site for NRC and NASEM (Table 9).The mean biases of Phe were 5.0% obs.mean for NRC and NAS-EM in duodenal studies, but of concern only for NRC Mean bias or slope within row and outflow differ at P ≤ 0.05 (Tukey test; refer to the text).

A-C
Mean bias or slope within row and outflow differ at P ≤ 0.001. 2 n = number of treatment means; minimum (Min) and maximum (Max).CCC = concordance correlation coefficient (Lin, 1989); RMSPE = root mean squared prediction error (Theil, 1966); RPE = relative prediction error (RMSPE as a % of mean observed); ECT = error in central tendency; ER = error due to the regression (Bibby and Toutenburg, 1978); RSR = ratio of RMSPE and SD of observed values (the smaller, the better; Moriasi et al., 2007).
in omasal studies (Table 10).The mean biases of Thr were within acceptable limits in duodenal studies but, respectively, 10.1 and 4.9% obs.mean for NRC and NASEM in omasal studies (Table 10).Regarding the slopes, only Leu predicted with NASEM presented different slopes between sampling site (Table 9); the associated linear biases were not of concern in the duodenal studies but reached 5.0% obs.mean in the omasal studies (Table 10).
Potential reasons, both biological and methodological, for the observed differences between omasal and duodenal studies for the EAA presenting the largest discrepancy, Met, are discussed below and in more detail in Supplemental File I (https: / / doi .org/ 10 .17632/xxxxx, Martineau et al., 2024), but no satisfactory resolution of this problem can be proposed.A further step in the estimation of EAA supply to the cow, which would be independent of the site of sampling, would be to compare the predictions of the flows of digestible EAA with their net portal absorption, acknowledging however, the challenges in this comparison with the potential use of EAA by the gut.
Diet Characteristics.The correlation matrix among dietary characteristics in each feed evaluation system is reported in Supplemental Table S4 (https: / / doi .org/ 10 .17632/xxxxx, Martineau et al., 2024).The correlation between residual errors and dietary characteristics was tested in separate multiple regression models summarized in Table 11.Starch, Rum_dcNDF, and Rum_dcSt were not evaluated with NRC, whereas   8).
Rum_dcNDF was P > 0.10 with NASEM and CNCPS.Multiple regressions can suffer in interpretability due to correlations among the independent variables; for example, a slope with respect to starch might appear, but when considered in the context of NDF it might be nonsignificant because of the correlation between these factors.The correlation was strongest (−0.80;P < 0.001) between NDF and starch, however, both were never included together in the multiple regression models (due to a threshold of P > 0.10 in univariate models).An in-depth discussion of results from the multiple regression analysis is reported in Supplemental File II (https: / / doi .org/ 10 .17632/xxxxx, Martineau et al., 2024).
Overall, within each feed system, factors that were usually significant in the multiple regressions of N outflows (Martineau et al., 2023a) were also significant for EAA outflows.Because Lys outflows were overpredicted with NASEM but not differently in duodenal and omasal studies (data not shown), the discussion that follows will focus on moderators influencing the residual errors of Lys from NASEM.Being significant in their respective univariate model, CP, EE, and RDP were selected to be included in the full multiple regression model: CP (coefficient = −1.2;SE = 0.54; P = 0.03), EE (coefficient = −1.7;SE = 0.97; P = 0.08), and RDP (coefficient = 0.30; SE = 0.147; P = 0.04; data not shown).In the reduced multiple regression model, only CP and RDP tended (P ≤ 0.09) to be correlated with the residual errors of Lys (Table 11).In the correlation matrix, the correlation was ≤ 0.19 (for the absolute values) between CP, EE, and RDP with NASEM (Supplemental Table S4).The results indicate that, globally and in absolute terms, the error in the overprediction of Lys outflows with NASEM tends to increase further with incremental values of CP (negative coefficient) or decreasing values of RDP (positive coefficient; Figure 8).The residual errors of Lys (or 2 n = number of treatment means; minimum (Min) and maximum (Max).CCC = concordance correlation coefficient (Lin, 1989); RMSPE = root mean squared prediction error (Theil, 1966); RPE = relative prediction error (RMSPE as a % of mean observed); ECT = error in central tendency; ER = error due to the regression (Bibby and Toutenburg, 1978); RSR = ratio of RMSPE and SD of observed values (the smaller, the better; Moriasi et al., 2007).
mean bias) averaged −18.0 g/d (Table 6); therefore, it can be estimated that they would average −15.9 g/d with a variation of 1 unit of SD in either CP and RDP (2.06 and 8.0, respectively, for CP and RDP; Table 2).The multiple regression analysis indicated that diet characteristics explained partly the overprediction of Lys with NASEM.Although CP and RDP should be investigated further in NASEM, it is still unclear why only Lys is specifically overpredicted with NASEM (Tables 6, 7, and 8).

Observed Met outflows versus NAN outflows.
A clear effect of the site of sampling on the mean biases of Met outflows was observed for the 3 feed evaluation systems, and this difference was relatively larger for Met compared with the other 3 EAA presenting a difference in mean biases between sampling site (Table 9).This could be related to a greater ratio of observed Met on NAN outflows compared with the other EAA.This hypothesis was evaluated for all EAA in regression models including the interaction between observed NAN outflows and the site of sampling: Table 12 and Figure 9 detail the EAA for which the effect of sam-pling site was significant.The difference in intercept at mean NAN values was significant for Lys, Met, Leu, and Val.For Met, it was on average 26% higher (P < 0.001) in omasal studies relative to duodenal studies.This proportion is similar to that found for the difference in mean biases between sampling sites reported for Met in Table 9.For the 3 other EAA, Lys, Leu and Val, the intercept was lower in omasal compared with duodenal studies.
Because the difference was larger for Met than for the other EAA in Table 9, we focused our investigation on this EAA.A more in depth discussion on the difference of observed Met relative to NAN outflows between digesta sampled at the omasum or at the duodenum can be found in Supplemental File I.A potential explanation for this difference between sampling site could be the insufficient protection of sulfur-AA before acid hydrolysis in older duodenal studies; however, the bias was still present in the subset of studies using performic acid to protect Met.Therefore, this hypothesis was discarded.The bias might also originate from the sieving out (or loss) of large particle (LP) during the omasal  9).The vertical dotted line corresponds to the average of predictions.
sampling procedure.The reconstitution of the omasal true digesta (OTD) would result in greater contributions of fluid (FP) and small particle (SP) phases at the expense of LP.Because microbes are mostly associated with SP and FP, the contribution of MiN to NAN would be overestimated at the expense of NANMN (or RUP).This would be in line with observed MiN outflows being on average 23% higher than NAN outflows in omasal versus duodenal studies (Supplemental Table S3).A greater contribution of FP and SP in OTD could induce a Met bias because microbial protein contains a greater concentration of Met compared with most RUP sources (NRC, 2001;Table 5-10).To evaluate this hypothesis, studies were categorized into low or high level of different dietary factors (e.g., intake of corn) and the bias was evaluated within each level.The bias was not diet-dependent; therefore, a potential bias related to the ratio of MiN: NAN in OTD was not supported.
Another potential contributing factor to the difference in mean biases between sampling sites could involve Met from endogenous secretions, due to the low concentration of Met in ECP relative to feed ingredients and microbial protein.Endogenous N outflow is 63% at the omasum versus the duodenum (Martineau et al., 2023a).Based on DMI in omasal treatments, sampling at the duodenal site would have added, on average, 1.2 g Met and 15.4 g NAN per day to the omasal outflows (data not shown).These increased outflows would, however, not have affected the ratio of total Met: NAN outflows in omasal treatments.
At this point, we cannot find other thoughts to elucidate why the difference in mean biases between omasal versus duodenal studies are higher for Met compared with Arg, Phe, and Thr.However, this bias helps explain some results reported in Tables 9 and 10 for Met outflows.To our knowledge, no study reported EAA outflows from both sampling sites; therefore, more research is needed to investigate this issue.

CONCLUSIONS
Overall, the results of the current study indicate that both NRC and NASEM feed evaluation systems are yielding accurate predictions of EAA outflows, with a small superiority of NASEM to predict absolute values (from the analysis on raw data) and a slight superiority of NRC to predict the responses to dietary changes (from the analysis on values adjusted for random study effects).In comparison, CNCPS feed evaluation system presented mean and linear biases of concern for many EAA.Measured chemistry of CP and EAA, reported in 1 or more feed ingredients of the diet in 36% of the studies used, resulted in decreased linear biases in the 3 feed evaluation systems.Improving predictions  of NAN, MiN, and NANMN outflows should improve predictions of EAA outflows because common moderators were correlated with residual errors.Inclusion or re-evaluation of rumen degradability coefficients of CP and starch is advocated in the prediction equation of EAA outflows.Further research is also needed to improve the inclusion of other variables in NASEM and CNCPS, e.g., NDF, CP, and EE.The estimation of more accurate predictions of EAA outflows is the first step in the process of balancing dairy rations for EAA.From these, will be derived the flows of digestible EAA.Future research objectives need to improve and verify the proportion of microbial protein of protozoal origin in various dietary regimen.The determination of the functions pulling EAA "irreversibly" from the pool of free AA and the efficiency with which EAA are used to support these functions are important.These are factors that will subsequently affect the ability of The effects of sampling site (duodenal versus omasal) on residual errors (observed minus predicted) were determined in regression models, which included the interaction between predicted EAA outflows (g/d) centered around their mean, and the sampling site (duodenal = duodenum and abomasum; omasal = omasum and reticulum).Regression models were adjusted for random study effects, and observations were weighted by the standardized SEM.Regression models are shown for those with a difference of P ≤ 0.10 in mean bias or slope between sampling sites.9. feed evaluation systems to correctly predict milk true protein yield and face nutritional challenges besides optimizing performances, such as reduce losses to the environment, sustain animal health, and improve production and quality of products. 4

Figure 1 .
Figure 1.Relationships between observed His, Lys and Met outflows and values predicted by National Research Council (2001; NRC), National Academies of Sciences, Engineering and Medicine (2021; NASEM), and Cornell Net Carbohydrate and Protein System v6.5.5 (CNCPS).Solid bold blue lines represent the best-fit regression line (refer toTable 3), and black lines represent unity.
Martineau et al.: Predictions of ruminal amino acid outflows slope within row and outflow differ at P ≤ 0.001. 1 Statistics were computed for EAA outflows (g/d) predicted by National Research Council (2001; NRC), National Academies of Sciences, Engineering and Medicine (2021; NASEM), and Cornell Net Carbohydrate and Protein System v6.5.5 (CNCPS).
Martineau et al.: Predictions of ruminal amino acid outflows Martineau et al.: Predictions of ruminal amino acid outflows meta-analysis was that the data set included 164 individual cow data that were summarized in 6 studies.Pacheco et al. (2012) compared observed EAA outflows with predictions from NRC (2001) and a variation of the CNCPS (Agricultural Modeling and Training Systems LLC version 2.0.15,Cortland, NY) using 154 treatment means from 40 studies.All the relevant sources used by Bateman et al. (2001) and Pacheco et al. ( Martineau et al.: Predictions of ruminal amino acid outflows slope within row and outflow differ at P ≤ 0.001. 1 Statistics were computed for EAA outflows (g/d) predicted by National Research Council (2001; NRC), National Academies of Sciences, Engineering and Medicine (2021; NASEM), and Cornell Net Carbohydrate and Protein System v6.5.5 (CNCPS).

Figure 2 .
Figure 2. Relationships between observed branched-chain AA outflows and values predicted by National Research Council (2001; NRC), National Academies of Sciences, Engineering and Medicine (2021; NASEM), and Cornell Net Carbohydrate and Protein System v6.5.5 (CNCPS).Solid bold blue lines represent the best-fit regression line (refer toTable 4), and black lines represent unity.

Figure 3 .
Figure 3. Relationships between observed Arg, Phe and Thr outflows and values predicted by National Research Council (2001; NRC), National Academies of Sciences, Engineering and Medicine (2021; NASEM), and Cornell Net Carbohydrate and Protein System v6.5.5 (CNCPS).Solid bold blue lines represent the best-fit regression line (refer toTable 5), and black lines represent unity.
Martineau et al.: Predictions of ruminal amino acid outflows

Figure 4 .
Figure 4. Relationships between observed values adjusted for the effect of study and His, Lys and Met outflows (g/d) predicted by National Research Council (2001; NRC), National Academies of Sciences, Engineering and Medicine (2021; NASEM), and Cornell Net Carbohydrate and Protein System v6.5.5 (CNCPS).Solid bold blue lines represent the best-fit regression line (refer to Table6).

Figure 5 .
Figure 5. Relationships between observed values adjusted for the effect of study and branched-chain AA outflows (g/d) predicted by National Research Council (2001; NRC), National Academies of Sciences, Engineering and Medicine (2021; NASEM), and Cornell Net Carbohydrate and Protein System v6.5.5 (CNCPS).Solid bold blue lines represent the best-fit regression line (refer to Table7).
Martineau et al.: Predictions of ruminal amino acid outflows

Figure 6 .
Figure 6.Relationships between observed values adjusted for the effect of study and Arg, Phe, and Thr outflows (g/d) predicted by National Research Council (2001; NRC), National Academies of Sciences, Engineering and Medicine (2021; NASEM), and Cornell Net Carbohydrate and Protein System v6.5.5 (CNCPS).Solid bold blue lines represent the best-fit regression line (refer to Table8).

Figure 7 .
Figure 7. Effects of sampling site on residual values adjusted for the effect of study versus predictions of Arg, Leu, Met, Phe, and Thr outflows (g/d) by National Research Council (2001; NRC), National Academies of Sciences, Engineering and Medicine (2021; NASEM), and Cornell Net Carbohydrate and Protein System v6.5.5 (CNCPS).Sampling sites were categorized as duodenal (brown; solid line) or omasal (blue; dashed line).The size of circles corresponds to the standardized SEM and the best-fit regression line is in bold (refer to Table9).The vertical dotted line corresponds to the average of predictions.

Figure 8 .
Figure 8. Relationships between residual errors of Lys (g/d) and predictions of CP (% DM) and RDP (% CP) with National Academies of Sciences, Engineering and Medicine (2021; NASEM).The blue lines represent the experiments in the data set, the solid bold black lines represent the best-fit regression lines, and the vertical dotted lines correspond to the averages of CP and RDP (refer toTable 11).

21
National Research Council (2001; NRC), National Academies of Sciences, Engineering and Medicine (2021; NASEM), and Cornell Net Carbohydrate and Protein System v6.5.5 (CNCPS). 3n = number of treatment means.4 P-values are given for the difference in mean bias and slope between sampling sites.Coefficients are given with their SE in parentheses with a symbol for their significance level.σe = square root of the estimated amount of (residual) heterogeneity.AICc = corrected Akaike's information criterion.5 Outliers were identified based on an absolute studentized residual value > 3 using an inner StudentResid function.Additional observations were identified as outliers by Cook's distance (refer to the text).$ P ≤ 0.10; * P ≤ 0.05; ** P ≤ 0.01; *** P ≤ 0.001.Table 10.Summary of feed evaluation system performance for predictions of EAA outflows in duodenal and omasal studies (all data; data adjusted for the effect of study) Statistics were computed separately for EAA outflows (g/d) predicted by National Research Council (2001; NRC), National Academies of Sciences, Engineering and Medicine (2021; NASEM), and Cornell Net Carbohydrate and Protein System v6.5.5 (CNCPS) in each sampling site (duodenal = duodenum and abomasum; omasal = omasum and reticulum).Results are shown for models reported in Table 2 n = number of treatment means.3 Average of the observed (Obs) and (Pred) outflows.4 CCC = concordance correlation coefficient(Lin, 1989); RMSPE = root mean squared prediction error(Theil, 1966); RPE = relative prediction error (RMSPE as a % of mean observed); ECT and ER = error in central tendency and error due to the regression, respectively (as a % of mean squared prediction error [MSPE]; Bibby and Toutenburg, 1978); RSR = ratio of RMSPE and SD of observed values (the smaller, the better; Moriasi et al., 2007); coefficient of the slope is from the simple linear regression of observed versus predicted values; P-values of the mean bias and of the slope being different from 1.0 are shown with a symbol for their significance level; linear bias = absolute difference between biases computed at first and third quantiles of predicted values (adapted from St-Pierre, 2003), and used to assess the biological relevance of the slope; mean and linear biases in bold character have biological relevance (>5.0% of observed mean; refer to the text).$ P ≤ 0.10; * P ≤ 0.05; ** P ≤ 0.01; *** P ≤ 0.001.
of sampling site (duodenal versus omasal) on observed EAA and NAN outflows (g/d) were determined in regression models which included the interaction between NAN outflows (g/d) and the sampling site.Observed outflows were centered around their mean, and regression models were adjusted for random study effects, with observations weighted by the standardized SEM.Regression models are shown for those with a difference of P ≤ 0.10 in intercept or slope between sampling sites.2n = number of treatment means.3Average and SD of observed outflows.4P-values are given for the difference in intercept and slope between sampling sites.Coefficients are given with their SE in parentheses with a symbol for their significance level.σe = square root of the estimated amount of (residual) heterogeneity.AICc = corrected Akaike's information criterion.5Outlierswere identified based on an absolute studentized residual value > 3 using an inner StudentResid function (refer to the text).$P ≤ 0.10; * P ≤ 0.05; ** P ≤ 0.01; *** P ≤ 0.001.
Martineau et al.: Predictions of ruminal amino acid outflows

Table 1 .
Martineau et al.:Predictions of ruminal amino acid outflows Summary statistics for the studies included in the data set 1 1 Data as reported in the publications.The final data set included 354 treatments from 94 studies in which one or more EAA outflows were reported.2 MiN = microbial N (MiN); NANMN = nonammonia nonmicrobial N. 3 n = number of treatment means.

Table 2 .
Summary statistics of dietary characteristics predicted by 3 feed evaluation systems 1 3 Rum_dc = apparent rumen degradability coefficient.Starch, Rum_dcNDF, and Rum_dcSt are not available for NRC.

Table 3 .
Summary of feed evaluation system performance for predictions of outflows of His, Lys, and Met (data not adjusted for the effect of study) 1 a, bMean bias or slope within row and outflow differ at P ≤ 0.05 (Tukey test; refer to the text).

Table 4 .
Summary of feed evaluation system performance for predictions of outflows of the branched-chain AA (data not adjusted for the effect of study) 1 a, bMean bias or slope within row and outflow differ at P ≤ 0.05 (Tukey test; refer to the text).A-C Mean bias or slope within row and outflow differ at P ≤ 0.001. 1 Statistics were computed for EAA outflows (g/d) predicted by National Research Council (2001; NRC), National Academies of Sciences, Engineering and Medicine (2021; NASEM), and Cornell Net Carbohydrate and Protein System v6.5.5 (CNCPS).

Table 5 .
Summary of feed evaluation systems performance for predictions of outflows of Arg, Phe, and Thr (data not adjusted for the effect of study) 1 a-cMean bias or slope within row and outflow differ at P ≤ 0.05 (Tukey test; refer to the text).

Table 6 .
Summary of feed evaluation system performance for predictions of outflows of His, Lys, and Met (data adjusted for the effect of study) 1 Mean bias or slope within row and outflow differ at P ≤ 0.05 (Tukey test; refer to the text).A-C Mean bias or slope within row and outflow differ at P ≤ 0.001. 1 Statistics were computed for EAA outflows (g/d) predicted by National Research Council (2001; NRC), National Academies of Sciences, Engineering and Medicine (2021; NASEM), and Cornell Net Carbohydrate and Protein System v6.5.5 (CNCPS).

Table 7 .
Martineau et al.:Predictions of ruminal amino acid outflows Summary of feed evaluation system performance for predictions of outflows of the branched-chain AA (data adjusted for the effect of study) 1

Table 8 .
Martineau et al.:Predictions of ruminal amino acid outflows Summary of feed evaluation system performance for predictions of outflows of Arg, Phe, and Thr (data adjusted for the effect of study) 1Mean bias or slope within row and outflow differ at P ≤ 0.05 (Tukey test; refer to the text).Statistics were computed for EAA outflows (g/d) predicted by National Research Council (2001; NRC), National Academies of Sciences, Engineering and Medicine (2021; NASEM), and Cornell Net Carbohydrate and Protein System v6.5.5 (CNCPS). 1

Table 9 .
Martineau et al.:Predictions of ruminal amino acid outflows Effects of sampling site on predictions of EAA outflows 1

Table 12 .
Relationships between observed Lys, Met, Leu and Val, and NAN outflows 1 EAA