Meta-analysis of apparent ruminal synthesis and postruminal flow of B vitamins in dairy

As milk production has significantly increased over the past decade(s), existing estimates of the B-vitamin needs of the modern dairy cow are currently being re-considered, as suboptimal B-vitamin supply may affect metabolic efficiency. At the same time, however, “true” (i.e., biologically active forms, excluding nonfunctional analogs) B-vitamin supply also cannot be adequately estimated by dietary intake, as the rumen microbiota has been shown to play a significant role in synthesis and utilization of B vitamins. Given their complex impact on the metabolism of dairy cows, incorporating these key nutrients into the next generation of mathematical models could help to better predict animal production and performance. Therefore, the purpose of this study was to generate hypotheses of regulation in the absence of supplemental B vitamins by creating empirical models, through a meta-analysis, to describe true B-vitamin supply to the cow (postruminal flow, PRF) and apparent ruminal synthesis (ARS). The database used for this meta-analysis consisted of 340 individual cow observations from 15 studies with 16 experiments, where diet and postruminal digesta samples were (post hoc) analyzed for content of B vitamins (B 1 , B 2 , B 3 , B 6 , B 9 , B 12 ). Equations of univariate and multivariate linear form were considered. Models describing ARS considered dry matter intake (DMI, kg/d), B-vitamin dietary concentration [mg/kg of dry matter (DM)] and rumen-level variables such as rumen digestible neutral detergent fiber (NDF) and starch (g/kg of DM), total volatile fatty acids (VFA, m M ), acetate, propionate, butyrate, and valerate molar proportions (% of VFA), mean pH, and fractional rates of degradation of NDF and starch (%/h). Models describing PRF considered dietary-level driving variables such as DMI, B-vitamin dietary concentration (mg/kg of DM), starch and crude protein (g/kg of DM) and forage NDF (g/kg of DM). Equations developed were required to contain all significant slope parameters and contained no significant collinearity between driving variables. Concordance correlation coefficient was used to evaluate the models on the developmental data set due to data scarcity. Overall, modeling ARS yielded better-performing models compared with modeling PRF, and DMI was included in all prediction equations as a scalar variable. The B-vitamin dietary concentration had a negative effect on the ARS of B 1 , B 2 , B 3 , and B 6 but increased the PRF of B 2 and B 9 . The rumen digestible NDF concentration had a negative effect on the ARS of B 2 , B 3 , and B 6 , whereas rumen digestible starch concentration had a negative effect on the ARS of B 1 and a positive effect on the ARS of B 9 . In the best prediction models, the dietary starch increased PRF of B 1 , B 2 , and B 9 but decreased PRF of B 12 . The equations developed may be used to better understand the effect of diet and ruminal environment on the true supply of B vitamins to the dairy cow and stimulate the development of better-defined requirements in the future.


INTRODUCTION
B vitamins act as enzyme cofactors and are therefore crucial in carbohydrate, protein, and lipid metabolism (Girard and Matte, 2006).As a result of the rumen microbial population's ability to synthesize B vitamins, little attention was previously placed on these components of lactating dairy cow rations (NRC, 2001).However, the milk production efficiency of dairy cows has increased drastically since the 1940s (Capper et al., 2009), thereby challenging previous assumptions and knowledge of B-vitamin supply and needs and suggesting that B-vitamin requirements may now be higher (Girard and Matte, 2006).As Girard and Graulet (2021) noted, although symptoms of clinical deficiency are rare due to the rumen microbiota's ability to synthesize B vitamins for its host, underlying subclinical deficiencies may still impair metabolic functions.Numerous studies have reported positive effects of dietary supplementation of B vitamins on milk yield, milk fat and milk protein (Shaver and Bal, 2000;Schwab et al., 2005;Evans et al., 2020).Other studies have also suggested that supplementing B vitamins could improve reproductive performance (Juchem et al., 2012;Duplessis et al., 2014;Li et al., 2016), decrease incidences of diseases (Fronk and Schultz, 1979;Niehoff et al., 2009;Duplessis et al., 2014), and reduce culling rates (Juchem et al., 2012).This may be particularly relevant during periods of stress (e.g., immediately postpartum; Evans et al., 2006;Yuan et al., 2012) or high energy and nutrient requirements (e.g., in high-producing cows; Li et al., 2016).
Although the above-mentioned findings warrant further research to deduce metabolic needs and roles of individual B vitamins in the dairy cow, knowledge of the rumen microbiota's ability to synthesize and use these crucial co-enzymes remains limited (Dehority, 2003;Franco-Lopez et al., 2020).Recent studies demonstrate the potential effect of forage characteristics such as wilting time, forage family, and forage particle length on the dietary concentration of some B vitamins, as well as B-vitamin apparent ruminal synthesis (ARS; Castagnino et al., 2014aCastagnino et al., , 2016aCastagnino et al., , 2017a)).These authors also observed a marked decrease in ARS of some B vitamins under certain conditions, thereby reducing the amounts available to the cow.Consequently, increased understanding of ruminal synthesis and utilization of B vitamins-first, when no additional supplementation occurs-is essential to better examine the relationship between dietary supply, true supply, and metabolic needs.As a result, the objective of this study was to perform a meta-analysis on available data to produce empirical models that (1) generate hypothesis of regulation (key drivers and modes of action) for the variation observed in synthesis and utilization (ARS) of B vitamins in the rumen, and (2) predict the postruminal flow (PRF) of B vitamins (true supply to the cow), resulting in better quantification of B-vitamin supply and thus supporting future attempts to establish Bvitamin needs of dairy cows.

Database Development and Diet Description
For this analysis, no animals were used and therefore animal ethical approval was not necessary.Data from 340 individual cow observations, representing 36 treatment means and 16 experiments from 15 studies conducted by 3 research groups [Michigan State Uni-versity (MSU), the National Institute for Agriculture, Food and Environment (INRAe), and Agriculture and Agri-Food Canada (AAFC)] were collected (Harvatine and Allen, 2006;Voelker Linton andAllen, 2007, 2008;Allen et al., 2008;Allen andYing, 2008, 2012;Kammes et al., 2012a,b;Kammes and Allen, 2012a,b,c;Fanchone et al., 2013;Ferlay et al., 2013;Jolicoeur et al., 2014;Brito et al., 2015) and are summarized in Table 1.None of the diets used in these experiments were supplemented with B vitamins.
Among the studies included, the experiments conducted at MSU examined the effect of varying agronomic or dietary factors on intake, digestion, and milk production responses, and used crossover experimental designs (Voelker Linton andAllen, 2007, 2008;Allen et al., 2008;Allen and Ying, 2012;Kammes and Allen, 2012a,b,c;Kammes et al., 2012a,b) or a 4 × 4 Latin square design (Harvatine and Allen, 2006;Allen and Ying, 2008).The agronomic treatments investigated in these studies included the comparison of legume versus grass silages, early versus late cut, and long versus short particle length forages in both legume and grass silage, as well as the endosperm type (floury or vitreous) and particle size (medium or fine) of dry ground corn grain.Other dietary factors examined at MSU included the comparison of low and high dietary forage content, the supplementation of fatty acids, the supplementation of monensin (Rumensin, Elanco Animal Health) and the supplementation of Saccharomyces cerevisiae fermentation product (Harvatine and Allen, 2006;Voelker Linton and Allen, 2007;Allen andYing, 2008, 2012).Only the control observations from the Allen andYing (2008, 2012) and Brito et al. (2015) studies were used, as the dietary treatments (monensin, Saccharomyces cerevisiae, and 5,6-dimethylbenzimidazole supplementation) may affect the rumen microbiota's ability to synthesize B vitamins, and the database had insufficient replication of these effects to consider incorporating them as fixed effects into the models.
The 3 experiments conducted at INRAe (Fanchone et al., 2013;Ferlay et al., 2013) used a 4 × 4 Latin square design and studied the effects of low or high N levels with starch or fiber as the main energy source on N partitioning, as well as the effect of increasing extruded linseed supplementation in hay-based or corn silage-based diets on milk production.
Finally, of the 2 experiments conducted at AAFC (Jolicoeur et al., 2014;Brito et al., 2015), Jolicoeur et al. (2014) used a randomized block design to study the effect of short dry period management on ruminal function during the transition period, whereas Brito et al. (2015), used a crossover design and studied the effect of supplementing a cobalamin precursor on the ARS of cobalamin.Observations from the control group only were used for the latter study, as the dietary treatment may have affected the rumen microbiota's ability to synthesize B vitamins.
The measurements available for each cow (which varied between studies), generally included DMI (kg/d), cobalt concentration in the diet (mg/kg of DM), as well as the intake (mg/d), PRF (mg/d), and ARS (mg/d) of B vitamins, the latter of which was calculated as the difference between PRF and intake of thiamin (B 1 ), riboflavin (B 2 ), niacin (B 3 ), vitamin B 6 , folates (B 9 ), and cobalamin (B 12 ).Other variables that were available in the majority of studies were dietary NDF (g/kg of DM), rumen digestible NDF (dNDF; g/kg of DM), dietary forage NDF (DFNDF; g/kg of DM), dietary starch (ST; g/kg of DM), rumen digestible starch (dS; g/kg of DM), dietary CP (g/kg of DM), rumen total VFA concentration (mM), rumen acetate (AC), propionate (PR), and butyrate (BT) molar proportions (% of VFA), acetate-to-propionate ratio, mean ruminal pH, fractional rates of degradation of potentially digestible NDF (kdNDF; %/h) and starch (kdS; %/h) in the rumen.Postruminal flow of digesta was determined as described by Kammes et al. (2012b), Fanchone et al. (2013), andJolicoeur et al. (2014).This database is unique, as no other group of studies has previously reported this type of information (B-vitamin content of diet and PRF).

Statistical Analysis
Model Development and Outlier Removal.The effects of diet and rumen parameters on ARS and PRF were modeled using SAS Studio (University Edition 9.4, SAS Institute Inc.).First, a Spearman correlation matrix, using the PROC CORR procedure, was constructed to assess for collinearity between all possible driving variables (Tables 2-4).Any 2 driving variables having a Spearman correlation coefficient (|r|) ≥0.3 were deemed to be collinear and thus were not both included in a model at the same time (Akoglu, 2018).From this correlation matrix, driving variables having an |r| ≥0.6 with the response variable were likely to have the largest influence on the models and thus guided model creation.
Dietary variables were used exclusively in PRF models to produce equations to predict the true amount of B-vitamin supply (PRF) from diet composition and DMI (easy to apply in practice and an outcome relevant to formulation PRF).The driving variables considered to model B-vitamin PRF included DMI, NDF, dNDF, ST, dS, B-vitamin dietary concentration (DC; mg/kg of DM), DFNDF, CP, and cobalt (Table 5).The ARS models included B-vitamin dietary concentrations in addition to ruminal variables, to aid in understanding of underlying causes and correlations (with focus placed on understanding mechanisms in the rumen).As a result, the driving variables considered to model Bvitamin ARS included DMI, dNDF, dS, DC, AC, PR, BT, VFA, pH, kdNDF, and kdS.Due to the limited data available on rumen microbiota in the database, dNDF and dS were included in ARS models to account for the variations in cellulolytic microbe (M C ) and amylolytic microbe (M A ) pool sizes.
Once all the relevant X variables (and combinations) were identified, linear univariate and linear multivariate mixed model analysis using PROC GLIMMIX was performed, treating study as a random effect on the model intercept term after consideration of the significance of the random slope effect (St-Pierre, 2001) and the random effect variance-covariance structure.A stepwise procedure, using forward selection of driving variables based on biological relevance and avoiding collinearity, resulted in the development of a series of multivariate models for each B vitamin.The corrected Akaike information criterion (AICC) as well as visual examination of the conditional studentized residuals obtained upon model fitting (via Q-Q plot, using Proc SGPLOT and Proc UNIVARIATE) was used to ensure that the addition of variables improved the models.The following statistical model was used when creating linear univariate and multivariate models: where Y ij is the predicted outcome of the dependent variable, β 0 is the intercept, S i is the random study effect on the intercept, B 1 x 1ij , B 2 x 2ij , …, B n x nij are the fixed effect slope estimates multiplied by the X variable, and e ij is the residual error (i = 1, …, n studies; and j = 1, …, n i observations).
Only driving variables with a significant slope parameter (P ≤ 0.05) were retained within the statistical model(s) developed.The number of observations used in each equation varied because the driving and dependent variables included were not reported by all studies.
Outliers were identified for each model using the Cook's distance test using SAS (v9.4,SAS Institute Inc.) and the same outliers were then removed in all models.The threshold to identify an observation as an outlier was if the Cook's distance value was greater than 4/n, where n is the number of observations, and if its removal improved the normality of the residual distribution.The procedure resulted in the removal of 15 outliers from the database, leaving 318 observations from 16 experiments after the removal of an additional 7 observations where DMI was not reported.
Model Selection and Evaluation.Models developed were further evaluated against the development data set to determine the amount and sources of error, using the concordance correlation coefficient (CCC) method.The predicted values used for model evaluation were the Y ij values adjusted for the random study effect.The CCC was calculated, as described in Equation [2a], where the Pearson correlation coefficient (r; Equation [2b]) represents a measure of precision of the model and C b (Equation [2c]) represents model accuracy (Lin, 1989).The CCC model evaluation metric also includes a measure of scale shift (υ; Equation [2d]) and a measure of location shift (µ; Equation [2e]), where υ quantifies the difference between the standard deviation (SD) for the observed (o) and predicted (p) values, and µ indicates underprediction (positive value) or overprediction (negative value) (Lin, 1989).Finally, the models were assessed visually, using observed versus predicted plots (Figures 1 and 2) and studentized residuals versus predicted plots.For each ARS and PRF B-vitamin  5-7).
Behavior Analysis.Given the complexity of the multivariate models developed, a behavior analysis was conducted to quantify the magnitude of the X variable effect on the predicted ARS or PRF flow of B vitamins.The behavior analysis of the model(s) was completed by individually increasing or decreasing each driving variable by +10% and −10% to determine the direction and magnitude of changes in the Y response variable.

RESULTS AND DISCUSSION
The results obtained from this meta-analysis provide insight into a process-net synthesis of B vitamins by the ruminal microbiota-for which we currently have limited knowledge.In this study, modeling (an empirical meta-analysis) was used as a tool to synthesize our limited knowledge with relationships observed in the novel B-vitamin database to increase knowledge.The significant linear multivariate mixed models resulting from the meta-analysis that describes the ARS of all 6 B vitamins considered are given in Table 6.Fewer mod-els (4 of the 6 B vitamins) could be fit to the PRF data.This may be as a result of (1) the difference in driving variables considered for ARS versus PRF models; (2) the much more muted variation in PRF compared with ARS due to the compensation that seems to be occurring by the rumen microbiota in response to high or low B-vitamin rumen levels; or (3) due to the limited dietary variables available from the database to generate these models, including the ration characteristics.Although in vitro/in vivo measurement errors can also contribute to some variation in the observed relationships, it could not be quantified for these data.The significant linear multivariate mixed models resulting from the meta-analysis to describe the PRF of B vitamins are given in Table 7.The corresponding model evaluation results for both ARS and PRF are described in Table 8.The residual analysis of all models showed no bias and normally distributed residuals.
The equally important ARS and PRF empirical models obtained from the meta-analysis described below offer a better understanding of the apparent ruminal synthesis of B vitamins and the variables affecting the amounts of B vitamins available for absorption by the cow, where a negative ARS indicates net use and a positive ARS indicates net synthesis.Discussions of the possible mechanisms behind the equations are only hypotheses, which will require validation in both controlled conditions and field trials.It must also be noted that these models were developed on a unique yet limited database, and thus should only be used within the data range of the developmental database.The current models are descriptions of the empirical relationship between various factors and individual B-vitamin PRF and ARS at the rumen microbiota level.

Thiamin (B 1 ) Models
Thiamin ARS Model and Interpretation.The ARS of thiamin was best predicted by a negative relationship with DMI, thiamin DC, and dS (Table 6), with a CCC of 0.913 (Table 8).The behavior analysis indicates that an increase of 10% in the thiamin DC has the greatest effect on thiamin ARS, resulting in a decrease of 51%, followed by DMI (21% decrease) and dS (6% decrease; Table 9).
The model indicates that increasing the dietary concentration of thiamin decreases ARS.This may be due to an increased utilization of preformed thiamin from dietary sources over de novo synthesis of the vitamin.The observed negative effect of DMI on ARS may be via an increased ruminal rate of passage (ROP), which could favor the growth of amylolytic microbes, which have a faster turnover rate, to a greater extent than that of cellulolytic microbes (Van Soest, 1994).This hypothesis around the relationship to M A is supported by the model's negative relationship between ARS and the amount of rumen digestible starch, which would be associated with an increased M A population.For instance, Streptococcus bovis, which belongs within the M A group, has thiamin requirements, and may thus be considered a thiamin user (Hobson and Stewart, 1997).Alternatively, the increased ROP and rumen digestible starch may create a rumen environment that does not favor the growth of cellulolytic microbes, subsequently resulting in decreased thiamin synthesis.It has previously been demonstrated that increasing the proportion of grain in the diet of dairy cows decreases the proportions of genera Fibrobacter, Pyramidobacter, and Bacteroidetes in the rumen, all 3 genera being known as thiamin-synthesizing bacteria (Pan et al., 2017).Moreover, increasing the proportion of grain in the diet promotes pyruvate formation, and the conversion of pyruvate to acetyl-CoA requires thiamin as a coenzyme for the pyruvate formate-lyase, increasing the microbial requirements for thiamin (Pan et al., 2018).
Thiamin PRF Model and Interpretation.The PRF of thiamin was best predicted by positive relationships with DMI and ST (Table 7),with a CCC of 0.838 (Table 8).The behavior analysis indicated that an increase of 10% in DMI has the greatest effect on thiamin PRF, resulting in an increase of 6%, followed by ST (3% increase; Table 9).
Although increasing DMI and ST can both increase the net utilization of thiamin by M A in the thiamin ARS model, this PRF model showed that, overall, increasing the dietary intake of starch leads to greater amounts of thiamin reaching the duodenum.These changes in PRF indicate that the higher concentration of thiamin in starch containing grains compared with forages (Tables 2-4; Schwab et al., 2006) compensated for the reduced ARS.The current observation is in accordance with Schwab et al. (2006), who observed a decrease in thiamin duodenal flow when increasing the diet's forage content from 30% to 60%, whereas no changes resulted from increasing the dietary starch content through the inclusion of corn and barley grains.The effect of DMI on thiamin PRF may simply be explained by increased  flows of nutrients to the duodenum in general, due to their increased intakes.

Riboflavin (B 2 ) Models
Riboflavin ARS Model and Interpretation.The ARS of riboflavin was best predicted by a negative re-lationship with DMI, riboflavin DC, and dNDF (Table 6), with a CCC of 0.941 (Table 8).The behavior analysis indicates that an increase of 10% in the riboflavin DC has the greatest effect on riboflavin ARS, resulting in a decrease of 176% (still within the observed biological range), followed by dNDF (44% decrease) and DMI (37% decrease; Table 9).The model indicates that increasing the amount of riboflavin reaching the rumen, through an increase of the DC of riboflavin and DMI, may promote the growth of riboflavin-utilizing microbes or decrease the activity of riboflavin-synthesizing microbes.The negative relationship between riboflavin ARS and the amount of dNDF suggests that the riboflavin-utilizing microbes are likely to be M C , increasing the use of riboflavin with increased fiber digestion.The hypothesis that M C bacteria mostly depend on an exogenous riboflavin supply is supported by the observation that in dairy bulls, supplementary riboflavin increased populations of the major M C species as well as activity of cellulolytic enzymes in the rumen but had no effect on activity of α-amylase and protease (Wu et al., 2021).
Riboflavin PRF Model and Interpretation.The PRF of riboflavin was best predicted by positive relationships with DMI, riboflavin DC, ST, and CP (Table 7), with a CCC of 0.848 (Table 8).The behavior analysis indicates that an increase of 10% in the CP had the greatest effect on riboflavin PRF, resulting in an increase of 13%, followed by DMI (9% increase), ST No significant models were found to describe the PRF from diet composition for niacin and vitamin B 6 .The dietary parameters available in the current database are therefore insufficient to predict changes in the amount of niacin and vitamin B 6 reaching the duodenum.(5% increase), and riboflavin DC (2% increase; Table 9).The observations of Magnúsdóttir et al. (2015) and Wu et al. (2021), suggesting that M A and proteolytic bacteria species are riboflavin producers, could explain the positive effects of increasing ST and CP on the amounts of riboflavin reaching the small intestine.As might be expected, DMI also has a large effect on riboflavin PRF because it subsequently leads to larger amounts of digesta reaching the duodenum (g/d), increasing the amount of riboflavin available for absorption by the host, especially when riboflavin DC is high.

Niacin (B 3 ) Models
Niacin ARS Model and Interpretation.The ARS of niacin was best predicted by a positive relationship with DMI and a negative relationship with DC, dNDF, and pH (Table 6), with a CCC of 0.954 (Table 8).The behavior analysis indicates that an increase of 10% in pH had the greatest effct on niacin ARS, resulting in a decrease of 52%, followed by niacin DC (27% decrease), DMI (12% increase), and dNDF (10% decrease; Table 9).
With ruminal pH being the variable of greatest influence in the model, ruminal environment, rather than B-vitamin intake, appears to have the greatest effect on niacin ARS.The negative relationship between pH and niacin ARS, further supported by the inclusion of DMI (positive effect) and dNDF (negative effect) variables in the model, also suggest that M c may use niacin, whereas M A synthesize it.Indeed, Luo et al. (2017) observed that dietary supplement of niacin on a high concentrate diet tends to reverse the symptoms of subacute ruminal acidosis by inhibiting starch utilization and decreasing the proportion of Prevotella while stimulating fibrolytic degradation by increasing the abundance of Succiniclasticum, Acetivibrio, and Treponema.Nevertheless, numerous studies reported a positive impact of niacin supplementation on rumen protozoa (Samanta and Harjit Kaur, 2000;Kumar and Dass, 2005) primarily attributable to an increase of Entodinia (Doreau and Ottou, 1996;Aschemann et al., 2012), which can regulate the ruminal environment by consuming and temporarily storing starch (Erickson et al., 1991).Hence, we cannot rule out the possibility that the effect of increasing niacin supply on the microbial population is mediated through protozoa that compete for substrate with M A , potentially reducing the populations of niacin-producing bacteria.Niehoff et al. (2009) observed that in 6 studies reporting niacin ARS, the ration with the highest niacin content within a study resulted in the lowest apparent niacin synthesis.Niacin PRF Model and Interpretation.No significant models were found to describe the PRF of niacin from diet composition (Table 7).Previous authors (Hannah and Stern, 1985;Niehoff et al., 2009), based on in vitro and review work, have suggested that the dietary concentration of the vitamin and the rumen parameters influencing its net synthesis may have antagonistic effects resulting in little variation in PRF.The dietary parameters available in the current database were insufficient to clarify this hypothesis.

Vitamin B 6 Models
Vitamin B 6 ARS Model and Interpretation.The ARS of vitamin B 6 was best predicted by a negative relationship with DMI, DC, dNDF, and pH (Table 6), with a CCC of 0.977 (Table 8).The behavior analysis indicates that an increase of 10% in the vitamin B 6 DC has the greatest effect on vitamin B 6 ARS, resulting in a decrease of 17%, followed by pH (15% decrease), DMI (8% decrease), and dNDF (3% decrease; Table 9).
Like thiamin and riboflavin, the apparent synthesis of vitamin B 6 is negatively affected by the dietary concentration of the vitamin and DMI.Vitamin B 6 use or degradation in the rumen with increasing dietary supply was also observed by Santschi et al. (2005a).The negative relationship of vitamin B 6 ARS with both mean ruminal pH and digestible NDF also suggests that as NDF digestion or ruminal pH increases, it creates an environment that promotes the growth of M C populations or alternatively, decreased M A populations.Indeed, vitamin B 6 stimulates cellulose digestion by mixed rumen bacteria in vitro (MacLeod and Murray, 1956), whereas Amin and Onodera (1998) reported that cellulolytic rumen bacteria such as Ruminococcus flavefaciens and Bacteroides (Fibrobacter) succinogenes require the vitamin.In further agreement with the current empirical model, Schwab et al. (2006) observed an overall positive vitamin B 6 ARS when increasing the dietary starch content.
Vitamin B 6 PRF Model and Interpretation.No significant models were found to describe the PRF of vitamin B 6 from diet composition (Table 7), suggesting an effect similar to that observed for niacin PRF.

Folates (B 9 ) Models
Folates ARS Model and Interpretation.The ARS of folates was best predicted by a positive relationship with DMI, PR, and dS (Table 6), with a CCC of 0.789 (Table 8).The behavior analysis indicates that an increase of 10% in DMI has the greatest effect on folate ARS, resulting in increases of 11%, followed by PR and dS, which both lead to a 3% increase (Table 9).
Unlike the models for thiamin, riboflavin, niacin, and vitamin B 6 , the DC of folates did not have a significant effect on the ARS of the vitamin, and all variables included in the model represent a positive relationship with folate ARS.From the large effect of DMI and PR on the model, together with the positive relationship with dS, it could be proposed that M A populations are responsible for synthesizing folates.This is supported by the concept that increasing DMI leads to increased digesta ROP, thus favoring fast-growing rumen bacteria such as those found within the M A population (Van Soest, 1994).Additionally, increased PR is generally the result of increased starch fermentation or of increased DMI, which is expected to be facilitated by increased M A populations (Robinson et al., 1986;Van Soest, 1994).Although to our knowledge there are no studies on the requirements of amylolytic bacteria for folates, in vitro and in vivo studies demonstrated that M C require folates and that a supplement of folic acid increases fiber digestion, promoting growth of M C and activity of bacterial cellulolytic enzymes in the rumen (Ayers, 1958;Ragaller et al., 2010;Wang et al., 2016).
Folates PRF Model and Interpretation.The PRF of folates was best predicted by a positive relationship with DMI, folates DC, and ST (Table 7), with a CCC of 0.760 (Table 8).The behavior analysis indicates that an increase of 10% in the DMI has the greatest effect on folate PRF, resulting in an increase of 11%, followed by folate ST (6% increase) and DC (3% increase; Table 9).
The amount of folates reaching the duodenum is increased by DMI, resulting from an increased amount of digesta reaching the duodenum and by increasing dietary starch, resulting in increased folate PRF by increasing ARS, as discussed above.The dietary concentration of the vitamin also increases folate PRF, suggesting that a significant proportion of dietary folates reaches the small intestine intact.

Cobalamin (B 12 ) Models
Cobalamin ARS Model and Interpretation.The ARS of cobalamin was best predicted by positive relationships with DMI and total VFA (Table 6), with a CCC of 0.914 (Table 8).The behavior analysis indicates that an increase of 10% in the DMI has the greatest effect on cobalamin ARS, resulting in an increase of 9%, followed by VFA (5% increase; Table 9).
Because cobalamin is not present in the plant material that makes up dairy cow diets and is entirely synthesized by the rumen bacteria, unless the diet is supplemented with cobalamin, the B-vitamin dietary concentration was not considered in the development of cobalamin ARS.Increasing DMI increases rumen pool size and therefore the growth of both microbial pools, M A and M C , which could consequently augment VFA production and, as a result, VFA concentration (Van Soest, 1994).This increased microbial population may thus result in a greater concentration of cobalamin in the rumen, as the vitamin is mostly present within the bacteria (Santschi et al., 2005a).Finally, although cobalt is essential to cobalamin ARS, this important mineral was not a significant variable in the models generated, possibly due to the dietary cobalt content already being higher (Table 5) than the minimal requirements of 0.11 mg/kg of DM in the diet (NRC, 2001).
Cobalamin PRF Model and Interpretation.The PRF of cobalamin was best predicted by a positive relationship with DMI and a negative relationship with ST (Table 7), with a CCC of 0.852 (Table 8).The behavior analysis indicates that an increase of 10% in the DMI has the greatest effect on folate PRF, resulting in an increase of 9%, followed by ST (2% decrease; Table 9).
As is the case for thiamin and folate PRF, DMI has the largest effect on cobalamin PRF because it subsequently affects the level of microbial activity in the rumen.Unlike thiamin, riboflavin, and folates, however, increased ST decreases the amount of cobalamin reaching the duodenum, possibly due to an increased ruminal bacteria population utilizing the vitamin.Increasing the proportion of concentrate in the diet decreases the concentration of cobalamin and increases the concentration of analogs of the vitamin in bacteria or rumen contents in dairy cattle (Hayes et al., 1966;Walker and Elliot, 1972;Santschi et al., 2005b) and sheep (Elliot et al., 1971;Sutton and Elliot, 1972).Recently, Franco-Lopez et al. (2020) suggested that variations in the bovine ruminal abundance of cobalamin are due to the shift toward microbial genera identified as cobalamin users, including Bacteroidetes, Ruminiclostridium, and Butyrivibrio and their increased ruminal concentration.For cobalamin, any changes in the ARS of the vitamin directly affect the resulting PRF, because no cobalamin is coming from the diet, unless supplemented.

CONCLUSIONS
The results obtained from both the ARS and PRF models suggest that diet composition and rumen dynamics correlate with the synthesis and resulting variations in PRF of each B vitamin differently.We hypothesized that cobalamin is likely to be synthesized mainly by M C , with riboflavin, niacin, vitamin B 6 , and folates mainly by M A , emphasizing that B-vitamin intake is not the major factor controlling B-vitamin PRF.The models generated from this meta-analysis offer insight into the supply of B vitamins and may be used to guide further experimental work, formulate diets with improved estimates of B-vitamin supply, and eventually be incorporated into existing dairy models to improve performance predictions.Moreover, they highlight the need for additional research on the rumen microbiome, which-combined with a more comprehensive understanding of B-vitamin requirements of dairy cows, their passage through the abomasum and the small intestine, and the gut's absorptive capacity for B vitamins-would allow prediction of when cows may benefit from dietary supplementation.

2Figure 1 .
Figure 1.Observed versus predicted plots for the best-performing prediction equations of B-vitamin apparent ruminal synthesis (ARS; mg/d), as evaluated on the developmental data set.Solid line = line of unity; dashed line = regression line.Numbers/symbols correspond to study IDs inTable 1.

Figure 2 .
Figure 2. Observed versus predicted plots for the best-performing prediction equations of B-vitamin postruminal flow (PRF; mg/d), as evaluated on the developmental data set.Solid line = line of unity; dashed line = regression line.Numbers/symbols correspond to study IDs in Table1.
Brisson et al.: MODELING OF B VITAMINS IN DAIRY COWS Table 9. Behavior analysis 1 of the B-vitamin apparent ruminal synthesis (ARS) and postruminal flow (PRF) expected change (in %) in the predicted Y-variable (either ARS or PRF), with a ±10% change in the driving X variable.2 DC = B-vitamin dietary concentration; dNDF = digestible NDF; dS = digestible starch; pH = mean ruminal pH; PR = propionate; VFA = total VFA concentration; ST = dietary starch.

Table 1 .
Brisson et al.: MODELING OF B VITAMINS IN DAIRY COWS Brisson et al.: MODELING OF B VITAMINS IN DAIRY COWS Studies used to generate database 1 Brisson et al.: MODELING OF B VITAMINS IN DAIRY COWS

Table 2 .
Brisson et al.: MODELING OF B VITAMINS IN DAIRY COWS Spearman correlation matrix of dietary driving variables considered for model development before removal of outliers equation, those with a CCC value closest to 1 were selected as the best-performing models (Tables

Table 3 .
Brisson et al.: MODELING OF B VITAMINS IN DAIRY COWS Spearman correlation matrix of B-vitamin DC driving variables considered for model development before removal of outliers 1DMI is expressed in kg/d; all other dietary parameters are expressed in g/kg of DM. 2 DC = dietary concentration, mg/kg of DM. 3 Cobalamin dietary concentration is not included because no cobalamin comes from the diet.4Acetate,propionate, and butyrate are expressed as % of total VFA; total VFA concentration is expressed in mM, and fractional rate of potentially digestible NDF (pdNDF) and starch are expressed as %/h.*P ≤ 0.05, **P ≤ 0.001.

Table 4 .
Brisson et al.: MODELING OF B VITAMINS IN DAIRY COWS Spearman correlation matrix of rumen driving variables considered for model development before removal of outliers

Table 5 .
Brisson et al.: MODELING OF B VITAMINS IN DAIRY COWS Summary descriptive statistics of variables in the data sets used for the development and evaluation of the models 1 1After removal of outliers.Predictive models should be used within these biological ranges.

Table 7 .
Brisson et al.: MODELING OF B VITAMINS IN DAIRY COWS Best-performing prediction equations of B-vitamin 1 postruminal flow (PRF; mg/d)

Table 8 .
Model performance evaluation 1 of all prediction equations Brisson et al.: MODELING OF B VITAMINS IN DAIRY COWS