Carbohydrate feed fractions are generally divided into at least four fractions: degradable starch, degradable fiber, undegradable fiber, and soluble carbohydrates (Nozière et al., 2010). Below is a detailed review of how carbohydrate fractions are represented in various models.

Nitrogenous feed fractions are generally disaggregated into at least two fractions in complex rumen models: soluble protein (amino acids) and non-protein nitrogen (NPN; ammonia and/or urea). Most models also include insoluble protein that is hydrolyzed to soluble protein, and fewer models include an undegradable protein fraction. The representations of growth substrates in each model are reviewed below and an overview is presented in Figure 2A.

Despite the impact of long chain fatty acids (LCFA) on fiber degradation and CH₄ production via the biohydrogenation H₂ sink, representations of lipid metabolism in mechanistic rumen are generally less complex than those of carbohydrates and N compounds (Figure 2B). In fact, they are not present at all in France et al. (1982). Dijkstra et al. (1992) includes a “lipids” pool, while Baldwin et al. (1987) and Dijkstra et al. (1996b) include a “LCFA” pool. In these models, fluxes to both pools include input from the diet and outflow from the rumen. Additionally, Baldwin et al. (1987) and Dijkstra et al. (1996b) account for the incorporation of LCFA into microbial lipid. Lipids are hydrolyzed to LCFA, which can then undergo biohydrogenation as in Baldwin et al. (1977), which has a relatively complex representation of lipids with “lipid,” triglycerides, and LCFA pools. Similarly, Danfær et al. (2006) includes a rumen fat pool which corresponds to dietary crude fat, assumed to be triglycerides, as well as a free fatty acids pool. Triglycerides pass to free fatty acids by lipolysis, are taken up by rumen microbes, and flow out of the rumen. Baldwin (1995) empirically represents inhibition of fiber hydrolysis by fat but this effect is not related to the degree of LCFA saturation (Dijkstra et al., 2000).

Dijkstra (1994) extends the limited representation of lipid metabolism in Dijkstra et al. (1992) by including an input to the lipid pool from the lysis of protozoa and the release of engulfed lipid not utilized for protozoal growth. It also includes the uptake of lipid by protozoa for growth. Dijkstra et al. (2000) further extends Dijkstra et al. (1992) to more comprehensively represent rumen lipid metabolism, including dietary lipids and both saturated and unsaturated free LCFA. An updated version of Baldwin et al. (1987) described in Benchaar et al. (1998) also includes the biohydrogenation of unsaturated fatty acids to calculate hydrogen balance in the rumen. Similarly, Mills et al. (2001) updated Dijkstra et al. (1992) to predict CH₄ production via H₂ balance, including biohydrogenation. However, neither of these updated models includes a LCFA pool, so biohydrogenation is represented as a lipid uptake with an empirical constant accounting for proportion of saturated fat in dietary lipid.

Some specialized models of rumen lipid metabolism focus on kinetically representing the processes of unsaturated fatty acid biohydrogenation and the production of specific fatty acids (Moate et al., 2008). However, extant rumen models incorporating CH₄-inhibiting additives (Muñoz-Tamayo et al., 2021; van Lingen et al., 2021) do not include biohydrogenation. As it is recommended that models incorporate alternative H₂ sinks in light of H₂ redirection with inhibited methanogenesis (Morgavi et al., 2023), increasingly complex representation of rumen lipid metabolism should become more common in rumen mechanistic models.

The simplest representation of fermentative microbes included in mechanistic rumen models is a single aggregated pool of microbes. This approach is utilized in Baldwin et al. (1977, 1987), Dijkstra et al. (1996b), and France et al. (1982). In the Baldwin models, the aggregated microbe pool is distributed across particle pools of different sizes, where microbes associated with different particle sizes access different substrates. This distribution implicitly distinguishes microbes based on substrate utilization. In a different approach, Danfær et al. (2006) models one microbial population that is disaggregated into pools of microbial components (microbial protein, starch, etc.), but uses one maintenance requirement that encompasses both amylolytic and fibrolytic bacteria. In contrast, Dijkstra et al. (1992) disaggregates microbes into amylolytic and fibrolytic microbial pools, where the amylolytic pool encompasses both bacteria and protozoa. Dijkstra (1994) further refines this by creating a fibrolytic bacteria pool and splitting amylolytic “microbes” into amylolytic bacteria and protozoa. In the Dijkstra models, inputs to a given microbial pool are represented as a microbial growth yield constant multiplied by the corresponding uptake of growth substrate (e.g., soluble protein or ammonia) for growth, with growth substrate requirement factors adapted from Reichl and Baldwin (1975). Additionally, these inputs apply specifically to the polysaccharide-free microbial dry matter, as amylolytic storage polysaccharides are represented as a separate state variable pool. While most kinetic parameters are shared between the amylolytic and fibrolytic groups, they differ in outflow rates and composition (Dijkstra et al., 1992), as only amylolytic bacteria synthesize storage polysaccharides. While amylolytic bacteria do not utilize this polysaccharide to power cellular processes, amylolytic hexose is taken up for formation of amylolytic bacterial storage polysaccharide. This may impact microbial growth, which depends on energy substrate availability, and distinguish the growth dynamics of each bacterial pool.

Mills et al. (2014) extends Dijkstra (1994) by splitting the amylolytic bacterial pool into lactate-producing bacteria and lactate-utilizing bacteria. Lactate-producers ferment amylolytic hexose to either lactate or VFA, depending on specific growth rate and rumen pH, while lactate-utilizers use both lactate and amylolytic hexose as energy sources. Lactate utilization by protozoa is also included. The growth of these microbial pools is represented similarly to that of Dijkstra (1994) and Dijkstra et al. (1992). Muñoz-Tamayo et al. (2016) uses a different approach from the prevailing method of disaggregation by carbohydrate utilization type, instead representing the rumen microbiota with three functional groups: sugar (glucose) utilizers, amino acids utilizers, and hydrogen utilizers. In Muñoz-Tamayo et al. (2016), ammonia is assumed to be the sole N source for sugar utilizers, and microbial growth is represented as a growth yield constant multiplied by the corresponding substrate uptake flux.

In Dijkstra et al. (1996b), uptakes of the aggregated microbial pool include outflow from the rumen, where the outflow rate for the aggregated microbial group is estimated by assuming that the total microbial biomass comprises 40% protozoa and 60% bacteria, that particle-associated bacteria make up 75% of the total bacterial biomass, and that the fractional outflow rate of protozoa is half of that of the fluid outflow rate. The need for such assumptions demonstrates the limitations of using aggregated microbial pools for more complex modeling exercises. This approach does not account for protozoal predation and resultant microbial N recycling in the rumen. In contrast, the 1992 and 1994 Dijkstra models with disaggregated amylolytic and fibrolytic microbe include outflows from each pool corresponding with the appropriate fraction, e.g., all amylolytic microbes flow out with the fluid and that all fibrolytic microbes with the solid fraction. In addition, microbes can be taken up via predation by protozoa and protozoa can also die due to lysis.

In Muñoz-Tamayo et al. (2016), the only uptakes of each functional microbial group are through death, represented as a mass-process where the death rate is constant across microbial groups. In France et al. (1982), uptake from the aggregated microbial group also includes microbial death, parameterized with a death rate dependent on the specific rate of microbial catabolism, which itself depends sigmoidally on the microbial growth rate, as well as washout to the omasum. Baldwin et al. (1977) includes microbial uptakes such as outflow of liquid-associated microbes with the rumen fluid, while particle-associated microbes pass out in association with insoluble particles. In Baldwin et al. (1987), it is assumed that large-particle associated microbes do not pass out of the rumen, while those in the small-particle-associated microbial pool (corresponding to the earlier model’s particle-associated pool) and fluid-associated pools do.

As rumen mechanistic models have evolved to predict CH₄ production, the increasingly complex representations of fermentative pathways and other controls have not been matched by increasing complexity in representations of fermentative microbial groups. The only models currently incorporating thermodynamic control of fermentation pathways (van Lingen et al., 2019, 2021) represent all fermentative microbes by a single pool. Sensitivity analysis in van Lingen et al. (2019) identified the fiber degradation rate constant as influential on CH₄ predictions, so distinguishing between cellulolytic and amylolytic bacteria may improve representation of substrate degradation, fermentative substrate availability, and CH₄ production (van Lingen et al., 2019). Less aggregation of bacteria solely based on carbohydrate utilization and inclusion of additional bacterial functional groups in the rumen may also be necessary to improve CH₄ predictions, especially under supplementation of CH₄-inhibitors. AFA targeting methanogens may provide an advantage to reductive acetogens to compete for H₂ (Ellis et al., 2008)_, but utilization of H₂ by reductive bacteria is not included in any extant model of rumen fermentation. Similarly, sulfate-reducing bacteria, while minor under normal conditions, may become more prevalent H₂-utilizers under CH₄-inhibition or alternative feeding practices that include sulfur-containing feeds, such as corn co-products, but are not included in any extant rumen model (Ellis et al., 2008). Inclusion of additional microbial functional groups may be an important next step for more biologically realistic representation of H₂ balance in the rumen. This endeavor can be supported by the increased knowledge of the diversity and function of the rumen microbiome generated through genomic approaches (Seshadri et al., 2018). However, this expanded genomic information has not yet been matched by representations of microbial metabolism in rumen mechanistic models (Bannink et al., 2016), although recent work has integrated microbial “omics” data into dynamic models of the metabolism of Fibrobacter succinogenes (Fakih et al., 2023) and the entire rumen microbiome (Davoudkhani et al., 2024). Further integration of omics data into rumen mechanistic models can improve representation of both microbial metabolism and fermentation stoichiometry (Muñoz-Tamayo et al., 2023) and mechanisms of CH₄-inhibition by AFA (Indugu et al., 2024; Tan et al., 2024), potentially improving predictions of CH₄ emissions.

The only extant rumen model that explicitly includes protozoa is Dijkstra (1994) and its derivatives. In Dijkstra (1994), inputs to the protozoa pool represent the uptake by protozoa of many substrates, and protozoal growth is determined by the minimum of either the growth supported by engulfed carbohydrates or protein. Inputs to the protozoal storage polysaccharide pool are yield constants multiplied by the corresponding uptakes of energy substrates. The representation of protozoal growth in Mills et al. (2014) is the same as in Dijkstra (1994), with the addition of lactate as an energy substrate for protozoal growth, and maximum protozoal uptake of bacterial protein and feed protein depends on rumen fluid pH.

To represent the high observed rate of protozoal lysis in the rumen in Dijkstra (1994), thought to be caused by unrestricted soluble sugar uptake and intracellular accumulation of acidic fermentative end products, protozoal lysis is included as an uptake, which is sigmoidally dependent on the rate of VFA production from hexose fermentation and protozoal biomass. Uptakes of protozoa also include outflow from the rumen, which, due to protozoal sequestration, is assumed to be 45% of the solid outflow rate. Thus, all protozoa are eligible for lysis, regardless of whether they are sequestered with less access to soluble substrates, leading to a rapid increase in protozoal death rates at high nutrient availabilities and mimicking the high protozoal lysis rates observed in vitro. However, recent work has questioned the applicability of these rates in vivo, due to limitations in studies that led to high observed lysis rates (Firkins et al., 2007). Diaz et al. (2014) postulated that extensive autolysis by isotrichids in culture tubes may result from their inability to migrate away from lytic conditions, unlike in the in vivo environment, where they could sequester in the ventral rumen. Therefore, the true in vivo protozoal lysis rate may be lower than that represented in Dijkstra (1994). Given the important role of protozoa in sequestering soluble substrates, revisiting the representation of protozoal lysis may improve predictions of VFA production and CH₄ emissions.

No mechanistic rumen model includes anaerobic fungi, perhaps because of their complex life cycle and relatively poorly characterized metabolism. However, France et al. (1990) uses a mechanistic, differential equation-based model to predict the proportion of the fungal population in each life stage (zoospore, immature thalli, and mature thalli) and total population size. Inclusion of anaerobic fungi in future models is important due to their impact on insoluble particle degradation (Kennedy and Murphy, 1988) and, consequently, particle retention and outflow rates. In addition, rumen anaerobic fungi play an important role in interspecies H₂ transfer, and therefore, CH₄ production. Methanogens are thought to be ecto-symbionts of anaerobic fungi, which, like protozoa, produce large amounts of H₂ gas via specialized hydrogenosome organelles (López-García et al., 2022; Valle et al., 2015). Therefore, representing interspecies H₂ transfer between anaerobic fungi and methanogens may improve predictions of CH₄ production and H₂ accumulation under CH₄-inhibition. To advance representation of anaerobic fungi in future models, the approach of France et al. (1990) could potentially be incorporated into a full rumen model.

The production of the major VFA (acetic, butyric, and propionic acids) is generally represented in the same manner mathematically, using empirically-derived stoichiometric yield factors to give relative proportions of each VFA species, based on high-forage or high-starch diets and usually interpolated for intermediate diets. This approach is more thoroughly examined in Alemu et al. (2011) and Bannink et al. (2006). Inputs to each VFA pool (acetic, butyric, propionic, and valeric acids) in Dijkstra (1994), include VFA content of the feed and fermentation of hexose, additional energy substrates available to protozoa, or soluble protein for growth, non-growth, and storage polysaccharide formation by microbes, according to stoichiometric yield factors. Dijkstra et al. (1996b), a simplified version of Dijkstra (1994) and Dijkstra et al. (1992), contains five inputs to an aggregated VFA pool: intake with diet, fermentation of soluble carbohydrates for microbial growth and for non-growth processes, and soluble protein fermentation. However, instead of predicting the VFA species, it uses an empirical average VFA profile for the diet simulated by the model.

Baldwin et al. (1977) represents VFA production using a relatively high degree of aggregation. Total VFA production is calculated using a fermentation balance equation, while acetic, propionic, butyric, and unspecified “higher” acids are given as proportions of total VFA using static stoichiometric relationships. Baldwin et al. (1987) disaggregates the major VFA and explicitly represents acetic, propionic, and butyric acid pools using empirical stoichiometric yield factors; Danfær et al. (2006) use a similar approach. Muñoz-Tamayo et al. (2016) uses a novel approach to modeling the production of the three major VFA, defining fermentation stoichiometry through biochemical reactions. This approach reduces the number of model parameters by avoiding unknown stoichiometric factors based on diet, arguably making it more mechanistic. van Lingen et al. (2019) uses a similar approach, utilizing biochemical reactions to predict individual VFA species formation.

In Dijkstra (1994) and Dijkstra et al. (1992), uptakes from each VFA pool include outflow from the rumen with the fluid fraction and absorption through the rumen wall. The latter is represented using modified Michaelis–Menten kinetics, where the maximum absorption rate is dependent on rumen wall surface area and is modified sigmoidally by rumen fluid pH to represent acid disassociation, with slower absorption rates of disassociated acids at higher pH. Dijkstra et al. (1996b) simplifies this representation by assuming a constant absorption rate based upon empirical VFA absorption data at rumen fluid pH values typical of sugarcane-based diets. Baldwin et al. (1987) represents the uptake of each major VFA with one aggregated mass-action reaction representing both outflow and absorption. Muñoz-Tamayo et al. (2016) includes an uptake of acid disassociation to the ionized conjugate base.

More complex representations of VFA production have developed in concert with increased interest in representing CH₄ production. It is likely that using empirical stoichiometric yield factors leads to errors in predicting relative VFA proportions and production, partly due to measurement errors in the data upon which the empirical factors are developed. Because direct observation of VFA production rates in vivo is technically difficult, it is typically assumed that molar proportions of VFA in rumen fluid are representative of the proportions in which VFA are produced (Alemu et al., 2011). However, this assumption is not necessarily valid given differential rates of VFA absorption and utilization in the rumen epithelium or by the rumen microbiota. Such stoichiometric constants also assume a fixed fermentative pattern for all microbial subpopulations, even though fungi and protozoa produce very little propionate, and a fixed microbial growth efficiency with substrate fermentation to each VFA. Finally, VFA interconversion cannot be represented using these fixed factors, nor do they incorporate the effect of pH on rumen VFA stoichiometric coefficients, potentially affected through interplay with thermodynamics and hydrogenase-mediated conversion of H+ to H₂ (see Section 4.5 and Figure 4). Only recently have models of Muñoz-Tamayo et al. (2016) and van Lingen et al. (2019) used yield factors from balanced fermentation reaction equations for hexose and protein fermentation. This type of representation requires its own assumptions, e.g., that non-hexose monosaccharides have the same fermentation stoichiometry as hexose or the structure of the “average” amino acid.

Mills et al. (2014) modifies Dijkstra (1994) to include lactic acid metabolism in the rumen (Figure 3B). The production of lactic acid is similar to that of the major VFA in Dijkstra (1994). Inputs to the lactic acid pool include intake with the diet and fermentation of hexose by lactate-producing amylolytic bacteria. The proportion of hexose fermented to lactic acid is assumed to increase as specific growth rate increases and as pH decreases. Uptakes of lactic acid in Mills et al. (2014) include outflow with fluid, absorption through rumen wall, and fermentation to VFA by lactate-utilizing bacteria and protozoa; uptakes for fermentation to VFA are all inputs to the corresponding VFA pool.

While the balance of lactic acid production and utilization usually prevents its accumulation in rumen, at high microbial growth rates and increased glycolytic flux, the production of more reduced products like lactic acid is a means to rapidly regenerate NAD+, whereas production of more oxidized products like acetic acid would be inhibited by the high H₂ partial pressure (Mackie et al., 1984) (Figures 4A,C). Therefore, the inclusion of lactic acid metabolism may gain importance as thermodynamic control of fermentative pathways becomes more prominent in rumen models. In addition, including lactic acid metabolism allows for more mechanistic prediction of rumen fluid pH.

In addition to the major VFA and lactic acid, some models also include minor VFA species. For example, Dijkstra (1994) and Dijkstra et al. (1992) incorporate hexose fermentation to valeric acid. However, no current mechanistic models of rumen fermentation include minor VFA (such as caproate), formate, or organic acids like fumaric or malic acid, despite their potential importance as intermediates in propionate or CH₄ production (Ellis et al., 2008). Only Danfær et al. (2006) includes an aggregated branched-chain VFA pool, produced through protein fermentation. While branched-chain VFA are minor species, they are important intermediates in branched-chain amino acid catabolism and microbial growth, suggesting that their inclusion could improve the representation of microbial growth dynamics and protein metabolism in the rumen. Additionally, incorporating alternative fermentative substrates and products, such as formate, malate, and fumarate, may improve predictions of fermentative shifts under CH₄-inhibition (Ellis et al., 2008).

Early representations of H₂ production in the rumen treated H₂ as a “zero pool^” (France et al., 1992), whereby the difference between all explicitly represented H₂ inputs and outputs was used for CH₄ production as seen in Baldwin (1995), Benchaar et al. (1998) and Mills et al. (2001). Similarly, Danfær et al. (2006) models CH₄ production based on empirically based on stoichiometric fermentation coefficients without representing methanogens. Mills et al. (2001) modified the Baldwin (1995) model to include H₂ production from the fermentation of carbohydrate and protein substrates to acetate and butyrate and microbial growth on amino acids. H₂ uptake was represented for microbial growth on NPN, biohydrogenation of unsaturated fatty acids and fermentation of substrates to propionate and valerate. Vetharaniam et al. (2015) also adapted Baldwin (1995) to simulate the rumen of a sheep and predict CH₄ emissions, using the same H₂-balance approach as Mills et al. (2001).

More recent models (e.g., van Lingen et al., 2019) instead represent an H₂ pool using the rate: state formalism. Inflows include carbohydrate fermentation to acetate and butyrate, with absorption and outflow of dissolved H₂ explicitly represented using Henry’s law and the ideal gas law. Eructation of gaseous H₂ is represented using a mass-action process and H₂ uptake for methanogen growth is modeled using Michaelis–Menten kinetics. While van Lingen et al. (2019) does not represent protein metabolism or H₂ production through amino acid fermentation, this flux is included in Muñoz-Tamayo et al. (2016) via mass-action equations. Muñoz-Tamayo et al. (2016) also explicitly represents non-equilibrium liquid–gas transfer of H₂ from dissolved to gaseous state using mass-action kinetics with dissolved H₂ uptake for methanogenesis and microbial growth on NPN, both represented by Michaelis–Menten kinetics.

No rumen mechanistic model currently represents methanogenic electron donors or substrates besides H₂ and CO₂. Formate, produced by anaerobic fungi and protozoa, may contribute up to 18% of CH₄ production (Hungate et al., 1970) and serve as an electron donor for reducing fumarate and malate to succinate and then propionate. Including formate and other potential electron donors like acetate, methanol, and methylamines in models could improve predictions of CH₄ emissions and VFA profiles, especially under CH₄-inhibition (Ungerfeld, 2020).

Accurate CH₄ prediction depends on correctly modeling relative concentrations of VFA produced through fermentation (Alemu et al., 2011), which typically first proceeds via glycolysis (Figure 4A). NADH and reduced ferredoxin, cofactors carrying electrons, must be re-oxidized for glycolysis to proceed (Hegarty and Gerdes, 1999) (Figure 4B). Although acetate is the most abundant VFA, its production from pyruvate is not directly coupled to the re-oxidation of reduced cofactors, unlike propionate (Figure 4C). When acetate is produced from pyruvate, cofactors must be re-oxidized via hydrogenase-catalyzed oxidation, which results in production of H₂. This is thermodynamically inhibited when the rumen hydrogen partial pressure (pH₂) is elevated (van Lingen et al., 2016) (Figure 4B). Thus, pH₂ thermodynamically controls fermentation pathways via the ratio of oxidized to reduced cofactors (van Lingen et al., 2016), impacting VFA molar ratios, H₂ balance, and ultimately CH₄ production. Thermodynamic favorability of fermentation pathways may also interact with other rumen conditions, such as pH, as hydrogen ions are taken up for hydrogenase-catalyzed NADH oxidation to NAD+ (van Lingen et al., 2016). Incorporation of thermodynamically controlled cofactor dynamics improved the prediction of VFA under different pH, glucose concentration, and pH₂ conditions in a model of in vitro mixed culture fermentation (Zhang et al., 2013). Only two models, van Lingen et al. (2019, 2021) and Offner and Sauvant (2006) represent microbial fermentative cofactors and their thermodynamic control on fermentation pathways mechanistically.

van Lingen et al. (2019, 2021) explicitly represents the NAD+/NADH ratio, controlling flux allocation between carbohydrate fermentation pathways. Inflows to the oxidized NADH pool include hexose fermentation to acetate, while outflows include hexose fermentation to propionate and hydrogenase-catalyzed reoxidation. Elevated pH₂ inhibits NADH reoxidation by modifying the mass-action reoxidation process via the thermodynamic potential factor (Jin and Bethke, 2007). Offner and Sauvant (2006) use a more complex approach, predicting thermodynamically favorable fermentation pathways by explicitly modeling Gibbs free energy changes. Muñoz-Tamayo et al. (2021) uses a hybrid approach assuming a linear relationship between NADH/NAD+ and pH₂, with pH₂ controlling flux allocation parameters. More widespread adoption of thermodynamic control in rumen models could further improve CH₄ predictions.

Only van Lingen et al. (2019, 2021) explicitly include methanogens and methane using the rate: state formalism (Figure 3A), while Muñoz-Tamayo et al. (2016, 2021) include a “hydrogen-utilizers” microbial pool, corresponding to methanogenic archaea. In van Lingen et al. (2019), methanogen growth via hydrogenotrophic methanogenesis is modeled by a growth yield constant multiplied by H₂ uptake. Methanogen outflow is set to 40% of the liquid and solid outflow rates, reflecting the slower outflow of methanogens due to their adherence to rumen epithelium. The CH₄ production rate is then modeled by multiplying the H₂ uptake flux for methanogen growth by a yield rate. In Muñoz-Tamayo et al. (2016), dissolved CH₄ production is represented as a yield factor multiplied by the H₂ uptake for H₂-utilizer growth, and conversion to gaseous CH₄ occurs via liquid–gas transfer.

Future models could benefit from more detailed representation of methanogenic subpopulations. Methanogen species vary in several respects that are relevant to predicting the impact of AFA, such as sensitivity to CH₄-inhibitors, H₂ affinity, and methanogenic pathways. Methanobrevibacter ruminantium is particularly sensitive to halogenated sulfonated methyl–coenzyme M reductase (MCR) inhibitors (Patra et al., 2017), potentially due to this species’ inability to synthesize coenzyme M (Ungerfeld and Pitta, 2024). Halogenated CH₄ analogs such as bromoform reduce CH₄ production by inhibiting cobamide-dependent methyl transfer (Wood et al., 1968). It is speculated that differences in methanogen sensitivity to halogenated CH₄ analogs may also be due to differences in cobamide structures and affinities for these analogs, but this has yet to be investigated experimentally (Ungerfeld and Pitta, 2024). Differences in expression of MCR isozymes may also contribute to variability in sensitivity to AFA, as well as H₂ affinity, across methanogen species (Pitta et al., 2022b; Ungerfeld and Pitta, 2024).

Methanogens also differ in methanogenic pathways, although extant mechanistic rumen models incorporate only hydrogenotrophic methanogenesis. Methylotrophic methanogenesis requires only one mole of H₂ to produce CH₄ from methyl group-bearing substrates, while hydrogenotrophic methanogenesis requires three or four moles of H₂ (Ungerfeld and Pitta, 2024). Thus, increased abundance of methylotrophic methanogens could contribute to greater CH₄ yields, but is limited by the availability of methyl group-bearing substrates (Feldewert et al., 2020). On the other hand, the lower H₂ threshold of methylotrophic methanogens may be less of a competitive advantage under CH₄-inhibition, when pH₂ in the rumen is higher. As pectin and xylan are rich in methyl groups (Feldewert et al., 2020), basal diet also may partially determine methanogen population structure and the impact of AFA on methanogenesis. However, the representation of non-hexose soluble carbohydrates is simplified in rumen models. Baldwin et al. (1987) specifies pectin as its own input, but simulates its fermentation using a combined soluble carbohydrates pool, and the α-hexose group in France et al. (1982) includes pectin. This simplified representation of complex plant polysaccharides and methanogen community structure could impact CH₄ prediction accuracy by underestimating methylotrophic methanogenesis under normal conditions and overestimating it under CH₄-inhibition.

Methanogenic microbiomes are likely influenced by many interacting factors such as basal diet, host genetics (Pitta et al., 2022b), and bacterial community composition, which has complex dynamics itself under CH₄-inhibition (Ungerfeld and Pitta, 2024). Mechanistic models may be an ideal tool for predicting changes in methanogen community structure under CH₄-inhibition. However, mechanistically modeling methanogens with more complexity would require model inputs (such as initial conditions of methanogen population distributions) and parameters (such as affinity constants and growth yields) that are difficult to obtain or may yet be unknown, making modeling methanogenic subpopulations under typical or CH₄-inhibited conditions challenging.

Only two mechanistic models incorporate AFA: van Lingen et al. (2021) for 3-nitroxypropanol (3NOP) and Muñoz-Tamayo et al. (2021) for bromoform from Asparagopsis taxiformis. While these models assume that AFA only act directly on methanogens, it is possible but currently unknown if AFA directly affect some rumen bacteria as well (Ungerfeld and Pitta, 2024). In addition to directly inhibiting MCR, 3NOP may redirect fermentation pathways toward propionate formation (van Gastelen et al., 2022), possibly through thermodynamic inhibition of NADH re-oxidation (van Lingen et al., 2021). A potential scheme of this redirection is shown in Figure 4D. These interactions emphasize the need for models to include both AFA and microbial cofactor dynamics.

The potential loss of persistent CH₄-inhibition by 3NOP in some studies (Schilde et al., 2021; Van Gastelen et al., 2024) suggests that microbial adaptation to AFA may be possible. However, such adaptation is not included in any rumen mechanistic model, and mechanistic models are often evaluated assuming quasi-steady state conditions (Danfær et al., 2006; Dijkstra, 1994; van Lingen et al., 2019, 2021). However, the time-dependent nature of microbial adaption aligns with suggestions by Muñoz-Tamayo et al. (2019) that models using substrate utilization kinetics alone cannot accurately predict methanogen dynamics, underscoring the importance of incorporating spatial and temporal information in models of H₂ utilization. For example, 3NOP supplementation may reduce MCR expression (Pitta et al., 2022a), so methanogenic adaptation to AFA may also be related to upregulation of MCR expression or expression of alternate MCR isoenzymes or subunits. Explicit modeling of fluctuations in MCR expression over time, potentially incorporating genomic data (e.g., Pitta et al., 2022a), may allow for predictions of methanogen adaptation to AFA.

AFA may also have indirect effects on net GHG reductions. For example, 3NOP is metabolized to NO₃− and NO₂−in the rumen (Duin et al., 2016), which can further be reduced to nitric oxide (NO) and ultimately nitrous oxide (N₂O). While enteric N₂O emissions are typically minor, denitrifying genes are present within the rumen bacterial and archaeal metagenome (Latham et al., 2016) and 3NOP supplementation may increase enteric N₂O emissions (Petersen et al., 2015). In addition, application with manure from cows fed 3NOP led some soils to emit more N₂O (Weber et al., 2021), suggesting potential alterations to N-excretion. As N₂O is a potent GHG with a greater global warming potential than CH₄ (IPCC, 2023), models of enteric fermentation under CH₄-inhibition should consider the potential indirect and downstream impacts on GHG production.

Approaches that assume the anti-methanogenic action of Asparagopsis species is due to solely its bromoform content allow for standardization of the inhibitory effect of various macroalgae species but may overlook compounds that act synergistically with bromoform (Ahmed and Nishida, 2024; Machado et al., 2016). Because different AFA have different mechanisms of CH₄-inhibition, it is possible they can also act synergistically (Villar et al., 2020), although this effect has not been seen consistently in vivo (Guyader et al., 2015; Maigaard et al., 2023; Zhang et al., 2021). Currently, no rumen mechanistic model represents direct supplementation of multiple AFA of different mechanisms, although van Lingen et al. (2021) does includes 3NOP catabolism to NO₃− and NO₂−.