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* The University of Reading, School of Agriculture, Policy and Development, Earley Gate, Reading RG6 6AR, United Kingdom;
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Institute for Grassland and Environmental Research, Plas Gogerddan, Aberystwyth, Dyfed SY23 3EB, United Kingdom;
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Agricultural Research Institute of Northern Ireland, Hillsborough, Co Down BT26 6DR, Northern Ireland; and
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Department of Animal and Poultry Science, University of Guelph, Guelph, ON, N1G2W1 Canada
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Abstract |
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 Top Abstract IntroductionMaterials and MethodsResultsDiscussionImplicationsLiterature Cited |
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Key Words: Dairy Cows • Methane • Modeling
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Introduction |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionImplicationsLiterature Cited |
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). There have been several attempts to formulate mathematical models to predict methane emissions from cattle (Wilkerson et al., 1995), and these models can be used to identify suitable mitigation options. The models can be classified within two groups. Firstly, there are the statistical models that relate directly the nutrient intake with methane output. Secondly, there are the dynamic mechanistic models that attempt to simulate methane emissions based on a mathematical description of ruminal fermentation biochemistry. Previously, these mechanistic models have been applied successfully (Mills et al., 2001). However, they do not deliver quick solutions based on limited dietary information. The statistical models have provided a better alternative in practical circumstances. Wilkerson et al. (1995) reviewed several statistical models and recommended adoption of the Moe and Tyrrell (1979) equation for dairy cows. However, this model, along with many others, was developed solely on the basis of North American data. Also, it requires cellulose and hemicellulose to be known. Such data are unavailable on many United Kingdom (U.K.) farms. Statistical models have also suffered from an inability to give reliable predictions outside the range of intake used in their formulation. Our hypotheses were that improved statistical models for U.K. systems can be developed from U.K. research data and that mechanistic models would prove superior to statistical models.
The first objective of this research was to develop statistical models for U.K. dairy systems using conventional linear regression techniques. The second objective was to evaluate these models and the Moe and Tyrrell (1979) equation for U.K. and North American systems. The third objective was to consider alternative techniques to develop a model with universal application to a wide range of intake and production systems.
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Materials and Methods |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionImplicationsLiterature Cited |
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Data Origin.
Data consisting of 159 treatment means from 11 experiments with 43 lactating cows conducted at the Metabolism Unit of the Center for Dairy Research (CEDAR), at the University of Reading, were used to develop the models. All animal procedures were licensed and conducted in accordance with U.K. Home Office regulations under the Animals (Scientific Procedures) Act of 1986 and were approved by the local ethics committee. Animals in Trials 1 and 6 were fed a total mixed ration (TMR) ad libitum that comprised on a DM basis: maize (19%) and grass (13%) silages together with dried alfalfa (6%) and a concentrate mixture (62%) (Beever et al., 1998). Trial 2 involved feeding a 3:1 (DM basis) maize silage and grass silage mixture with four different concentrates. The concentrates varied in starch source and degradability and were fed at 8.7 kg DM/d with ad libitum access to the forage (Cammell et al., 2000). The same forage mixture was fed in Trials 3 and 4 on a 1:1 (DM basis) ratio with either a high- or low-starch concentrate in a TMR. The TMR was fed at either ad libitum or restricted intake (85% of ad libitum DM). The diets for Trials 5 and 11 comprised ad libitum fresh cut grass fed three times daily with a 16% crude protein concentrate fed at 5 kg DM/d. Trial 7 involved feeding whole-crop wheat (WCW) silage together with grass silage on a 1:2 (DM basis) ratio. Treatments involved the replacement of WCW with NaOH-treated WCW and changing the forage concentrate ratio (Sutton et al., 2001). Trial 8 also consisted of diets containing WCW and grass silage with a 2:1 (DM basis) forage-to-concentrate ratio (Sutton et al., 1998). In Trials 9 and 10, cows were fed maize silage and concentrates on a 2:1 (DM basis) ratio, with the maize silage harvested at two stages of maturity (low and high).
Statistical Analysis.
The correlations among the variables analyzed were determined using the CORR procedure of SAS (SAS Inst. Inc., Cary, NC). The MIXED procedure of SAS (St-Pierre, 2001) was used to determine individual regression coefficients, and the strength of the relationship between methane output and the other independent variables are listed in Table 1.
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where Yijklmnop = methane (MJ/d); Ti = trial effect; Dj = DMI (kg/d); Nk = N (g/kg DM); Fl = NDF (g/kg DM); Am = ADF (g/kg DM); Sn = starch (g/kg DM); Wo = water-soluble carbohydrate (WSC) (g/kg DM); Mp = ME (MJ/kg DM); DNjk, DFjl, DAjm, DSjn, DWjo, DMjp, NFkl, NAkm, NSkn, NWko, NMkp, FAlm, FSln, FWlo, FMlp, ASmn, AWmo, AMmp, SWno, SMnp, and WMop = interactions of corresponding main effects; ß0 to 35 = regression coefficients; and ejklmnop = residual error. Third-degree interactions were not included to prevent overparameterization of the initial model.
The backward elimination procedure for multiple regression in SAS was used to develop the linear models, and the criteria for selecting the best-fit model were as described by Oldick et al. (1999). The main effects were also analyzed using the MIXED procedure of SAS. Initially, both the intercept and the independent variables were assigned a random component (in addition to the overall fixed effect). However, the data suggested that only the intercept was affected by the Trial. A full model with independent variables interacting with the trial was not possible because the data structure did not permit it and the model would not solve (G matrix was not positive definite; N. R. St. Pierre, personal communication). A significance level of P < 0.10 was used in all analyses.
The model of Moe and Tyrrell (1979) relating the intake of carbohydrate fractions to methane production was used for intermodel comparison. This model is described as follows:
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where NFC is nonfiber carbohydrate, HC is hemicellulose, and C is cellulose.
Nonlinear Modeling
Data Origin. The same data set used to construct the linear models was fit to the nonlinear models.
Techniques. Conventional methods of analysis for the relationship between methane emissions and nutrient intake have relied upon linear relationships, given a predefined intake range. However, a nonlinear, diminishing returns relationship may be more appropriate (see discussion). The nonlinear models tested in this instance were based on the Mitscherlich equation form:
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where a and b are the maximum and minimum values of y, respectively, and c is a shape parameter determining the change of y with increasing x. The data were gathered from multiple trials, so a meta-analytic approach was adopted. Therefore, the nonlinear mixed procedure (PROC NLMIXED in SAS, SAS Inst. Inc., which took into account the fixed and random effects of trials (and their interaction), was used to fit parameter values to the CEDAR data (see results section) (Littell et al. 1996).
Model Evaluation
Data Origin.
Two independent data sets were used to evaluate the new models and the model of Moe and Tyrrell (1979). The first data set (American) was the same as that used by Benchaar et al. (1998) and Mills et al. (2001) to evaluate mechanistic models of methanogenesis. These data were summarized by Benchaar et al. (1998) and represent both lactating and nonlactating dairy cows fed North American diets, with corn silage and alfalfa hay being the principal forage sources. The second data set (U.K.), comprised calorimetry data from experiments conducted at the Agricultural Research Institute of Northern Ireland (ARINI; Unsworth et al., 1994). These data were based on lactating Holstein cows fed typical U.K. diets with grass or grass silage as the only forage sources. A summary of the American and U.K. data sets is displayed in Table 2. The U.K. data contained four experiments. In Experiments 1, 3, and 4, cows received a diet of grass silage with 8 kg of general-purpose concentrates. The grass silage was either ensiled directly or following a wilting period, corresponding to the two treatments. Experiment 2 involved four treatments based on inoculant or formic acid-based silage additive, applied with or without a sugar solution at ensiling. The diets fed in Exp. 2 consisted of 100% forage. Additional U.K. data from the Grassland Research Institute at Hurley, were used to further evaluate the model predictions (Cammell et al., 1986). However, these data did not provide a full characterization of nutrient intake. Therefore, they were suitable only for evaluation with four of the eight models selected. These data are taken from experiments with traditional Friesian cows fed a diet of grass silage (66% DMI) and general-purpose concentrates (34% DMI).
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. Following this adjustment, the comparison of observed and predicted values was performed using the mean square prediction error (MSPE):
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where i = 1, 2, ..., n; n is the number of experimental observations; and Oi and Pi are the observed and predicted values, respectively. The MSPE was decomposed into error due to overall bias of prediction (ECT), error due to deviation of the regression slope from unity (ER), and error due to the disturbance or random variation (ED) (Bibby and Toutenburg, 1977). The square root of MSPE is expressed in the same units as the observed values and a comparison of the root MSPE as a percentage of the observed mean provides an indication of the overall error of prediction.
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Results |
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Linear Modeling.
Table 3 shows that, among the variables studied, only DMI explained a significant amount of variation in daily methane production. None of the correlations between individual nutrient concentrations (grams per kilogram of DM) and methane output were significant, highlighting the need to define such relationships in terms of total nutrient intake (grams per day) and methane output.
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). The Trial effects were significant and the best-fit model, Linear 1, was defined as follows:
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The DMI is not the only measure of total intake available. Description of intake in terms of calculated metabolizable energy intake (MEI) is accessible for most diets. In theory, MEI accounts for methane emissions within its derivation. As such, using MEI to describe intake accounts for the higher proportion of feed energy lost as methane on high-fiber or forage-based diets. Therefore, a second model, Linear 2, was developed using MEI as the independent variable:
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Linear Models 1 and 2 have the advantage of being simple equations, requiring minimal dietary information. However, to account for methane production on diets of similar DMI but differing nutrient profiles, a third model was developed without an explicit term for DMI or MEI. Intake was considered on a nutrient basis (grams of nutrient per day), and these were correlated with methane output. Selected on the same criteria described above, Linear 3 was defined as follows:
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A subset of the data set (n = 64) that contained details of dietary forage intake was used to assess whether methane prediction could be improved with an equation considering forage proportion (Forage DMI/DMI) as an independent variable. The same procedure and selection criteria as outlined above were used to select the best-fit model. Linear 4 was defined as follows:
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Nonlinear Modeling.
The Mitscherlich equation was reparameterized with biologically meaningful parameters. Mitscherlich 1 used DMI as the independent variable, whereas Mitscherlich Models 2 and 3 used MEI. For all three models, parameter b was fixed at zero, representing cessation of methanogenesis at nil intake. Parameter a represents the maximum potential methane production and was fitted for each model against the CEDAR data set using the NLMIXED procedure, giving values of 56.27, 45.98, and 45.98 for Mitscherlich 1, 2, and 3, respectively. For Mitscherlich 1 and 2, c was fitted to these data using the same procedure, giving values of 0.028 and 0.003, respectively. The hypothesis behind Mitscherlich 3 was that the increase in methane output with increasing MEI would depend on dietary composition. Previous research has established a tendency for fibrous diets (high ADF) to increase methane, whereas the reverse is true for diets high in starch (Mills et al., 2001). Therefore, for Mitscherlich 3, c represents the ratio of dietary starch to ADF as follows:
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This equation was derived from the CEDAR data set by splitting these data into five subgroups according to starch-to-ADF ratio. Following this procedure, c was fitted for each subgroup using SAS. The resulting linear regression between c and starch-to-ADF ratio yields the above equation.
Model Evaluation
Table 5 details the results of the model evaluation. Analyses of model predictions for the American and ARINI data are shown in Figures 1 and 2, respectively. The most noteworthy aspects of these results are highlighted below according to the particular data set used for evaluation.
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gave improved estimates of between 17 and 31% above the observed mean. For all models, this substantial overprediction meant that ECT contributed towards the majority of MSPE. The lowest error of prediction was demonstrated by Moe and Tyrell (1979) and Mitscherlich 3 with the root MSPE equivalent to 34% of the observed mean. The four linear models developed from the CEDAR data were unable to match the ability of the Moe and Tyrrell (1979) model in this instance. Figure 1
displays an important distinction between the linear and nonlinear models, whereby the linear models tended to show regression slopes of significantly less than 1 (mean = 0.78). Hence, they tended to underpredict emissions for the highest observed values and vice versa. However, the nonlinear models displayed regression slopes nearer to unity (mean = 0.92).
U.K. Data.
In contrast to evaluation against the American data, all models except Mitscherlich 3 underpredicted methane production for the ARINI data. Also, the degree of deviation from the observed mean was reduced, with the greatest underprediction being only 12% (Moe and Tyrrell, 1979). Of particular note, however, was the improved level of prediction for Mitscherlich 3 in comparison to Mitscherlich 2. Mitscherlich 3 showed the lowest root MSPE of all models (16.3%). Figure 2 shows that all models yielded a regression slope of less than 1 for observed versus predicted plots. However, a similar pattern emerges for the nonlinear models as seen with the American data. In particular, Mitscherlich 2 and 3 show regression slopes of 0.58 and 0.63, respectively, in comparison to 0.17 to 0.54 for the U.K. linear models and Mitscherlich 1. Of those models suitable for evaluation against the Hurley data, both linear and nonlinear models gave very low root MSPE percentages and this reflected the similarity of these data to the data from CEDAR on which the models were developed.
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Discussion |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionImplicationsLiterature Cited |
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), with the exception of Axelsson (1949), who derived a model with a quadratic term for DMI. However, the Axelsson (1949) model is inadequate when used to predict methane production over a range of intakes outside of those used to develop the relationship (Wilkerson et al., 1995). Hence, this model suffers from many of the same limitations as linear alternatives, in that it is unsuitable for extrapolation, although it may describe better the data used for model construction. If the model of Axelsson (1949) is examined over a wider range of DMI, it predicts a maximal methane output at 12.5 kg DMI/d followed by a decline in total methane emissions with increasing DMI until emissions become negative, where DMI is greater than 24 kg DM/d. In contrast, given the declining proportion of GE lost as methane with increasing intake, one would expect any linear model developed within a limited range of intake to overpredict for extrapolations at higher or lower levels of intake.
Within this study, the application of the nonlinear models to predict methane emissions avoids many of the pitfalls associated with both linear alternatives and the quadratic approach demonstrated by Axelsson (1949). By adopting a model that applies biologically sensible constraints (e.g., zero methane at zero intake and an upper limit to emissions), the value of the model as a predictive tool is enhanced. At the same time, the scope for misapplication of the model is reduced. In contrast, previous studies have correlated methane production from dairy cows with parameters that include milk composition measurements (Holter and Young, 1992). It is difficult to see the biological rationale behind such approaches.
The model evaluation summarized in Table 5 demonstrates the utility of the Mitscherlich models in comparison to the linear equations. Although there is minimal difference in root MSPE percentage between the models when used to redescribe the CEDAR data, the benefits become apparent for the American and ARINI data. Besides the reduced error of prediction, the Mitscherlich models display much less absolute error of prediction due to regression as depicted by the regression slopes in Figures 1 and 2. Previous studies evaluating linear models have also shown substantial errors due to regression of observed and predicted methane emissions (Wilkerson et al., 1995). The ability of the nonlinear models to account better for those observations at the extreme methane output-to-feed intake ratios is encouraging.
Of the linear models, the Moe and Tyrrell (1979) model was the most successful for predicting both American and U.K. data sets. For the U.K. data, this is somewhat surprising given that this model was derived from American data. However, the large volume of data used to construct this model may have contributed to its utility in this case. Where only the most basic dietary profile is available (as with the Hurley data set), the simple models play an important role. In these situations, the model of Moe and Tyrrell (1979) and the other more complex models are not applicable. Linear 1 and 2 and Mitscherlich 1 and 2 show low errors of prediction for the Hurley data (Table 5), although Mitscherlich 1 and 2 are able to better describe the American and ARINI data.
Even though the Moe and Tyrrell (1979) model gives reasonable predictions of methane emissions, the positive influence of nonfiber carbohydrate (NFC) on methane production could be misleading when using the model to develop low-emission feed rations. The principal components of NFC are starch and WSC. It has been shown both here and elsewhere (Mills et al., 2001) that starch inclusion leads to a much higher recovery of feed energy as net energy, in direct contrast to WSC. Therefore, for the purposes of ration formulation and providing that sufficient data are available, Mitscherlich 3 should provide a more robust option. Figure 2 shows the uneven distribution of evaluation data between high- and low-emission groups. The low-emission group describes those cows fed 100% forage diets in Exp. 2 of the ARINI data. It is evident that the regressions for the linear models in Figure 2 were affected to a greater degree by these data than was the case for the nonlinear models. A greater spread in evaluation data throughout the range of methane emissions shown would help to clarify this occurrence. However, such data, typically involving animals at low intakes, were unavailable in this instance.
When the dynamic model of Mills et al. (2001) was used to simulate different feeding strategies, estimates of methane energy as a proportion of ME ranged from 9.5 to 10.2%. The higher starch diets (corn silage or concentrate vs. grass silage) showed increased rates of decline in the proportion of GE lost as methane, as ME intake increased. The relatively low proportion of ME lost as methane in these simulations can be explained by the tendency of the model to underestimate emissions for the CEDAR data (Mills et al., 2001). However, the direct contrast between the results for Mitscherlich 3 (Figure 3) and the dynamic model with regard to the effect of starch content are less clear. The nature of the dynamic model is such that many more nutritional factors are considered during simulation. Therefore, the application of the dynamic model to the various diets represents more than just the effect of starch-to-ADF ratio. Although both the Mitscherlich 3 and dynamic models predict reduced methane emissions for isoenergetic diets as starch concentration increases, the models do not agree as to the marginal benefit in energy retention for increases in intake.
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There are benefits to be gained by refining the calculation of the shape parameter in Mitscherlich 3. A larger database with a broader range of starch-to-ADF ratios would provide an opportunity to improve the model further. Other dietary parameters could be included to estimate this shape parameter, but for every extra descriptor there is a trade-off between improved methane prediction and increased model complexity. Also, more data are required for animals fed at low intakes, and for different breeds and sexes.
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Implications |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionImplicationsLiterature Cited |
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Footnotes |
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2 Correspondence—phone +44 (0) 1189 316783; E-mail: j.a.n.mills{at}reading.ac.uk.
Received for publication June 12, 2002. Accepted for publication July 30, 2003.
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Literature Cited |
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TopAbstractIntroductionMaterials and MethodsResultsDiscussionImplicationsLiterature Cited |
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