Evaluation of methane prediction equations for Australian feedlot cattle fed barley and wheat-based diets

Description of the evaluation and new equation parametrisation database

The database used for evaluation of extant equations and development of a new equation in this study was pooled from four open circuit respiration chamber studies (published and unpublished; Tables S1, S2) conducted at the Large Animal Facility at the Centre for Animal Research and Teaching (CART) of the University of New England (Armidale, NSW Australia), 2018 to 2022. All experiments followed animal care and handling procedures in accordance with approvals granted by the Animal Ethics Committee of the University of New England (authorities numbers: AEC-18-028, ARA21-106, AEC-20-061, and ARA22-013).

An initial database of 384 individual records from 53 feedlot cattle was assembled for validation of extant literature equations and new model parametrisation (Database 1, Table 1, Table S1). In these studies, feedlot cattle were fed transition and finisher diets based on tempered rolled barley. Diets differed in roughage, grain, and canola oil content, resulting in variation in the neutral detergent fibre (NDF), ether extract (EE) and starch concentration within the database (Table 1). The diets in all studies contained 25 mg/kg DM of monensin. Study cattle were managed as closely as possible to commercial feedlot conditions (please refer to the Supplementary material for further information on diets). No study cattle were treated with hormonal growth promotants (HGP) or fed other additives to stimulate growth, feed efficiency or CH₄ production.

Study ARA22-013 (A. Almeida, unpubl. data) was the largest proportion of the database (82.03%). A steering committee consisting of consulting feedlot nutritionists designed diet specifications to reflect a range of diets representative of the Australian lot feeding industry. A total of 16 different diets containing four levels of NDF (19.4%, 24.7%, 29.8%, and 34.4% of DM) and four levels of EE (3.1%, 4.3%, 5.3%, and 6.7% of DM) were evaluated over a 112-day feeding period. Two blocks of 20 Angus steers with initial body weight (BW) of 336 ± 21 kg (five animals per EE level; 40 total), were stepped down from 34.4% to 19.4% NDF, using four 28-day periods on each NDF level. The CH₄ production was individually measured eight times, on days 20, 27, 48, 55, 76, 83, 104, and 111, resulting in a total of 320 observations. One steer was injured on day 56 and was excluded from measurement periods on days 62, 69, 76, 83, 90, 97, 104 and 111. In addition, one other individual chamber observation on day 7 was removed, due to low DMI of one steer during CH₄ measurement. The final number of observations used in the analyses were 315.

Study AEC-20-061 (previously published as Almeida et al. 2023) involved four Angus steers with CH₄ measured over a 112-day feeding period. Steers were transitioned to a final finisher diet by day 21, utilising three transition diets (7 days each). Mean analysed NDF (40.5%, 33.7%, 31.3% and 29.0%) and EE (4.35%, 4.70%, 5.57% and 6.66%) were recorded for starter, transition 1, transition 2 and finisher diets, respectively. The CH₄ production was individually measured eight times, on days 7, 14, 21, 28, 49, 70, 91, and 112, resulting in a total of 32 observations. Two individual chamber observations were removed from the dataset on day 28 because of low DMI of two steers during CH₄ measurement. The final number of observations used in the analyses were 30 (7.81% of database).

Study ARA-21-106 (previously published as Cowley et al. (2024a) involved five Angus heifers (initial BW 346 ± 6 kg) fed for an 81-day period. Heifers were transitioned to a final finisher diet by day 23, by feeding three transition diets. Starter was fed for 8 days, transition 1 for 8 days, and transition 2 for 7 days. Mean analysed NDF (42.0%, 33.8%, 28.5% and 28.0%) and EE (4.6%, 4.6%, 4.7%, and 5.2%) were recorded for starter, transition 1, transition 2 and finisher diets, respectively. The CH₄ was individually measured seven times, on days 6, 14, 21, 34, 48, 62 and 76. One heifer contracted ruminal acidosis on day 52 and was excluded from measurement periods on days 62 and 76. In addition, one other individual chamber observation at day 21 was removed due to low DMI of one heifer during CH₄ measurement. The final number of observations used in the analysis were 32 (8.33% of database).

Study AEC-18-028 (A. Nortup, unpubl. data) involved four Lowline Angus cattle (198 ± 39 kg initial BW) fed for 28 days. Steers were fed 2.0% BW (DM basis), and were progressively adapted through starter, transition 1, and transition 2 and finisher diets with 1 week on each diet (45%, 56%, 67% and 79% tempered barley respectively, DM basis). The CH₄ was individually measured on days 6 and 7 of the finisher period only. One individual chamber observation on day 7 was removed due to low DMI of one steer during CH₄ measurement. The final number of observations used in the analyses were seven (1.82% of database).

Description of the new model validation database

For validation of the new equation, a second database of 329 individual records from 122 feedlot cattle was assembled (Database 2; Table 1, Tables S1 and S3), pooled from eight open circuit respiration chamber studies conducted at the Large Animal Facility at CART at the University of New England from 2022 to 2024. All experiments followed animal care and handling procedures in accordance with approvals granted by the Animal Ethics Committee of the University of New England (Authorities numbers: ARA22-094, ARA 23-018, ARA22-038, ARA24-020, ARA22-101, ARA23-069, ARA23-069.1, and ARA24-030). In these studies, HGP-free feedlot cattle of Angus, Shorthorn, Santa Gertrudis, Wagyu and Brahman × Bos taurus composite breeds were fed transition and finisher diets based on tempered rolled barley or steam-flaked barley or wheat, or combinations of steam-flaked wheat and barley.

Study ARA22-094 (previously published as Chowdhury et al. 2024) involved four Brahman × Bos taurus composite steers (initial BW: 361 ± 35.5 kg) fed for 77 days. The steers were transitioned to a 50% steam-flaked barley- and 50% steam-flaked wheat-based finisher diet by day 22, using three intermediate transition diets, each fed for 7 days. Mean analysed NDF (35.9%, 30.1%, 29.6%, and 26.2% DM) and EE (2.6%, 4.9%, 3.7%, and 6.2% DM) were recorded for the starter, transition 1, transition 2, and finisher diets, respectively. Methane emissions were measured individually seven times, on days 7, 14, 21, 35, 49, 63, and 77, resulting 28 observations in total. Due to a chamber malfunction on day 7, one reading was excluded, leaving 27 observations (7.7% of the database) for the final analysis.

Study ARA22-038 (previously published as Cowley et al. (2024b)) involved eight Brahman × Bos taurus composite steers (initial BW: 374 ± 16.3 kg) and four Angus steers (initial BW: 346 ± 15.2 kg) fed for a 55-day period. Steers were transitioned to three different finisher diets, based on either steam-flaked barley, steam-flaked wheat or a mix of equal parts steam-flaked barley and steam-flaked wheat by day 22, utilising three transition diets fed for 7 days each. Mean NDF (40.1%, 38.2%, 34.2%, and 29.0% DM) and EE (3.4%, 2.9%, 2.3%, and 6.2% DM) were recorded for the starter, transition 1, transition 2, and finisher diets, respectively. A total of 48 CH₄ emission observations were collected, with individual measurements conducted four times, on days 13, 20, 27, and 34. Observations included in the final analysis represented 13.6% of the database.

Study ARA24-020 (F. Cowley, unpubl. data) involved 10 Shorthorn steers (initial BW: 267 ± 19.5 kg) fed a tempered barley-based transition 1 diet over a 21-day period. Steers underwent a 7-day adaptation to housing and a total mixed ration (TMR), followed by a 14-day experimental phase. The diet contained 27.3% NDF and 3.8% EE on a DM basis. Enteric CH₄ emissions were measured five times, on days 7, 8, 13, and 14, resulting in a total of 40 observations. For the final analysis, baseline measurements from all 10 steers, (n = 20) and control group (n = 4) observations were included, representing 6.8% of the database.

Study ARA22-101 (F. Cowley, unpubl. data) involved 20 Angus steers (initial BW: 425 ± 35.5 kg) fed over a 63-day period. Steers were transitioned to a tempered barley-based finisher diet by day 22, using the starter, transition 1 and transition 2 diets, each fed for 7 days. Mean NDF (31.4%, 28.9%, 29.6%, and 30.1% DM) and EE (3.9%, 4.3%, 3.9%, and 4.6% DM) concentrations were recorded for the starter, transition 1, transition 2, and finisher diets, respectively. Methane emissions were recorded five times, on days 22, 28, 35, 49, and 63. The final analysis included baseline methane data (n = 20) from day 22 and control group measurements (n = 20) from subsequent sampling days, contributing 40 observations (11.4% of the database).

Study ARA23-018 (F. Cowley, unpubl. data) involved five pureblood Wagyu steers (initial BW: 530 ± 31.2 kg) fed tempered barley and corn-silage based grower and then finisher diets for 42 days each, following a 4-day period of adaptation to housing. Mean NDF (26.2 and 25.5%) and EE (4.1 and 4.0%) concentrations were recorded for the grower and finisher diets, respectively. Methane emissions were recorded four times per diet, on days 34 and 41 (grower diet), and days 76 and 83 (finisher diet). The final observations used in the analysis were 24, representing 7% of the database.

Study ARA23-069 (F. Cowley, unpubl. data) involved 40 Santa Gertrudis steers (initial BW: 342 ± 35.8 kg) fed a tempered barley-based finisher diet over an 83-day period, with a 5-day adaptation to housing and the finisher ration followed by a 78-day experimental phase. The diet had an NDF and EE concentration of 34.1% and 3.5% on DM basis, respectively. Methane was individually measured on days 7, 8, 19, 20, 50, 51, 82, and 83. Due to a chamber malfunction on day 20, one reading was excluded. In the final analysis, only baseline measurements (n = 79) and control group data (n = 30) were included, accounting for 30% of the database.

Study ARA23-069.1 (F. Cowley, unpubl. data) involved 20 Angus cross steers (initial BW: 311 ± 46.6 kg) fed a tempered barley-based finisher diet over a 56-day period. After a 5-day adaptation to housing and the finisher diet, the experimental phase spanned 51 days and included a 23-day washout period between two 14-day sampling periods. The diet had an NDF concentration of 32.6% and an EE concentration of 4.0% on a DM basis. Enteric CH₄ emissions were measured individually on days 7, 8, 19, 20, 55, and 56. Only baseline observations (n = 40) measured at day 7 and 8 were included in the final analysis, which contributed 11.4% of the database.

Study ARA24-030 (F. Cowley, unpubl. data) was conducted using 20 Shorthorn × Hereford steers (initial BW: 306 ± 19.1 kg) fed for a period of 96 days. After a 14-day adaptation to housing and a tempered barley-based transition 1 diet, the steers underwent an 82-day experimental phase, which included a 3-day baseline measurement and three 13-day sampling periods, separated by a 20-day washout period. Steers were transitioned to the finisher diet by day 22, using three successive transition diets each fed for 7 days. The transition 1 diet had an NDF and EE concentration of 33.0% and 3.7% on DM basis. Individual CH₄ measurements were recorded on days 0, 1, 13, 14, 46, 47, 79, and 80. For the final analysis, only baseline observations (n = 40) collected on day 0 and 1 with the transition 1 diet were included, comprising 11.4% of the database.

Feeding and feed chemical composition

For the evaluation of extant equations and new model parametrisation, a total of 25 unique tempered rolled barley-based diets were used across all studies. For the validation of the new models, a total of 12 unique tempered rolled barley- and steam-flaked barley and/or wheat-based diets were used across all studies. The average chemical composition of the diets observed in the databases is reported in Table 1 (see Tables S2, S3 for further details). All studies adopted similar mixing procedures and feed chemical analyses. Dry matter (DM) of feed offered and refusals were measured (AOAC 1990, method 924.05) and feed offered was analysed for chemical analysis and fractions. Approximately three grab samples (~500 g) were collected at mixing of each batch of the diet. The samples were sealed and frozen at −20°C before analysis in duplicate. Gross energy was determined by using an adiabatic calorimetric bomb (Parr Instrument Co., Moline, IL, USA). Fat content (EE; AOAC 1990, method 930.15), starch (AOAC Method 996.11) and crude protein (CP) content by N analysis with Dumas combustion, by using Leco FP-528LC (Etheridge et al. 1998), were also analysed. The NDF content was determined with amylase and without sodium sulfate (Van Soest et al. 1991), and acid detergent fibre (ADF) and detergent lignin (ADL) were determined (Goering and Van Soest 1970) in an ANKOM 2000 Fiber Analyzer (ANKOM Technology, Macedon NY, USA). All ANKON F57 bags were then analysed for ash (AOAC 1990; method number 924.05) and fibre fractions were corrected for ash content. Hemicellulose was calculated by difference (NDF – ADF), cellulose was calculated as the difference between ADF and ADL, and soluble residue (SR) was calculated by subtracting CP and EE from the neutral detergent solubles (Database 1 only).

Measurements of CH₄ production

For measurement of CH₄ production, the cattle were confined over 23 h in open circuit respiration chambers (~20 m³) after at least 7 days adaptation to each diet. Briefly, chambers were sealed in the morning when cattle were fed. When in chambers, the cattle had ad libitum access to feed and water. Air temperature was controlled centrally and kept at ~21 °C for all chambers. Air temperature and relative humidity were measured in each chamber using sensors (BME280, Bosch Sensortec, Gerlingen, Germany). Air flow through each chamber (mean = 1.6 m³/min) was controlled using a flow meter (Model ST75V, Fluid Components International, San Marcos, CA, USA). For AEC-18-028, ARA21-106, AEC-20-061, ARA22-013, ARA22-094, and ARA22-038, the concentration of CH₄ (parts per million per volume) was measured in the chamber incoming (ambient) and exhaust air streams using a Servomex Multigas Analyzer (Servomex 4100 Gas Purity Analyzer) calibrated for CH₄, CO₂ and O₂, before each measurement day. Moisture was removed by a drying column before a multiplexer was used to direct the dried sample air from each chamber and the ambient air into the analyser in turn. CH₄, CO₂ and O₂ concentrations were measured over 10 s after a 40 s purge time, by the Servomex analyser. Air flow and gas concentration data from the sampled air were loaded directly into a daily workbook with separate Excel spreadsheets for each chamber every 9 min, and used to calculate g of CH₄/L air. For ARA24-020, ARA22-101, ARA23-069, ARA23-069.1, and ARA24-030, the concentration of CH₄ (parts per million per volume) was measured in the chamber incoming (ambient) and exhaust air streams using a low-pressure sampling Optical Feedback Cavity Enhanced Absorption Spectroscopy Analyser, (Proceas®, AP2E, Aix-en-Provence, France), auto-calibrated for CH₄, CO₂, O₂, H₂, NH₃, and N₂O. A multiplexer was used to direct the dried sample air from each chamber and the ambient air into the analyser in turn. CH₄, CO₂, O₂, H₂, NH₃, and N₂O concentrations were measured over 90 s after a 30 s purge time, by the Proceas® analyser. For all data, air flow was corrected to standard temperature and pressure, accounting for altitude, and hourly variation in temperature and barometric air pressure. CH₄ production was averaged hourly and daily CH₄ production estimated by the area under the curve by the approximate integral using the trapezoidal rule. In all cases, recovery of CH₄ through the chambers was assessed pre-measurement and post-measurement by introducing pure CH₄ at a known rate via a mass flow controller (Smart Trak 2 Series 100, Sierra Instruments, Monterey, CA, USA) and the gas analyser was used to quantify CH₄ concentration. All daily CH₄ emission data was corrected for 100% of CH₄ recovery. Mean CH₄ recovery was 96.8 ± 4.48% (AEC-18-028), 92.8 ± 1.36% (AEC-20-061), 97.5 ± 2.05% (ARA-21-106) 101 ± 3.28% (AEC-22-013), 97.4 ± 1.46% (ARA22-038), 92.9 ± 2.93% (ARA22-094), ARA24-020, 91.9 ± 2.95% (ARA22-101), 94.1 ± 3.11% (ARA23-018) and 98.0 ± 3.07% (ARA23-069.1). CH₄ yield (g CH₄/kg DMI) was calculated by dividing the CH₄ production by DMI recorded at the CH₄ measurement day. Please refer to Hegarty et al. (2012) for further details on the use of the open circuit respiration chambers and CH₄ measurement protocols.

Selection of CH₄ prediction equations

The prediction equations evaluated for CH₄ emissions from feedlot cattle fed grain-based diets were from Moe and Tyrrell (1979), IPCC (2006, 2019), Escobar-Bahamondes et al. (2017a), and Galyean and Hales (2022) (Table 2). We reviewed several candidate equations and selected the ones that were likely derived from datasets similar to the one we used in the present study, required input variables that were available in our database and included predictor variables that can be easily determined by commercial feed analysis laboratories. The Moe and Tyrrell (1979) equation, which is currently used to predict CH₄ emissions of feedlot cattle in the Australian National Inventory Report (Commonwealth of Australia 2023), takes into account the intake of cell wall carbohydrates (HC and CEL) and cell contents (SR = 100 – NDF – EE – CP) (Eqn 1, Table 2). The IPCC (2006) tier 2 equation uses an emission conversion factor (Y_m) based on daily gross energy intake (GEI, MJ/day) (Eqn 2, Table 2). For diets containing 90% or more concentrate (typical of feedlot finisher diets), the IPCC specifies Y_m is 3.0 ± 1.0% of GEI. For all other diets and cattle categories, the IPCC specifies Y_m is 6.5 ± 1.0%. The IPCC (2019) tier 2 approach uses CH₄ yield (MY) of 21.0 g CH₄/kg dry matter intake (DMI, equivalent to Y_m = 6.3%; total mixed rations with 15–75% of high-quality forage), MY = 13.6 g CH₄/kg DMI (equivalent to Y_m = 4.0%; non-steam-flaked corn-based diets, forage from 0 to 15%) (Eqn 3a – used MY and Eqn 3b used Y_m, Table 2). The equations proposed by Escobar-Bahamondes et al. (2017a) included as inputs BW, crude protein intake, CP:NDF and dietary starch:NDF ratios, and polynomial effects of fat², DMI² and (NDF – ADF)³ (Eqns 4a, 4b, Table 2, see supplementary material in Escobar-Bahamondes et al. (2017a) for further details on the database used to derive Eqns 4a, 4b). Finally, Galyean and Hales (2022) proposed modified Ellis et al. (2009) equations that can predict CH₄ production (g/day) from DMI, dietary starch:NDF ratio with or without dietary ether extract (EE) concentration, assuming an energy value of 55.65 MJ/kg CH₄ (Eqns 5a, 5b, Table 2, please refer to supplementary data in Galyean and Hales (2022) for further details on the database used to derive Eqns 5a, 5b).

Evaluation of equation adequacy

Each equation was assessed by regressing residual (observed – predicted) values on the predicted values, centred on their mean values (St-Pierre 2003). This procedure makes the intercept and slope estimates independent. We performed the analysis using the PROC MIXED of SAS 9.4 (SAS Systems Inc., Cary, NC; St-Pierre 2001). The slopes and intercepts of each equation were estimated using the ESTIMATE statement of the MIXED procedure in SAS, along with the root mean square error (RMSE) of this regression. The intercepts of the regression equations were the mean biases, whereas the slopes of such regression equations were the linear biases. When linear bias was significant (P ≤ 0.05) the bias and minimum and maximum predicted values were calculated. Additionally, observed CH₄ was regressed on predicted CH₄ for each equation. The coefficient of determination (r²) was obtained as a measure of the strength of the relationship between observed and predicted CH₄. To evaluate model precision, several commonly used measures of adequacy were employed, including mean absolute error (MAE), mean square prediction error (MSPE), as described in Table S4. The MSPE was decomposed into mean bias, systematic bias, and random variation to assess sources of variation (Table S4, McMeniman et al. 2009). Additionally, the concordance correlation coefficient (CCC; Lin 1989) was estimated for each equation. The closer the CCC of a model to 1, the better the equation (accuracy and precision).

Sensitivity analysis

Pearson’s correlation coefficients were calculated using the CORR procedure to determine the strength of the linear relationship between the input variables and CH₄ emissions in feedlot cattle, as well as between the input variables themselves. Then sensitivity analysis was performed to evaluate the variability of existing empirical equations to predict feedlot cattle CH₄ emission predictions using Monte Carlo simulations. This involved varying the input of independent variables within each equation using the minimum and maximum values of each input variable in the database to simulate the local sensitivity of CH₄ predictions, while the other input variables within a given equation was kept at its mean value. The resulting range of CH₄ predictions for each equation was then illustrated using tornado plots.

New equation parametrization and validation

Based on the correlation analysis and graphical exploration on the input variables in the database, we identified variables that exhibited a strong association with CH₄ production, had low correlation among themselves, and could be easily measured. To assess the potential for adjusting coefficients in predicting daily CH₄ production in g/day, we conducted stepwise regression analyses using SAS software (STEPWISE procedure; SAS Systems Inc., Cary, NC). Variables tested included: DMI, CP, EE, starch, and NDF content. Significance was declared at P < 0.05. Statistical analysis in all models was performed using the MIXED procedure of SAS software. Linear mixed model regressions were fitted assuming the effect of study as a random effect. The slopes and intercepts of each equation were estimated using the ESTIMATE statement of the MIXED procedure in SAS.

The general statistical model used was as follows:

CH_4ijk = is the dependent variable for the jth animal of the ith study, X_ij is the independent variable for the jth animal of the ith study, a_j and b_j are the parameters to be estimated, s_j is the random effect of the ith study ~ N(0,σs2), e_ijk is residual error ~ N(0,σe2).

Multiple mixed model equations were also fitted considering study as random effect. The slopes and intercepts of each equation were estimated using the ESTIMATE statement of the MIXED procedure in SAS.

CH_4ijk = is the dependent variable for the jth animal of the ith study, X1_ij and X2_ij are significant independent variables for the jth animal of the ith study, a_j, b_1i and b_2i are the parameters to be estimated, s_j is the random effect of the ith study ~ N(0,σs2), e_ijk is residual error ~ N(0,σe2).

Equation assessment using Database 1

Upon evaluating the equations for predicting CH₄ from the published literature (Table 2), we observed that without exceptions, all equations exhibited both mean bias and systematic bias (Fig. 1). Based on the data presented in (Table 3; Fig. 1a), it can be observed that the equation proposed by Moe and Tyrrell (1979; Eqn 1) overestimated enteric CH₄ emissions by 115 ± 1.37 g/day (P < 0.01). Similarly, Eqn 2 (IPCC 2006) overestimated CH₄ by 75.9 ± 1.34 g/day. The prediction Eqns 3a, 3b from the IPCC (2019), overestimated CH₄ by 86.4 ± 1.36 g/day and 81.8 ± 1.36 g/day, respectively. The equation proposed Escobar-Bahamondes et al. (2017a; Eqn 4b), that required as inputs BW, CP:NDF, STARCH:NDF ratios, and polynomial effects of DMI and fat was the best fit of the extant equations, yet still over-predicted CH4 by 17.8 ± 1.41 g/day, with significant systematic bias. This overestimate increased to 24.0 ± 1.40 g/day when BW, CP, and polynomial effects of hemicellulose and fat were used as inputs (Eqn 4a). The equations proposed by Galyean and Hales (2022) that considered DMI and ratio of dietary starch to NDF concentrations alone or in combination with EE concentration overestimated CH₄ predictions by 80.9 ± 1.38 g/day and 76.7 ± 1.37 g/day, respectively (Eqns 5a, 5b, Table 3).

Fig. 1.

Plot of observed CH₄ (g/day) vs predicted CH₄ (g/day) from literature equations. r² = coefficient of determination, MAE = mean absolute error, MSPE = mean square prediction error.

As shown in Table 3, all equations displayed significant linear bias, indicating the presence of a systematic bias in CH₄ predictions (Table 3 and Fig. 1). This result indicates that the error in CH₄ prediction varies with the predicted CH₄ value. In all instances, there are negative slopes in Table 3, indicating that increasing the CH₄ predictions results in greater overestimation of CH₄. All variables in Table 1 were tested as covariates in an attempt to eliminate the linear bias, but this was unsuccessful (P ≥ 0.12).

The decomposition of MSPE revealed that the greatest proportion was due to mean bias (93.3%), only 1.66% was due to systematic bias and 5.08% was random bias in the equation proposed by Moe and Tyrrell (1979; Eqn 1; Fig. 1a). Both IPCC (2019) equations showed unbalanced bias decomposition. Eqn 3a had 79.6%, 12.9% and 7.53% of the MSPE as mean, systematic and random bias, respectively (Fig. 1c). Similarly, Eqn 3b had 77.6%, 14.1% and 8.26% of the MSPE as mean, systematic and random bias, respectively (Fig. 1d). Both equations proposed by Escobar-Bahamondes et al. (2017a; Eqns 4a, 4b; Fig. 1e, f) showed balanced distribution of the errors. In this sense, mean bias represented 27.4% and 20.6% of the MSPE, systematic bias was 36.6% and 30.3% of the MSPE and random bias was 36.0% and 49.1% of the MSPE in Eqns 4a, 4b, respectively. The majority of the errors in equations proposed by Galyean and Hales (2022; Eqns 5a, 5b; Fig. 1g–h) were due to mean bias (82.1% and 81.5% respectively). Systematic bias corresponded to 8.03% and 8.49% respectively (Eqns 5a and 5b). Random bias was 9.28% and 9.97% respectively (Eqns 5a and 5b).

Correlation and sensitivity analysis

When investigating the impact of input values (independent variables) on the uncertainty of CH₄ output (dependent variable) in the evaluated equations, we utilised tornado diagrams. Our findings revealed that the quantity of soluble residues had the greatest influence on the Moe and Tyrrell (1979) equation. It is worth noting that there is a high correlation between SR and HC (0.43), as well as CEL and HC (0.43), as depicted in Fig. 2. This high correlation raises concerns regarding potential collinearity issues.

Fig. 2.

Linear relationship (Pearson correlation = r) of input variables required to predict methane in evaluated literature equations. CH₄ = methane, DMI = dry matter intake, BW = body weight, Y_m = emission factor, CP = crude protein, EE = ether extract, NDF = neutral detergent fibre, HC = hemicellulose, ADF = acid detergent fibre, CEL= cellulose, SR = soluble residue, STA = starch.

Body weight was ranked the most influential input in predicting CH₄ in Eqns 4a, 4b (Fig. 3e–f), both proposed by Escobar-Bahamondes et al. (2017a). It is important to note that there is a high correlation between BW and DMI with a coefficient of 0.77 (Fig. 2), which indicates a strong relationship between these two variables. Additionally, a similar observation can be made for HC and DMI, which is the second most influential input in Eqn 4a (Fig. 3e).

Fig. 3.

Tornado plot depicting low (blue zone) and high (red zone) input variables of existing equations to predict daily CH₄ emission (g) in feedlot cattle. White values inside the blue and red bars represent the predicted CH₄ emission (g/day) at the minimum (blue) and maximum (red) values of each input variable. GEI = gross energy intake, SR = soluble residue, CEL = cellulose, HC = hemicellulose, DMI = dry matter intake, BW = body weight, NDF = neutral detergent fibre, ADF = acid detergent fibre, CP = crude protein, STA = starch.

In the analysis of the equations proposed by Galyean and Hales (2022), the tornado plot revealed that the input variables DMI, NDF, and starch were ranked as the first, second, and third most influential variables, respectively (Fig. 3g, h). However, it is important to note that these input variables exhibited a high correlation among themselves (Fig. 2), which raises the potential issue of collinearity as mentioned earlier.

The mean predicted values estimated by Eqns 1, 2, 3a, 3b, 4a, 4b, 5a, 5b were 151, 87.9, 158, 160, 139, 93.6, 147, and 142 g/day; respectively. Thus, Eqn 2 displayed mean predicted value closer to the average CH₄ production observed in the dataset (i.e. 79.9 g/day; Table 2). Additionally, it is worth noting that in all the evaluated equations, the relationships between the input variables observed in the sensitivity analysis were consistent with the existing correlations reported in Fig. 2. This means that the size and direction of the relationships observed in the tornado plots align with the correlations between the variables within the database used in the present study.

New equation parametrization

In accordance with the specified criteria to identify input variables that could improve the accuracy of predicting CH₄ production by feedlot cattle, we conducted a stepwise procedure to test the variables DMI, NDF, EE, starch, and CP to produce a regression that minimised the RMSE and maximised the adjusted-r² (Liu et al. 2017). The stepwise regression analysis revealed that DMI, EE, and dietary NDF met the P-value threshold (≤ 0.05) for entry into the equation. NDF was the first variable selected in the stepwise analysis (r² = 0.892), followed by DMI (r² = 0.909) then EE (r² = 0.912). Thus, a multiple regression with intercept = 0 was fitted to predict CH₄ production from feedlot cattle (Eqn 6; n = 384; P < 0.05; RMSE = 22.2; g/d; σs2 = 8.02; r² = 0.91):

where CH₄ is methane emissions in grams per day; DMI is dry matter intake in kg/day; EE is ether extract in % DM; NDF is neutral detergent fibre in % of DM, each parameter estimate is followed by its standard error after the ‘±’.

These findings suggest that a 1% increase in dietary EE results in a 4.0 g reduction in CH₄ emissions, while each percentage point increase in dietary NDF contributes to a 2.3 g increase in CH₄ production.

Alternatively, a simple linear equation (Eqn 7) with intercept = 0 was fitted between CH₄ production (g/day) and DMI (kg), in which the slope represented the CH₄ yield in g/kg DMI (Fig. 4; n = 384; P < 0.01; RMSE = 32.6 g/day; r² = 0.85):

where CH₄ is methane emissions in grams per day; DMI is dry matter intake in kg/day ± s.e.

Fig. 4.

Linear relationship between daily CH₄ (methane, g) and DMI (dry matter intake, kg) in feedlot cattle fed tempered barley-based diets: CH_4(g/day) = 9.89 ± 1.54 × DMI_(kg/day) (Eqn 7; n = 384; P < 0.01; RMSE = 32.6 g/day; r² = 0.85).

New equations validation

This newly developed equations (Eqns 6, 7) were tested with an independent evaluation dataset (n = 352; Fig. 5). Eqn 6 showed a mean bias of −5.42 ± 1.51 (Fig. 5a; P < 0.01; overestimation, but the smallest among all tested equations), with no evidence of linear bias (−0.0136 ± 0.113; P = 0.90;). Furthermore, Eqn 6 showed a smaller MSPE (829) and a higher CCC (0.296), indicating the best fit among the evaluated models (Fig. 5a). Eqn 7 overestimated CH₄ production by 10.9 ± 1.598 g/day (Fig. 5b; P < 0.01) and exhibited a linear bias (−0.509 ± 0.0893; P < 0.01). Additionally, it demonstrated a poorer goodness of fit compared to Eqn 6, with an MSPE of 1098 and a CCC of 0.222.

Fig. 5.

Validation of Eqns 6 (a), 7 (b) using the independent dataset. MAE = mean absolute error, MSPE = mean square prediction error.