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The objective of this study was to investigate the effects of starch varying in rate of fermentation and level of inclusion in the diet in exchange for fiber on methane (CH4) production of dairy cows. Forty Holstein-Friesian lactating dairy cows of which 16 were rumen cannulated were grouped in 10 blocks of 4 cows each. Cows received diets consisting of 60% grass silage and 40% concentrate (dry matter basis). Cows within block were randomly assigned to 1 of 4 different diets composed of concentrates that varied in rate of starch fermentation [slowly (S) vs. rapidly (R) rumen fermentable; native vs. gelatinized corn grain] and level of starch (low vs. high; 270 vs. 530g/kg of concentrate dry matter). Results of rumen in situ incubations confirmed that the fractional rate of degradation of starch was higher for R than S starch. Effective rumen degradability of organic matter was higher for high than low starch and also higher for R than S starch. Increased level of starch, but not starch fermentability, decreased dry matter intake and daily CH4 production. Milk yield (mean 24.0±1.02kg/d), milk fat content (mean 5.05±0.16%), and milk protein content (mean 3.64±0.05%) did not differ between diets. Methane expressed per kilogram of fat- and protein-corrected milk, per kilogram of dry matter intake, or as a fraction of gross energy intake did not differ between diets. Methane expressed per kilogram of estimated rumen-fermentable organic matter (eRFOM) was higher for S than R starch-based diets (47.4 vs. 42.6g/kg of eRFOM) and for low than high starch-based diets (46.9 vs. 43.1g/kg of eRFOM). Apparent total-tract digestibility of neutral detergent fiber and crude protein were not affected by diets, but starch digestibility was higher for diets based on R starch (97.2%) compared with S starch (95.5%). Both total volatile fatty acid concentration (109.2 vs. 97.5mM) and propionate proportion (16.5 vs. 15.8mol/100mol) were higher for R starch- compared with S starch-based diets but unaffected by the level of starch. Total N excretion in feces plus urine and N retained were unaffected by dietary treatments, and similarly energy intake and output of energy in milk expressed per unit of metabolic body weight were not affected by treatments. In conclusion, an increased rate of starch fermentation and increased level of starch in the diet of dairy cattle reduced CH4 produced per unit of eRFOM but did not affect CH4 production per unit of feed dry matter intake or per unit of milk produced., (Copyright © 2015 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

An isotope dilution model for partitioning phenylalanine and tyrosine uptake by the mammary gland of the lactating dairy cow is constructed and solved in the steady state. The model contains four intracellular and four extracellular pools and conservation of mass principles are applied to generate the fundamental equations describing the behaviour of the system. The experimental measurements required for model solution are milk secretion and plasma flow rate across the gland in combination with phenylalanine and tyrosine concentrations and plateau isotopic enrichments in arterial and venous plasma and free and protein bound milk during a constant infusion of [1-(13)C]phenylalanine and [2,3,5,6-(2)H]tyrosine tracer. If assumptions are made, model solution enables determination of steady state flows for phenylalanine and tyrosine inflow to the gland, outflow from it and bypass, and flows representing the synthesis and degradation of constitutive protein and phenylalanine hydroxylation. The model is effective in providing information about the fates of phenylalanine and tyrosine in the mammary gland and could be used as part of a more complex system describing amino acid metabolism in the whole ruminant., (Copyright © 2014 Elsevier Ltd. All rights reserved.)

A dynamic, mechanistic model of the sulfur hexafluoride (SF6) tracer technique, used for estimating methane (CH4) emission rates from ruminants, was constructed to evaluate the accuracy of the technique. The model consists of six state variables and six zero-pools representing the quantities of SF6 and CH4 in rumen and hindgut fluid, in rumen and hindgut headspace, and in blood and collection canister. The model simulates flows of CH4 and SF6 through the body, subsequent eructation and exhalation and accumulation in a collection canister. The model predicts CH4 emission by multiplying the SF6 release rate of a permeation device in the rumen by the ratio of CH4:SF6 in collected air. This prediction is compared with the actual CH4 production rate, assumed to be continuous and used as a driving variable in the model. A sensitivity analysis was conducted to evaluate the effect of changes in several parameters. The predicted CH4 emission appeared sensitive to parameters affected by the difference in CH4:SF6 ratio in exhaled and eructed air respectively, viz., hindgut fractional passage rate and hindgut CH4 production. This is caused by the difference in solubility of CH4 and SF6 and by hindgut CH4 production. In addition, the predicted CH4 emission rate appeared sensitive to factors that affect proportions of exhaled and eructed air sampled, i.e., eructation time fraction, exhalation time fraction, and distance from sampling point to mouth/nostrils. Changes in rumen fractional passage rate, eructation rate, SF6 release rate, background values and air sampling rate did not noticeably affect the predicted CH4 emission. Simulations with (13)CH4 as an alternative tracer show that the differences and sensitivity to parameters greatly disappear. The model is considered a useful tool to evaluate critical points in the SF6 technique. Data from in vivo experiments are needed to further evaluate model simulations., (Copyright © 2014 Elsevier Ltd. All rights reserved.)

A meta-analysis investigation based on literature data was conducted to estimate the effect size of nutritional and animal factors on phosphorus (P) excretion in feces and concentrations of P in milk. Two data sets were created for statistical analysis: One to derive prediction equations for P in feces (25 studies; 130 treatments) and another for P in milk (19 studies; 94 treatments). Prediction equations were derived using mixed model regression analysis with a random effect for study, and equations were evaluated based on values for Bayesian information criterion (BIC), root mean square prediction error (RMSPE), and concordance correlation coefficient (CCC) statistics. In terms of RMSPE and CCC values, fecal P excretion was best predicted by P intake, where P in feces (g/d)=-3.8(±3.45) + 0.64(±0.038) × P intake (g/d) (RMSPE: 18.3%, CCC: 0.869). However, significant effects of crude protein [g/kg of dry matter (DM)], neutral detergent fiber (g/kg of DM), and milk yield (kg/d) on fecal P excretion were also found. Despite a lack of improvement in terms of RMSPE and CCC values, these parameters may still explain part of the variation in fecal P excretion. For milk P, expressed as a fraction of P intake, the following equation had the highest CCC and the lowest RMSPE value: P in milk as a fraction of P intake (g/g)=0.42(±0.065) + 0.23(±0.018) × feed efficiency (i.e., fat- and protein-corrected milk yield/dry matter intake) - 0.11(±0.0199) × P in feed (g/kg of DM) (RMSPE: 19.7%; CCC: 0.761). Equations derived to predict fecal P as a fraction of P intake (g/g) or milk P content (g/kg) could not adequately explain the observed variation and did not perform well in terms of RMSPE and CCC values. Examination of the residuals showed that P balance was a seemingly confounding factor in some of the models. The results presented here can be used to estimate P in feces and milk based on commonly measured dietary and milk variables, but could also be used to guide development of mechanistic models on P metabolism in lactating dairy cattle. Factors to consider in future research and modeling efforts regarding efficiency of P use include the effects of dietary neutral detergent fiber, crude protein, starch, variation in P content of milk, and effects of P resorption from bone and body tissues during early lactation., (Copyright © 2013 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

Monensin is a common feed additive used in various countries, where 1 of the associated benefits for use in beef cattle is improved efficiency of energy metabolism by the rumen bacteria, the animal, or both. Modeling fermentation-altering supplements is of interest, and thus, it is the purpose of this paper to quantify the change in VFA profile caused by monensin dose in high-grain-fed beef cattle. The developmental database used for meta-analysis included 58 treatment means from 16 studies from the published literature, and the proportional change in molar acetate, propionate, and butyrate (mol/100 mol) as well as total VFA (mM) with monensin feeding dose (mg/kg DM, concentration in the feed) was evaluated using the MIXED procedure (SAS Inst. Inc., Cary, NC) with the study treated as a random effect. The mean monensin dose in the literature database was 30.9 ± 3.70 mg/kg DM and ranged from 0.0 to 88.0 mg/kg DM. Mean DMI was 7.8 ± 0.26 kg DM/d, mean concentrate proportion of the diet was 0.87 ± 0.01, and mean treatment period was 42 ± 5.6 d. Results produced the following equations: proportional change in acetate (mol/100 mol) = -0.0634 (± 0.0323) × monensin (mg/kg DM)/100 (P = 0.068), proportional change in propionate (mol/100 mol) = 0.260 (± 0.0735) × monensin (mg/kg DM)/100 (P = 0.003), and proportional change in butyrate (mol/100 mol) = -0.335 (± 0.0916) × monensin (mg/kg DM)/100 (P = 0.002). The change in total VFA was not significantly related to monensin dose (P = 0.93). The results presented here indicate that the shift in VFA profile may be dose dependent, with increasing propionate and decreasing acetate and butyrate proportions (mol/100 mol). These equations could be applied within mechanistic models of rumen fermentation to represent the effect of monensin dose on the VFA profile in high-grain-fed beef cattle.

High-sugar grass varieties have received considerable attention for their potential to reduce nitrogen (N) excretion and increase milk yield in cattle. However, considerable variation exists in the magnitude of response in published results. The purpose of this study is to explain the variation in response using a dynamic mechanistic model to predict observed N and milk yield results from the literature, and from simulated data. Examined effects were (1) water-soluble carbohydrate [WSC; g/kg of dry matter (DM)] increase; (2) change in crude protein (CP) and neutral detergent fiber (NDF) content of the plant with WSC increase; and (3) the level of N fertilization. The database for evaluation of model N and milk yield predictions consisted of 4 published studies with 28 treatment means for which high-sugar grasses were being evaluated. Water-soluble carbohydrate content of the diets ranged from 95 to 248 g/kg of DM, CP content ranged from 115 to 263 g/kg of DM, and the NDF content ranged from 400 to 568 g/kg of DM. Urine N, milk N, and total N excretion were predicted well by the model and followed the directional pattern of observed values within each study. Simulation results showed that the N utilization ratio increased as the WSC content of the diet increased, but to varying degrees depending on the grass scenario examined. The greatest benefit in terms of N utilization ratio and urine N levels were seen when the WSC content of grass increased at the expense of CP, followed by a 50:50 CP and NDF mix, followed by a trade for NDF. Simulated milk yield decreased slightly when WSC increased at the expense of CP, increased slightly when it increased at the expense of a CP and NDF mix, and increased most when WSC increased at the expense of NDF. Results were amplified slightly under conditions of low-N fertilization and in the absence of grain feeding. Overall, modeling is useful as an explanatory tool. The variation from results in the literature with high-WSC grass feeding may be, at least in part, the result of the level of WSC (g/kg of DM) increase, concurrent changes occurring within the CP and NDF fractions of the plant, and the plane of nutrition of the diet (grain feeding and N fertilization levels)., (Copyright © 2011 American Dairy Science Association. Published by Elsevier Inc. All rights reserved.)

Canada is committed to reducing its greenhouse gas emissions to 6% below 1990 amounts between 2008 and 2012, and methane is one of several greenhouse gases being targeted for reduction. Methane production from ruminants is one area in which the agriculture sector can contribute to reducing our global impact. Through mathematical modeling, we can further our understanding of factors that control methane production, improve national or global greenhouse gas inventories, and investigate mitigation strategies to reduce overall emissions. The purpose of this study was to compile an extensive database of methane production values measured on beef cattle, and to generate linear and nonlinear equations to predict methane production from variables that describe the diet. Extant methane prediction equations were also evaluated. The linear equation developed with the smallest root mean square prediction error (RMSPE, % observed mean) and residual variance (RV) was Eq. I: CH(4), MJ/d=2.72 (+/-0.543) + [0.0937 (+/-0.0117) x ME intake, MJ/d] + [4.31 (+/-0.215) x Cellulose, kg/d] - [6.49 (+/-0.800) x Hemicellulose, kg/d] - [7.44 (+/-0.521) x Fat, kg/d] [RMSPE=26.9%, with 94% of mean square prediction error (MSPE) being random error; RV=1.13]. Equations based on ratios of one diet variable to another were also generated, and Eq. P, CH(4), MJ/d=2.50 (+/-0.649) - [0.367 (+/-0.0191) x (Starch:ADF)] + [0.766 (+/-0.116) x DMI, kg/d], resulted in the smallest RMSPE values among these equations (RMSPE=28.6%, with 93.6% of MSPE from random error; RV=1.35). Among the nonlinear equations developed, Eq. W, CH(4), MJ/d=10.8 (+/-1.45) x (1-e([-0.141 (+/-0.0381) x DMI, kg/d])), performed well (RMSPE=29.0%, with 93.6% of MSPE from random error; RV=3.06), as did Eq. W(3), CH(4), MJ/d=10.8 (+/-1.45) x [1-e({-[-0.034 x (NFC/NDF)+0.228] x DMI, kg/d})] (RMSPE=28.0%, with 95% of MSPE from random error). Extant equations from a previous publication by the authors performed comparably with, if not better than in some cases, the newly developed equations. Equation selection by users should be based on RV and RMSPE analysis, input variables available to the user, and the diet fed, because the equation selected must account for divergence from a "normal" diet (e.g., high-concentrate diets, high-fat diets).

Methane (CH4) is one of the major greenhouse gases being targeted for reduction by the Kyoto protocol. The focus of recent research in animal science has thus been to develop or improve existing CH4 prediction models to evaluate mitigation strategies to reduce overall CH4 emissions. Eighty-three beef and 89 dairy data sets were collected and used to develop statistical models of CH4 production using dietary variables. Dry matter intake (DMI), metabolizable energy intake, neutral detergent fiber, acid detergent fiber, ether extract, lignin, and forage proportion were considered in the development of models to predict CH4 emissions. Extant models relevant to the study were also evaluated. For the beef database, the equation CH4 (MJ/d) = 2.94 (+/- 1.16) + 0.059 (+/- 0.0201) x metabolizable energy intake (MJ/d) + 1.44 (+/- 0.331) x acid detergent fiber (kg/d) - 4.16 (+/- 1.93) x lignin (kg/d) resulted in the lowest root mean square prediction error (RMSPE) value (14.4%), 88% of which was random error. For the dairy database, the equation CH4 (MJ/d) = 8.56 (+/- 2.63) + 0.14 (+/- 0.056) x forage (%) resulted in the lowest RMSPE value (20.6%) and 57% of error from random sources. An equation based on DMI also performed well for the dairy database: CH4 (MJ/d) = 3.23 (+/- 1.12) + 0.81 (+/- 0.086) x DMI (kg/d), with a RMSPE of 25.6% and 91% of error from random sources. When the dairy and beef databases were combined, the equation CH4 (MJ/d) = 3.27 (+/- 0.79) + 0.74 (+/- 0.074) x DMI (kg/d) resulted in the lowest RMSPE value (28.2%) and 83% of error from random sources. Two of the 9 extant equations evaluated predicted CH4 production adequately. However, the new models based on more commonly determined values showed an improvement in predictions over extant equations.

In the dynamic modeling of dairy cow performance over a full lactation, the difference between net energy intake and net energy used for maintenance, growth, and output in milk accumulates in body reserves. A simple dynamic model of net energy balance was constructed to select, out of some common dry matter intake (DMI) prediction equations, the one that resulted in a minimum cumulative bias in body energy deposition. Dry matter intake was predicted using the Cornell Net Carbohydrate and Protein System, Agricultural Research Council, or National Research Council (NRC) DMI equations from body weight (BW) and predicted fat-corrected milk yield. The instantaneous BW of cows at progressive weeks of lactation was simulated as the numerical integral of the BW change obtained from the predicted net energy balance. Predicted DMI and BW from each DMI equation, using either of 2 equations to describe maintenance energy expenditures, were compared statistically against observed data from 21 herd average published full lactation data sets. All DMI equations underpredicted BW and DMI, but the NRC DMI equation resulted in the minimum cumulative error in predicted BW and DMI. As a general solution to prevent predicted BW from deviating substantially over time from the observed BW, a lipostatic feedback mechanism was integrated into the NRC DMI equation as a 2-parameter linear function of the relative size of simulated body reserves and week of lactation. Residual sum of squares was reduced on average by 52% for BW predictions and by 41% for DMI predictions by inclusion of the negative feedback with parameters taken from the average of all 21 least squares fits. Similarly, root mean square prediction error (%) was reduced by 30% on average for BW predictions and by 23% for DMI predictions. Inclusion of a feedback of energy reserves onto predicted DMI, simulating lipostatic regulation of BW, solved the problem of final BW deviation within a dynamic model and improved its DMI prediction to a satisfactory level.

Equations that predict daily dry matter intake (DMI) of a lactating cow could be evaluated by comparing the predicted accumulation of energy in body weight (BW) over the course of lactation with the observed BW evolution. However, to do so requires that first the energy balance calculations from observed DMI are evaluated. The purpose of the work reported here was to determine the degree of deviation of predicted from observed BW, according to net energy for lactation (NE(L)) balance calculated from weekly observations of DMI, BW, and fat-corrected milk production in 21 sets of full-lactation data, and to determine an appropriate correction of the NE(L) bias for subsequent DMI prediction evaluations. When the National Research Council maintenance equation 0.08 x BW(kg)(0.75) was used in energy balance calculation, BW was overpredicted with an increasing difference between the cumulative predicted BW and observed BW as lactation progressed. Placing all the error of BW prediction into maintenance energy expenditures resulted in a best-fit equation of 0.096 +/- 0.003 Mcal/kg of BW(0.75). A time-dependent equation was also developed, in which weekly maintenance expenditures were determined as the NE(L) expenditure to yield a zero NE(L) balance and could be described by a second-order polynomial equation related to week of lactation (WOL) where maintenance NE(L) = [-0.0227(+/- 0.0098) x WOL2 + 1.352(+/- 0.456) x WOL + 78.09(+/- 4.92) Mcal/kg of BW(0.75)] x 10(-3). Average maintenance energy expenditure at the onset of lactation was approximately 0.08 Mcal/kg of BW(0.75), and this value increased to a plateau at wk 15 of lactation of approximately 0.098 Mcal/kg of BW(0.75). Standard deviations between data sets of weekly maintenance parameter estimates throughout lactation were large but consistent at approximately 25% of the mean. Revision of the maintenance energy expenditure estimate substantially improved BW prediction by the energy balance model. On average, the 0.096 Mcal of NE(L)/kg of BW(0.75) equation resulted in the best BW predictions, although substantial variation existed around this value.