Dynamic sensitivity analysis of a mathematical model describing the effect of the macroalgae Asparagopsis taxiformis on rumen fermentation and methane production under in vitro continuous conditions
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Abstract
Ruminants play an important role in global warming by emitting enteric methane (CH 4 ) through the degradation of feeds by the rumen microbiota. To better understand the dynamics fermentation outputs, including CH 4 and volatile fatty acids (VFA) production, mathematical models have been developed. Sensitivity analysis (SA) methods quantify the contribution of model input parameters (IP) to the variation of an output variable of interest. In animal science, SA are usually conducted in static condition. In this work, we hypothesized that including the dynamic aspect of the rumen fermentation to SA can be useful to inform on optimal experimental conditions aimed at quantifying the key mechanisms driving CH 4 and VFA production. Accordingly, the objective of this work was to conduct a dynamic SA of a rumen fermentation model under in vitro continuous conditions (close to the real in vivo conditions). Our model case study integrates the effect of the macroalgae Asparagopsis taxiformis (AT) on the fermentation. AT has been identified as a potent CH 4 inhibitor via the presence of bromoform, an anti-methanogenic compound. We computed Shapley effects over time for quantifying the contribution of 16 IPs to CH 4 (mol/h) and VFA (mol/l) variation. Shapley effects integrate the three contribution types of an IP to output variable variation (individual, via the interactions and via the dependence/correlation). We studied three diet scenarios accounting for several doses of AT relative to Dry Matter (DM): control (0% DM of AT), low treatment (LT: 0.25% DM of AT) and high treatment (HT: 0.50% DM of AT). Shapley effects revealed that hydrogen (H 2 ) utilizers microbial group via its Monod H 2 affinity constant highly contributed (> 50%) to CH 4 variation with a constant dynamic over time for control and LT. A shift on the impact of microbial pathways driving CH 4 variation was revealed for HT. IPs associated with the kinetic of bromoform utilization and with the factor modeling the direct effect of bromoform on methanogenesis were identified as influential on CH 4 variation in the middle of fermentation. Whereas, VFA variation for the three diet scenarios was mainly explained by the kinetic of fibers degradation, showing a high constant contribution (> 30%) over time. The simulations computed for the SA were also used to analyze prediction uncertainty. It was related to the dynamic of dry matter intake (DMI, g/h), increasing during the high intake activity periods and decreasing when the intake activity was low. Moreover, CH 4 (mol/h) simulations showed a larger variability than VFA simulations, suggesting that the reduction of the uncertainty of IPs describing the activity of the H 2 utilizers microbial group is a promising lead to reduce the overall model uncertainty. Our results highlighted the dynamic nature of the influence of metabolic pathways on CH 4 productions under an anti-methanogenic treatment. SA tools can be further exploited to design optimal experiments studying rumen fermentation and CH 4 mitigation strategies. These optimal experiments would be useful to build robust models that can guide the development of sustainable nutrition strategies.
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Reducing enteric methane emissions remains one of the key environmental and economic challenges in ruminant livestock systems. The red macroalgae Asparagopsis taxiformis has emerged as a promising natural feed additive for methane mitigation due to its bioactive compounds such as bromoform, which can inhibit methanogenesis in the rumen (Machado et al., 2014). While experimental studies have demonstrated its effect on reducing methane output, there is still a need to better understand the mechanistic underpinnings of this mitigation and how they interact dynamically within the rumen microbial ecosystem. In particular, modeling its impact under continuous fermentation conditions and assessing the sensitivity of key model parameters over time have not been extensively explored.
The present study by Blondiaux et al. (2024) addresses this …
Reducing enteric methane emissions remains one of the key environmental and economic challenges in ruminant livestock systems. The red macroalgae Asparagopsis taxiformis has emerged as a promising natural feed additive for methane mitigation due to its bioactive compounds such as bromoform, which can inhibit methanogenesis in the rumen (Machado et al., 2014). While experimental studies have demonstrated its effect on reducing methane output, there is still a need to better understand the mechanistic underpinnings of this mitigation and how they interact dynamically within the rumen microbial ecosystem. In particular, modeling its impact under continuous fermentation conditions and assessing the sensitivity of key model parameters over time have not been extensively explored.
The present study by Blondiaux et al. (2024) addresses this gap by performing a dynamic sensitivity analysis using the Shapley effects method on a previously developed mathematical model describing the effect of A. taxiformis on rumen fermentation and methane production under in vitro continuous conditions. This approach provides a robust global measure of parameter influence over time. The model outputs assessed include methane production, volatile fatty acid (VFA) profiles, and hydrogen concentration.
One of the most notable contributions of this study is the demonstration that sensitivity is not static but evolves dynamically over the course of the simulation. The analysis reveals that different parameters dominate influence at different time points and for different output variables. For example, the rate of bromoform release and its interaction with methanogenic inhibition are shown to exert varying levels of influence over time on methane concentration. These findings underscore the complex temporal interactions in the rumen microbial ecosystem and the value of using Shapley values to unravel them.
The manuscript is clearly written, logically structured, and demonstrates strong methodological rigor. The authors made commendable efforts to respond to reviewer feedback and further improved the clarity of their figures, terminology, and explanation of model assumptions. Their discussion of the rationale for using the Shapley procedure and their reflection on the implications of parameter influence over time are particularly insightful.
Nonetheless, the authors acknowledge that the model’s applicability to in vivo conditions still requires empirical validation, particularly for its assumptions around hydrogen dynamics and methanogen inhibition. Despite this, the study provides meaningful advances in the use of mathematical modeling for guiding experimental design and optimizing mitigation strategies in ruminant systems.
In conclusion, this study stands out for its scientific clarity, methodological depth, and relevance to ongoing efforts in precision livestock feeding and environmental sustainability. It contributes meaningful insights into the use of computational tools to complement empirical research and optimize methane mitigation strategies. I strongly recommend the publication of this preprint in PCI Animal Science.
References
Blondiaux P, Senga Kiessé T, Eugène M, Muñoz-Tamayo R. 2024. Dynamic sensitivity analysis of a mathematical model describing the effect of the macroalgae Asparagopsis taxiformis on rumen fermentation and methane production under in vitro continuous conditions. bioRxiv 2024.06.19.599712 ver. 2 peer-reviewed and recommended by PCI Animal Science. https://doi.org/10.1101/2024.06.19.599712
Machado L, Magnusson M, Paul NA, de Nys R, Tomkins N. 2014. Effects of marine and freshwater macroalgae on in vitro total gas and methane production. PLoS One 9,932 e85289. https://doi.org/10.1371/journal.pone.0085289 -
