Prediction of enteric methane emission from buffaloes using statistical models

Agriculture, Ecosystems and Environment xxx (2014) 139–148

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Prediction of enteric methane emission from buffaloes using statistical models Amlan Kumar Patra * Department of Animal Nutrition, West Bengal University of Animal and Fishery Sciences, 37 K. B. Sarani, Belgachia, Kolkata 700037, India

A R T I C L E I N F O

A B S T R A C T

Article history: Received 27 December 2013 Received in revised form 19 April 2014 Accepted 10 June 2014 Available online xxx

Methane (CH4) production from world buffalo population contributes a substantial share to the global greenhouse gas production by livestock. However, there is no model for predicting enteric CH4 production in buffaloes, though there are several models developed for prediction of enteric CH4 from cattle. Thus, the objective of this study was to develop linear and nonlinear statistical models to predict CH4 production from dietary and animal characteristic variables. A database from 24 publications was constructed, which included 64 mean observations of CH4 outputs measured on 394 buffaloes. Extant equations developed for cattle were also evaluated for suitability of those CH4 prediction equations in buffaloes. The simple linear equations that predicted with high precision and accuracy were CH4 (MJ/ day) = 1.29(
0.576) + 0.788(
0.099)  dry matter (DM) intake (kg/day) [RMSPE = 19.4%, with 94% of mean square prediction error (MSPE) being random error; R2 = 0.81] and CH4 (MJ/day) = 0.135(
0.767) + 1.717(
0.233)  neutral detergent fiber (NDF) intake (kg/day) [RMSPE = 18.3%, with 99.7% of MSPE being random error; R2 = 0.79]. Multiple regression equations that predicted CH4 slightly better than simple prediction equations were CH4 (MJ/day) = 0.436(
0.665) + 0.678(
0.184)  DM intake (kg/day) + 0.697(
0.347)  NDF intake (kg/day) [RMSPE = 16.1%, with 99.9% of MSPE from random error; R2 = 0.85] and CH4 (MJ/ day) = 0.819(
0.801) + 0.690(
0.432)  crude protein (CP) intake (kg/day) + 1.527(
0.215)  NDF intake (kg/ day) + 0.930(
0.413)  non-fibrous carbohydrate (NFC) intake (kg/day) [RMSPE = 16.5%, with 99.7% of MSPE accounting random error; R2 = 0.84]. Among the nonlinear equations developed, monomolecular model, CH4, MJ/day = 39.99(
17.23)  {1  exp(0.0276(
0.0132)  DM intake (kg/day)) [RMSPE = 19.1%, with 99.9% of MSPE accounting random error; R2 = 0.80]}, performed better than other nonlinear models, but the predictability and robustness of the equation did not improve compared with the linear models. Extant equations overestimated the methane production, and had low accuracy and precision. The equations developed in this study would be useful for national inventory preparation to improve an estimation of methane production in buffaloes particularly for tropical feeding situations. ã 2014 Elsevier B.V. All rights reserved.

Keywords: Buffalo Methane production Statistical model Regression equation

1. Introduction Greenhouse gas (GHG) emissions from livestock production system have emerged as great concerns in the recent decades owing to the contribution of a considerable share to the global anthropogenic GHG emissions (Opio et al., 2013). A life cycle analysis of GHG emissions assessed that livestock sectors and animal protein production contribute about 12–18% of total GHG (Steinfeld et al., 2006; Westhoek et al., 2011) accounting 9%, 35– 40% and 65% of carbon dioxide, methane and nitrous oxide of global anthropogenic emissions, respectively (Steinfeld et al., 2006). Major share of methane emissions from livestock arises

* Tel.: +91 33 25569234. E-mail address: [email protected] (A.K. Patra). http://dx.doi.org/10.1016/j.agee.2014.06.006 0167-8809/ ã 2014 Elsevier B.V. All rights reserved.

from enteric fermentation in ruminants (Patra, 2012, 2014). Annually, an estimated 94.9 million tonnes of enteric methane was contributed by different livestock species of the world in 2010 (Patra, 2014). Although enteric methane by cattle largely represented an estimated 74% of total enteric methane, buffalo population was the second most contributor of enteric methane emissions accounting about 11.3% of total enteric methane, followed by sheep (6.4%), goats (4.9%) and other animals (Patra, 2014). Besides, the annual growth rate of enteric methane from buffaloes was 1.57% after goats (2.0%), while growth rate of enteric methane emission from cattle was 0.87% (Patra, 2014). Despite a significant share of enteric methane contributed by buffaloes, methane production from this animal species has not been assessed adequately. Several statistical and dynamic mechanistic models had been recommended for prediction of methane from cattle and sheep

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(Kriss, 1930; Axelsson, 1949; Blaxter and Clapperton, 1965; Mills et al., 2003; Ellis et al., 2007; Kebreab et al., 2008; Ramin and Huhtanen, 2013). Statistical models predict methane production from nutrient intake directly, while dynamic mechanistic models estimate methane emission using mathematical descriptions of rumen fermentation biochemistry (Kebreab et al., 2006; Ellis et al., 2007). These models have been quite useful to predict enteric methane emission from cattle without undertaking extensive and costly experiments. Although numerous statistical models were developed and evaluated from database of dairy and beef cattle, and sheep feeding studies, development of models for predicting enteric methane production in buffaloes has not received attention so far. The models developed for cattle may not have precise predictive ability of methane production for buffaloes. Therefore, the objective of this study were to develop statistical models for prediction of enteric methane production in buffaloes using commonly measured dietary variables, and to validate different existing methane prediction models for cattle using a database of buffaloes. 2. Materials and methods 2.1. Construction of database A database was compiled from the studies published in journals and conference proceedings for this meta-analytic approach. Criteria for inclusion of studies in the database were that the studies provided an adequate description of the animals, chemical composition and intake of the diet, and in vivo methane production in buffaloes measured using either respiration chamber or sulphur hexafluoride tracer technique. Overall, 24 publications (Barman et al., 2001; Garg et al., 2012; Haque et al., 2004; Kannan and Garg, 2009; Kannan et al., 2010; Khan et al., 1988; Lal et al., 1987; Malik and Singhal, 2009; Mehra et al., 2006; Mohini and Singh, 2001, 2003, 2008; Murarilal et al., 1999; Pattanaik et al., 1996; Prakash et al., 2000; Prusty et al., 2013; Sahoo et al., 1995; Sakthivel, 2012; Santra et al., 1994; Saraswat et al., 2001; Singhal et al., 2006; Tiwari et al., 2000; Turnbull et al., 2000; Varma et al., 2012) that reported data on animal characteristics, composition of diets, methane production, intake and digestibility of nutrients fulfilled the criteria for inclusion in this database. All the studies in these publications were conducted in India as no publication that could fulfill the inclusion criteria was available from other countries to the best of knowledge of the author. This is to mention that most of the buffalo population is centered in South-Asia, and other tropical countries. Thus, dietary and animal characteristics of other buffalo-rearing countries would adequately be similar to this database. There were a total of 64 treatment means obtained from 394 observations from buffaloes. However, treatments (n = 6) containing feed additives that have antimethogenic properties were removed before statistical analysis. The investigated dietary and animal factors (independent variables) were body weight (BW), intake (dry matter (DM), individual nutrients, gross energy (GE) and metabolizable energy (ME)) and nutrient composition of diets that were used for regression equation development. Since all variables were not available for all studies in the data set, the number of observations used for regression analyses varied between dietary and response variables depending on the regressor variables available. Data reported in differing units of measure were transformed to the same units. Some records were incomplete or not reported uniformly, which necessitated the calculations from the reported data. Whenever possible, missing chemical composition of the diets was calculated from book values of ingredients (Feedipedia, 2013) or studies included in this dataset with similar ingredients. When a study did not report all possible outcomes and it was not

possible to calculate from the reported data, missing variables were considered as missing data. 2.2. Statistical analysis 2.2.1. Linear model Statistical analysis procedure used for prediction of methane production from this database has been described elsewhere (Patra, 2010). In brief, all statistical computations were carried out using the PROC MIXED, PROC REG and PROC CORR procedures of the SAS software system. Data were analyzed according to St-Pierre (2001) taking into account the random effect of the study because studies represented random samples of larger population of studies, using PROC MIXED (SAS, 2001) with the following model: Y ij ¼ B0 þ B1 X ij þ B2 X 2ij þ si þ bi X ij þ eij where: Yij = the expected outcome for the dependent variable Y observed at level j of the continuous variable X in the study i. B0 = the overall intercept across all studies (fixed effect). B1 and B2 = the overall linear and quadratic regressing coefficient of Y on X, respectively, across all studies (fixed effect). Xij = the value j of the variable X in study i. si = the random effect of study i. bi = the random effect of study i on the regression coefficient of Y on X in study i, and, eij = the unexplained residual error. However, squared term of predictors were not significant (P > 0.10) for any equations, and they were removed from the final models. Observed methane production was weighted by the number of animals in each study to take into consideration of unequal variance among studies. The slopes and intercepts by study were included as random effects, and an unstructured variance–covariance matrix (type = un) or a variance component (type = vc) of variance–covariance structure was performed at the random part of the model (St-Pierre, 2001). If random covariance or random slope, they were removed from the model. All significant predictors (P < 0.10) of methane outputs and twoway interactions were further used to develop multiple regression equations employing the backward elimination multiple regression procedure following the algorithm reported by Oldick et al. (1999) and Patra (2009). To limit overparameterization of the models, a variance inflation factor less than 100 for every continuous independent variable tested was assumed, as suggested by Oldick et al. (1999). The best-fit equations of multiple regression equations that further improved the relationship obtained from linear regression are presented. 2.2.2. Nonlinear models Since DM intake as sole independent variable predicted methane emission with highest degree of determination in the linear model, DM intake was used as a determinant for development of non-linear relationships between DM intake and methane outputs, if prediction could be further improved. These were relationships exhibiting diminishing returns (monomolecular), sigmoidal (Gompertz) and exponential behaviours. The PROC NLMIXED of SAS was used to parameterize the nonlinear functions with a little modification of the equation used by Schulin-Zeuthen et al. (2007) and the exponential model in the following forms: Monomolecular :Y ¼ a  ða þ bÞ  expðc  xÞ Gompertz : Y ¼ b  exp


 ð1  expðc  xÞ  lnða þ 2bÞ  2b b

A.K. Patra / Agriculture, Ecosystems and Environment xxx (2014) 139–148

Exponential : Y ¼ b  expðc  xÞ where the parameter a and b represent the upper asymptote and Y intercept of the nonlinear models, respectively and c determines the shape of the response curve in the nonlinear functions. Study including parameters a, b and c was considered random in the models (Schinckel and Craig, 2002; Schulin-Zeuthen et al., 2007) The lowest value of Akaike’s Information Criteria (AIC, a measure of regression fit), greater values of determination (R2) and biological relevance of the parameters were considered to find out the bestfit non-linear models. 2.2.3. Model evaluation There are no models for prediction of methane emissions from buffaloes. Thus, predictive abilities of a range of existing models of Kriss (1930), Axelsson (1949), Mills et al. (2003), IPCC (2006) tier II, Ellis et al. (2007), Yan et al. (2009) and Ramin and Huhtanen (2012, 2013),) that were developed from dairy and beef cattle, and sheep were compared using inputs from this databases (Table 1). These equations were selected for comparison because they were commonly evaluated in different studies (Ellis et al., 2007, 2009; Yan et al., 2009), and their input variables were available from this compiled database. Equations developed in this study and extant equations were compared using mean square prediction error (MSPE), root of MSPE (RMSPE) expressed as a percentage of the observed mean (Theil, 1966) and coefficient of determination (R2) (Draper and Smith, 1998). The MSPE value was calculated as: n X ðOi  Pi Þ2

MSPE ¼

i¼1

141

respectively; and r is the coefficient of correlation between predicted and observed values. The ECT values indicate how the average of predicted values deviates from the average of observed values. Error due to regression measures deviation of the least squares regression coefficient (r  SO/SP) from 1, the value where the predictions are completely accurate. A large ER value indicates inadequacies in the ability of the model to predict the variable. Error dPue to disturbance represents the variation in observed values unexplained after the mean and the regression biases have been removed. Concordance correlation coefficient (CCC) or reproducibility index was used to evaluate the precision and accuracy of predicted versus observed values for each model (Lin, 1989); which has been described previously (Ellis et al., 2009). The CCC estimate represents as a product the correlation coefficient (r) and the bias correction factor (Cb). Another estimate (m) that measures location shift relative to the scale (difference of the means relative to the square root of the product of two standard deviations). An internal evaluation was undertaken for cross-validation to evaluate the accuracy and predictability of the equations. For this purpose, the whole data set was randomly divided into three subsets and the split was made experiment-wise so that all data from one study were in the same subset (Yan et al., 2009; Ramin and Huhtanen, 2013). The equations were then evaluated using the two-third of data and the MSPE. The prediction bias of good equations (simple, multiple and non-linear models) developed in this study and extant models were further evaluated in the form of residual plots in which the residuals (observed  predicted) were plotted against predicted values as described by St-Pierre (2003).

n

where Oi is the observed value for the ith observation, Pi is the predicted value for the ith observation, and n is the number of observations. Square root of the MSPE (RMSPE), which provides an estimate of the overall prediction error, was expressed as a proportion (MSPE divided by the observed mean) of the observed 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 value was decomposed into mean bias or error in central tendency (ECT), slope bias or error due to regression (ER), and random or error due to disturbance (ED). These three fractions were calculated as follows (Bibby and Toutenburg, 1977): ECT ¼ ðP  OÞ2 ER ¼ ðSP  r  SO Þ2

3. Results 3.1. Description of dataset A description of the dietary and animal characteristics included in this meta-analysis such as nutrient intake, feed digestibility, BW and CH4 production are shown in Table 2. The mean concentrations of crude protein (CP) and neutral detergent fiber (NDF) ranged from 76 to 236 g/kg DM and 430 to 717 g/kg DM, respectively, which suggested that quality of diets varied widely. Concentration of ether extract though ranged widely had low mean concentration. The wide range of digestibilities of DM, NDF, CP and fats in the dataset signified that digestibilities varied substantially depending upon dietary chemical composition. The methane emissions expressed in terms of MJ/day, g/kg DM intake, % of gross energy intake also ranged extensively in the dataset.

ED ¼ ð1  r2 Þ  S2O

3.2. Correlations between methane production and animal and dietary variables

and expressed as a percentage of MSPE. The entities P and O are the averaged predicted and observed values, respectively; SP and SO are the standard deviations of the predicted and observed values,

Daily methane emission (MJ/day) was positively (P = 0.01– <0.001) correlated (r = 0.39–0.90) with body weight and intakes of

Table 1 List of extant cattle equations used to predict methane production from buffaloes. Source

Equation

Kriss (1930) Axelsson (1949) Mills et al. (2003)

CH4 (MJ/d) = 0.996 + 1.246  DM intake (kg/d) CH4 (MJ/d) = 2.067 + 2.636  DM intake (kg/d)  0.105  DM intake (kg/d)2 CH4 (MJ/d) = 5.93 + 0.92  DM intake (kg/d) CH4 (MJ/d) = 8.25 + 0.07  ME intake (MJ/d) CH4 (MJ/d) = 56.27  (56.27 + 0)  exp[0.028  DM intake (kg/d)] CH4 (MJ/d) = 0.065  GE intake (MJ/d) CH4 (MJ/d) = 3.272 + 0.736  DM intake (kg/d) CH4 (MJ/d) = 0.582 + 1.40  DM intake (kg/d) CH4 (MJ/d) = 0.797 + 1.427  DM intake (kg/d)  0.020  DM intake (kg/d)2 CH4 (L/d) = 976  [(1  exp (0.0407  DM intake (kg/d))]

IPCC (2006) Ellis et al. (2007) Yan et al. (2009) Ramin and Huhtanen (2013) Ramin and Huhtanen (2012)

GE: gross energy; DM: dry matter; ME: metabolizable energy.

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Table 2 Descriptive statistics of the variable in the database used to evaluate methane prediction equations in buffalo. Items

Unit

N

Minimum

Maximum

Mean

SD

Body weight Chemical composition Organic matter Crude protein Ether extract Neutral detergent fiber Acid detergent fiber Crude fiber Nitrogen free extract Roughage proportion Nutrient intake Dry matter intake Gross energy intake TDN intake ME intake Digestibility Dry matter Organic matter Crude protein Neutral detergent fiber Acid detergent fiber Crude fiber Ether extract Nitrogen free extract Methane production Methane Methane Methane Methane

kg

58

107.3

537.0

327.4

121.5

DM DM DM DM DM DM DM DM

58 58 48 41 38 45 48 58

861.6 76.2 6.8 430.0 254.2 199.3 262.8 367.2

942.6 236.0 74.7 717.2 461.6 394.1 674.2 100.0

903.2 116.4 24.5 571.4 356.8 275.9 482.3 699.4

19.2 40.3 16.1 84.5 65.7 52.1 74.1 168.3

kg/day Mcal/day kg/day Mcal/day

58 58 58 58

2.6 9.6 1.3 4.6

14.7 64.2 11.3 37.8

6.4 27.0 3.7 13.0

2.7 11.6 1.8 6.1

% % % % % % % %

46 48 44 13 10 28 37 28

40.4 44.7 34.8 44.2 43.1 43.0 22.4 40.1

79.7 84.1 86.8 70.3 68.4 71.7 78.6 72.0

57.4 60.5 58.5 55.4 59.7 60.5 63.2 56.2

8.4 8.4 12.1 9.5 9.5 8.1 13.2 7.9

MJ/d g/kg DM intake g/kg DDM intake % of GE intake

58 58 46 58

2.1 9.3 17.9 3.0

14.5 33.6 51.8 9.7

6.4 18.6 33.6 5.9

2.7 4.7 10.0 1.5

g/kg g/kg g/kg g/kg g/kg g/kg g/kg g/kg

SD: standard deviation; DM: dry matter; DDM: digestible dry matter; GE: gross energy.

all nutrients except ether extract (Table 3). Intake of ether extract tended (P = 0.09) to negatively correlated (r = 0.24) with methane production (MJ/day). Intake of nutrients and energy except ether extract and non-fibrous carbohydrate (NFC) explained significant amount of variation (R2 = 0.49–0.81) in methane output. However, concentrations of any nutrients were not correlated (P > 0.10) with daily methane emission (MJ/day). Methane outputs expressed as g/ kg DM intake tended to correlate positively with NDF concentration (P = 0.08; R2 = 0.28) and acid detergent fiber (ADF) intake (P = 0.07; 0.29), and positively correlated with ADF concentration (P = 0.04; R2 = 0.32); however, correlations between methane emission (as g/kg DM intake) and intake and concentrations of other nutrients and energy were not significant (P > 0.10) in this database (data not shown). 3.3. Prediction equations for methane production Individually, intake of all nutrients (DM, GE, ME, total digestible nutrients (TDN), NDF, ADF, CP, EE and NFC) significantly predicted

methane outputs (Table 4). However, prediction of methane output was high (R2 = 0.68–81) for intake of DM, GE, ME, TDN, NDF and ADF and they are presented in Table 4. Among the nutrient composition (CP, EE, NDF, ADF and NFC), NDF and ADF concentrations predicted methane output, though the prediction was low (R2 = 0.38–0.40). Digestible organic matter intake used as a single predicted methane production similar to only DM intake. Methane emission was not predicted by the concentrations of CP, NFC and EE in this database. Multiple regression models were developed utilizing significant independent variables, if they could improve the methane prediction further compared with individual variables. Inclusion of intakes of DM and NDF or DM and ADF or CP, NDF and NFC as predictors marginally improved (R2 = 0.81 for intake of DM as a predictor to 0.84–0.85 for all models) methane prediction, although inclusion of each of these variables had a significant effect on the prediction of methane production. None of the other variables and interaction terms improved prediction of methane emission further.

Table 3 Pearson correlation coefficients (r) for dietary variables and methane production (MJ/d) in the database. Items Body weight (kg) DM intake, kg/d GE intake, MJ/d ME intake, MJ/d

Total digestible nutrient Crude protein Ether extract Neutral detergent fiber Acid detergent fiber Crude fiber Nitrogen free extract Non-fibrous carbohydrate

r 0.76 0.88 0.90 0.84 Intake (kg/d) 0.85 0.70 0.24 0.89 0.85 0.78 0.77 0.39

DM: dry matter; GE: gross energy; CP: crude protein; ME: metabolizable energy.

P-value

r

P-value

<0.001 <0.001 <0.001 <0.001

– – – –

– – – –

<0.001 <0.001 0.09 <0.001 <0.001 <0.001 <0.001 0.01

Composition (g/kg of DM) <0.01 0.03 0.20 0.07 0.02 0.08 0.06 0.22

1.0 0.84 0.20 0.65 0.90 0.62 0.67 0.16

A.K. Patra / Agriculture, Ecosystems and Environment xxx (2014) 139–148

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Table 4 List of developed statistical models used to predict methane production (MJ/d) from buffaloes. Equation no.

Equation

Linear 1 Linear 2 Linear 3 Linear 4 Linear 5 Linear 6 Linear 7 Linear 8 Linear 9 Linear 10 Linear 11 Linear 12 Linear 13 Linear 14 Monomolecular 1 Monomolecular 2 Exponential Gompertz

CH4 CH4 CH4 CH4 CH4 CH4 CH4 CH4 CH4 CH4 CH4 CH4 CH4 CH4 CH4 CH4 CH4 CH4

(MJ/d) = 1.29(
0.576) + 0.788(
0.099)  DM intake (kg/d) (MJ/d) = 2.93(
0.599) + 0.0618(
0.0135)  ME intake (kg/d) (MJ/d) = 1.577(
0.572) + 0.0423(
0.0057)  GE intake (MJ/d) (MJ/d) = 2.89(
0.585) + 0.907(
0.191)  TDN intake (kg/d) (MJ/d) = 0.135(
0.767) + 1.717(
0.233)  NDF intake (kg/d) (MJ/d) = 0.614(
0.984) + 2.588(
0.484)  ADF intake (kg/d) (MJ/d) = 3.35(
0.899) + 2.364(
0.492)  NFC intake (kg/d) (MJ/d) = 8.66(
2.63)  0.00449(
0.0024)  NDF (g/kg) (MJ/d) = 7.56(
2.45)  0.0038(
0.00266)  ADF (g/kg) (MJ/d) = 0.436(
0.665) + 0.678(
0.184)  DM intake (kg/d) + 0.697(
0.347)  NDF intake (kg/d) (MJ/d) = 0.412(
0.757) + 0.753(
0.175)  DM intake (kg/d) + 0.915(
0.549)  ADF intake (kg/d) (MJ/d) = 1.83(
0.728) + 0.0143(
0.0026)  BW (kg) (MJ/d) = 0.819(
0.801) + 0.690(
0.432)  CP intake (kg/d) + 1.527(
0.215)  NDF intake (kg/d) + 0.930(
0.413)  NFC intake (kg/d) (MJ/d) = 3.40(
0.456) + 0.685(
0.171)  digestible OM intake (kg/d) (MJ/d) = 21.71(
3.84)  {21.71(
3.84)  0.732(
0.637)}  exp{0.0485(
0.0094)  DM intake (kg/d)} (MJ/d) = 39.88(
17.23)  (1  exp{0.0276(
0.0132)  DM intake (kg/d)} (MJ/d) = 3.019(
0.290)  exp{0.108(
0.0160)  DM intake (kg/d)} (MJ/d) = 0.836(
0.493)  exp{(1  exp(0.277(
0.0314)  DM intake (kg/d))  ln(12.05(
1.28) + 2  0.836(
0.493)/0.836(
0.493)}  2  0.836(
0.493)

The subscripted data in parentheses are s.e. values. BW: body weight; DM: dry matter; OM: organic matter; NDF: neutral detergent fiber; ADF: acid detergent fiber; CP: crude protein; NFC: non-fibrous carbohydrate.

Dry matter intake was used to predict methane emission using non-linear models. However, monomolecular (R2 = 0.79), exponential (R2 = 0.80) and Gompertz (R2 = 0.81) models did not improve prediction of methane outputs further compared to the linear model using DM intake (R2 = 0.80) as single predictor. 3.4. Comparison of models Analyses of MSPE and CCC of the developed and extant methane prediction equations are presented in Table 5. The examination of the equations with one variable revealed that equation based on NDF intake (RMSPE% = 18.3) was the best predictor of methane production considering smaller RMSPE (97.7% of its error from random sources) and greater precision (CCC values = 0.88) and

accuracy (Cb = 0.99), followed by DM intake (RMSPE% = 20.2 with 93.7% error from random sources and CCC value of 0.87). The equations with two variables, which included the effects of DM intake and NDF intake, and DM intake and ADF intake, respectively, resulted in the lowest RMSPE values (RMSPE% = 16.1–16.9) with random error sources of 98.6% and 99.9%) and greater precision and accuracy. The equations with three variables, which included intakes of CP, NDF and NFC had RMSPE% value of 16.5, and had 99.7% of error from random sources. No added advantage in terms of RMSPE was achieved by increasing the complexity of the equations. Some of the simpler equations had lower RMSPE values than the more complex equations, and hence they were not presented here. Two-third of the treatments in this database were randomly used for cross-validation to evaluate the accuracy and

Table 5 Mean square prediction error and concordance correlation coefficient analyses of developed and extant methane prediction equations. Study

Equation no.

RMSPE (%)

ECT (%)

ER (%)

ED (%)

CCC

R2

Cb

m

This study

Linear 1 Linear 2 Linear 3 Linear 4 Linear 5 Linear 6 Linear 7 Linear 8 Linear 9 Linear 10 Linear 11 Linear 12 Linear 13 Linear 14 Monomolecular 1 Monomolecular 2 Exponential Gompertz Linear Linear Linear 1 Linear 2 Exponential Linear Linear 1 Linear Linear Non-linear

19.4 26.4 20.36 25.8 18.3 22.0 40.1 41.4 39.9 16.1 16.9 28.2 16.5 22.7 21.2 19.1 21.5 20.9 47.4 58.8 87.8 92.9 49.6 27.2 32.4 57.4 46.0 42.8

0.053 0.022 0.009 0.22 0.077 0.34 2.22 0.005 0.067 0.053 0.94 1.75 0.15 0.022 1.35 0.001 1.69 3.73 74.5 81.0 95.4 92.5 74.8 31.2 61.4 75.4 78.3 73.0

6.28 16.5 8.63 13.9 0.26 1.95 6.01 25.8 32.2 0.01 0.49 1.98 0.13 38.7 14.9 0.05 18.2 18.7 9.67 2.20 0.08 0.66 10.2 17.2 4.80 13.8 4.04 6.50

93.7 83.3 91.4 85.9 99.7 97.7 91.8 74.1 67.7 99.9 98.6 96.2 99.7 61.0 83.7 99.9 80.1 77.5 15.8 16.8 4.63 6.86 15.0 51.6 33.8 10.8 17.6 20.5

0.87 0.71 0.85 0.73 0.88 0.81 0.30 0.18 0.12 0.92 0.91 0.68 0.92 0.74 0.85 0.89 0.83 0.90 0.65 0.48 0.28 0.19 0.63 0.84 0.70 0.58 0.63 0.67

0.81 0.68 0.79 0.69 0.79 0.70 0.12 0.38 0.40 0.85 0.84 0.56 0.84 0.79 0.79 0.80 0.80 0.82 0.81 0.69 0.81 0.68 0.80 0.79 0.81 0.81 0.789 0.796

0.97 0.86 0.96 0.88 0.99 0.96 0.86 0.296 0.19 0.99 0.99 0.91 0.99 0.82 0.95 0.99 0.93 0.99 0.72 0.56 0.32 0.23 0.70 0.94 0.70 0.65 0.709 0.755

0.012 0.038 0.052 0.037 0.014 0.037 0.190 0.016 0.078 -0.023 -0.102 -0.11 -0.016 0.002 -0.039 -0.002 0.077 0.088 0.85 1.21 2.08 2.57 0.89 0.33 0.69 0.98 0.90 0.79

Kriss (1930) Axelsson (1949) Mills et al. (2003)

IPCC (2006) Ellis et al. (2007) Yan et al. (2009) Ramin and Huhtanen (2013) Ramin and Huhtanen (2012)

RMSPE%: root mean square prediction error (RMSPE) expressed as a percentage of the observed mean; ECT, ER, and ED, error due to bias, regression and disturbance, respectively, as a percentage of total RMSPE; CCC: concordance correlation coefficient; r: correlation coefficient estimate; Cb: bias correction factor; m: location shift relative to the scale.

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Fig. 1. Plots of predicted versus observed methane (MJ/d) production. For Eq. (1), Y = 1.894 (
0.362) + 0.688 (
0.050)  X, R2 = 0.845, RMSPE% = 19.4, CCC = 0.88 and Cb = 0.96, n = 38 (top left); Eq. (5), Y = 1.447 (
0.467) + 0.738 (
0.069)  X, R2 = 0.81, RMSPE% = 18.0, CCC = 0.88 and Cb = 0.97, n = 28 (top right); Eq. (10), Y = 0.883 (
0.471) + 0.840 (
0.069)  X, R2 = 0.854, RMSPE% = 15.8, CCC = 0.92 and Cb = 0.99, n = 27 (bottom left); and Gompertz, Y = 0.456 (
0.584) + 1.027 (
0.082)  X, R2 = 0.82, RMSPE% = 21.6, CCC = 0.89 and Cb = 0.99, n = 38 (bottom right).

predictability of the equations. A plot of predicted versus observed methane for the Eqs. (1), (5), (10) and Gompertz is presented in Fig. 1, which indicated a good relationship between observed and predicted methane production, and had low RMSPE, high accuracy and predictability. Methane outputs were overpredicted by all extant models as indicated by high negative m values and these models had greater ECT ranging from 31 to 95% of the RMSPE. Among these models, the mean bias (difference between predicted and actual data) was the lowest with IPCC (2006) model (0.33 MJ/day) and the largest bias (2.08–2.57 MJ/day) with Mills et al. (2003) linear models. The RMSPE followed a similar trend. Similar results were also found when the total error was separated into mean bias, line bias and random variation. Only 5–7% of the error was attributed to random variation for linear models of Mills et al. (2003) along with lower CCC and Cb values; while with IPCC (2006), 52% of the error was derived from random variation with highest precision (CCC = 0.84) and accuracy (Cb = 0.94). Six prediction equations, two from each of simple, multiple and non-linear models that predicted methane outputs highly, were used from residual analysis. There was no significant mean and linear biases (P > 0.05) for all models except for non-linear models (Figs. 2 and 3). The mean and slope biases of the non-linear equations, although significant statistically resulted in a maximum bias of less than 1.13 and 1.52 MJ/day over the full range of predicted values for monomolecular and Gompertz equations, respectively. In contrast, the mean and linear biases of two best

extant equations (one each from linear and non-linear models) were significant (P < 0.001) and resulted in a maximum bias of 3.28 and 4.31 MJ/day over the full range of predicted values for models of IPCC (2006) and Ramin and Huhtanen (2012), respectively. 4. Discussion The mean concentrations of CP and NDF in the diets were 116 and 571 g/kg DM. This suggested that low to medium quality diets were included in this dataset. The average methane production per kg DM intake in this database for buffalo was 18.6 g/kg DM intake, which was lower than the values (ranging from 20.2 to 23.0 g/kg DM) reported for dairy and beef cattle (Moe and Tyrrell, 1979; Mills et al., 2003; Ellis et al., 2007; Ramin and Huhtanen, 2013). The lower value of methane production (g/kg DM intake) in the present study was likely due to the lower quality of diets fed to the buffaloes in Indian situations compared with the diets offered to cattle in temperate countries, and consequently low digestibility (mean digestibility of 57%) of feeds. Differences in methane production between cattle and buffaloes may also exist. Various models developed in this study demonstrated that DM or GE or NDF intake as a single predictor had a stronger relationship with methane production than other predictors. A number of studies had also reported several prediction equations with high precisions for methane outputs using feed intake (DM or energy) as a primary predictor in dairy and beef cattle (Holter and Young, 1992; Yan et al., 2000, 2009; Mills et al., 2003). In this

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145

Fig. 2. Plot of observed minus predicted methane production (residual) vs. predicted methane production from buffaloes. The independent variable (predicted methane production) was centered around the mean predicted value before the residuals were regressed on the predicted values, where for Eq. (1), Y = 0.028 (
0.16) + 0.15 (
0.077) (X  6.33), R2 = 0.06, P = 0.065 (top left); for Eq. (5), Y = 0.032 (
0.18) + 0.026 (
0.083) (X  6.14), R2 = 0.002, P = 0.75 (top right); for Eq. (10), Y = 0.102 (
0.16)  0.0086 (
0.068) (X  5.98), R2 = 0.0004, P = 0.90 (bottom left); for Eq. (13), Y = 0.038 (
0.16)  0.016 (
0.069) (X  6.0), R2 = 0.001, P = 0.82 (bottom right).

study, R2 values (0.79–0.81) obtained in the relationship between methane and DM or GE and NDF intake were relatively high compared with other studies (Ellis et al., 2007; Yan et al., 2009). The prediction equations using DM intake or ME intake as primary predictors of methane emission had low R2 values (0.44 or 0.36) in studies with beef cattle in North American feeding situations (Ellis et al., 2007) and moderate R2 values (0.68 with DM intake or 0.70 with GE intake) in UK feeding conditions (Yan et al., 2009). It is likely that less variability of the chemical composition of diets especially, NDF and ADF contents and DM intake in the present dataset compared with the datasets of Yan et al. (2009) and Ellis et al. (2007) resulted in better relationship between methane emissions and nutrient intake. It was expected that ME intake could be a better determinant of methane outputs than DM intake as the former accounts for methane production within its derivation (Mills et al., 2003). However, ME intake predicted methane production with less precision compared with DM intake (R2 = 0.80 versus 0.68). The reason is not clear, but may be due to inclusion of calculated ME values for many studied included in this dataset instead of direct observations from studies, thus imposing errors in ME values. Nonetheless, Ellis et al. (2007) also noted a lower predictability of methane using ME intake than DM intake in dairy (R2 = 0.64 versus 0.53) and beef cattle (R2 = 0.44 versus 0.36) datasets. No quadratic term of the dependent variables were significant (P > 0.05) in predicting methane emission in this study. However, Ramin and Huhtanen (2013) found that the quadratic

model containing DM intake as single predictor improved the goodness of fit compared with linear model, but did not perform better than the newly developed equations. A number of prediction equations were attempted to develop using chemical composition of diets and BW of animals, which could be useful in situations where intake data could not be available. However, only concentrations of NDF and ADF, and BW resulted in reasonable degrees of prediction of methane production, and these equations predicted methane outputs with less accuracy. Dietary fats were negatively associated with methane production and the prediction model for methane production included fats as a predictor when the database included the studies with dietary ether extract supplementation (Patra, 2013). However, fats in this study were not associated with methane production, which was most likely due to the presence of low concentrations of fats in the diets. Ellis et al. (2007) reported that the multiple regression equation containing DM intake and fat intake improved the prediction model in beef database, but not in dairy database. Multiple regression equations were presented when they improved the prediction compared with simple regression equations. Multiple regression models containing intakes of DM and NDF or DM and ADF or NDF, CP and NFC improved the predictive ability of methane emission to a little extent (R2 = 0.80– 0.85). The multiple regression models developed by Ellis et al. (2007), which had the highest R2 values, included ME intake, ADF intake and lignin intake as determinants with R2 = 0.85 for the beef

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Fig. 3. Plot of observed minus predicted methane production (residual) versus predicted methane production from buffaloes. The independent variable (predicted methane production) was centered around the mean predicted value before the residuals were regressed on the predicted values, where for monomolecular equation, Y = 0.024 (
0.159) + 0.28 (
0.082) (X  6.45), R2 = 0.19, P = 0.001 (top left); for Gompertz equation, Y = 0.28 (
0.16)  0.19 (
0.052) (X  5.97), R2 = 0.19, P = 0.008 (top right); For IPCC (2006), Y = 0.97 (
0.17)  0.23 (
0.054) (X  7.33), R2 = 0.25, P = <0.001 (bottom left); for equation of Ramin and Huhtanen (2012), Y = 2.33 (
0.17)  0.22 (
0.054) (X  8.70), R2 = 0.24, P = <0.001 (bottom right).

dataset, 0.65 for the dairy dataset and 0.71 for the combined beef and dairy dataset. In the present database, lignin was not evaluated as most of the studies did not report lignin concentrations in diets. Biological responses rarely follow a linear trend over a wide range of values, and thus nonlinear relationships between methane production and DM intake were also evaluated for prediction of methane emissions in buffaloes. However, these nonlinear models did not further improve the relationship between methane production and DM intake though they were comparable with the linear model. Among these non-linear models, monomolecular 2 and Gompertz model had the highest precision and accuracy, though error due to regression bias for Gompertz model had higher than the monomolecular models. Mills et al. (2003) noted that there was minor difference in RMSPE percentage between the linear and non-linear models for the UK data, but the benefits were evident for the American and Northern Ireland data for lactating cows. However, non-linear models may be more appropriate and reliable for predicting methane outputs in a wide range of intake and dietary variables (Mills et al., 2003). For example, the non-linear models of Ramin and Huhtanen (2012) and Mills et al. (2003) performed slightly better than the linear models of Ramin and Huhtanen (2013) and Mills et al. (2003), respectively, when challenged in this database. The present dataset was used to validate a range of extant prediction equations for methane production for dairy and beef cattle. The extant equations were developed using methane

production data based on beef cattle (Kriss, 1930; Axelsson, 1949; Yan et al., 2009), dairy cattle (Mills et al., 2003), dairy and beef cattle (Ellis et al., 2007), and cattle and sheep (Ramin and Huhtanen, 2012, 2013). The IPCC (2006) tier II model was chosen as most countries use this model for their methane emission inventory preparation. The newly developed models performed better than the extant models as these equations except the equations predicted by NDF and ADF concentrations had the lowest RMSPE values compared with the extant models evaluated with this database although they should also be challenged on an external database if these new equations perform better than the extant equations. The higher inaccuracy and imprecision of the extant models developed from cattle of North America and European situations compared with new equations developed in this study may be attributed to the animal type, geographical and dietary differences. The diets in this study were of low to medium quality whereas the diets for cattle in North America and European countries comprised of medium to high quality. There are also differences of rumen fermentation, nutrient utilization and microbial populations between cattle and buffaloes (Calabro et al., 2004; Chanthakhoun et al., 2012). Based on the model of IPCC (2006) tier II model, the enteric methane production from buffaloes in India was estimated to be 4584 Gg/year in 2007 (Patra, 2012). However, the estimates of enteric methane from buffaloes based on the data of DM intake by buffaloes (Patra, 2012) and prediction Eq. (1) developed in this study was 4203 Gg/year, which

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was 8.3% lower than IPCC (2006) model based prediction. Thus, the models reported in this study should be considered for more accurately estimating the enteric methane emission inventories for buffalo-rearing countries. 5. Conclusions Linear models developed based on DM intake or NDF intake as single predictor, and both of these determinants predicted methane production precisely and accurately. Although nonlinear models did not perform better than linear models, they could be suitable when data range is outside of this database. Any extant models developed for cattle in North American and European situations did not perform adequately and overpredicted methane outputs. These equations developed in this study would be useful for preparing national methane emission inventory from buffaloes. Nonetheless, these newly developed models should be evaluated on an external database for suitability of prediction of methane production from buffaloes. Acknowledgement The research grant provided by Indian Council of Agricultural Research, New Delhi is gratefully acknowledged. References Axelsson, J., 1949. The amount of produced methane energy in the European metabolic experiments with adult cattle. Ann. Roy. Agric. Coll. Sweden 16, 404– 419. Barman, K., Mohini, M., Singhal, K.K., 2001. Effect of supplementation of rumensin and level of roughage on methane production. Indian J. Anim. Nutr. 18, 325–329. Bibby, J., Toutenburg, H., 1977. Prediction and Improved Estimation in Linear Models. John Wiley & Sons, London, UK. Blaxter, K.L., Clapperton, J.L., 1965. Prediction of the amount of methane produced by ruminants. Br. J. Nutr. 19, 511–522. Calabro, S., Williams, B.A., Piccolo, V., Infascelli, V., Tamminga, S., 2004. A comparison between buffalo (Bubalus bubalis) and cow (Bos taurus) rumen fluids in terms of the in vitro fermentation characteristics of three fibrous feed. J. Sci. Food Agric. 84, 645–652. Chanthakhoun, V., Wanapat, M., Kongmun, P., Cherdthong, A., 2012. Comparison of ruminal fermentation characteristics and microbial population in swamp buffalo and cattle. Livest. Sci. 143, 172–176. Draper, N.R., Smith, H., 1998. Applied Regression Analysis, third ed. John Wiley & Sons, New York, NY. Ellis, J.L., Kebreab, E., Odongo, N.E., Beauchemin, K., McGinn, S., Nkrumah, J.D., Moore, S.S., Christopherson, R., Murdoch, G.K., McBride, B.W., Okine, E.K., France, J., 2009. Modeling methane production from beef cattle using linear and nonlinear approaches. J. Anim. Sci. 87, 1334–1345. Ellis, J.L., Kebreab, E., Odongo, N.E., McBride, B.W., Okine, E.K., France, J., 2007. Prediction of methane production from dairy and beef cattle. J. Dairy Sci. 90, 3456–3467. Feedipedia, 2013. Animal Feed Resources Information System. INRA CIRAD AFZ and FAO.www.feedipedia.org. Garg, M.R., Kannan, A., Phondba, B.T., Shelke, S.K., Sherasia, P.L., 2012. A study on the effect of ration balancing for improving milk production and reducing methane emission in lactating buffaloes under field conditions. Indian J. Dairy Sci. 65, 250–255. Haque, N., Saraswat, M.L., Hassan, Q.Z., Bhar, R., Mehra, U.R., Khan, M.Y., Verma, A.K., Dass, R.S., 2004. Metabolizable energy value of some cereal grain on wheat straw based diets of buffaloes. Indian J. Anim. Sci. 74, 973–976. Holter, J.B., Young, A.J., 1992. Methane production in dry and lactating Holstein cows. J. Dairy Sci. 75, 2165–2175. (2006), I.P.C.C., 2006. 2006 IPCC Guidelines for National Greenhouse Gas Inventories. IGES, Hayama, Kanagawa, Japanhttp://www.ipcc-nggip.iges.or.jp. Kannan, A., Garg, M.R., 2009. Effect of ration balancing on methane emission reduction in lactating animals under field conditions. Indian J. Dairy Sci. 62, 292–296. Kannan, A., Garg, M.R., Singh, P., 2010. Effect of ration balancing on methane emission and milk production in lactating animals under field conditions in Rae Bareli district of Uttar Pradesh. Indian J. Anim. Nutr. 27, 103–108. Kebreab, E., Clark, K., Wagner-Riddle, C., France, J., 2006. Methane and nitrous oxide emissions from Canadian animal agriculture: a review. Can. J. Anim. Sci. 86, 135– 158. Kebreab, E., Johnson, K.A., Archibeque, S.L., Pape, D., Wirth, T., 2008. Model for estimating enteric methane emissions from United States dairy and feedlot cattle. J. Anim. Sci. 86, 2738–2748.

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