Development of methane conversion factor models for Zebu beef cattle fed low‐quality crop residues and by‐products in tropical regions

Abstract The enteric methane conversion factor (Y m) is an important country‐specific value for the provision of precise enteric methane emissions inventory reports. The objectives of this meta‐analysis were to develop and evaluate the empirical Y m models for the national level and the farm level for tropical developing countries according to the IPCC's categorization. We used datasets derived from 18 in vivo feeding experiments from 1999 to 2015 of Zebu beef cattle breeds fed low‐quality crop residues and by‐products. We found that the observed Y m value was 8.2% gross energy (GE) intake (~120 g methane emission head−1 day−1) and ranged from 4.8% to 13.7% GE intake. The IPCC default model (tier 2, Y m = 6.5% ± 1.0% GE intake) underestimated the Y m values by up to 26.1% compared with its refinement of 8.4% ± 0.4% GE intake for the national‐level estimate. Both the IPCC default model and the refined model performed worse in predicting Y m trends at the farm level (root mean square prediction error [MSPE] = 15.1%–23.1%, concordance correlation coefficient [CCC] = 0.16–0.18, R 2 = .32). Seven of the extant Y m models based on a linear regression approach also showed inaccurately estimated Y m values (root MSPE = 16.2%–36.0%, CCC = 0.02–0.27, R 2 < .37). However, one of the developed models, which related to the complexity of the energy use efficiencies of the diet consumed to Y m, showed adequate accuracy at the farm level (root MSPE = 9.1%, CCC = 0.75, R 2 = .67). Our results thus suggest a new Y m model and future challenges for estimating Zebu beef cattle production in tropical developing countries.


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KAEWPILA And SOMMART are recommended for diets with poorer digestibility and energy values (IPCC, 2006). Because the Y m default model was developed from a dataset based on Bos taurus fed temperate feedstuffs, research that adopts country-or region-specific Y m models is also significant for reducing possible errors in the estimates of Y m for different livestock and feed combinations (Lassey, 2007).
In addition to emissions at the national level, those at the farm level are also significant for applying methane mitigation strategies that may increase feed energy deposition in animals (Hristov et al., 2013). Y m values at the farm level show extremely high variability (Johnson & Johnson, 1995;Lassey, 2007). Indeed, models that describe this circumstance at the farm level are too complex to be used in national inventories at low tier levels. Overall, extant models for estimating enteric methane emissions can be classified into two principal groups: empirical (statistical) or dynamic mechanistic models (Kebreab, Johnson, Archibeque, Pape, & Wirth, 2008). In terms of the former, independent variables such as animal and diet as well as energy utilization efficiency have been selected to develop empirical Y m models (Blaxter & Clapperton, 1965;IPCC, 2006, Jaurena et al., 2015. Regarding the latter, a Danish-specific Y m model has been developed using a mathematical description of ruminal fermentation biochemistry (Nielsen et al., 2011).
One challenge is the lack of data available to predict Y m for Zebu and Zebu crossbred beef cattle in tropical countries. This is a particular problem given that stocks of Zebu (Bos indicus) beef cattle in developing countries in tropical regions now account for more than half of the global beef cattle population (FAO, 2015). Both Kurihara, Magner, Hunter, and McCrabb (1999) and our previous studies (Chaokaur, Nishida, Phaowphaisal, & Sommart, 2015;Chuntrakort et al., 2014;Tangjitwattanachai, Phaowphaisal, Otsuka, & Sommart, 2015) have consistently found the Y m value of Zebu beef cattle production in tropical regions to be much higher than those estimated by IPCC (2006).
As the diets fed to these Zebu beef cattle typically consist of poorquality crop residues and by-products compared with those fed to B. taurus (Kearl, 1982;NRC, 2000, WTSR, 2010, extant Y m models may be inaccurate for the Zebu beef population.
Based on this gap in the body of knowledge on this topic, this meta-analysis aimed to develop new and evaluate existing regional diet-specific empirical Y m models for Zebu beef cattle production in tropical regions at the national level and the farm level from on-farm accessible data.

| Extant Y m model selection
The extant Y m models from the published works (Blaxter & Clapperton, 1965;FAO, 2010;IPCC, 2006, Jaurena et al., 2015, Patra, 2013Ramin & Huhtanen, 2013;Yan, Agnew, Gordon, & Porter, 2000) presented in Table 2 were selected to predict the Y m of the beef cattle dataset and to guide the model development. The model selection criteria were based on the model's possible use at the national or farm level as well as the existence of independent NFC = 1,000 − (Ash + CP + EE + NDF),  (Kebreab et al., 2008). These Y m estimates are a rough guide based on the beef farm practices in most developed and developing countries (IPCC, 2006).
A default model (Y m = 6.5% ± 1.0% of GE intake, namely model A) was selected to emphasize the IPCC's recommendation for cattle fed low-quality crop residues and by-products in developing countries. At the farm level, regression models are typically used to estimate the Y m values related to the complex variable(s) of the animal and its diet. Seven regression models (namely model B, C, D, E, F, G, and H) were thus selected to increase the levels of the complexity variable(s).

| Model development for the national level
This model (Table 3, namely model I) was simulated according to the tier 2 level of IPCC (2006), which developed a Y m model based on the quotient of mean methane energy emissions to mean GE intake across the measured herd, while the conversion from methane energy to flux in mass units was 55.56 MJ/kg (Lassey, 2007). Thus, the calculation was where Y m , methane conversion factor (% of GE intake); CH 4i , the ith

| Model development for the farm level
This investigation was carried out using a subsampling dataset (n = 36, termed the two-thirds dataset) from the total dataset (n = 53). The models were developed using a multiple linear regression analysis, which relates the independent variable(s) to Y m . This investigation was conducted in a sequential manner to increase model complexity at each level and thus increase the model's predictive power, which is based on complex information (IPCC, 2006, Moraes, Strathe, Fadel, Casper, & Kebreab, 2014. According to the dataset availability and extent models (Table 2), five complexity levels were performed, namely dietary, intake, digestibility, integrated dietary, intake and digestibility, and energy levels ( Table 3). All variables were computed under the selected most probable model at these levels of complexity. Specifically, the regression analysis for model complexity at each level was analyzed using the REG procedure (stepwise and collinearity diagnostics) of the SAS statistical software version 6.12 (SAS Institute Inc. Cary, NC, USA). The statistical model was where Y m = methane conversion factor (% of GE intake); β 0 = intercept, β 1 , β 2 , …, β n = slopes, X 1 , X 2 , …, X n = independent variables, and ɛ = error.

| Cross-evaluation
Three statistical parameters, namely the coefficient of determination (R 2 ), root-mean-square prediction error (RMSPE), and variance inflation factors (VIFs), were undertaken to evaluate the developed models against the observed Y m to assess model performance. The predicted Y m dataset for each model was developed using the model regressor. Model I, developed for the national level, was excluded as it did not exactly mimic the real regression system. The R 2 (stepwise) and VIFs (collinearity diagnostics) were obtained during the model development process previously described via the REG procedure of the SAS. This R 2 was used as an index of the goodness of fit of the Y m models, determining the proportion of variance in the observed Y m explained by the model (Nakagawa & Schielzeth, 2013). Thus, R 2 of 1 indicates that the regression line perfectly fits the data, while an R 2 of 0 indicates that the line does not fit the data at all.
The VIFs measure the inflation in the variances of the parameter estimates due to collinearities that exist among the independent variables (Belsley, Kuh, & Welsch, 1980). The largest VIF was used as the formal criterion for deciding if it is larger than 10 (i.e., sufficient to affect the predicted values; Moraes et al., 2014).
The RMSPE was calculated as servation number, and Ō = mean observed Y m value. The RMSPE was used as an index to describe the predictive accuracy of every developed model (Tedeschi, 2006). RMSPE values are expressed as a percentage of the observed Y m , and range from 0 to positive infinity. An RMSPE value equal to 0 indicates a perfect score in the predictive accuracy model.

| Comparison of the extant and developed Y m models using on-farm accessible data
This comparison aimed to evaluate the performance of the extant and developed models in predicting Y m using on-farm accessible data (the one-third dataset, n = 17). The predicted Y m values were constructed as a dataset by adding the independent variable(s) into the Y m models.
Y m values for models A and I were generated around their mean value using their specific uncertainty value, namely 6.5% ± 1.0% GE intake and 8.4% ± 0.4% GE intake, respectively. The mean was presumed to be the lower bounds if the diet had a greater DE/ME value (due to the negative relationship between the energy use efficiency and Y m values), and thus, the upper bounds were used on the opposite side.
The MSPE analysis was divided into RMSPE (3) and total MSPE.
Total MSPE was decomposed to compile the sources of variation in the MSPE (Bibby & Toutenburg, 1977), ECT, ER, and ED were expressed as a percentage of total MSPE.
The CCC and derivative statistics (Lin, 1989)  The observed versus predicted plots were analyzed using the method described by Ellis et al. (2010). Briefly, the slope was determined by regressing the observed Y m values (independent variable) against the predicted Y m values (dependent variable) using the REG procedure. This response aims to test the significance of the slope against 0, which assesses the existence of linear relationship between the observed and predicted values.

| Dataset description
The dataset for this meta-analysis, including beef cattle characteristics (age and body weight), diet composition, digestibility, feeding level, (4) Total MSPE = ECT + ER + ED,

| Development of the models
The Y m models developed and categorized using the levels of predictive possibility discussed herein are listed in Table 3

| Comparison of the extant and developed models using on-farm accessible data
The MSPE analysis (Table 4)  Once again, the analysis of the observed versus predicted values plots ( Figure 2) indicated that only model N had moderate predictive power (R 2 = .67). For most of the models here, although the statistical significance of the slope was reached (p < .05 or <.01), predictive power was very low considering an R 2 less than .50.

| Perspectives of the dataset
Because of the importance of Y m in determining the accuracy of enteric methane emissions for national and global inventories (IPCC, 2006), we analyzed a range of Y m models of the associated beef cattle production system. The present dataset (  (Marcondes, Tedeschi, Valadares Filho, & Gionbelli, 2013;Ogino et al., 2016). Nellore beef cattle, wide spread in Brazil and India, are also a small breed size, with a mature body weight of ~530 kg according to Marcondes et al. (2013). The diet compositions and nutritive values such as crude protein (40-213 g/kg DM), total digestible nutrients (454-737 g/kg), and ME content (6.7-12.9 MJ/kg DM) showed several available feeding systems for tropical developing countries. The mean enteric methane emission rate in our records (~120 g methane head −1 day −1 ) could result from frame size and voluntary feed intake of cattle (Smith, Lyons, Wagner, & Elliott, 2015).
The range of Y m values of 4.8%-13.7% of GE intake in this study agreed with that in Johnson and Johnson (1995). The many attempts to estimate Y m variability emphasize the difficulty because of the number of factors related to Y m (Blaxter & Clapperton, 1965;Hill, McSweeney, Wright, Bishop-Hurley, & Kalantar-Zadeh, 2016). What and roughage (fresh forage, conserved forage, straw) are the primary factors affecting Y m values. Conventionally, it has been known that Y m values reduce as ME intake (Blaxter & Clapperton, 1965;Chaokaur et al., 2015), feed quality (starch content), energy content (IPCC, 2006;Johnson & Johnson, 1995;Kurihara et al., 1999), and fat content rise (Chuntrakort et al., 2014;Patra, 2013). Our previous studies showed that an increase in feeding level not only reduces Y m values, but also improves beef productivity; thus, reducing the intensity of enteric methane is a strategic feeding management approach (Chaokaur et al., 2015;Tangjitwattanachai et al., 2015).

| Predicting Y m values at the national level for Zebu beef cattle in tropical regions
The predicted Y m values are used in a complex algorithm standardized by IPCC (2006). If inventory compliers are chosen at the tier 2 level, the aim is to control errors of less than 20% around the mean of the enteric methane emission inventory of a country. IPCC (2006) suggested that a 10% error in a variable will result in methane errors ranging up to 20% depending on the circumstances. Our result ( Figure 1) showed room to improve Y m predictions for Zebu beef cattle fed low-quality crop residues and by-products in tropical regions. and mechanistic model of fermentation biochemistry in the enteric to calculate enteric methane emission inventories, instead of a tier 2 one (Bannink et al., 2011). The Y m tabulation for the cattle fed blooming grasses, legumes, and high-quality crop residues should be related to the IPCC's data because there is evidence in Brazil and Australia that the Y m response to this diet is rather similar given the overall range of uncertainty (Kennedy & Charmley, 2012;Pedreira et al., 2013;Tomkins et al., 2015). Additionally, a main reason for this difference is the degree to which Y m depends on feed quality (Jaurena et al., 2015;Kurihara et al., 1999;Lassey, 2007).

| Predicting the Y m values at the farm level for Zebu beef cattle in tropical regions
Predicting the Y m values at the farm level is a different task compared with tier 2. Indeed, describing the Y m trends from the direct measurements in cattle is challenging for a variety of reasons such as the importance of data on methane mitigation throughout the assessment of the carbon footprint values (Ogino et al., 2016). According to Kebreab et al. (2008), predicted values equal observed values in a perfect model.
Thus, the best model should have a low RMSPE, high CCC, and high R 2 (observed vs. predicted). Some researchers have shown that regression models may also be capable of describing the changes in Y m values considering the effects of dietary changes (Blaxter & Clapperton, 1965;Jaurena et al., 2015;Patra, 2013;Ramin & Huhtanen, 2013;Yan et al., 2000). In particular, as the regression approach statistically relates the factors of animal and diet to Y m output, it was thus effective to refine to the IPCC (2006) default Y m model when predicting at the farm level because the latter is designed to enumerate nationallevel emissions (Crosson et al., 2011). Our results ( farmers impose changes in beef herd composition and feeding regime to improve beef productivity. These considerations challenge the enteric methane inventory method (Lassey, 2007).
For the case of extent models, the lack of data representativeness of the cattle used in this analysis could be a major source of error. This kind of model error typically calls for extrapolation, which is associated with a lack of correspondence between the circumstances associated with the available data and those associated with the predictions (IPCC, 2006). In this case, the Y m data of the extent models may be available for situations in which high diet quality is stimulating at high voluntary intake load but not for situations involving the intake limited changes due to low diet quality ( Finally, although these findings contribute to our understanding of Zebu beef cattle populations in tropical regions and offer better model applications for estimating their presented Y m values, the lack of information obtained from feedlot and grazing herds is a limitation of this study. Thus, the scopes for further research should be to develop the Y m models using feedlot and grazing datasets to provide more implications in estimating enteric methane emissions of Zebu cattle.