# Sensitivity analysis of the INRA 2018 feeding system for ruminants by a one-at-a-time approach: Effects of dietary input variables on predictions of multiple responses of dairy cattle

Seoyoung Jeon, Sophie Lemosquet, Anne-Cécile Toulemonde, Tristan Senga

Kiessé, Pierre Nozière

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Seoyoung Jeon, Sophie Lemosquet, Anne-Cécile Toulemonde, Tristan Senga Kiessé, Pierre Nozière. Sensitivity analysis of the INRA 2018 feeding system for ruminants by a one-at-a-time approach: Effects of dietary input variables on predictions of multiple responses of dairy cattle. Journal of Dairy Science, 2024, 10 (7), pp.4558-4577. 10.3168/jds.2023-24361 . hal-04510660

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# Sensitivity analysis of the INRA 2018 feeding system for ruminants by a one-at-a-time approach: Effects of dietary input variables on predictions of multiple responses of dairy cattle

Seoyoung Jeon,<fnref n="1" /> ◊ Sophie Lemosquet,<fnref n="2" /> ◊ Anne-Cécile Toulemonde,<fnref n="1" /> ◊ Tristan Senga Kiessé,<fnref n="3" /> ◊
and Pierre Nozière<fnref n="1" />* ◊

## ABSTRACT

In the feeding system for ruminants developed in 2018 by the French National Institute of Agricultural Research (INRA), the prediction of multiple animal responses is based on the integration of the characteristics of the animal and the available feedstuff characteristics, as well as the rationing objectives. In this framework, the characterization of feedstuffs in terms of net energy, digestible protein, and fill units requires information on their chemical composition, digestibility, and degradability. Despite the importance of these feed characteristics, a comprehensive assessment of their impact on the responses predicted by the INRA 2018 feeding system has not been carried out. Thus, our study investigated how variables predicted by the INRA feeding system (i.e., outputs) for dairy cows are affected by variation in feed characterization (i.e., inputs). We selected 5 input variables for the sensitivity analysis: CP, OM apparent digestibility (OMd), gross energy (GE), effective degradability of nitrogen assuming a passage rate of 6%/h (ED6_N), and true intestinal digestibility (dr_N) of nitrogen. A one-at-a-time sensitivity analysis was performed on predicted digestive, productive, and environmental output variables for dairy cows with 6 contrasted diets. These 6 diets were formulated to meet 95% of the potential daily milk production (37.5 kg) of a multiparous cow at wk 14 of lactation. The values of the 5 key input variables of each feedstuff were then randomly sampled around the INRA 2018 feed table values (reference point). The response of the output variable to the variation of the input variable was quantified and compared using the tangent value at the reference point and the normalized sensitivity coefficient. Among the major final output variables, CP and dr_N had the

greatest impact on N excretion in urine (as a proportion of total fecal and urinary N excretion; UN/TN); OMd and GE had the greatest impact on N utilization efficiency (NUE; N in milk as proportion of intake N); and ED6_N had the greatest impact on milk protein yield (MPY). Additionally, CP, GE, and dr_N had the least effect on methane emission, OMd had the least effect on UN/TN, and ED6_N had the least effect on NUE. The responses of most output variables to ED6_N and dr_N variations were highly dependent on diet and were related to the ratio between protein truly digestible in the intestine (PDI; i.e., MP) and net energy for lactation (UFL; i.e., NE_L) at the reference point of each diet. Overall, we were able to analyze the response of output variables to the variations of the input variables, using the tangent and its normalized value at the reference point. The predicted final outputs were more affected by variations in CP, GE, and OMd. The other 2 input variables, ED6_N and dr_N, had a smaller effect on the final output variables, but the responses varied between the diets according to their PDI/UFL ratio. Our present study was conducted using 6 representative diets for dairy cattle fed at their potential, but should be completed by the analysis of more diverse conditions.

**Key words:** INRAtion V5, dairy cattle, sensitivity analysis, normalized sensitivity coefficient

## INTRODUCTION

The French national feeding system for ruminants published in 1978 (INRA, 1978) is widely adopted in France and several other countries and is regularly updated (INRA, 1988, 2007). The scientific basis of the latest version of the Institut national de la recherche agronomique (INRA) feeding system was published in 2018 (INRA, 2018) and is accompanied by the reference rationing software (INRAtion V5). The INRA feeding system consists of an energy system (defined by INRA

<footnote n="1">¹UMR Herbivores, INRAE, VetAgro Sup, 63122 Saint-Genès-Chamanelle, France</footnote>

<footnote n="2">²UMR PEGASE, INRAE, Institut Agro, 35590 Saint-Gilles, France</footnote>

<footnote n="3">³UMR SAS, INRAE, Institut Agro, 35000 Rennes, France</footnote>
as “UF”), a protein system (protein truly digestible in the intestine; **PDI**), and a fill unit (**UE**) system. The characteristics of each feedstuff and diet are determined based on these 3 systems. And for that, in addition to their chemical composition, total-tract digestibility, the estimation of ruminal degradability and true intestinal digestibility are needed. Accordingly, it is necessary to evaluate through sensitivity analysis (**SA**) how the output variables of the INRA 2018 feeding system are affected by variation in several input variables, such as chemical composition, degradability, and digestibility values.

Sensitivity analysis of ruminant feeding systems has been already conducted. An SA of the whole nutritional system has been performed for American nutritional models or feeding systems, such as Molly (Baldwin, 1995), the Cornell Net Carbohydrate and Protein System (Lanzas et al., 2007a,b; Higgs et al., 2015), and the Nutrient Requirements of Beef (NASEM, 2016) and Dairy Cattle (NRC, 2001; NASEM, 2021). Lanzas et al. (2007a,b) performed SA to study the effect of carbohydrate and protein fractionation in feed on microbial growth. Bateman II et al. (2008) conducted SA on the effect of changes in dietary nutrient composition on milk components predicted by both Molly and NRC. In NASEM (2016), the effect of the nutrient value of feed on ME requirement, growth, and methane emission was evaluated. NASEM (2021) also recognized that the dairy model was evaluated by an SA, but the method and results were not detailed. Binggeli et al. (2022) conducted SA to evaluate the contributions of DMI, BW, potential milk production, and dietary nutrients (NDF, ADF, CP, and starch) to MP supply and predicted milk protein yield (MPY), which are 2 variables included in the INRA 2018 system. However, SA has not been performed on the entire INRA 2018 feeding system applied to dairy cattle, and the variation in key output variables relative to the variation in input variables has not been quantified.

Therefore, we quantified to what extent the main output variables of the INRA 2018 model (including prediction of intake, milk production, nitrogen excretion, and methane emission) are affected by variations in the main input variables of feedstuffs. For this purpose, among several SA methods, the one-at-a-time (OAT) method was applied as an easy approach (Groen et al., 2014) that allows evaluation of the individual effect of independent input variables by varying one at a time (Saltelli, 1999; Bar Massada and Carmel, 2008).

## MATERIALS AND METHODS

A screening process was first carried out on the feed to select a limited number of key input variables among

all input variables of the model, mainly to simplify the SA carried out on the diet in a second step. This screening was conducted using 22 feedstuffs which are widely used for dairy cattle rations; it was performed using OAT analysis and generalized additive models (GAM), which can consider interactions among the input variables (Hastie and Tibshirani, 1990), unlike the OAT method. Five input variables were selected from this screening process. We varied the values of these 5 input variables of each feedstuff and conducted OAT analysis in terms of diet. Through this, we were able to analyze the relations between feed ingredients and the responses of animals to dietary factors. Abbreviations, meanings, units, and North American terms for the input and output variables included in this study are listed in Table 1.

### Feedstuff: Screening for Selection of Key Input Variables

To use the INRAtion V5 software, more than 10 input variables (corresponding to the chemical composition, and ruminal, intestinal, and total-tract digestibilities of feedstuffs) are needed. To avoid a high calculation cost due to an SA performed on all input variables, a previous screening procedure was carried out to select key input variables (Ge et al., 2015). We calculated the effects of all mandatory input variables on the main output variables for 13 concentrates (barley, corn, dehydrated alfalfa, 2 mixed concentrates, faba bean, soybean, beet pulp, wheat bran, corn gluten feed, corn gluten meal, rapeseed meal, and soybean meal) and 9 forages (fresh grass, fresh perennial ryegrass, fresh corn, fresh white clover, alfalfa hay, first and second growth grass hay, grass silage, and corn silage) frequently used in France as feedstuffs for dairy cattle (Supplemental Tables S1 and S2, see Notes; Jeon et al., 2024). The output variables were the main dietary variables related to energy, protein, or fill values and are detailed in each section. All calculations were performed using the PrevAlim application (included in INRAtion V5 software), which calculates the feed value based on the INRA 2018 feeding system model.

**OAT Method.** All input variables were considered as being independent. The OAT analysis evaluated output variables by varying each input variable at a time when fixing the other input variables at a nominal value (Iooss and Lemaître, 2015). Output variables were calculated based on random values of each input variable generated through Latin hypercube sampling (LHS, with a sample size n = 50), which used the density function of each input in terms of feedstuff. As a sensitivity index (SI), we calculated the ratio of the CV of each input simulated through LHS, and the CV of the output was calculated according to the OAT analysis as follows:
$$CV_{ratio}(\%) = \frac{CV_{Output}}{CV_{Input}} \times 100.$$

When the CV<sub>ratio</sub> was over 50%, an input variable was assumed to be influential on the output variable considered. This cut-off threshold was considered as a compromise that enables selection of a reasonable number of influential input variables. The input variables were gross energy (GE), Ash, CP, NDF, ADF, ether extract (EE), OM apparent digestibility (OMd), effective degradability of nitrogen assuming a passage rate of 6%/h (ED6_N), and true intestinal digestibility (i.e., “digestibilité réelle”) of nitrogen (dr_N) for all feedstuffs (forages and concentrates), as well as ADL, starch, the effective degradability of starch assuming a passage rate of 6%/h (ED6_St) for concentrates, and DM for forages. We assumed that all input variables have a normal distribution. Mean values for random sampling were based on the INRA feed table (INRA, 2018), with a range assumed to be ± 10% of the mean value, but if the actual interlaboratory variability was available, the observed value was used (BIPEA, 2022). The variability of 10% used in the present study is close to the interlaboratory variability value for a given feedstuff (BIPEA, 2022), and has been considered as reasonable. Additionally, in cases where the theoretical maximum value cannot exceed 100% (i.e., OMd, ED6_N, ED6_St, dr_N), the range was adjusted so that all random sample values were 99.9% or less. The output variables were GE, ED6_N, dr_N, OMd, PDI of alimentary (PDIA) or microbial (PDIM) origin, net energy for lactation (UFL, i.e., “Unité Fourragère Lait”; 1 UFL = 1.76 Mcal of NE<sub>L</sub>), rumen protein balance (RPB), lysine and methionine

truly digestible in the intestine (LysDI and MetDI, respectively) for all feedstuffs, as well as the basal fill value (bFVc) and ED6_St for concentrates, feeding level of reference, and fill value for sheep and dairy (UEM and UEL, i.e., “Unité d’Encombrement Moutons” and “Unité d’Encombrement Lait,” respectively) for forages. When GE, OMd, ED6_N and dr_N are not measured, the INRA 2018 feeding system calculates these values using chemical components, so these 4 items were considered as both input and output variables. If no output variable was affected by the input variable (i.e., CV<sub>ratio</sub> = 0%), the result was not reported; this concerned only ED6_N and ED6_St for concentrates.

**Generalized Additive Models.** Generalized additive models describe an output variable y (response) as a function of some input variables x<sub>0</sub>, x<sub>1</sub>, x<sub>2</sub>, x<sub>3</sub>, ..., x<sub>n</sub>, (predictors) by using unknown smooth functions. Two kinds of models were fitted:

1. A model that contains all input variables given by

$$y \sim s(x_0) + s(x_1) + s(x_2) + s(x_3) + \dots + s(x_n); \quad [1]$$

2. A model including all input variables except the target input variable (x<sub>0</sub> in the following equation)

$$y \sim s(x_1) + s(x_2) + s(x_3) + \dots + s(x_n). \quad [2]$$

The output data set y from PrevAlim is restricted to the main output variables (i.e., PDIA, PDIM, and UFL for all feedstuffs, UEM for forages, and bFVc for concentrates); x<sub>n</sub> are the input variables of the data set obtained using

<table><caption>**Table 1.** Glossary of inputs and outputs used in sensitivity analysis</caption><thead><tr><th>Abbreviation</th><th>Definition</th><th>Unit</th></tr></thead><tbody><tr><td>bFVc</td><td>Basal fill value of concentrate</td><td>UEL/kg DM</td></tr><tr><td>dr_N</td><td>True intestinal digestibility (“digestibilité réelle”) of nitrogen</td><td>%</td></tr><tr><td>ECH4</td><td>Energy in methane</td><td>kcal/kg DM</td></tr><tr><td>ED6_N</td><td>Effective degradability of nitrogen assuming a passage rate of 6%/h</td><td>%</td></tr><tr><td>ED6_St</td><td>Effective degradability of starch assuming a passage rate of 6%/h</td><td>%</td></tr><tr><td>EE</td><td>Ether extract</td><td>g/kg DM</td></tr><tr><td>FLref</td><td>Feeding level of reference</td><td>% BW</td></tr><tr><td>GE</td><td>Gross energy</td><td>kcal/kg DM</td></tr><tr><td>LysDI</td><td>Lysine truly digestible in the intestine</td><td>% PDI</td></tr><tr><td>MetDI</td><td>Methionine truly digestible in the intestine</td><td>% PDI</td></tr><tr><td>MPY</td><td>Milk protein yield</td><td>g/d</td></tr><tr><td>NUE</td><td>Nitrogen utilization efficiency</td><td>g/g</td></tr><tr><td>OMd</td><td>Organic matter apparent digestibility (also known as OMD)</td><td>%</td></tr><tr><td>PDI</td><td>Protein truly digestible in the intestine</td><td>g/kg DM</td></tr><tr><td>PDIA</td><td>Protein truly digestible in the intestine of alimentary origin (also known as digestible RUP)</td><td>g/kg DM</td></tr><tr><td>PDIM</td><td>Protein truly digestible in the intestine of microbial origin (also known as digestible MCP)</td><td>g/kg DM</td></tr><tr><td>RPB</td><td>Rumen protein balance</td><td>g/kg DM</td></tr><tr><td>SRg</td><td>Global substitution rate of concentrate</td><td>kg DM/kg DM</td></tr><tr><td>UEL</td><td>Fill value for dairy cows and dairy goats (“Unité d’Encombrement Lait”)</td><td>/kg DM</td></tr><tr><td>UEM</td><td>Fill value for sheep (“Unité d’Encombrement Mouton”)</td><td>/kg DM</td></tr><tr><td>UFL</td><td>Net energy for lactation (“Unité fourragère Lait”; 1 UFL = 1.76 Mcal of NE<sub>L</sub>)</td><td>/kg DM</td></tr><tr><td>UN/TN</td><td>Urinary nitrogen/total (urinary + fecal) nitrogen excretion</td><td>g/g</td></tr></tbody></table>
the LHS method (n = 50). The input variables for GAM included all variables and the same distribution as that used in the OAT analysis in terms of feedstuff (i.e., GE, Ash, CP, NDF, ADF, EE, OMD, ED6_N, and dr_N for all feedstuffs, as well as ADL, starch and ED6_St for concentrates, and DM for forages). The GAM consider interactions among 2 or 3 (or more) input variables by including the terms s(xᵢ, xⱼ) or s(xᵢ, xⱼ, xₖ), and so on, respectively, in Equation 1, unlike OAT analysis. In addition, GAM can model complex (e.g., nonlinear) relationships between output and input variables.

The difference between the R² of both previous models (Equations 1 and 2) was calculated to evaluate the contribution of the predictor of interest, x₀, to the variation in the output variable. Thereby, an input variable x₀ that gives a difference higher than 0.4 between the R² of both models was considered to be influential on the output variable. Results concerning average differences in R² of less than 0.01 were not reported. This concerned Ash, NDF, EE, ADL, starch, and DM as input variables. All statistical analyses were conducted using R software (R Core Team, 2022; version 4.1.3, R Foundation for Statistical Computing, Vienna, Austria). The R package “mgcv” was used for the fitting of GAM (Wood et al., 2022). A random sample matrix that comprises the values of all input variables was needed. Therefore, 50 samples were randomly sampled using the LHS method. Here, the randomLHS function of R was used (Carnell, 2017), assuming intra-feedstuff variability was independent between input variables, except between dr_N and ED6_N for mixed concentrate and forage (INRA, 2018). Because the intra-feedstuff relationship between dr_N and ED6_N is not linear, the relationship between both values was considered with the Spearman's correlation, using the corr.test function (Revelle, 2023).

## Diet: Quantification of the Impact of Input Variables

In terms of diet, 5 input variables were included, which were selected based on results from the OAT and GAM approaches in terms of feedstuff. The impact of each input variable on diet was estimated by studying variation in these 5 input variables around the reference point. These variations are described in the next section.

**Reference Diets for Sensitivity Analysis.** The initial diets selected for SA were called the reference diets. They were conceived according to diets observed in the field, using INRAtion V5 software, to satisfy intake capacity and reach an objective of 95% of the potential daily milk production (37.5 kg) by a multiparous cow at wk 14 of lactation, at 50 mo of age and 608 kg of BW. Diets were formulated using forages (fresh perennial ryegrass [RF]; first [GH1], second [GH2], and first and second [GH3] growth grass hay; grass silage [GS]; corn silage [CS]),

protein concentrates (soybean meal and rapeseed meal), and energy concentrate (barley and corn). The feed table for INRAtion V5 used for reference diet calculation was constructed with PrevAlim as follows: for each feedstuff, the values for each mandatory input variable (Ash, CP and NDF) and nonpredictable variable were the values of the INRA 2018 feed table, and the others (e.g. UEL, PDI, UFL) were calculated using the PrevAlim model. The diet composition and the predicted responses of the animal (e.g. intake, production) were calculated by INRAtion V5 based on the theoretical basis of the INRA 2018 feeding system: the fill value of the diet satisfies the animal's intake capacity, and the UFL, PDI, MetDI, and LysDI dietary supplies allow to cover the milk yield objective. It is defined as the reference diet or reference point in this study. The composition of the reference diets is shown in Table 2.

**Simulation.** The feed table for INRAtion V5 for OAT analysis was constructed with PrevAlim as described for the reference diet, except that the value for each of the 5 input variables (CP, GE, OMD, ED6_N, and dr_N) selected through the above-described (feedstuff) approach varied around the reference values (around ± 10% of mean value; refer to feedstuff). We performend LHS for each of the 5 input variables, by assuming that they are independent, to construct a data set containing a total of 250 data points (5 variables × 50 replications). For each input variable combination, each feed composing the diet was sorted in the same order based on the value of the target input variable. At this time, the proportions of each feedstuff were fixed to their proportion in the reference diets. Thus, the nutritional content (i.e., GE, CP, ED_N), affecting dietary UEL, UFL, PDI, MetDI, and LysDI concentration, varied around the “reference diet” values. The DMI and nutrient supplies (that determine the animal responses) were then calculated using INRAtion V5 so that the fill value the diet satisfies the animal's intake capacity.

**Sensitivity Index.** To quantify the influence of each input variable (i) on each output variable (j), the tangent (T) and normalized tangent (NT) called normalized sensitivity coefficient were used according to Hughes et al., (2013), as follows:

$$T_{ij}(\text{y unit/x unit}) = \frac{\Delta y_j}{\Delta x_i} = \frac{y_{2j} - y_{1j}}{x_{2i} - x_{1i}},$$

$$NT_{ij}(\%) = \frac{\Delta y_j}{\Delta x_i} \times \frac{Avg(x_{1i}, x_{2i})}{Avg(y_{1j}, y_{2j})} \times 100 =$$

$$\frac{y_{2j} - y_{1j}}{x_{2i} - x_{1i}} \times \frac{Avg(x_{1i}, x_{2i})}{Avg(y_{1j}, y_{2j})} \times 100.$$
<table><caption>**Table 2.** Diet formulation and nutritive values for multiparous cows<fnref n="1" /></caption><thead><tr><th rowspan="2">Item</th><th colspan="6">Diet</th></tr><tr><th>RF</th><th>GH1</th><th>GH2</th><th>GH3<sup>2</sup></th><th>GS</th><th>CS</th></tr></thead><tbody><tr><td colspan="7">Diet ingredient (% DM)</td></tr><tr><td>Fresh perennial ryegrass</td><td>72.9</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>Grass hay (first growth)</td><td>—</td><td>54.2</td><td>—</td><td>—</td><td>—</td><td>—</td></tr><tr><td>Grass hay (second growth)</td><td>—</td><td>—</td><td>84.2</td><td>52.9</td><td>—</td><td>—</td></tr><tr><td>Grass silage</td><td>—</td><td>—</td><td>—</td><td>—</td><td>62.1</td><td>—</td></tr><tr><td>Corn silage</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>75.6</td></tr><tr><td>Barley</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>10.8</td></tr><tr><td>Corn</td><td>23.6</td><td>24.7</td><td>15.8</td><td>28.6</td><td>33.7</td><td>—</td></tr><tr><td>Soybean meal</td><td>3.6</td><td>—</td><td>—</td><td>—</td><td>4.2</td><td>13.6</td></tr><tr><td>Rapeseed meal</td><td>—</td><td>21.1</td><td>—</td><td>18.6</td><td>—</td><td>—</td></tr><tr><td>Predicted DMI (kg/d)</td><td>21.4</td><td>25.4</td><td>22.0</td><td>24.9</td><td>22.6</td><td>22.6</td></tr><tr><td colspan="7">Nutritive value</td></tr><tr><td>OM (g/kg DM)</td><td>926</td><td>937</td><td>922</td><td>939</td><td>928</td><td>955</td></tr><tr><td>CP (g/kg DM)</td><td>143</td><td>150</td><td>183</td><td>150</td><td>140</td><td>141</td></tr><tr><td>NDF (g/kg DM)</td><td>414</td><td>443</td><td>486</td><td>446</td><td>389</td><td>345</td></tr><tr><td>ADF (g/kg DM)</td><td>199</td><td>239</td><td>245</td><td>237</td><td>207</td><td>175</td></tr><tr><td>EE (g/kg DM)</td><td>36.8</td><td>25.4</td><td>30.7</td><td>26.1</td><td>33.8</td><td>27.9</td></tr><tr><td>GE (kcal/kg DM)</td><td>4,339</td><td>4,448</td><td>4,527</td><td>4,456</td><td>4,481</td><td>4,495</td></tr><tr><td>UFL (/kg DM)</td><td>0.98</td><td>0.81</td><td>0.93</td><td>0.83</td><td>0.94</td><td>0.93</td></tr><tr><td>OMd (% DM)</td><td>73.9</td><td>61.3</td><td>70.2</td><td>62.6</td><td>69.8</td><td>68.3</td></tr><tr><td>ED6_N (% DM)</td><td>66.3</td><td>58.2</td><td>63.1</td><td>58.7</td><td>64.5</td><td>62.5</td></tr><tr><td>dr_N (% DM)</td><td>86.0</td><td>79.3</td><td>86.9</td><td>80.6</td><td>82.7</td><td>83.5</td></tr><tr><td>PDI (g/kg DM)</td><td>94.5</td><td>97.6</td><td>109.2</td><td>98.0</td><td>89.3</td><td>92.6</td></tr><tr><td>PDI/UFL (g/UFL DM)</td><td>96.4</td><td>120.7</td><td>117.5</td><td>118.8</td><td>94.6</td><td>99.2</td></tr></tbody></table>

$T_{ij}$ represents the tangent value around the reference point, $NT_{ij}$ represents the sensitivity of the model output to input variable variation around the reference point; for each input variable $i$, $x_{2i}$ represents the closest $x$ value larger than the reference value, $x_{1i}$ represents the closest $x$ value smaller than the reference value; for each output variable $j$, $y_{2j}$ represents the value of $y$ when $x = x_{2i}$; $y_{1j}$ represents the value of $y$ when $x = x_{1i}$. The input variables ($x_i$) considered were CP, GE, OMD, ED6_N, and dr_N, and the output variables ($y_j$) came from INRAtion V5, including milk protein yield, energy in methane (ECH4), nitrogen utilization efficiency (NUE; N in milk as proportion of intake N), the ratio between urine and total N excretion (UN/TN), the global substitution rate (SRg), DMI, PDI, UFL, and PDI/UFL. For a given $NT_{ij}$, the sign may vary depending on the diet. To assess both the magnitude and the variability of this indicator, the mean and SE of $NT_{ij}$ has thus been calculated using the absolute value ($|NT_{ij}|$).

# RESULTS

## Feedstuff: Screening for Selection of Key Input Variables

Crude protein, GE, OMD, ED6_N, and dr_N showed a $CV_{ratio}$ higher than 50% for at least one output variable in both forage and concentrate (Tables 3 and 4). In for-

age, ADF and NDF showed a $CV_{ratio}$ >50% for UFL and RPB, through an effect on OMD. Thus, CP, GE, OMD, ED6_N, and dr_N, which were influential input variables for both concentrate and forage, appeared as key input variables. As a result of GAM fitting, the average of $R^2$ differences in all feedstuffs, when the input variables were GE, CP, ADF, dr_N, and ED6_St, was not higher than the threshold value of 0.4 (Table 5). Organic matter digestibility was found to have a high influence on protein, energy, and fill values (i.e., PDIM for both forages and concentrates, UFL and bFVc for concentrates, and UEM for forages). Effective degradability of nitrogen mainly affected protein (PDIA) for concentrate feeds (0.61 ± 0.078), but did not have a significant effect on the others. Therefore, based on an $R^2$ difference of 0.4 with GAM fitting, OMD and ED6_N, but not GE, CP and dr_N, appeared as key input variables. Finally, based on results of both the OAT and GAM fitting approaches, CP, GE, OMD, ED6_N, and dr_N were retained as key input variables for SA in terms of diet.

## Diet Approach: Quantification of the Impact of Input Variables

**Crude Protein.** The UN/TN ratio was the final animal response most affected by CP (with a range of absolute values such as $|NT_{CP,UN/TN}| = 131 ± 12.6\%$), followed by NUE ($|NT_{CP,NUE}| = 83.5 ± 4.47\%$) and MPY ($|NT_{CP,MPY}|$

<footnote n="1">¹Second parity; BW 608 kg; 50 mo of age; wk 14 of lactation; 10,000 kg of milk yield per year.</footnote>

<footnote n="2">²GH3 diet contained 3-kg fixed amount of first growth grass hay.</footnote>
<table><caption>**Table 3.** Average of CV<sub>ratio</sub><sup>1</sup> across all concentrate feedstuffs<sup>2</sup></caption><thead><tr><th rowspan="2">Input</th><th colspan="10">Output</th></tr><tr><th>GE</th><th>OMd</th><th>dr_N</th><th>PDIA</th><th>PDIM</th><th>PDI</th><th>UFL</th><th>bFVc</th><th>RPB</th><th>LysDI</th><th>MetDI</th></tr></thead><tbody><tr><td>ADF</td><td>1.3</td><td>8.6 (1)</td><td>—</td><td>—</td><td>5.2</td><td>2.4</td><td>10.5 (1)</td><td>14.3</td><td>33.1 (1)</td><td>0.4</td><td>0.6</td></tr><tr><td>ADL</td><td>—</td><td>3.2</td><td>—</td><td>3.2</td><td>0.2</td><td>1.6</td><td>—</td><td>—</td><td>0.6</td><td>0.3</td><td>0.3</td></tr><tr><td>Ash</td><td>5.3</td><td>—</td><td>—</td><td>—</td><td>3.8</td><td>1.5</td><td>7.0</td><td>—</td><td>7.5 (1)</td><td>0.3</td><td>0.4</td></tr><tr><td>CP</td><td>8.9</td><td>—</td><td>—</td><td>100<sup>3</sup> (13)</td><td>10.8</td><td>54.7<sup>3</sup> (5)</td><td>5.9</td><td>—</td><td>226<sup>3</sup> (9)</td><td>10.3</td><td>9.6</td></tr><tr><td>dr_N</td><td>—</td><td>—</td><td>—</td><td>99.8<sup>3</sup> (13)</td><td>10.7</td><td>54.5<sup>3</sup> (5)</td><td>—</td><td>—</td><td>9.1 (1)</td><td>10.3</td><td>9.7</td></tr><tr><td>ED6_St</td><td>—</td><td>—</td><td>—</td><td>—</td><td>8.3</td><td>4.3</td><td>—</td><td>—</td><td>6.5</td><td>1.1</td><td>0.7</td></tr><tr><td>ED6_N</td><td>—</td><td>—</td><td>—</td><td>139<sup>3</sup> (11)</td><td>9.8</td><td>69.1<sup>3</sup> (8)</td><td>—</td><td>—</td><td>147<sup>3</sup> (9)</td><td>13.1</td><td>17.2 (1)</td></tr><tr><td>EE</td><td>—</td><td>—</td><td>—</td><td>—</td><td>1.5</td><td>0.5</td><td>—</td><td>—</td><td>0.9</td><td>0.1</td><td>0.1</td></tr><tr><td>NDF</td><td>1.6</td><td>—</td><td>7.4</td><td>—</td><td>4.8</td><td>2.3</td><td>8.3</td><td>13.8</td><td>4.3</td><td>0.4</td><td>0.4</td></tr><tr><td>OMd</td><td>—</td><td>—</td><td>—</td><td>—</td><td>71.8<sup>3</sup> (13)</td><td>29.2</td><td>140<sup>3</sup> (13)</td><td>80.9<sup>3</sup> (13)</td><td>42.9 (6)</td><td>6.8</td><td>6.1</td></tr><tr><td>Starch</td><td>—</td><td>—</td><td>—</td><td>—</td><td>4.2</td><td>2.2</td><td>—</td><td>10.5</td><td>3.8</td><td>0.6</td><td>0.3</td></tr><tr><td>GE</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>114<sup>3</sup> (13)</td><td>—</td><td>—</td><td>—</td><td>—</td></tr></tbody></table>

= 32.6 ± 5.58%; Table 6). These responses differed little according to diet (CV of T<sub>CP,UN/TN</sub> = 22.7%; CV of T<sub>CP,NUE</sub> = -25.4%; CV of T<sub>CP,MPY</sub> = 34.3; Table 7). In contrast, ECH4 was on average less affected by CP (|NT<sub>CP,ECH4</sub>| = 7.4 ± 3.27%), but the response differed greatly according to diet (CV of T<sub>CP,ECH4</sub> = 214%), the GH2 diet being the most affected (Figure 1). Dry matter intake showed a positive response to CP related to the increase in SRg (Figure 2; |NT<sub>CP,DMI</sub>| = 16.1 ± 2.10%; |NT<sub>CP,SRg</sub>| = 43.2 ± 12.83%). Although the response of SRg, one of the factors regulating DMI, differed depending on diet (CV of T<sub>CP,SRg</sub> = 61.4%), the response of DMI differed little according to diet (CV of T<sub>CP,DMI</sub> = 30.5%). Overall, variations in CP logically affected PDI more than UFL (|NT<sub>CP,PDI</sub>| = 51.4 ± 3.43%; |NT<sub>CP,UFL</sub>| = 13.7 ± 5.39%; |NT<sub>CP,PDI/UFL</sub>| = 37.7 ± 3.78%). The response of PDI and PDI/UFL to CP variations was homogeneous among diets (CV of T<sub>CP,PDI</sub> = 13.1%; CV of T<sub>CP,PDI/UFL</sub> = 32.1%), whereas the response of UFL varied according to diet (CV of T<sub>CP,UFL</sub> = 86.3%), and it was more marked with the GH2 diet (Figure 3).

**Gross Energy.** The most affected final animal responses in terms of GE were NUE and UN/TN ratio (|NT<sub>GE,NUE</sub>| = 85.8 ± 7.38%; |NT<sub>GE,UN/TN</sub>| = 52.4 ± 4.97%). Responses were comparable among diets (CV of T<sub>GE,NUE</sub> = 12.9%; CV of T<sub>GE,UN/TN</sub> = -16.7%). Milk protein yield and ECH4 were less affected by GE variations (|NT<sub>GE,MPY</sub>| = 47.0 ± 17.38%; |NT<sub>GE,ECH4</sub>| = 17.3 ± 4.82%; Figure 4), although the responses differed slightly among diets (CV of T<sub>GE,MPY</sub> = 115%; CV of T<sub>GE,ECH4</sub> = 73.1%). In addition, the effect on MPY was marked with grass hay-based diets, and the effect on ECH4 was marked with the RF, GS, and CS diets. As GE increased, SRg increased and DMI decreased in all diets (Figure 5; |NT<sub>GE,SRg</sub>| = 201 ± 41.9%; |NT<sub>GE,DMI</sub>| = 44.0 ± 12.56%). The responses differed according to diet (CV of T<sub>GE,SRg</sub> = 60.1%; CV of T<sub>GE,DMI</sub> = -67.8%) and were more pronounced with the RF, GS, and CS diets. Variation in GE logically influenced UFL more than PDI (|NT<sub>GE,UFL</sub>| = 118 ± 2.9%; |NT<sub>GE,PDI/UFL</sub>| = 122 ± 3.0%; |NT<sub>GE,PDI</sub>| = 3.8 ± 1.0%; Figure 6). A low variability in response across diets was seen with PDI (CV of T<sub>GE,PDI</sub> = -60.4%), but not with UFL and PDI/UFL (CV of T<sub>GE,UFL</sub> = 9.5%; CV of T<sub>GE,PDI/UFL</sub> = -12.1%).

**OM Digestibility.** Nitrogen utilization efficiency, ECH4, and MPY were the final animal responses the most affected by OMd variations, whereas UN/TN was less affected (|NT<sub>OMd,NUE</sub>| = 108 ± 6.4%; |NT<sub>OMd,ECH4</sub>| = 103 ± 3.8%; |NT<sub>OMd,MPY</sub>| = 98.0 ± 17.44%; |NT<sub>OMd,UN/TN</sub>| = 40.0 ± 4.27). The responses of NUE, ECH4, and UN/TN were homogeneous among diets (CV of T<sub>OMd,NUE</sub> = 9.7%; CV of T<sub>OMd,ECH4</sub> = 10.6%; CV of T<sub>OMd,UN/TN</sub> = -19.3%). In contrast, the nonlinear increase in MPY varied slightly according to diet (CV of T<sub>OMd,MPY</sub> = 46.6%), with the tangent values for the RF and GS diets (T<sub>OMd,MPY</sub> = 8.76 and 4.42, respectively) being lower than those of the other 4 diets (T<sub>OMd,MPY</sub> = 20.2 ± 0.94; Figure 7). Although SRg was greatly changed by OMd (|NT<sub>OMd,SRg</sub>| = 262 ± 77.9%), DMI was less affected (|NT<sub>OMd,DMI</sub>| = 26.5 ± 10.45%) on average. The response of DMI was quadratic, and the response of SRg was exponential and highly variable between diets (Figure 8; CV of T<sub>OMd,DMI</sub> = -443%; CV of T<sub>OMd,SRg</sub> = 81.8%). In addition, the tangent value of DMI was negative or positive depending on the respective location of the inflection and the reference points (Figure 8). The variations in OMd had a greater effect on UFL than on PDI (|NT<sub>OMd,UFL</sub>| = 133 ± 1.4%; |NT<sub>OMd,PDI</sub>| = 31.0 ± 1.62%). The responses of PDI and UFL differed little according to diet (CV of T<sub>OMd,PDI</sub> = 14.8%; CV of T<sub>OMd,UFL</sub> = 3.5%; CV of T<sub>OMd,PDI/UFL</sub> = -18.9%; Figure 9).

<footnote n="1">¹CV of input variable/CV of output variable × 100; values in parentheses represent the number of feedstuffs with CV<sub>ratio</sub> > 50%.</footnote>

<footnote n="2">²Barley, corn, dehydrated alfalfa, 2 mixed concentrate, faba bean, soybean, beet pulp, wheat bran, corn gluten feed, corn gluten meal, rapeseed meal, and soybean meal.</footnote>

<footnote n="3">³Average of CV<sub>ratio</sub> >50%.</footnote>
<table><caption>Table 4. Average of CV<sub>ratio</sub><sup>1</sup> across all forage feedstuffs<sup>2</sup></caption><thead><tr><th rowspan="2">Input</th><th rowspan="2">GE</th><th rowspan="2">OMd</th><th rowspan="2">ED6_N</th><th rowspan="2">dr_N</th><th rowspan="2">PDIA</th><th rowspan="2">PDIM</th><th rowspan="2">PDI</th><th colspan="6">Output</th></tr><tr><th>UFL</th><th>UEM</th><th>UEL</th><th>RPB</th><th>LysDI</th><th>MetDI</th><th>FLref<sup>3</sup></th></tr></thead><tbody><tr><td>ADF</td><td>—</td><td>36.8 (3)</td><td>—</td><td>—</td><td>6.3</td><td>22.1</td><td>16.9</td><td>51.1<sup>4</sup> (3)</td><td>21.4 (1)</td><td>12.3</td><td>44.4 (3)</td><td>1.2</td><td>1.4</td><td>19.3 (1)</td></tr><tr><td>Ash</td><td>8.5</td><td>0.1</td><td>—</td><td>—</td><td>—</td><td>5.3</td><td>3.3</td><td>8.6</td><td>—</td><td>0.1</td><td>8.5 (1)</td><td>0.4</td><td>0.5</td><td>—</td></tr><tr><td>CP</td><td>5.6</td><td>8.0</td><td>10.9</td><td>24.9 (1)</td><td>108<sup>4</sup> (9)</td><td>4.7</td><td>39.9 (2)</td><td>13.0</td><td>23.6</td><td>13.2</td><td>256<sup>4</sup> (5)</td><td>8.6</td><td>9.9</td><td>23.0</td></tr><tr><td>dr_N</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>2.7</td><td>33.7</td><td>—</td><td>—</td><td>—</td><td>4.2</td><td>8.2</td><td>9.4</td><td>—</td></tr><tr><td>DM</td><td>—</td><td>—</td><td>—</td><td>—</td><td>46.3 (5)</td><td>2.0</td><td>2.0</td><td>0.1</td><td>1.0</td><td>—</td><td>—</td><td>0.8</td><td>0.2</td><td>24.2</td></tr><tr><td>ED6_N</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>263<sup>4</sup> (9)</td><td>7.0</td><td>86.8<sup>4</sup> (7)</td><td>—</td><td>—</td><td>164<sup>4</sup> (5)</td><td>21.5</td><td>—</td><td>4.3</td></tr><tr><td>EE</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>0.8</td><td>—</td><td>—</td><td>—</td><td>0.9</td><td>—</td><td>0.1</td><td>—</td></tr><tr><td>NDF</td><td>—</td><td>56.8<sup>4</sup> (4)</td><td>—</td><td>—</td><td>2.0</td><td>11.0</td><td>34.1 (3)</td><td>25.9 (1)</td><td>78.9<sup>4</sup> (5)</td><td>34.6 (2)</td><td>17.8</td><td>65.1<sup>4</sup> (3)</td><td>1.8</td><td>2.2</td><td>31.5 (2)</td></tr><tr><td>OMd</td><td>—</td><td>—</td><td>—</td><td>—</td><td>2.8</td><td>16.4</td><td>62.6<sup>4</sup> (9)</td><td>47.6 (3)</td><td>138<sup>4</sup> (9)</td><td>168<sup>4</sup> (6)</td><td>47.1 (2)</td><td>121<sup>4</sup> (5)</td><td>3.8</td><td>3.9</td><td>47.3 (4)</td></tr><tr><td>GE</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td><td>—</td></tr></tbody></table>

<table><caption>Table 5. Differences in average R<fnref n="2" /> between models including and excluding input variables of interest in generalized additive models fitting<fnref n="1" /></caption><thead><tr><th rowspan="3">Input</th><th colspan="10">Output</th></tr><tr><th colspan="2">PDIA</th><th colspan="2">PDIM</th><th colspan="2">UFL</th><th colspan="2">FV<sup>2</sup></th><th rowspan="2">SE</th></tr><tr><th>Mean</th><th>SE</th><th>Mean</th><th>SE</th><th>Mean</th><th>SE</th><th>Mean</th><th>SE</th></tr></thead><tbody><tr><td colspan="10"><strong>Concentrate</strong></td></tr><tr><td>ADF</td><td>6.8 × 10<sup>-5</sup></td><td>6.43 × 10<sup>-5</sup></td><td>0</td><td>—</td><td>6.2 × 10<sup>-5</sup></td><td>6.05 × 10<sup>-5</sup></td><td>0.025</td><td>8.8 × 10<sup>-3</sup></td><td></td></tr><tr><td>CP</td><td>0.040</td><td>0.0124</td><td>7.3 × 10<sup>-3</sup></td><td>5.90 × 10<sup>-3</sup></td><td>2.3 × 10<sup>-4</sup></td><td>1.19 × 10<sup>-4</sup></td><td>0</td><td>—</td><td></td></tr><tr><td>GE</td><td>9.0 × 10<sup>-5</sup></td><td>9.16 × 10<sup>-5</sup></td><td>0</td><td>—</td><td>0.28</td><td>0.040</td><td>0</td><td>—</td><td></td></tr><tr><td>OMd</td><td>1.1 × 10<sup>-4</sup></td><td>6.2 × 10<sup>-5</sup></td><td>0.53<sup>3</sup></td><td>0.057</td><td>0.69<sup>3</sup></td><td>0.045</td><td>0.60<sup>3</sup></td><td>0.050</td><td></td></tr><tr><td>ED6_Si</td><td>1.3 × 10<sup>-4</sup></td><td>7.7 × 10<sup>-5</sup></td><td>0.020</td><td>0.0109</td><td>7.2 × 10<sup>-5</sup></td><td>6.24 × 10<sup>-5</sup></td><td>0</td><td>—</td><td></td></tr><tr><td>ED6_N</td><td>0.61<sup>3</sup></td><td>0.078</td><td>0.10</td><td>0.052</td><td>6.6 × 10<sup>-5</sup></td><td>3.69 × 10<sup>-5</sup></td><td>0</td><td>—</td><td></td></tr><tr><td>dr_N</td><td>0.17</td><td>0.049</td><td>0.015</td><td>9.3 × 10<sup>-3</sup></td><td>3.9 × 10<sup>-5</sup></td><td>5.18 × 10<sup>-5</sup></td><td>0</td><td>—</td><td></td></tr><tr><td colspan="10"><strong>Forage</strong></td></tr><tr><td>ADF</td><td>8.9 × 10<sup>-6</sup></td><td>9.29 × 10<sup>-6</sup></td><td>9.7 × 10<sup>-7</sup></td><td>1.252 × 10<sup>-6</sup></td><td>3.1 × 10<sup>-5</sup></td><td>2.93 × 10<sup>-5</sup></td><td>2.9 × 10<sup>-3</sup></td><td>2.10 × 10<sup>-3</sup></td><td></td></tr><tr><td>CP</td><td>0.055</td><td>0.0114</td><td>1.2 × 10<sup>-3</sup></td><td>3.8 × 10<sup>-4</sup></td><td>3.9 × 10<sup>-4</sup></td><td>1.98 × 10<sup>-4</sup></td><td>0.060</td><td>0.0245</td><td></td></tr><tr><td>GE</td><td>0</td><td>—</td><td>1.0 × 10<sup>-6</sup></td><td>1.18 × 10<sup>-6</sup></td><td>0.36</td><td>0.042</td><td>2.6 × 10<sup>-3</sup></td><td>1.87 × 10<sup>-3</sup></td><td></td></tr><tr><td>OMd</td><td>2.3 × 10<sup>-3</sup></td><td>7.8 × 10<sup>-4</sup></td><td>0.65<sup>3</sup></td><td>0.049</td><td>0.36</td><td>0.032</td><td>0.62<sup>3</sup></td><td>0.100</td><td></td></tr><tr><td>ED6_N</td><td>0.076</td><td>0.0179</td><td>2.7 × 10<sup>-3</sup></td><td>9.2 × 10<sup>-4</sup></td><td>4.5 × 10<sup>-5</sup></td><td>4.40 × 10<sup>-5</sup></td><td>2.7 × 10<sup>-3</sup></td><td>1.96 × 10<sup>-3</sup></td><td></td></tr><tr><td>dr_N</td><td>0.071</td><td>0.0323</td><td>5.6 × 10<sup>-4</sup></td><td>1.67 × 10<sup>-4</sup></td><td>3.7 × 10<sup>-5</sup></td><td>3.80 × 10<sup>-5</sup></td><td>2.7 × 10<sup>-3</sup></td><td>1.92 × 10<sup>-3</sup></td><td></td></tr></tbody></table>

<footnote n="1">¹CV of input variable/CV of output variable × 100; (n) = the number of feedstuffs with CV<sub>ratio</sub> >50%</footnote>

<footnote n="2">²Grass silage, grass hay first and second growth, corn silage, alfalfa hay, fresh grass, fresh perennial ryegrass, fresh corn, and fresh white clover.</footnote>

<footnote n="3">³FLref = reference feeding level.</footnote>

<footnote n="4">⁴Average of CV<sub>ratio</sub> >50%.</footnote>

<footnote n="1">¹Output ~s(Input<sub>0</sub>) + s(Input<sub>1</sub>) + s(Input<sub>2</sub>) + ... + s(Input<sub>n</sub>); Output ~s(Input<sub>0</sub>) + s(Input<sub>1</sub>) + s(Input<sub>2</sub>) + ... + s(Input<sub>n</sub>).</footnote>

<footnote n="2">²FV = fill value (for the concentrates, it was the basal fill value; for the forages, it was the fill value for sheep).</footnote>

<footnote n="3">³Average of R² difference >0.4.</footnote>
<table><caption>**Table 6.** Changes in output variables predicted by INRAtion V5 according to changes in input variables, expressed as a normalized tangent<fnref n="1" /> (NTᵢⱼ, %)</caption><thead><tr><th rowspan="2">Item<sup>2</sup></th><th colspan="9">Output</th></tr><tr><th>MPY</th><th>ECH4</th><th>NUE</th><th>UN/TN</th><th>SRg</th><th>DMI</th><th>PDI</th><th>UFL</th><th>PDI/UFL</th></tr></thead><tbody><tr><td>CP</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>RF</td><td>30.6</td><td>1.7</td><td>-86.1</td><td>154</td><td>56.0</td><td>16.7</td><td>39.7</td><td>10.2</td><td>29.4</td></tr><tr><td>GH1</td><td>14.3</td><td>-0.2</td><td>-95.2</td><td>122</td><td>9.6</td><td>9.5</td><td>51.3</td><td>3.3</td><td>48.0</td></tr><tr><td>GH2</td><td>55.7</td><td>22.4</td><td>-64.1</td><td>77.7</td><td>97.4</td><td>19.9</td><td>65.4</td><td>38.2</td><td>27.2</td></tr><tr><td>GH3</td><td>25.6</td><td>4.2</td><td>-87.4</td><td>125</td><td>18.0</td><td>13.0</td><td>53.9</td><td>11.6</td><td>42.3</td></tr><tr><td>GS</td><td>33.9</td><td>-7.5</td><td>-89.9</td><td>165</td><td>35.0</td><td>23.7</td><td>49.2</td><td>2.0</td><td>47.2</td></tr><tr><td>CS</td><td>35.4</td><td>8.2</td><td>-78.5</td><td>142</td><td>43.4</td><td>13.9</td><td>48.9</td><td>16.9</td><td>32.0</td></tr><tr><td>SE</td><td>5.58</td><td>4.12</td><td>4.47</td><td>12.6</td><td>12.83</td><td>2.10</td><td>3.43</td><td>5.39</td><td>3.78</td></tr><tr><td>|Average|</td><td>32.6</td><td>7.4</td><td>83.5</td><td>131</td><td>43.2</td><td>16.1</td><td>51.4</td><td>13.7</td><td>37.7</td></tr><tr><td>|SE|</td><td>5.58</td><td>3.27</td><td>4.47</td><td>12.6</td><td>12.83</td><td>2.10</td><td>3.43</td><td>5.39</td><td>3.78</td></tr><tr><td>GE</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>RF</td><td>4.2</td><td>26.3</td><td>74.9</td><td>59.4</td><td>300</td><td>-70.7</td><td>-6.0</td><td>118</td><td>-124</td></tr><tr><td>GH1</td><td>82.8</td><td>6.2</td><td>96.5</td><td>50.2</td><td>60.6</td><td>-13.8</td><td>-1.4</td><td>113</td><td>-115</td></tr><tr><td>GH2</td><td>83.4</td><td>5.3</td><td>99.1</td><td>28.8</td><td>216</td><td>-15.7</td><td>-1.9</td><td>111</td><td>-114</td></tr><tr><td>GH3</td><td>90.7</td><td>9.2</td><td>109</td><td>57.3</td><td>90.6</td><td>-19.3</td><td>-1.5</td><td>131</td><td>-133</td></tr><tr><td>GS</td><td>-15.0</td><td>33.0</td><td>64.4</td><td>57.0</td><td>243</td><td>-79.5</td><td>-6.3</td><td>115</td><td>-121</td></tr><tr><td>CS</td><td>5.9</td><td>23.5</td><td>70.8</td><td>61.5</td><td>295</td><td>-64.9</td><td>-5.8</td><td>121</td><td>-127</td></tr><tr><td>SE</td><td>19.78</td><td>4.82</td><td>7.38</td><td>4.97</td><td>41.91</td><td>12.56</td><td>1.00</td><td>2.9</td><td>3.0</td></tr><tr><td>|Average|</td><td>47.0</td><td>17.3</td><td>85.8</td><td>52.4</td><td>201.0</td><td>44.0</td><td>3.8</td><td>118</td><td>122</td></tr><tr><td>|SE|</td><td>17.38</td><td>4.82</td><td>7.38</td><td>4.97</td><td>41.91</td><td>12.56</td><td>1.00</td><td>2.9</td><td>3.0</td></tr><tr><td>OMd</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>RF</td><td>60.5</td><td>109</td><td>98.0</td><td>41.2</td><td>392</td><td>-37.4</td><td>31.0</td><td>129</td><td>-97.7</td></tr><tr><td>GH1</td><td>127</td><td>97.8</td><td>118</td><td>39.2</td><td>46.4</td><td>8.6</td><td>29.8</td><td>134</td><td>-104</td></tr><tr><td>GH2</td><td>135</td><td>98.8</td><td>128</td><td>21.8</td><td>283</td><td>6.2</td><td>30.6</td><td>137</td><td>-107</td></tr><tr><td>GH3</td><td>121</td><td>98.4</td><td>115</td><td>38.0</td><td>47.6</td><td>6.0</td><td>29.7</td><td>130</td><td>-100</td></tr><tr><td>GS</td><td>29.4</td><td>119</td><td>101</td><td>47.0</td><td>269</td><td>-71.2</td><td>26.4</td><td>132</td><td>-105</td></tr><tr><td>CS</td><td>116</td><td>93.8</td><td>86.1</td><td>52.7</td><td>531</td><td>29.7</td><td>38.3</td><td>136</td><td>-97.9</td></tr><tr><td>SE</td><td>17.44</td><td>3.80</td><td>6.36</td><td>4.27</td><td>77.95</td><td>15.20</td><td>1.62</td><td>1.4</td><td>1.59</td></tr><tr><td>|Average|</td><td>98.0</td><td>102.7</td><td>107.7</td><td>40.0</td><td>261.6</td><td>26.5</td><td>31.0</td><td>133</td><td>101.9</td></tr><tr><td>|SE|</td><td>17.44</td><td>3.780</td><td>6.36</td><td>4.27</td><td>77.95</td><td>10.45</td><td>1.62</td><td>1.4</td><td>1.59</td></tr><tr><td>ED6_N</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>RF</td><td>-48.9</td><td>13.5</td><td>-15.7</td><td>0.6</td><td>30.6</td><td>-33.1</td><td>-92.1</td><td>5.3</td><td>-97.4</td></tr><tr><td>GH1</td><td>-2.9</td><td>4.5</td><td>&lt;0.1</td><td>16.2</td><td>7.4</td><td>-2.9</td><td>-64.4</td><td>4.7</td><td>-69.1</td></tr><tr><td>GH2</td><td>-6.0</td><td>3.0</td><td>0.6</td><td>0.4</td><td>40.7</td><td>-6.5</td><td>-101</td><td>1.8</td><td>-102</td></tr><tr><td>GH3</td><td>-5.4</td><td>4.6</td><td>-1.5</td><td>12.9</td><td>11.0</td><td>-4.1</td><td>-68.1</td><td>4.2</td><td>-72.3</td></tr><tr><td>GS</td><td>-55.6</td><td>16.3</td><td>-20.2</td><td>1.8</td><td>17.4</td><td>-35.4</td><td>-92.7</td><td>6.6</td><td>-99.2</td></tr><tr><td>CS</td><td>-33.6</td><td>15.3</td><td>-7.6</td><td>24.3</td><td>54.7</td><td>-26.0</td><td>-65.1</td><td>11.2</td><td>-76.2</td></tr><tr><td>SE</td><td>9.69</td><td>2.49</td><td>3.59</td><td>4.41</td><td>7.52</td><td>6.19</td><td>6.67</td><td>1.28</td><td>6.17</td></tr><tr><td>|Average|</td><td>25.4</td><td>9.5</td><td>7.6</td><td>9.4</td><td>27.0</td><td>18.0</td><td>80.5</td><td>5.6</td><td>86.1</td></tr><tr><td>|SE|</td><td>9.69</td><td>2.49</td><td>3.51</td><td>4.06</td><td>7.52</td><td>6.19</td><td>6.67</td><td>1.28</td><td>6.17</td></tr><tr><td>dr_N</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>RF</td><td>23.3</td><td>-5.5</td><td>8.3</td><td>54.5</td><td>-11.9</td><td>15.0</td><td>43.3</td><td>-1.6</td><td>44.9</td></tr><tr><td>GH1</td><td>3.9</td><td>-0.7</td><td>2.1</td><td>57.9</td><td>-4.0</td><td>1.9</td><td>49.0</td><td>-0.1</td><td>49.1</td></tr><tr><td>GH2</td><td>4.5</td><td>-1.0</td><td>1.2</td><td>33.6</td><td>-19.1</td><td>3.3</td><td>51.5</td><td>-0.3</td><td>51.9</td></tr><tr><td>GH3</td><td>4.9</td><td>-1.1</td><td>2.5</td><td>57.6</td><td>-6.1</td><td>2.5</td><td>48.9</td><td>-0.3</td><td>49.2</td></tr><tr><td>GS</td><td>26.0</td><td>-6.7</td><td>9.5</td><td>59.5</td><td>-6.1</td><td>16.5</td><td>45.3</td><td>-2.0</td><td>47.3</td></tr><tr><td>CS</td><td>25.1</td><td>-5.4</td><td>9.5</td><td>61.6</td><td>-24.9</td><td>15.5</td><td>47.0</td><td>-1.9</td><td>48.9</td></tr><tr><td>SE</td><td>4.57</td><td>1.13</td><td>1.63</td><td>4.22</td><td>3.42</td><td>2.95</td><td>1.20</td><td>0.36</td><td>0.94</td></tr><tr><td>|Average|</td><td>14.6</td><td>3.4</td><td>5.5</td><td>54.1</td><td>12.0</td><td>9.1</td><td>47.5</td><td>1.0</td><td>48.6</td></tr><tr><td>|SE|</td><td>4.57</td><td>1.13</td><td>1.63</td><td>4.22</td><td>3.42</td><td>2.95</td><td>1.20</td><td>0.36</td><td>0.94</td></tr></tbody></table>

²|Average| = average of absolute NTᵢⱼ values; |SE| = standard error of absolute NTᵢⱼ values.

**Effective Degradability of Nitrogen.** The final animal response most affected by ED6_N was MPY (|NTED6_N,MPY| = 25.4 ± 9.69%), the others being less affected (|NTED6_N,ECH4| = 9.5 ± 2.49%; |NTED6_N,NUE| = 7.6 ± 3.51%; |NTED6_N,UN/TN| = 9.4 ± 4.06%). All 4 of the these

responses differed according to diet (CV of TED6_N,MPY = -92.0%; CV of TED6_N,ECH4 = 67.1%; CV of TED6_N,NUE = -118%; CV of TED6_N,UN/TN = 121%; Figure 10), with MPY being most affected by the RF, GS, and CS diets. Global substitution rate varied nonlinearly and DMI decreased

<footnote n="1">¹Normalized sensitivity coefficient (%); NTᵢⱼ (%) = $\frac{\Delta y_j}{\Delta x_i} \times \frac{Avg(x_{1i}, x_{2i})}{Avg(y_{1j}, y_{2j})} \times 100 = \frac{y_{2j} - y_{1j}}{x_{2i} - x_{1i}} \times \frac{Avg(x_{1i}, x_{2i})}{Avg(y_{1j}, y_{2j})} \times 100$; where i is one input variable, j is one output variable, xᵢ and xⱼ are the input variable values closest to the reference value, and yᵢ and yⱼ are the values of the output variable when x is xᵢ and xⱼ, respectively.</footnote>
<table><caption>**Table 7.** Variation of the response of output to input variabilities around the reference situation, expressed as the CV (SD/mean value of tangent, %)</caption><thead><tr><th rowspan="2">Input</th><th colspan="9">Output</th></tr><tr><th>MPY</th><th>ECH4</th><th>NUE</th><th>UN/TN</th><th>SRg</th><th>DMI</th><th>PDI</th><th>UFL</th><th>PDI/UFL</th></tr></thead><tbody><tr><td>CP</td><td>34.3</td><td>214</td><td>-25.4</td><td>22.7</td><td>61.4</td><td>30.5</td><td>13.1</td><td>86.3</td><td>32.1</td></tr><tr><td>GE</td><td>115</td><td>73.1</td><td>12.9</td><td>-16.7</td><td>60.1</td><td>-67.8</td><td>-60.4</td><td>9.5</td><td>-12.1</td></tr><tr><td>OMd</td><td>46.6</td><td>10.6</td><td>9.7</td><td>-19.3</td><td>81.8</td><td>-443</td><td>14.8</td><td>3.5</td><td>-18.9</td></tr><tr><td>ED6_N</td><td>-92.0</td><td>67.1</td><td>-118</td><td>121</td><td>78.6</td><td>-80.7</td><td>-21.8</td><td>58.3</td><td>-15.2</td></tr><tr><td>dr_N</td><td>76.2</td><td>-83.6</td><td>77.2</td><td>14.3</td><td>-80.3</td><td>77.3</td><td>12.5</td><td>-86.9</td><td>17.3</td></tr></tbody></table>

in response to ED6_N (Figure 11; $|NT_{ED6_N,SRg}| = 27.0 \pm 7.52\%$; $|NT_{ED6_N,DMI}| = 18.0 \pm 6.19\%$). The responses differed according to diet (CV of $T_{ED6_N,SRg} = 78.6\%$; CV of $T_{ED6_N,DMI} = -80.7\%$), with the decrease in DMI being

more marked for the RF, GS, and CS diets. Variation in ED6_N affected PDI more than UFL ($|NT_{ED6_N,PDI}| = 80.5 \pm 6.67\%$; $|NT_{ED6_N,PDI/UFL}| = 86.1 \pm 6.17\%$; $|NT_{ED6_N,UFL}| = 5.6 \pm 1.28\%$). The responses of PDI and PDI/UFL

<figure><img src="image_2.png" /><figcaption>**Figure 1.** Responses of (a) milk protein yield (g/d), (b) energy in methane (kcal/kg DM), (c) nitrogen utilization efficiency (N in milk, g/N intake g), and (d) urinary nitrogen/total excreted nitrogen (g/g) when CP (g/kg DM) is varied. The white square with a solid green line is RF, the black square with a dashed orange line is GH1, the white circle with a dotted yellow line is GH2, the black circle with a dotted-dashed brown line is GH3, the white triangle with a long-dashed blue line is GS, and the black triangle with a 2-dashed purple line is CS. Each mark indicates the reference point for each diet, and the accompanying numbers are the tangent values at each point (output unit/input unit).</figcaption></figure>
<figure><img src="image_3.png" /><figcaption>**Figure 2.** Responses of (a) global substitution rate of concentrate (kg DM/kg DM) and (b) DMI (kg/d) when CP (g/kg DM) is varied. The white square with a solid green line is RF, the black square with a dashed orange line is GH1, the white circle with a dotted yellow line is GH2, the black circle with a dotted-dashed brown line is GH3, the white triangle with a long-dashed blue line is GS, and the black triangle with a 2-dashed purple line is CS. Each mark indicates the reference point for each diet, and the accompanying numbers are the tangent values at each point (output unit/input unit).</figcaption></figure>

were not affected by diet (CV of $T_{ED6\_N,PDI} = -21.8\%$; CV of $T_{ED6\_N,PDI/UFL} = -15.2\%$), whereas the low average response of UFL differed slightly among diets (CV of $T_{ED6\_N,UFL} = 58.3\%$; Figure 12).

**True Intestinal Digestibility of Nitrogen.** The final animal response most affected by dr_N was UN/TN ratio ($|NT_{dr\_N,UN/TN}| = 54.1 \pm 4.22\%$), and to a lesser extent MPY, NUE, and ECH4 ($|NT_{dr\_N,MPY}| = 14.6 \pm 4.57\%; |NT_{dr\_N,NUE}| = 5.5 \pm 1.63\%; |NT_{dr\_N,ECH4}| = 3.4 \pm 1.13\%$).

The response of UN/TN ratio did not differ across the diets (CV of $T_{dr\_N,UN/TN} = 14.3\%$), but the other responses were more affected by diet (CV of $T_{dr\_N,MPY} = 76.2\%$; CV of $T_{dr\_N,ECH4} = -83.6\%$; CV of $T_{dr\_N,NUE} = 77.2\%$; Figure 13), particularly MPY with the RF, GS, and CS diets. The responses of SRg differed depending on diet. With the RF, GS, and CS diets, SRg increased and then decreased; with the other 3 diets, SRg decreased (Figure 14; $T_{dr\_N,SRg} = -5 \cdot 10^{-4} \pm 1.5 \cdot 10^{-4}$). Dry matter intake increased with

<figure><img src="image_4.png" /><figcaption>**Figure 3.** Responses of (a) protein truly digestible in the intestine (g/kg DM), (b) UFL (/kg DM), and (c) PDI/UFL (g PDI/UFL) when CP (g/kg DM) is varied. The white square with a solid green line is RF, the black square with a dashed orange line is GH1, the white circle with a dotted yellow line is GH2, the black circle with a dotted-dashed brown line is GH3, the white triangle with a long-dashed blue line is GS, and the black triangle with a 2-dashed purple line is CS. Each mark indicates the reference point for each diet, and the accompanying numbers are the tangent values at each point (output unit/input unit).</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Figure 4.** Responses of (a) milk protein yield (g/d), (b) energy in methane (kcal/kg DM), (c) nitrogen utilization efficiency (N in milk, g/N intake g), and (d) urinary nitrogen/total excreted nitrogen (g/g) when gross energy (GE, kcal/kg DM) is varied. The white square with a solid green line is RF, the black square with a dashed orange line is GH1, the white circle with a dotted yellow line is GH2, the black circle with a dotted-dashed brown line is GH3, the white triangle with a long-dashed blue line is GS, and the black triangle with a 2-dashed purple line is CS. Each mark indicates the reference point for each diet, and the accompanying numbers are the tangent values at each point (output unit/input unit).</figcaption></figure>

all diets as dr_N increased, and the response also differed depending on diet (CV of T<sub>dr_N,DMI</sub> = 77.3%), being greater with the RF, GS, and CS diets. Variation in dr_N affected PDI more than UFL (|NT<sub>dr_N,PDI</sub>| = 47.5 ± 1.20%; |NT<sub>dr_N,PDI/UFL</sub>| = 48.6 ± 0.94%; |NT<sub>dr_N,UFL</sub>| = 1.0 ± 0.36%). The responses of PDI and PDI/UFL were not affected by diet (CV of T<sub>dr_N,PDI</sub> = 12.5%; CV of T<sub>dr_N,PDI/UFL</sub> = 17.3%), whereas the low response of UFL differed slightly among the diets (CV of T<sub>dr_N,UFL</sub> = -86.9%; Figure 15).

DISCUSSION

**Feedstuff: Screening for Selection of Key**
**Input Variables**

The first step of SA is to analyze the contribution of
each input variable to the output variable to select key

input variables (Ge et al., 2015). The INRA 2018 feeding
system calculates the animal's responses according to the
characteristics of the diet, which are based on the char-
acteristics of the feedstuff. Consequently, input variables
with low impact at the feedstuff level could not have an
impact on the diet characteristics and animal responses.
Therefore, in this study, the screening of input variables
was first performed at the feedstuff level. For that, in
the present study, 2 types of analysis methods (OAT and
GAM) were used in terms of feedstuff to screen key input
variables for SA in terms of diet. In the OAT analysis
conducted using the CV<sub>ratio</sub>, it is possible to evaluate the
individual impact of each input variable on each output
variable. However, OAT analysis does not consider the
interaction between input variables. To address this
limitation, GAM fitting was used because, unlike OAT
<figure><img src="image_6.png" /><figcaption>**Figure 5.** Responses of (a) global substitution rate of concentrate (kg DM/kg DM) and (b) DMI (kg/d) when gross energy (GE, kcal/kg DM) is varied. The white square with a solid green line is RF, the black square with a dashed orange line is GH1, the white circle with a dotted yellow line is GH2, the black circle with a dotted-dashed brown line is CS, the white triangle with a long-dashed blue line is GS, and the black triangle with a 2-dashed purple line is CS. Each mark indicates the reference point for each diet, and the accompanying numbers are the tangent values at each point (output unit/input unit).</figcaption></figure>

analysis, it does not require varying one input variable at a time to evaluate output responses. Although 5 key input variables were selected based on this hypothesis, NT analysis at the diet and animal response levels was performed on all 12 input variables to verify that no influential input variables are lost through the screening process in terms of feedstuff level. This was confirmed by the results presented in Supplemental Tables S3 and S4 (Jeon et al., 2024). In the OAT analysis, CP, GE,

OMd, ED6_N, and dr_N showed a CV<sub>ratio</sub> higher than 50%, whereas in GAM only OMd and ED6_N showed models with a difference in R<sup>2</sup> higher than 0.4. Although only OMd and ED6_N were key input variables revealed by the GAM approach, it was decided to keep the 5 key input variables revealed by OAT for further SA in terms of diet. The significant impact of ADF and NDF on UFL and RPB revealed by the OAT approach for forages was related to their effect on OMd. Because the retained key

<figure><img src="image_7.png" /><figcaption>**Figure 6.** Responses of (a) protein truly digestible in the intestine (g/kg DM), (b) UFL (/kg DM), and (c) PDI/UFL (g PDI/UFL) when GE (kcal/kg DM) is varied. The white square with a solid green line is RF, the black square with a dashed orange line is GH1, the white circle with a dotted yellow line is GH2, the black circle with a dotted-dashed brown line is GH3, the white triangle with a long-dashed blue line is GS, and the black triangle with a 2-dashed purple line is CS. Each mark indicates the reference point for each diet, and the accompanying numbers are the tangent values at each point (output unit/input unit).</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>**Figure 7.** Responses of (a) milk protein yield (g/d), (b) energy in methane (kcal/kg DM), (c) nitrogen utilization efficiency (N in milk, g/N intake g), and (d) Urinary nitrogen/total excreted nitrogen (g/g) when OM apparent digestibility (OMd, %) is varied. The white square with a solid green line is RF, the black square with a dashed orange line is GH1, the white circle with a dotted yellow line is GH2, the black circle with a dotted-dashed brown line is GH3, the white triangle with a long-dashed blue line is GS, and the black triangle with a 2-dashed purple line is CS. Each mark indicates the reference point for each diet, and the accompanying numbers are the tangent values at each point (output unit/input unit).</figcaption></figure>

input variables already include OMd for both forages and concentrates, ADF and NDF were excluded from the list of input variable despite the importance of fiber in ruminant nutrition.

As the operational feed units in the INRA 2018 feed-
ing system are PDI, UFL, UE, the 5 key input variables
revealed by SA in terms of feedstuff appeared consistent.
Indeed, PDI mainly depends on CP, OMd, ED6_N, and
dr_N. In addition, PDI consists of a part originating
from diet (PDIA) and a part originating from microbes
(PDIM). It is known that ED6_N and dr_N mainly af-
fect PDIA and that OMd affects PDIM. Furthermore, se-
quential losses in energy between GE, DE, ME, and UFL
depend highly on energy in feces (i.e., on OMd), urine,
and gas (i.e., on CP and OMd, respectively), as well as

extra heat (i.e., on ME/GE). Lastly, UE is highly depen-
dent on OMd. The SA revealed OMd as a common major
input for PDI, UFL, and UE feed value, and that OMd
is also the main criterion to which digestive interactions
between feedstuffs are applied (INRA, 2018).

Diet: Quantification of the Impact of Key
Input Variables

**Sensitivity Analysis Methods.** The OAT approach allows the identification of input variables that are par- ticularly influential on the outputs and the determination of the significance of input variables (Lomas and Eppel, 1992). Therefore, the OAT approach has been widely used in various fields to evaluate the influence of each
<figure><img src="image_9.png" /><figcaption>**Figure 8.** Responses of (a) global substitution rate of concentrate (kg DM/kg DM) and (b) DMI (kg/d) when OM apparent digestibility (OMd, %) is varied. The white square with a solid green line is RF, the black square with a dashed orange line is GH1, the white circle with a dotted yellow line is GH2, the black circle with a dotted-dashed brown line is GH3, the white triangle with a long-dashed blue line is GS, and the black triangle with a 2-dashed purple line is CS. Each mark indicates the reference point for each diet, and the accompanying numbers are the tangent values at each point (output unit/input unit).</figcaption></figure>

variable on the model (Groen et al., 2014). However, in general, the SI in OAT analysis is calculated as the variation of the output variable compared with the variation of the input variable (Jouven et al., 2008; Binggeli et al., 2022), as applied to feedstuff in the present study. This is a method that can effectively quantify variability when all models are linear (Saltelli et al., 2005). However, as most responses relating input variables to output variables in terms of diet are nonlinear in the INRA 2018

feeding system, a different quantitative approach was needed. Therefore, in the present study, the sensitivity of the output variable to the variation per unit of the input variable was quantified as the tangent value at the reference point. In addition, by calculating the NT value, which is a normalized SI unit, it is possible to compare the respective variations of the output variables with respect to the variation of each input variable (Hughes et al., 2013).

<figure><img src="image_10.png" /><figcaption>**Figure 9.** Responses of (a) protein truly digestible in the intestine (g/kg DM), (b) UFL (/kg DM), and (c) PDI/UFL (g PDI/UFL) when OM apparent digestibility (OMd, %) is varied. The white square with a solid green line is RF, the black square with a dashed orange line is GH1, the white circle with a dotted yellow line is GH2, the black circle with a dotted-dashed brown line is GH3, the white triangle with a long-dashed blue line is GS, and the black triangle with a 2-dashed purple line is CS. Each mark indicates the reference point for each diet, and the accompanying numbers are the tangent values at each point (output unit/input unit).</figcaption></figure>
<figure><img src="image_11.png" /><figcaption>**Figure 10.** Responses of (a) milk protein yield (g/d), (b) energy in methane (kcal/kg DM), (c) Nitrogen utilization efficiency (N in milk, g/N intake g), and (d) urinary nitrogen/total excreted nitrogen (g/g) when effective degradability of nitrogen assuming a passage rate of 6%/h (ED6_N, %) is varied. The white square with a solid green line is RF, the black square with a dashed orange line is GH1, the white circle with a dotted yellow line is GH2, the black circle with a dotted-dashed brown line is GH3, the white triangle with a long-dashed blue line is GS, and the black triangle with a 2-dashed purple line is CS. Each mark indicates the reference point for each diet, and the accompanying numbers are the tangent values at each point (output unit/input unit).</figcaption></figure>

**Influence of Input Variables on PDI and UFL.** The 5 main input variables tested in this study can be broadly divided into energy-related (UFL) and protein-related (PDI) variables. As a result of the SA, and as expected, OMd and GE had more influence on UFL, whereas CP, ED6_N, and dr_N had more influence on PDI, and especially on the dietary (PDIA) fraction (Table 6). The contribution of CP and ED6_N to the variation of PDIM was smaller and depended mainly on microbial protein synthesis, and thus on OMd via fermentable OM (Sauvant and Nozière, 2016).

**Most Affected Output Variables Are Related to Nitrogen Efficiency.** Among the 4 main final output variables retained in the present study (i.e., MPY, UN/TN, ECH4, and NUE), UN/TN and NUE were the most highly in-

fluenced by variation in the input variables. These 2 variables are related to N partitioning. Indeed, variations in N excreted through urine mainly refer to the excess in the rumen degradable N and in metabolizable protein (i.e., PDI), and fecal N mainly refers to the apparently undigested N. The variations in the UN/TN ratio were highly and negatively correlated with the variations in NUE (N milk/N intake, i.e., nitrogen efficiency) when input variables were OMd, CP, or GE (r = -1.00; data not shown). However, when the input variable was dr_N, we found a strong positive linear correlation between both output variations (r = 0.95), and when the input variable was ED6_N, the correlation between both was weak (r = -0.21). This reflects the fact that for a given animal at a given level of N intake, the digestive utilization of
<figure><img src="image_12.png" /><figcaption>**Figure 11.** Responses of (a) global substitution rate of concentrate (kg DM/kg DM) and (b) DMI (kg/d) when effective degradability of nitrogen assuming a passage rate of 6%/h (ED6_N, %) is varied. The white square with a solid green line is RF, the black square with a dashed orange line is GH1, the white circle with a dotted yellow line is GH2, the black circle with a dotted-dashed brown line is GH3, the white triangle with a long-dashed blue line is GS, and the black triangle with a 2-dashed purple line is CS. Each mark indicates the reference point for each diet, and the accompanying numbers are the tangent values at each point (output unit/input unit).</figcaption></figure>

protein (ED6_N and dr_N) highly affects N partitioning between milk, urine, and feces. In other words, the responses of NUE and UN/TN are not always related, depending on the dietary variation factor. Thus, this emphasizes the need to assess indicators of N utilization not only for production (i.e., NUE), but also for its environmental impact (i.e., UN/TN).

**Least Affected Output Variable.** Among the 4 retained final output variables, ECH4 was the least affected by

the fluctuation of input variables, except by OMd. In the model (INRA, 2018), ECH4 is calculated with OM, OMd, proportion of concentrate, and feeding level. In our simulation, OM and proportion of concentrate were fixed values for each diet, and when considering the input variables other than OMd, the variation in dietary OMd was small, so we presume that the variation of ECH4 was small.

**Milk Protein Yield Response.** In the INRA 2018 feeding system, for a given animal, the MPY is calculated

<figure><img src="image_13.png" /><figcaption>**Figure 12.** Responses of (a) protein truly digestible in the intestine (g/kg DM), (b) UFL (/kg DM), and (c) PDI/UFL (g PDI/UFL) when effective degradability of nitrogen assuming a passage rate of 6%/h (ED6_N, %) is varied. The white square with a solid green line is RF, the black square with a dashed orange line is GH1, the white circle with a dotted yellow line is GH2, the black circle with a dotted-dashed brown line is GH3, the white triangle with a long-dashed blue line is GS, and the black triangle with a 2-dashed purple line is CS. Each mark indicates the reference point for each diet, and the accompanying numbers are the tangent values at each point (output unit/input unit).</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>**Figure 13.** Responses of (a) milk protein yield (g/d), (b) energy in methane (kcal/kg DM), (c) nitrogen utilization efficiency (N in milk, g/N intake g), and (d) urinary nitrogen/total excreted nitrogen (g/g) when true intestinal digestibility (dr_N, %) is varied. The white square with a solid green line is RF, the black square with a dashed orange line is GH1, the white circle with a dotted yellow line is GH2, the black circle with a dotted-dashed brown line is GH3, the white triangle with a long-dashed blue line is GS, and the black triangle with a 2-dashed purple line is CS. Each mark indicates the reference point for each diet, and the accompanying numbers are the tangent values at each point (output unit/input unit).</figcaption></figure>

from the PDI and UFL balances (supply – theoretical requirements) and their interactions, adjusted by the LysDI and MetDI contents. The response model, as well as the response model of DMI to the PDI/UFL ratio is nonlinear. In the model, MPY responds at a low level of UFL balance and reaches a plateau at a high level of UFL balance. This explains the variability of some responses to input variables between diets. Although MPY increased almost linearly with increasing CP with all diets, it increased with increasing GE with grass hay-based diets but showed a parabolic curve with the other diets (Figure 4). With grass hay-based diets, it is mainly related to a decrease in the PDI/UFL ratio, without a significant change in DMI in the range where MPY positively responds to change in UFL balance, whereas with the other

diets, both PDI/UFL and DMI decrease with increasing GE, leading to a less predictable nutritional balance and MPY response in the range where MPY is less responsive to changes in UFL balance.

**Response of DMI to Variations in Input Variables**

When the input variable was GE, ED6_N, or dr_N, the responses of SRg and DMI showed opposite tendencies, and when the input was OMd, SRg increased for all diets, but the response of DMI differed depending on the diet. In the INRA 2018 feeding system, for a given animal, SRg is one of the factors involved in the prediction of DMI. Likewise, other dietary factors, such as the fill value of forage and the proportion of concentrate, as well as the intake capacity (which is affected by the PDI/UFL ratio), are involved in the prediction of DMI (Vérité and
<figure><img src="image_15.png" /><figcaption>**Figure 14.** Responses of (a) global substitution rate of concentrate (kg DM/kg DM) and (b) DMI (kg/d) when true intestinal digestibility (dr_N, %) is varied. The white square with a solid green line is RF, the black square with a dashed orange line is GH1, the white circle with a dotted yellow line is GH2, the black circle with a dotted-dashed brown line is GH3, the white triangle with a long-dashed blue line is GS, and the black triangle with a 2-dashed purple line is CS. Each mark indicates the reference point for each diet, and the accompanying numbers are the tangent values at each point (output unit/input unit).</figcaption></figure>

Delaby, 2000; Faverdin et al., 2003; INRA, 2018), and the fill value of forage is itself regulated by DMI. This is why the responses of SRg and DMI to variations in input variables were not always correlated in our study.

**Variation According to Diet.** Some results differ according to diet. This is especially remarkable when the average |NT| value was low. When considering cases where the |CV| of the tangent at the reference point was greater than 62% (average CV value of all outputs; Table

7), the average |NT| value was less than 30%, except for some cases (|NT<sub>OMd,SRg</sub>| and |NT<sub>GE,MPY</sub>|; Table 6). At this time, when analyzing the results according to diet, 2 groups could be distinguished: grass hay-based diets (GH1, GH2, and GH3) versus the other diets (RF, GS, and CS). Furthermore, the correlations between tangent (or NT) values and diet characteristics (CP, GE, OMd, ED6_N, dr_N, PDI, UFL, PDI/UFL, and SRg) at reference points were calculated. For ECH4 (with GE, CP,

<figure><img src="image_16.png" /><figcaption>**Figure 15.** Responses of (a) protein truly digestible in the intestine (g/kg DM), (b) UFL (/kg DM), and (c) PDI/UFL (g PDI/UFL) when true intestinal digestibility (dr_N, %) is varied. The white square with a solid green line is RF, the black square with a dashed orange line is GH1, the white circle with a dotted yellow line is GH2, the black circle with a dotted-dashed brown line is GH3, the white triangle with a long-dashed blue line is GS, and the black triangle with a 2-dashed purple line is CS. Each mark indicates the reference point for each diet, and the accompanying numbers are the tangent values at each point (output unit/input unit).</figcaption></figure>
ED6_N, and dr_N as input variables), MPY (with GE, ED6_N, and dr_N), and DMI (with OMd, ED6_N, and dr_N), the correlation was the highest (average R² ≥ 0.72) with PDI/UFL than with other reference diet characteristics, such as GE and dr_N (average R² ≤ 0.13). In addition, this trend was remarkable when the input variable was dr_N or ED6_N, which may be linked to the fact that these variables have a great influence on PDI and the PDI/UFL ratio. Moreover, PDI/UFL regulates feed intake in the model (Vérité and Delaby, 2000; Favardin et al., 2003), and variations in MPY and ECH4 are highly related to DMI. In addition, responses of MPY depend on both UFL and PDI balances through their interactions (Brun-Lafleur et al., 2010; Daniel et al., 2016). Thus, if SI values differ according to diet, this may not be related to the characteristics of each feedstuff, but rather to the dietary PDI/UFL ratio of the reference diet.

## CONCLUSIONS

The methods developed through this study allowed to quantify and compare the responses of the output variables in relation to five main input variables variations of the INRA 2018 feeding system. Notably, the outputs were more influenced by changes in CP, GE, and OMd. In particular, OMd had a significant effect on MPY, ECH4, and NUE. Conversely, ED6_N and dr_N showed on average lower impact on DMI, ECH4, and MPY. However, responses varied across diets, primarily according to their PDI/UFL ratio. In addition, these results can be used to establish a safety margin when formulating a diet for dairy cattle, even if the variability of input variables is not well known. However, although the present study included 6 representative diets typically encountered for dairy cows in France, the study of more diverse diets, animal characteristics, and rationing objectives is needed to provide more predictive information.

## NOTES

This research was supported by the INRAE Animal Physiology and Livestock Systems Division (Toulouse, France). The authors thank the committees, Rémy Delagarde, René Baumont, Luc Delaby, Yayu Huang, Patrick Chapoutot, and Gaëlle Maxin, for advice on analysis of diet rationing and explaining the results. Supplemental material for this article is available at https://entrepot.recherche.data.gouv.fr/dataset.xhtml?persistentId=doi:10.57745/ERYQ18. No human or animal subjects were used, so this analysis did not require approval by an Institutional Animal Care and Use Committee or Institutional Review Board. The authors have not stated any conflicts of interest.

**Abbreviations used:** |Average| = average of absolute NTᵢⱼ values; |SE| = standard error of absolute NTᵢⱼ values; bFVc = basal fill value of concentrate; CS = corn silage; dr_N = true intestinal digestibility of nitrogen (digestibilité réelle); ECH4 = energy in methane; ED6_N = effective degradability of nitrogen assuming a passage rate of 6%/h; ED6_St = effective degradability of starch assuming a passage rate of 6%/h; EE = ether extract; FL-ref = feeding level of reference; FV = fill value; GAM = generalized additive model; GE = gross energy; GH1 = first growth grass hay-based diet; GH2 = second growth grass hay-based diet; GH3 = first and second growth grass hay-based diet; GS = grass silage-based diet; INRA = French National Institute of Agricultural Research; LHS = Latin hypercube sampling; LysDI = lysine truly digestible in the intestine; MetDI = methionine truly digestible in the intestine; MPY = milk protein yield; NT = normalized tangent; NUE = N utilization efficiency; OAT = one-at-a-time; OMd = OM apparent digestibility; PDI = protein truly digestible in the intestine; PDIA = PDI of alimentary origin; PDIM = PDI of microbial origin; RF = fresh perennial ryegrass-based diet; RPB = rumen protein balance; SA = sensitivity analysis; SI = sensitivity index; SRg = global substitution rate; T = tangent; UE = fill value; UEL; fill value for dairy (Unité d'Encombrement Lait); UEM = fill value for sheep (Unité d'Encombrement Moutons); UFL = net energy for lactation (Unité Fourragère Lait); UN/TN = ratio between urine and total N excretion.

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## ORCIDS

Seoyoung Jeon https://orcid.org/0000-0002-8276-317X

Sophie Lemosquet https://orcid.org/0000-0002-1077-1285

Anne-Cécile Toulemonde https://orcid.org/0009-0008-3999-9110

Tristan Senga Kiessé https://orcid.org/0000-0003-2710-5825

Pierre Nozière https://orcid.org/0000-0003-1727-8984