Prediction of enteric methane production, yield, and intensity in dairy cattle using an intercontinental database

Abstract Enteric methane (CH 4) production from cattle contributes to global greenhouse gas emissions. Measurement of enteric CH 4 is complex, expensive, and impractical at large scales; therefore, models are commonly used to predict CH 4 production. However, building robust prediction models requires extensive data from animals under different management systems worldwide. The objectives of this study were to (1) collate a global database of enteric CH 4 production from individual lactating dairy cattle; (2) determine the availability of key variables for predicting enteric CH 4 production (g/day per cow), yield [g/kg dry matter intake (DMI)], and intensity (g/kg energy corrected milk) and their respective relationships; (3) develop intercontinental and regional models and cross‐validate their performance; and (4) assess the trade‐off between availability of on‐farm inputs and CH 4 prediction accuracy. The intercontinental database covered Europe (EU), the United States (US), and Australia (AU). A sequential approach was taken by incrementally adding key variables to develop models with increasing complexity. Methane emissions were predicted by fitting linear mixed models. Within model categories, an intercontinental model with the most available independent variables performed best with root mean square prediction error (RMSPE) as a percentage of mean observed value of 16.6%, 14.7%, and 19.8% for intercontinental, EU, and United States regions, respectively. Less complex models requiring only DMI had predictive ability comparable to complex models. Enteric CH 4 production, yield, and intensity prediction models developed on an intercontinental basis had similar performance across regions, however, intercepts and slopes were different with implications for prediction. Revised CH 4 emission conversion factors for specific regions are required to improve CH 4 production estimates in national inventories. In conclusion, information on DMI is required for good prediction, and other factors such as dietary neutral detergent fiber (NDF) concentration, improve the prediction. For enteric CH 4 yield and intensity prediction, information on milk yield and composition is required for better estimation.

quantified accurately so that emission can be mitigated through management. Direct measurement of enteric CH 4 production from cattle can be conducted using various techniques including several bottom-up and some top-down approaches, i.e., based on national or regional activity data and emission factors for different CH 4 sources, or on atmospheric measurements, respectively. However, measurements of CH 4 production from individual animals, groups of animals, or at a regional level is expensive and requires specialized equipment (Hammond et al., 2016;Kebreab, Clark, Wagner-Riddle, & France, 2006). Proxies (i.e., indicators or indirect traits) for CH 4 emissions have also been qualitatively explored, but no single proxy was found to accurately predict CH 4 and combinations of proxies to date are not sufficiently robust for general applicability (Negussie et al., 2017). Therefore, quantitative approaches such as mathematical modeling have been used to estimate CH 4 production in cattle (Kebreab, Johnson, Archibeque, Pape, & Wirth, 2008). Both mechanistic and empirical approaches have been used to predict enteric CH 4 emissions. However, mechanistic models are usually more detailed and require numerous inputs that may not be readily available; therefore, their utility in practice is reduced. An empirical prediction approach requires fewer inputs and can generally be implemented by a much wider audience including scientists and policy makers. There are over 40 empirical prediction equations for enteric CH 4 production of lactating dairy cows in the literature (Appuhamy, France, & Kebreab, 2016). The majority of these models were based on measurements from relatively small numbers of animals in the same geographic region, which may limit their application in other regions. Therefore, a more comprehensive database needs to be collated to develop enteric CH 4 production prediction models at both global and regional scales. Furthermore, the performance of global models in each geographic region should be evaluated and compared with regional-specific prediction models.
The CH 4 conversion factor (Y m ) was introduced by the Intergovernmental Panel on Climate Change (IPCC) to indicate the proportion of the animal's gross energy intake (GEI) converted to enteric CH 4 energy, and it is widely used for national GHG emission inventories and global research on mitigation strategies. However, it has been consistently shown that CH 4 emissions are related not only to feed intake but also to feed nutrient compositions, which Y m -based models cannot adequately represent (Ellis, Bannink, France, Kebreab, & Dijkstra, 2010). Therefore, identifying relationships between dietary variables and CH 4 production and their impacts on prediction and model performance are critical. Several extant prediction models require inputs that may not be commonly available in a commercial dairy production system. Although predictive ability is likely to be enhanced with model complexity (Moraes, Strathe, Fadel, Casper, & Kebreab, 2014;Santiago-Juarez et al., 2016), the trade-off between availability of variable inputs on farm and prediction accuracy of enteric CH 4 production of dairy cows must be carefully considered. This is because more complex models may contain predictor variables that are expensive and not easy to obtain and thereby not applicable, especially in developing countries. Therefore, a categorization of model types which reflect different types and levels of data availability (e.g., diet composition, milk production and composition, and animal characteristics) needs to be conducted. Evaluation of model performance across various categories can be useful for different groups (e.g., researchers, regulators etc.).
The objectives of this study were to: (1) collate a global database of enteric CH 4 production in individual lactating dairy cows; (2) determine the availability of key variables for predicting enteric CH 4 production (g/day per cow), yield [g/kg dry matter intake (DMI)], and intensity [g/kg energy corrected milk (ECM)] and their respective relationships; (3) develop intercontinental and regional-specific prediction equations for CH 4 production, yield, and intensity using a large individual cow database and cross-validate their performance; and (4) assess the trade-off between the availability of on-farm variable inputs and prediction accuracy of enteric CH 4 production, yield, and intensity in lactating dairy cows.
Energy corrected milk (3.5% fat) was calculated based on an equation derived from Tyrrell and Reid (1965): ECM (kg/day) = 12.95 9 fat yield (kg/day) + 7.65 9 true protein yield (kg/day; i.e., crude protein 9 0.93) + 0.327 9 milk yield (kg/day). The majority of studies had measured GE. If the feed ingredients and proportions in the diets were known, the GE was calculated from book values (about 6%).
Methane yield (CH 4 production divide by DMI) and intensity (CH 4 production divide by ECM) were calculated for all records.
The majority of the studies in the database had investigated the impact of diet composition on enteric CH 4 production. However, about 20% of the studies tested the effect of feed additives or pure nutrient supplementation, so data from these studies were either completely excluded or only the control treatments were retained.
These feed additives included nitrate (Olijhoek et al., 2016), 3nitrooxypropanol (Hristov et al., 2015), and intragastric infusion of acetate, propionate, glucose, and cis-or trans-fatty acids. Measurements of enteric CH 4 production were conducted using various approaches although the observations from a given research group were usually measured using the same approach. To ensure data quality, only enteric CH 4 measurements from respiration chambers, the GreenFeed system (C-Lock Inc., Rapid City, SD), and sulfur hexafluoride (SF 6 ) tracer technique were retained for the analysis.
The variable selection and model evaluation approaches required complete data for all predictor and response variables. Therefore, records missing any predictor or response variable information were removed before being screened for outliers. Outliers in the database were screened using the interquartile range (IQR) method (Zwillinger & Kokoska, 2000) based on CH 4 yield and intensity records for each region. In this study, a factor of 1.5 for extremes was used in constructing markers to identify outliers, as shown in the Equations (i-iii): Unlike variable selection and model evaluation approaches, the construction of equations does not require data that contain a complete set of all predictor variables. Therefore, to be able to maximize the amount of data useful to construct prediction equations, subsets of data that contain complete information of CH 4 production and of the selected corresponding predictor variables were screened for outliers using the IQR method stated above and then used for the construction of equations. The same approaches were done for CH 4 yield and intensity models.

| Model development
Model development was conducted using a sequential approach, by incrementally adding different levels (e.g., dietary composition, milk production and composition, and animal traits) of variables to develop models with increasing complexity. In total, 11 CH 4 production prediction models with different complexity categories were developed ( Therefore, the amount of data was maximized for the development of equations at different complexity levels. Methane production was predicted by fitting a mixed effect model using the lmer (Bates, Maechler, Bolker, & Walker, 2015) procedure of R statistical language (R Core Team 2016; version 3.3.0).
The model was developed as shown in Equation (iv): where Y denotes the response variable of CH 4 production (g/day per cow), CH 4 yield (g/kg DMI) or CH 4 intensity (g/kg ECM); b 0 denotes the fixed effect of intercept; X 1 to X n denote the fixed effects of predictor variables and b 1 to b n are the corresponding slopes; S i (R j ) denotes the random study effects nested in research group; R j denotes the random research group effects (research groups that contributed data for analysis were used to capture variations such as different regional weather conditions, CH 4 measurement methods used, research protocols etc.); ε denotes the within-experiment error. Explanatory variables, which play a key role in predicting CH 4 production were selected for DMI + Com_C, Diet_Com_C, ECM + Com_C, Animal_C, and Animal_no_DMI_C using a comprehensive selection approach as follows: all of the subset models were fitted to the complete data set (total of 2,566 observations) and the corresponding Bayesian information criterion (BIC) scores were computed. The BIC was calculated as: n log SSEp n þ ðlog nÞ p, where p is the number of regression coefficients, n is the sample size, and SSE p is error sum of squares. A model with a smaller BIC is preferred because it reaches a balance between the goodness of fit and model complexity. In addition, the presence of multicollinearity of fitted models was examined conservatively based on variance inflation factor (VIF). A VIF in excess of 5 was considered an indicator of multicollinearity (Kutner et al., 2005), and identified predictor variables with the largest VIF were removed from the model one at a time. Similar variable selection procedures as described above were adopted for CH 4 yield (for Diet_Com_C, ECM + Com_C, and Animal_no_DMI_C) and CH 4 intensity (for DMI + Com_C, Diet_Com_C, Milk_Com_C, Animal_C, and Animal_no_DMI_C).

| Cross-validation and model evaluation
The predictive accuracy of fitted CH 4 prediction models at different categories was evaluated using the revised k-fold cross-validation method (James, Witten, Hastie, & Tibshirani, 2014), based on the refined complete data set (total of 2,566 observations), with folds composed of individual study (k = number of studies). Each individual fold was treated as a validation set. The prediction of CH 4 production of each fold was computed using the model that was fitted from the remaining folds as described by Moraes et al. (2014). The predictions of all folds were used to conduct model evaluation metrics as described below. Evaluation of all models developed at each category was assessed on intercontinental, EU, and US complete data sets. A combination of model evaluation metrics was used to assess model performance including mean square prediction error (MSPE), root MSPE (RMSPE), mean absolute error (MAE), and concordance correlation coefficient (CCC). The MSPE was calculated according to Bibby and Toutenburg (1977) where Y i denotes the observed value of the response variable for the ith observation,Ŷ i denotes the predicted value of the response variable for the ith observation, n denotes the number of observations. The RMSPE was used to assess overall model prediction accuracy because its output was in the same unit as the observations. In this study, RMSPE was reported as a proportion of observed CH 4 production means in order to compare the predictive capability of models developed from different data sets. The MAE was calculated as shown in Equation (vi) to quantify the prediction error as suggested by Chai and Draxler (2014): In both cases, smaller RMSPE or MAE implies better model performance. The RMSPE to standard deviation of observed values ratio (RSR) was calculated as shown in Equation (vii), where S o denotes the standard deviation of observations. It was used to compare the performance of a single model based on data from different regions accounting for the regional variability (Moriasi et al., 2007). Similarly, smaller RSR indicates better model predictive ability given the variability of data. MSPE was decomposed into mean bias (MB) and slope bias (SB) deviations to identify systematic biases. The MB and SB were calculated as shown in Equations (viii) and (ix), respectively: where P and O denote the predicted and observed means, S p denotes the standard deviation of predicted values, and r denotes the Pearson correlation coefficient.
Furthermore, CCC was conducted that includes a bias correction factor (C b ) and r, as measurements of accuracy and precision, respectively (Lin, 1989). The CCC was calculated as shown in Equation (x), approaches were conducted to test the performance of CH 4 yield and intensity models. Currently, most national enteric CH 4 inventories are based on models recommended by IPCC (1997IPCC ( , 2006. Therefore, IPCC models were also evaluated on both intercontinental and regional data sets. performed worse than any of the previous models. Using ECM and milk composition improved model performance compared with the equation that used MY only. All models using only milk production and composition variables tended to slightly under-predict at the higher end of production and overpredict at the low end of production ( Figure 1) Table 2) and the smallest MAE (47.5 and 48.5 g/day, respectively; Figure 1).

| Database
The predictive ability of intercontinental models on regional data set (EU and US) was also evaluated using RSR. The intercontinental models had a larger RSR (averaging 0.73) on EU observations compared to using all data (averaging 0.70). A greater amount of systematic biases (both MB and SB) was observed with CH 4 prediction for EU cows than for all cows when using intercontinental models (average 8% vs. 2%, respectively). The predictive ability of intercontinental models on US observations was similar to the overall evaluation, and systematic biases were also similar (

| Regional models (EU)
Models developed on the EU database and model evaluations are presented in Table 3. The internal EU model evaluations based on EU observations and model comparisons across different categories followed a trend similar to the intercontinental prediction models.
Adding NDF to DMI improved model accuracy compared to using either DMI or GEI alone or adding EE to DMI (  Table 3) and (MAE = 44.9 and 44.5 g/day, respectively; Figure 2). In addition, the intercontinental and EU models had similar overall performance for predicting enteric CH 4 production of EU cows (mean = 0.73 and 0.72, respectively). However, systematic biases were proportionally smaller for EU models compared to intercontinental models (4% vs. 8%, respectively). Furthermore, all categories of models based on the EU database had smaller RSR (mean = 0.72) when used to predict CH 4 production in EU cows compared to prediction for US cows (mean = 0.80). There was significant MB when EU models were evaluated against US data (Table 3).

| Regional models (US)
Models developed on US data and model evaluations are shown in were observed when predicting CH 4 production of EU cows using models based on the US data.

| Models for methane yield
Intercontinental CH 4 yield (g/kg DMI) prediction models of various complexity levels and with evaluations based on different datasets are shown in Table 5. Results for the regional based models of CH 4 yield are given in Tables S1 and S2 for EU and US, respectively. In both intercontinental and regional models, we observed positive   Table 5). The CCC and MAE analyses also confirmed that it was the best performing model (Tables 5, S1, and S2). Such findings were also observed in EU and US regional models (Equations 58 and 65, RMSPE = 14.8% and 18.6%, respectively; Tables S1 and S2, respectively). Using milk components as model variables resulted in the second-best model in all regions. Furthermore, the intercontinental models had a similar RSR while predicting EU or US observations (mean = 0.97 and 0.98, respectively), compared to predicting CH 4 yield using EU and US regional models ( Figures S1-S3).

| Models for methane intensity
Intercontinental CH 4 intensity (g/kg ECM) prediction models of various complexity levels and with model evaluations based on different datasets are shown in Table 6, and results for the regional models for EU, and the US are shown in Tables S3 and S4, respectively. We consistently observed negative relationships between GEI, DMI, and dietary EE concentration with CH 4 intensity, and positive relationships between MP, BW and dietary NDF concentration with CH 4 intensity. However, models that were based on GEI, DMI, or dietary composition did not predict CH 4 intensity well. Substantial improvement in prediction accuracy was observed when milk component and animal variables were included in the model. Similar to CH 4 production and yield models, intercontinental models performed well for both EU and US cows ( Figures S4-S6). Models that included the most variables had the greatest CCC and the smallest MAE compared to all other categories in all regions.

| Key predictor variables for methane emission
This study identified key predictor variables for CH 4 production (g/ day per cow), yield (g/kg DMI), and intensity (g/kg ECM) in lactating dairy cows from different regions of the world and evaluated the trade-off between the availability of input variables and prediction accuracy of models. The analysis confirmed that DMI is the most important variable to predict enteric CH 4 production in dairy cattle, which agrees with previous research (e.g., Hristov et al., 2013;Kriss, 1930;Reynolds, Crompton, & Mills, 2011). There was a significant positive relationship between DMI and CH 4 production demonstrating that as a dairy cow consumes more feed, more CH 4 is produced due to greater availability of substrate for microbial fermentation.
The majority of extant prediction models for CH 4 production included DMI as a predictor variable, and evaluation of models developed in this study across various complexity levels also indicated that DMI had the greatest effect on the amount of CH 4 produced. The slopes of DMI to CH 4 production ranged from 13.0 to 15.3 g of CH 4 /kg of DMI for EU cows (Table 3) when other covariates were kept constant. The corresponding values were smaller for US cows and ranged from 11.3 to 12.3 g of CH 4 /kg of DMI (Table 4). This is probably due to the difference in dietary composition between EU and US diets and the digestibility of these diets, as EU diets contained proportionally more forage. Practically, it is unlikely that one variable (e.g., dietary NDF concentration) would be different while the rest remain constant because of the associated exchange for other nutrients in ingredients used to formulate diets. In addition, the slopes can only be interpreted in combination with the intercept in all equations.
Nevertheless, these results provide insights in assessing the impact of explanatory factors on the variability of CH 4 production among different regions. Increased intake may potentially increase passage rate and shorten digesta retention time in the rumen, thus decreasing rumen fermentation and organic matter digestibility, which ultimately decrease CH 4 production per unit of feed (Boadi, Benchaar, Chiquette, & Masse, 2004). Methane yield has been reported to have a negative relationship with DMI (Moe & Tyrrell, 1979). Johnson and Johnson (1995) reported that for every kg of increase in DMI, there is, on average, a 1.6% decrease of feed GE lost through CH 4 . A more recent study also confirmed 2.1% reduction on Y m per kg of DMI increase from dairy cows (Warner, Bannink, Hatew, van Laar, & Dijkstra, 2017). Therefore, it is important to use different Y m values depending on level of production, which accounts for intake and digestibility of nutrients. In the present study, DMI was not considered as a predictor for CH 4 yield, and MY or ECM was not used for prediction of CH 4 intensity because these variables already have However, negative relationships between CH 4 yield and MY (or ECM), and between CH 4 intensity and DMI were observed because of the overall positive relationship between MY and DMI, which is in close agreement with previous reports (e.g., Johnson & Johnson, 1995;Moe & Tyrrell, 1979;Warner et al., 2017).
In agreement with Kebreab et al. (2008) and Appuhamy et al. (2016), IPCC (2006, the Tier 2 model overpredicted CH 4 production of US cows in our database by 22%, whereas it performed well on EU cows mainly because the Y m in IPCC Tier 2 (6.5%) was similar to the average Y m of EU cows (6.4%) in our database. There was a moderate SB of the IPCC (2006) Tier 2 model for EU cows probably due to the absence of an intercept in the IPCC model. The Y m for US cows in our database (5.4%) was close to that reported by Kebreab et al. (2008) and Appuhamy et al. (2016) for US cows. This illustrates that it is important to either use a regional model or intercontinental model that was developed using representative samples from each region.
Furthermore, the GEI-based models appear to perform better and are associated with small systematic biases when they include an intercept term as for the GEI_C models developed in the present study.
Dietary NDF concentration was selected previously as the key dietary variable to predict enteric CH 4 production of dairy cows across regions (Moe & Tyrrell, 1979;Nielsen et al., 2013). Dietary NDF, the majority of which is from forage, represents the amount of structural carbohydrates in the diet. The type of carbohydrates (structural or non-structural) in the diet has been shown to influence volatile fatty acid (VFA) profile in the rumen, and in turn, enteric CH 4 production (Russell & Wallace, 1997;Van Soest, 1994). Studies focused on the effect of type of carbohydrates indicate that diets rich in non-structural carbohydrates such as starch and sugars are more likely to favor propionate formation, resulting in less hydrogen (H) and CH 4 production, whereas diets rich in structural carbohydrates generally favor acetate and butyrate production by net H producers (Bannink et al., 2008;Johnson & Johnson, 1995;Moe & Tyrrell, 1979 The forage quality in the diet, specifically fiber digestibility, plays an important role in enteric CH 4 production (Brask, Lund, Hellwing, Poulsen, & Weisbjerg, 2013;Warner et al., 2016), and it has been shown that CH 4 production of cows tends to increase with increasing diet organic matter digestibility (Ramin & Huhtanen, 2013). The EU diets containing more forage have an inherently greater digestibility of NDF than more concentrate-based US diets where the lower ruminal pH in the high grain diets inhibits the growth of methanogens and protozoa, in turn, hampering NDF digestion and CH 4 production in the rumen (Hegarty, 1999 for the optimal amount of more digestible carbohydrate or low fiber sources will increase milk production, and decrease ruminal pH and fiber digestibility, and both lead to a reduction in CH 4 intensity (Boadi et al., 2004;Leng, 1993). Consistent with expectations, both enteric CH 4 yield and intensity declined as dietary NDF concentration decreased in the present evaluation.
Dietary EE concentration was also identified as a key dietary predictor variable in EU and intercontinental enteric CH 4 production prediction models, but its impact on the predictive ability of US models was minimal. Dietary EE concentration may be increased by using herbage in young, leafy stage rather than in more mature, stemmy stage (Warner et al., 2016), or by lipid supplementation of the diet, and is an indicator of the amount of lipid consumed relative to other dietary components (Martin et al., 2016). The effect of lipid supplementation on enteric CH 4 production has been extensively studied and lipid supplementation is a well-recognized mitigation strategy as reviewed by several groups (e.g., Beauchemin, Kreuzer, O'Mara, & McAllister, 2008;Knapp et al., 2014;Martin, Morgavi, & Doreau, 2010). Lipids reduce CH 4 production by suppressing the protozoa and methanogen population in the rumen, decrease NDF digestibility, and reduce the total amount of organic matter fermented, resulting in lower CH 4 production (Guyader et al., 2014;Machm€ uller & Kreuzer, 1999;Van Nevel & Demeyer, 1996). Finally, lipids may cause a reduction in DMI, due to their high energy density and effects on gut fill and appetite, which could lead to less CH 4 production (Allen, 2000;Hollmann et al., 2012). Consistent with the above-mentioned studies and data summarized by Grainger and Beauchemin (2011), slopes of the EE variable in the EU prediction models were significantly negative. The absence of dietary EE in US models, and small slope when EE was forced in US models, might be due to the relatively lower EE concentration in the US diets. In addition, the magnitude of reduction has not always been consistent, with some studies reporting a 3.5% (Moate et al., 2011) and a 5.6% (Beauchemin et al., 2008) (Hristov et al., 2013). However, such effects may strongly vary among studies, depending on the compensation of increased energy density to the reduction in fiber digestibility and DMI.
Body weight was one of the variables selected for prediction of CH 4 production. As noted by Smith and Baldwin (1974) and Demment and Van Soest (1985), ruminal volume and weight are proportional to BW of dairy cows. Consequently, smaller animals, with a lower maintenance energy requirement, ingest less feed and have less CH 4 production (Hristov et al., 2013). In addition, simulations with a dynamic mechanistic model indicated that the DMI/BW ratio is an important factor for CH 4 production; consuming same amount of feed intake, smaller cows tend to produce less CH 4 as ruminal passage rate is likely to be faster due to greater DMI/BW ratio (Huhtanen, Ramin, & Cabezas-Garcia, 2016;Huhtanen, Ramin, & Ud en, 2015), which has been shown to reduce CH 4 yield (Goopy et al., 2014). Therefore, BW could affect DMI and passage rate of ruminal digesta, which will lead to differences in feed digestibility and VFA production, ultimately affecting CH 4 production. A positive relationship was observed between BW and CH 4 production in our evaluation, which agrees with previous research (Hristov et al., 2013;Moraes et al., 2014).

| Selection of the best models
In the current study, the trade-off between model complexity and predictive ability has been evaluated. In general, improvement in model goodness-of-fit has been reported as the model structure becomes more complex (e.g., Moraes et al., 2014;Santiago-Juarez et al., 2016).
An evaluation of whole-farm CH 4 production models demonstrated poor performance and greater systematic biases when equations did not include dietary variables (Ellis et al., 2010). In the present study, models were categorized and different levels of potential predictor variables were sequentially added during the model development process. We observed that accuracy of prediction of CH 4 production improved in models that include DMI, dietary composition, milk production and composition, and BW. In particular, complex models that used all available variable information consistently improved prediction performance compared to simpler models. Models using only MY or dietary composition were the least accurate. When DMI was omitted from the model to predict CH 4 production, ECM was selected instead due to its high correlation with DMI, but model predictive ability was reduced. Although intercontinental models were developed based on a data set containing a slightly greater proportion of EU data compared to US data (55% vs. 42%, respectively), the intercontinental models seem to perform well on both regions without significant biases. In addition, the variable inputs required to improve predictions are not always available from commercial dairy farms, for example, DMI and BW of individual dairy cows. Milk yield and milk components are generally available in practice, but CH 4 production was not predicted well by these input variables. Considering the number of variables required and prediction performance we recommend the equation with DMI + NDF concentration to be used for enteric CH 4 production. A recent evaluation of extant models using estimated DMI vs. actual DMI measurements indicated enteric CH 4 emissions could be predicted satisfactorily without DMI measurements for North America, but not for Australia and New Zealand, with accuracy of prediction using Europe data in between . However, estimation of DMI is still a challenge for dairy farmers in practice because voluntary DMI prediction equations require individual animal information and, in particular BW (Fox, Sniffen, O'Connor, Russell, & Van Soest, 1992;NRC, 2001;Vazquez & Smith, 2000). In this respect, using average or total intake from a group of cows or the whole herd instead of individual measurements could be an alternative for wholefarm enteric CH 4 emission estimates, when cows are grouped by milk production, BW, or parity in commercial dairy farms.
Model evaluations across various complexity levels indicated that CH 4 yield of lactating dairy cows could be predicted successfully with milk production and composition or dietary composition based models. The corresponding intercontinental models were able to make comparable predictions for EU and US cows relative to the regional EU and US models. The best prediction of CH 4 intensity could be achieved with the most complex model (Animal_C), with the model for the intercontinental data set also able to make accurate predictions for both EU and US cows. Although overall predictive performance was similar, it should be noted that actual predictions based on the model derived from intercontinental data may differ from the model based on regional-specific data, because the slopes of the variables included in these models differ.
Finally, it is important to note that the majority of data used in this study was from temperate regions and there is a scarcity of dairy cow data from tropical regions, which differ in breeds and the quality of forage fed. Many developing countries are in the tropical regions, and milk production rather than GHG emissions is still the top priority in those countries (FAO, 2016). Therefore, further research on determinants and predictors of CH 4 emission applicable to animals in the tropics is warranted. In addition, spatial auto correlations should also be considered to incorporate the effects of environmental factors once a broader database becomes available in the future.
In summary, our analysis based on a relatively large dataset from the GLOBAL NETWORK project, indicated that the ability to predict enteric CH 4 production increases with increasing model complexity.
As observed previously, DMI is the key factor for enteric CH 4 production prediction. Although complex models that use DMI, NDF, EE, MF, and BW had the best performance for predicting CH 4 production, models requiring only DMI or DMI + NDF had the second best predictive ability and offer an alternative to complex models.
Milk production and composition variables are key factors to predict CH 4 yield, whereas milk composition and animal variables are key factors to predict CH 4 intensity. Model evaluation specific to individual regions compared with that of intercontinental based models suggests that enteric CH 4 production, yield, and intensity can be accurately predicted from both intercontinental models and regionalspecific models with similar performance. Although prediction performance was similar, intercepts and slopes of variables in optimal prediction equations developed on intercontinental basis differed from those developed on regional basis. Therefore, revised CH 4 emission conversion factors for specific regions are preferred to improve CH 4 production estimates in national inventories.

ACKNOWLEDG EMENTS
This study is part of the Joint Programming Initiative on Agriculture, Food Security and Climate Change (FACCE-JPI)'s "GLOBAL