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.

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., NEL) 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.

Generalized additive models reveal the intrinsic complexity of wood formation dynamics.

The intra-annual dynamics of wood formation, which involves the passage of newly produced cells through three successive differentiation phases (division, enlargement, and wall thickening) to reach the final functional mature state, has traditionally been described in conifers as three delayed bell-shaped curves followed by an S-shaped curve. Here the classical view represented by the 'Gompertz function (GF) approach' was challenged using two novel approaches based on parametric generalized linear models (GLMs) and 'data-driven' generalized additive models (GAMs). These three approaches (GFs, GLMs, and GAMs) were used to describe seasonal changes in cell numbers in each of the xylem differentiation phases and to calculate the timing of cell development in three conifer species [Picea abies (L.), Pinus sylvestris L., and Abies alba Mill.]. GAMs outperformed GFs and GLMs in describing intra-annual wood formation dynamics, showing two left-skewed bell-shaped curves for division and enlargement, and a right-skewed bimodal curve for thickening. Cell residence times progressively decreased through the season for enlargement, whilst increasing late but rapidly for thickening. These patterns match changes in cell anatomical features within a tree ring, which allows the separation of earlywood and latewood into two distinct cell populations. A novel statistical approach is presented which renews our understanding of xylogenesis, a dynamic biological process in which the rate of cell production interplays with cell residence times in each developmental phase to create complex seasonal patterns.