Sensitivity analysis of the INRA 2018 feeding system for ruminants by hybrid local and global approaches: Comparing the contribution of dietary input variables to multiple response prediction in dairy cattle

We conducted sensitivity analysis (SA) of the French National Institute of Agricultural Research (Institut national de la recherche agronomique; INRA) 2018 feeding system for ruminants applied to dairy cows. We evaluated which dietary input variables contribute most to changes in each output variable, considering the potential interactions presence among input variables. We applied a quantitative analysis (one-at-a-time analysis, OAT; i.e., local SA) and a relative comparative analysis (global SA; GSA) through variance-based SA considering potential interactions and nonmonotonicity. The 5 likely influential dietary input variables were selected: CP, gross energy (GE), OM apparent digestibility (OMd), effective degradability of nitrogen assuming a passage rate of 6%/h, and true intestinal digestibility of nitrogen. The sensitivity of 5 selected animal responses (output variables) to input variables was analyzed: DMI, milk protein yield (MPY), energy in methane (ECH4), nitrogen utilization efficiency (NUE), and the ratio between urine and total N excretion (UN/TN). Six diets for dairy cattle, reflecting the diversity of diets commonly used in practice, were formulated to meet 95% of the potential milk production (37.5 kg/d) of a multiparous dairy cow at wk 14 of lactation. For each diet, the 5 input variables were randomly sampled around the INRA 2018 feed table values (reference point), and the animal responses around this reference situation were calculated using the rationing software INRAtion V5. In OAT, the sensitivity of animal responses was quantified by calculating the normalized tangent value at the reference point, and in GSA, the Sobol indices were calculated for relative influence of each input and their interaction. The influence of the 5 key input variables on the 5 main animal responses predicted from the INRA feeding system was consistent across both SA approaches. With the 6 diets, GE and OMd appeared as the main contributors to changes in DMI, MPY, ECH4, and NUE. Crude protein was the main contributor to changes in UN/TN and another major contributor to changes in NUE. When considering OAT, the sensitivity of outputs showed differences depending on diet, more particularly for DMI and MPY. With grass hay–based diets (GH), DMI was less sensitive and MPY was more sensitive to variations in input variables than other diets. When considering GSA, interactions between input variables were also noticeable for DMI and MPY; the interactions were high with the GH diets for DMI, and with fresh ryegrass and grass silage diets for MPY. On the other hand, for MPY, the non-GH diets were less sensitive to variations in input variables, and the interaction between inputs was higher than with GH diets. Our results support the hypothesis that MPY, unlike DMI, is more responsive to energy-related factors at a high true intestinal digestible protein (PDI) to net energy for lactation (UFL) ratio (e.g., GH diets >117 g PDI/UFL), than at a lower PDI/UFL ratio. Hence, hybridizing the SA methods can help to interpret the system and facilitate a more precise evaluation thereof, especially GSA, which is amenable to nonmonotonic models such as those characterizing complex feeding systems integrating multiple nutritional and animal factors.