High-yielding ruminants necessitate high-concentrate diets to meet their nutritional demands and production goals. However, such diets often lead to sub-acute ruminal acidosis (SARA), a metabolic disorder characterized by a decrease in rumen pH below physiological levels (typically below 6.0). SARA negatively impacts dry matter intake, cellulolysis, and overall production performance. The susceptibility to SARA varies significantly among animals within a herd, with some individuals exhibiting tolerance while others are highly susceptible. This inter-animal variability highlights the need for a quantitative approach to assess individual adaptation capacity to high-concentrate diets. Current methods for evaluating SARA typically rely on single measurements or simple indices of rumen pH, failing to capture the dynamic nature of the animal's response. Therefore, there is a critical need for a more comprehensive approach that can accurately quantify individual responses and identify potential biomarkers associated with resilience to SARA. The development of such an approach is crucial for precision livestock farming, allowing for tailored feeding strategies to optimize production while minimizing health risks. This research aims to address this gap by developing a novel modeling framework to quantify individual dairy goat responses to a high-concentrate diet challenge, using rumen pH as the primary indicator of acid status. By providing a quantitative measure of adaptation capacity, this approach contributes to improved understanding of animal resilience and enables more targeted feeding practices in precision livestock farming.

Several studies have explored the consequences of SARA in ruminants, emphasizing the negative impact on feed efficiency and production traits (Owens et al., 1998; Krause & Oetzel, 2006). The variable response to high-concentrate diets, with some animals exhibiting tolerance and others susceptibility, has been documented (Krause & Oetzel, 2005). Various indicators have been proposed to assess rumen acid status and SARA occurrence, including initial and final pH values, pH variation amplitude, and time spent below a specific pH threshold (Dragomir et al., 2008). However, a quantitative measure of individual animal response to dietary challenges, especially concerning the dynamic nature of rumen pH, has been lacking. Quantifying individual animal responses to dietary changes using appropriate metrics is crucial for identifying potential biomarkers of resilience and guiding breeding strategies toward more robust animals (Friggens et al., 2017). Studies have used various approaches to quantify animal responses to different perturbations such as feed restriction and weaning (Friggens et al., 2016; Nguyen-Ba et al., 2020; Revilla et al., 2019; Ben Abdelkrim et al., 2019), but these often focus on single time-scale measurements. The current study addresses the need for a robust method integrating multiple time scales to assess individual resilience to dietary changes.

This study used eight rumen-cannulated dairy goats (four Alpine and four Saanen) habituated to a low-concentrate diet (20% concentrate on a dry matter basis). The diet was abruptly switched to a high-concentrate diet (50% concentrate), formulated to be isoprotein. Rumen fluid was sampled before and at 1, 2, 4, and 6 h after morning and afternoon feedings for nine days, including two days before the diet change (d1 and d2), four consecutive days after the change (d3-d6), and once a week for the following three weeks (d7-d9). Rumen pH was measured immediately. The data analysis comprised three steps. Step 1 involved summarizing the post-prandial kinetics of [H+] (the logarithmic transformation of pH) using a three-parameter quadratic function: [H+](t) = f(t, v₀, A, R). Here, v₀ is the initial [H+], A is the amplitude of acidosis (difference between maximum [H+] and v₀), and R represents the recovery capacity 6 h after feeding. Additional synthetic variables were calculated from this model, including the duration of acidosis (dur), the amplitude of acidosis relative to a threshold θ (AmpAc), and the [H+] value at 6 h (var_θ). Step 2 used a mixed model for each synthetic variable to analyze the short- and long-term effects of the diet change, with individual goats as random effects. Fixed effects included the sampling week and day, allowing for assessment of both short-term (daily) and long-term (weekly) responses. Step 3 developed a metric based on health trajectories (Schneider, 2011; Lough et al., 2015) to quantify individual adaptive capacity. For synthetic variables with significant long-term effects, a daily score (s) ranging from -2 to 2 was assigned based on the daily changes in these variables. A decrease in both variables indicated better adaptation, weighted by the time interval between sampling days using the relative Euclidean distance (Model 3). A global index (GI) was calculated as the sum of weighted daily scores. Statistical analyses included Spearman correlation tests (for non-Gaussian data), likelihood ratio tests (ANOVA), and mixed-model analysis (lme4 package in R). The Shapiro-Wilk test was applied to check for normality, and a Box-Cox transformation was used when necessary.

Post-prandial [H+] kinetics varied considerably among goats (Figure 5). The re-parameterized quadratic model yielded biologically meaningful parameters (Figure 6, Table 1). Correlation analysis showed strong positive relationships between A (amplitude of acidosis) and AmpAc (amplitude of acidosis relative to the threshold), and a strong negative correlation between a (curvature of the original quadratic function) and both A and AmpAc. This highlights the importance of the model's re-parameterization in addressing biological meaning. The mixed-model analysis (Table 2) revealed that v₀ (initial [H+]) and A (amplitude of acidosis) were significantly affected by the week effect but not the day effect, indicating that goats could cope with the high-concentrate diet in the short term but exhibited long-term changes in rumen pH. The proportion of variance explained by individual differences was substantial for v₀ (56%) and A (17%), while it was lower for R (recovery capacity, 10%). The health trajectory analysis (Table 3, Figure 7) assigned daily scores and a global index to each goat, allowing the ranking of goats according to their adaptive capacity. Goat 8 exhibited the most favorable response, while Goats 1 and 7 showed the least favorable responses. Two main adaptation strategies were identified: minimizing pH variations and oscillating between increases and decreases. Analysis of pH data yielded similar results, although the use of [H+] was crucial for the accuracy of statistical analyses.

This study presents a novel approach for quantifying individual goat responses to a high-concentrate diet challenge, incorporating both short-term (hourly) and long-term (weekly) dynamics of rumen pH. The findings demonstrate considerable inter-individual variability in adaptive strategies, confirming the hypothesis that some goats are better equipped to cope with the challenge of high-concentrate diets. The three-step modeling procedure effectively integrates the two distinct time scales of post-prandial kinetics and the overall experimental duration. The use of [H+] instead of pH was crucial for appropriate statistical analyses. The two major adaptation strategies identified – minimizing pH variations or oscillating between increases and decreases – warrant further investigation to understand the underlying physiological and microbial mechanisms. This information is critical for designing tailored feeding strategies in precision livestock farming. The approach provides a valuable tool for identifying potential biomarkers of resilience, which could contribute to future breeding programs focused on selecting more robust animals.

This research introduces a novel three-step modelling approach to quantify the adaptive response of dairy goats to a high-concentrate diet challenge. The method successfully integrates two time scales of data, allowing the assignment of daily scores and a global index representing individual resilience. This generic approach can be extended to other performance indicators and dietary changes, thereby improving our understanding of animal adaptation and enabling more precise feeding strategies in livestock farming. Future research should explore the integration of other physiological and behavioral measures to further elucidate the mechanisms underlying these adaptive strategies. Moreover, the application of this method to larger datasets would enhance the statistical power and generalizability of the findings.

The study used a relatively small sample size (eight goats), which might limit the generalizability of the findings. Although the study rigorously addressed the challenges of integrating two time scales in the analysis, the chosen weighting scheme for the daily scores (relative Euclidean distance) is a strong assumption that should be explored further. Further investigation into the optimal methods of weighting based on time interval is warranted. Finally, additional data from different breeds and environmental conditions will improve the robustness and reliability of the proposed modelling approach.