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* Centre for Nutrition Modelling, Department of Animal and Poultry Science, University of Guelph, Guelph, Ontario, N1G 2W1, Canada
Department of Agricultural, Food and Nutritional Science, University of Alberta, Edmonton, Alberta, T6G 2P5, Canada
1 Corresponding author: jellis{at}uoguelph.ca
| ABSTRACT |
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Key Words: cattle greenhouse gas methane modeling
| INTRODUCTION |
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Mathematical models allow us to predict CH4 production from cattle without undertaking extensive and costly experiments. The models used can be classified as either statistical models, which relate nutrient in-take to CH4 production directly, or dynamic mechanistic models, which estimate CH4 production using mathematical descriptions of rumen fermentation biochemistry (Kebreab et al., 2006). Although many statistical models have been fairly successful in predicting CH4 production, many have inputs that are not commonly measured and some may have difficulty predicting CH4 production outside the range of values on which they were developed (Wilkerson et al., 1995). These problems may be addressed by using commonly measured equation input variables and by developing models on expansive data sets compiled from multiple sources.
The objectives of this study were 1) to develop statistical models of CH4 production on beef and dairy data using commonly measured dietary variables, and to determine the factors that appear to have a significant relationship with CH4 production, and 2) to challenge extant CH4 prediction models against a CH4 database containing beef and dairy cattle data.
| MATERIALS AND METHODS |
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The main effects (DMI kg/d, MEI Mcal/d, ADF kg/d, NDF kg/d, EE kg/d, lignin kg/d, and forage proportion %) were analyzed using PROC MIXED (SAS Institute, 2000). The mixed model analysis was chosen because the data were gathered from multiple studies; therefore, it was necessary to consider analyzing not only fixed effects of the dependent variables, but also random effects (because the studies represented a random sample of a larger population of studies). Distribution of random effects was assumed to be normal and the dual quasi-Newton technique was used for optimization with an adaptive Gaussian quadrature as the integration method (SAS Institute, 2000). Analysis was performed with an assumption of variance distribution for the fixed factor to be normal or gamma (SAS Institute, 2000). Observed CH4 production rates were weighted by the n of the study (Table 1
), and if the random covariance or the random slope was not significant, they were removed from the model (St-Pierre, 2001).
The predictive ability of equations from Kriss (1930), Axelsson (1949), Blaxter and Clapperton (1965), Moe and Tyrrell (1979b), and Mills et al. (2003) was compared using inputs from the 3 databases. The extant equations used are presented in Table 3
. These equations were selected for comparison because they are commonly used and their input variables were obtainable from the compiled database.
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where Oi is the observed value, Pi is the predicted value, and n is the number of observations. Square root of the MSPE (RMSPE), expressed as a proportion of the observed mean, gives an estimate of the overall prediction error. Values of RMSPE are expressed relative to the observed mean, as opposed to the predicted mean, so that comparisons of RMSPE (%) values can be made between equations with different predicted means and so that deviation from observed values can be evaluated. The MSPE was decomposed into random error (ED), error due to deviation of the regression slope from unity (ECT), and error due to overall bias (ER; Bibby and Toutenburg, 1977).
| RESULTS AND DISCUSSION |
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Many older equations rely on DMI or MEI to predict CH4 production; therefore, DMI- and MEI-based prediction equations were developed on our database for comparison (Table 5
). Equations [1b] and [2b] predict CH4 production from beef cattle using only MEI and DMI, respectively; equations [1d] and [2d] predict CH4 production from dairy cattle using only MEI and DMI, respectively; and equations [1c] and [2c] predict CH4 production from the combined database using only MEI and DMI, respectively (Table 5
). Results of the MSPE analysis are presented in Table 6
. For all 3 databases, using DMI to predict CH4 production resulted in lower RMSPE and higher R2 values than using MEI. This is not surprising because all data sets reported DMI, but many MEI values were extrapolated from other information provided in the publication and are likely to contain some error compared with DMI values. In theory, MEI would be expected to have a stronger relationship with CH4 production than DMI because it accounts for CH4 production within its derivation (Mills et al., 2003).
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Although DMI and MEI appear to be adequate predictors of CH4 production on their own, a substantial level of variation is left unaccounted for by these models. There have been attempts to use more complex regression models with better descriptions of dietary composition (Wilkerson et al., 1995) with success, so regression analysis on our database was undertaken to determine which other factors contribute to improving the prediction of CH4 production.
Multiple Regression Equations
Several scenarios were set up in the current study from which CH4 prediction equations were developed. These included using either MEI or DMI, and measures of dietary variables expressed as either a percentage of DM or kilograms per day. However, a problem arose in using PROC MIXED when trying to develop equations based on dietary variables expressed as a percentage of DM, because for many of the studies, the percentage of DM of a variable was constant within a study (i.e., all animals were fed the same diet). The MIXED procedure would not converge on these data, or deemed them non- significant. An overall plot of CH4 production vs. percentage of DM for many of the variables did appear to have a significant relationship (Table 4
). However, PROC CORR does not account for the random effects of study; therefore, these results are likely biased. In addition, this analysis does not consider the interaction between variables. The relationship between CH4 production and dietary variables expressed as a percentage of DM was interesting to look at because it gave an indication of the influence of the variable if DMI were held constant, similar to the idea of a forage:concentrate ratio. Once this percentage was multiplied by the DMI to convert the variable to kilograms per day, the resulting relationship included the effects of both the variable being evaluated and DMI. For example, because the relationship between CH4 production and DMI is positive, if the relationship between CH4 production and a given variable were negative, these two lines would multiply and cancel each other out, resulting in a zero slope for the line when the variable is expressed in kilograms per day. Similarly, if the CH4 production vs. variable (%) line were positive, the CH4 production vs. variable (kg/d) line would become more positive, and if the CH4 production vs. variable (%) line had a zero slope, the CH4 production vs. variable (kg/d) line would become slightly positive. Although kilograms per day is the more common way of expressing a dietary component intake, looking at the percentage of DM of a variable would tease out its influence from the effect of total DMI. However, because the variable expressed as a percentage of DM did not consistently vary within the study, PROC MIXED equations could be developed only for variables expressed as kilograms per day.
The NDF fraction of a diet, evaluated here for inclusion in a CH4 prediction equation, is made up of cellulose, hemicellulose, lignin, and sometimes silica, and is commonly referred to as the cell-wall fraction (Van Soest et al., 1991). Neutral detergent fiber was positively correlated with CH4 production when expressed as kilograms per day; however, when expressed as a percentage of DM, the relationship was positive for only the beef database (Table 4
). The negative correlation for the dairy and combined databases could be due to the relative proportions of cellulose, hemicellulose, and lignin that make up the NDF fraction. The positive correlation of NDF (kg/d) with CH4 production is likely the result of increased ruminal fermentation, decreased rate of passage out of the rumen, and a favored high acetate:propionate ratio because of the actual NDF component and DMI (Hegarty and Gerdes, 1998; Benchaar et al., 2001; Boadi et al., 2004). Neutral detergent fiber (kg/d) showed a high correlation with CH4 production for the beef database (R2 = 0.63), and comparably high values for the dairy and combined databases (R2 = 0.44 and 0.42, respectively; Table 4
), suggesting that it may be an easily measured variable useful as a predictor of CH4 production within a regression equation.
Acid detergent fiber (the fraction containing cellulose, lignin, and silica), a less desirable measure of fiber than NDF (NRC, 2001), although examined because it is commonly measured, was negatively related to CH4 production when expressed as a percentage of DM for the dairy and combined databases (R2 = 0.39, and 0.061, respectively), but was positively related to CH4 production for the beef database (R2 = 0.19; Table 4
). When expressed as kilograms per day, ADF was positively related to CH4 production for the beef, dairy, and the combined databases (R2 = 0.55, 0.34, and 0.36, respectively; Table 4
).
Lignin, another frequently measured variable, is a noncarbohydrate component that binds to cellulose and hemicellulose, decreasing their availability and strengthening the structure of the plant cell wall (Van Soest, 1994). Lignin was significantly negatively related to CH4 production when expressed as a percentage of DM (P < 0.05; Table 4
); however, when expressed as kilograms per day, lignin was positively related to CH4 production but was not significant (Table 4
). When lignin (kg/d) was included in a complex regression equation (e.g., equation [11b]), its effect on overall CH4 production was negative. The negative relationship between lignin and CH4 production was likely through its limiting effect on digestion of cellulose and hemicellulose, thus limiting CH4 production by the rumen microbes.
It would have been desirable to have a description of the NFC component of the ration, composed of starches, sugars, and pectin, because similar components have been shown to be good predictors of CH4 production (Moe and Tyrrell, 1979b, used NSC and Mills et al., 2003, used starch). However, NFC was not commonly reported, and attempts to calculate it as NFC = 100 (CP + EE + ash + NDF) often resulted in unrealistic values, likely because at least one of the variables was from an average book value. Therefore, NFC was not included in the analysis. The fermentation of cell wall carbohydrates generally produces more CH4 than the fermentation of soluble sugars, which generally produces more CH4 than the fermentation of soluble starch (Johnson et al., 1996). Although NFC, starch, sugar, and pectin are good predictors of CH4 production, these variables are seldom measured in North America, so application of the CH4 prediction equation based on these variables may be severely limited.
Ether extract was positively related to CH4 production when expressed as kilograms per day, and nonsignificantly related to CH4 production when expressed as a percentage of DM (Table 4
). High levels of dietary fat have been shown to depress CH4 production (MJ/d) through biohydrogenation of unsaturated fatty acids (Dong et al., 1997; Machmuller and Kreuzer, 1999), decreased fiber degradation, and decreasing the amount of OM fermentable in the rumen (Mathison, 1997). When EE (kg/d) was included in a regression equation (e.g., equation [12b]), its effect on overall CH4 production became negative.
Forage proportion in the diet has also been used to predict CH4 production (Benchaar et al., 2001; Mills et al., 2003). Johnson and Johnson (1995) reported that very low forage diets (<10%) typically lose between 2 and 3% of gross energy intake as CH4, whereas the accepted average for more modest diets is 6%. A significant positive relationship existed between CH4 production and forage proportion for the beef database (Table 4
), whereas a significant negative relationship existed for the dairy database when all data points were included (Table 4
). However, when 100% forage diet data points were removed from the dairy database, the relationship became significantly positive (Table 4
). The combination of the positive relationship for the beef data, which covered lower values (down to 9% forage), and the negative relationship for the dairy data (with all data points), which covered mainly higher values (>40% forage), resulted in a significant nonlinear relationship in the combined database. Analysis using the nonlinear mixed procedure showed that the relationship between CH4 production and forage proportion in the diet for the combined database could be described by the relationship CH4 (MJ/d) = 0.00103 x (forage%)2 + 0.110 x (forage%) + 8.89. However, there was a high RMSPE value associated with the equation (RMSPE = 46.3%; ED = 30.4%). Lovett et al. (2003) observed a quadratic response of methane emissions to decreasing forage percentage of the diet, in agreement with the results of Moss et al. (1995). Rumen simulations performed by Benchaar et al. (2001) showed that CH4 production (MJ/d) increased when the percentage of forage in the diet was increased from 30 to 80%, and declined thereafter. The authors suggested that this was due to increased ruminal passage rate, decreased ruminal digestion of starch, increased digestion of NDF, and increased ruminal microbial efficiency. Decreasing the forage percentage of the diet also resulted in a shift in ruminal fermentation toward propionate production and decreased ruminal pH (Fahey and Berger, 1988). Propionate production favors competitive pathways for H2 use in the rumen, and would therefore decrease overall CH4 production (Hegarty, 1999; Moss et al., 2000).
The linear 4 equation of Mills et al. (2003) uses forage proportion of the diet in addition to DMI to predict CH4 production, similar to some of the equations developed here (Table 5
). However, among the extant equations, this equation had the highest RMSPE values when challenged against our database (Table 6
). Significant variation existed in the relationship between forage proportion and CH4 production, and this was likely due to variability in the composition of the forage and concentrate fractions within the ratio.
Comparison of Models
Regression equations developed from the beef, dairy, and combined databases are presented in Table 5
, and the results of the RMSPE analysis of them are presented in Table 6
. For the beef database, examination of the equations with one variable (equations [1b] to [6b]) revealed that equations [5b] and [6b] [based on NDF (+) and ADF (+), respectively, where (+) indicates a positive relationship] were the best predictors of CH4 production in terms of RMSPE (RMSPE% = 22.3 and 24.3, respectively). The ADF equation had 96% of its error from random sources (Table 6
). Of the equations with 2 variables (equations [7b] to [12b]), equations [11b] and [7b] had the lowest RMSPE values (RMSPE% = 18.7 and 20.6, respectively) and included the effects of DMI (+) and lignin (), and MEI (+) and NDF (+), respectively [where () indicates a negative relationship; Table 6
]. Of the equations with 3 variables (equations [13b] and [14b]) equation [14b], with the effects of MEI (+), ADF (+), and lignin (), resulted in the lowest RMSPE value (14.4%) and 88% of error from random sources (Table 6
).
For the dairy database, examination of the equations with one variable (equations [1d] to [5d]) revealed that equations [3d] and [2d] [based on forage% (+) and DMI (+), respectively] were the best predictors of CH4 production in terms of RMSPE (RMSPE% = 20.6 and 25.6, respectively), where the forage equation excluded 100% forage data sets, and the DMI equation had 91% of its error from random sources (Table 6
). Of the equations with 2 variables (equations [6d] and [7d]), equation [7d] had the lowest RMSPE value (RMSPE% = 29.5) and included the effects of MEI (+) and NDF () (Table 6
). The equation with 3 variables (equation [8d]), with the effects of DMI (+), ADF () and NDF (+), resulted in an RMSPE value of 28.2 and 86% of error from random sources (Table 6
). Whereas increasing the complexity of the equation for the beef database reduced the RMSPE value, increasing the complexity for the dairy database did not increase predictions significantly.
When the beef and dairy databases were combined, examination of the equations with one variable (equations [1c] to [4c]) revealed that equation [2c], based on DMI (+), was the best predictor of CH4 production in terms of RMSPE (RMSPE% = 28.2), and had 83% of its error from random sources. Of the equations with 2 variables (equations [5c] to [8c]), equations [7c] and [5c] had the lowest RMSPE values (RMSPE% = 29.7 and 29.9, respectively) and included the effects of MEI (+) and NDF (+), and MEI (+) and forage (+), respectively (Table 6
). Of the equations with 3 variables (equations [9c] and [10c]), equation [9c], with the effects of DMI (+), NDF (+), and lignin (), resulted in the lowest RMSPE value (RMSPE% = 29.6) and had 73% of error from random sources (Table 6
). No added advantage in terms of RMSPE was achieved by increasing the complexity of the equations for the combined database, likely because of the carryover effect from the dairy database. Some of the simpler equations had lower RMSPE values than the more complex equations.
Overall, equation [14b] had the lowest RMSPE value for the beef database, equation [3d] for the dairy database, and equation [2c] for the combined database. The lower RMSPE values achieved with more complex equations for the beef database was likely the result of a wider range of diets within the beef database and thus more variability. It could also be due to the relatively weaker relationship between CH4 production and DMI for the beef database compared with the dairy database. In this case, the addition of other variables to the model improved its predictive ability.
The weaker relationships and higher variability for the beef database could be caused by several factors. First, the dairy database is mostly calorimetry data, whereas the beef database is fairly equally divided between calorimetry and SF6 data. It is possible that combining techniques could introduce variability, and perhaps with a larger database of calorimetry vs. SF6 data, the effect of constructing regression equations based on one vs. the other method could be determined. Second, although most dairy cows are housed in confinement, beef cows can be confined in a feedlot or on pasture with correspondingly different diets that will vary more than dairy cow diets (Basarab et al., 2005). Although the cows included in the dairy database were all in the same physiological state (lactating), beef cows could be in a cow-calf (lactating), backgrounding, or feedlot operation and vary more in age, gender, BW, and ADG. Either of these explanations could suggest that these equations may need to be reexamined against a larger current beef database, possibly divided into cow-calf, feeder-stocker, and feedlot scenarios separating by collection technique, as was started by Nkrumah et al. (2006).
The extant equations of Blaxter and Clapperton (1965), Mills et al. (2003; linear 4), and Moe and Tyrrell (1979b) all used information on the composition of diet to improve the prediction of CH4 production and can be compared with the equations developed in this study as well as against each other. These equations were selected because they are commonly used and the required inputs are obtainable from the database compiled here or from North American book values.
Estimates of gross energy digestibility at maintenance intake, required for the equation of Blaxter and Clapperton (1965, adjusted by Wilkerson et al., 1995), are not commonly measured and were estimated as gross energy digestibility at production level intakes for most of the data. Despite this, the equation of Blaxter and Clapperton (1965) does well when challenged against the northern American database. Mean square prediction error values were comparable to those of the newly developed equations, and relatively high proportions of error came from random sources (Table 6
), particularity for the beef database. Conversely, the equation of Moe and Tyrrell (1979b) generally had high RMSPE values in all the databases (Table 6
). Many of the inputs for this equation (cellulose, hemicellulose, and NSC) were average book values because they were not reported in the published papers, and this might have affected its predictive ability. In addition, these variables were reported in feed tables for only a limited number of feeds; thus, assumptions were made and the accuracy of these estimates was likely low. However, Moe and Tyrrell (1979b) showed these dietary variables to be highly correlated with CH4 production. Contrary to the results of the current study, Wilkerson et al. (1995) found that the equation of Moe and Tyrrell (1979b) performed better than several other equations. However, this is part of the limitation of this equation; although it may predict CH4 production well, the inability to obtain accurate input values makes it a less practical choice.
Overall, for the beef database, among the extant equations, the equation of Blaxter and Clapperton (1965) performed the best in terms of the lowest RMSPE value (RMSPE% = 19.1, ED = 79%), followed by the nonlinear 2 equation of Mills et al. (2003; RMSPE% = 28.7, ED = 95%; Table 6
). For the dairy database, the nonlinear 2 equation of Mills et al. (2003) had the lowest RMSPE value (RMSPE% = 28.7, ED = 91%), followed closely by the nonlinear 1 equation of Mills et al. (2003) and equation of Kriss (1930; Table 6
). For the combined database, the equation of Blaxter and Clapperton (1965) had the lowest RMSPE value (RMSPE% = 27.9, ED = 100%), again followed by the nonlinear 2 equation of Mills et al. (2003; RMSPE% = 29.3, ED = 93%; Table 6
).
The average RMSPE (%) values for the beef database were 24.6 and 44.9 for the new and extant equations, respectively. For the dairy database, average RMSPE (%) values were 30.2 and 35.9 for the new and extant equations, respectively. For the combined database, the average RMSPE (%) values were 32.7 and 38.4 for the new and extant equations, respectively. For all 3 databases, numerical decreases in the RMPSE were obtained with the newly developed equations.
Newly developed individual equations had the lowest RMSPE values (compared with extant models) for the beef and dairy databases (equations [14b] and [3d], respectively; Table 6
), and came a close second for the combined dairy database (equation [2c] and the equation of Blaxter and Clapperton, 1965; Table 6
).
Although the average MSPE for the new models vs. the extant models was consistently numerically lower for all databases (see above), a simple Students t-test, assuming unequal variance, showed that the lower average MSPE value difference was significant only for the beef database (P = 0.013, 0.099, and 0.137, for the beef, dairy, and combined databases, respectively).
It appears that the new models performed comparably to, if not slightly better than, the extant models. They were also, for the most part, simpler equations containing input variables more easily obtainable at the farm level. The simplicity and easily obtainable input variables may make the new equations preferable over the extant models, although they should also be challenged on an external database.
| CONCLUSIONS |
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Received for publication October 16, 2006. Accepted for publication March 25, 2007.
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