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Predicting the metabolizable energy intake of ruminants using digestibility, ruminal methane production and fermentation data

Published online by Cambridge University Press:  21 November 2008

M. J. McPHEE  and
R. S. HEGARTY
M. J. McPHEE*
Affiliation:
NSW Department of Primary Industries, Armidale, NSW 2351, Australia
R. S. HEGARTY
Affiliation:
NSW Department of Primary Industries, Armidale, NSW 2351, Australia
*
*To whom all correspondence should be addressed. Email: malcolm.mcphee@dpi.nsw.gov.au
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Summary

Obtaining accurate estimates of the metabolizable energy (ME) intake (MEI; MJ/day) of individual grazing ruminants is an important requirement for effective nutritional management and genetic selection of energy efficient ruminants. Diet digestibility and the daily methane production rate (MPR; MJ/day) of ruminants can be closely linked with their MEI, so published data were examined to determine whether MEI could be accurately estimated from digestibility, MPR and other parameters able to be measured on grazing animals. Four modelling approaches were assessed or developed to estimate MEI: (i) a published fixed proportional relationship between the non-metabolizable losses of MPR and urinary energy (UE; MJ/day); (ii) the proportion of energy digestibility (EngDig); (iii) MPR and the ruminal factors that influence the stoichiometric relationships between MPR and MEI; and (iv) the calculated ME arising from rumen fermentation (MEf; MJ/day). Data to develop the models (n=61) were collected across three publications (Paper) where the Paper effect was treated as a random-effect variable. Each of the models (1–4) was challenged with an independent data set (n=19). The inclusion of MEf (P=0·01) to predict MEI [MEI=0·18 (2·03)+3·42 (0·36)×sqrt(MEf) (d.f.=57; residual log likelihood=173·6)] had the lowest mean square error of prediction (MSEP) when challenged with the independent data set; mean bias of −0·42 MJ/day (P<0·05), MSEP=0·68 MJ/day and the bias, slope and random components of the MSEP were, as a proportion, 0·26, 0·13 and 0·61, respectively. None of the models estimated MEI with sufficient accuracy to be useful for identifying individual animals with above average energetic efficiency. A critical limit to any model seeking to estimate MEI from MPR and fermentation traits appears to be the variation between animals and between diets, in the proportion of digested energy which is fermented relative to that which is made available by mammalian digestion, and this is evaluated.

Type
Modelling Animal Systems Paper
Information
The Journal of Agricultural Science , Volume 146 , Issue 6 , December 2008 , pp. 643 - 654
Copyright
Copyright © 2008 Cambridge University Press

INTRODUCTION

Metabolizable energy (ME) intake (MEI; MJ/day) is frequently the principal constraint to ruminant growth (Beauchemin et al. Reference Beauchemin, McClelland, Jones and Kozub1995; Hegarty et al. Reference Hegarty, Neutze and Oddy1999) and, as such, is an important input in feeding standards and models which seek to describe or predict animal growth (SCA 1990; AFRC 1993). MEI of grazing animals has traditionally been estimated indirectly from measures of dry matter (DM) intake (DMI) derived from markers or pasture cuts and from laboratory- or marker-based estimates of DM digestibility (Dove & Mayes Reference Dove and Mayes1991). In recent years, new field methods have been developed for estimating diet digestibility (Coates Reference Coates2000), methane production and perhaps CO2 production in grazing ruminants (Johnson et al. Reference Johnson, Huyler, Westberg, Lamb and Zimmerman1994; Pinares-Patiño et al. Reference Pinares-Patiño, D'Hour, Jouany and Martin2007). It was hypothesized that combining measurements such as digestibility, methane production rate (MPR; MJ/day), characteristics of fermentation stoichiometry and rumen volatile fatty acids (VFA) proportions would allow accurate prediction of the MEI of grazing ruminants. Estimating MEI from animal measurements only would dispense with the need to sample pasture, or pursue the complexities of diet selectivity and digestibility in order to determine MEI. Such a simple technique is required to provide a more cost-effective means of identifying animals of high feed-use efficiency without lengthy testing (Archer et al. Reference Archer, Arthur, Herd, Parnell and Pitchford1997). The current paper develops several models using digestibility, MPR and fermentation data obtained from controlled feeding and respiration studies. For the development and challenge of the models, we used published data.

Variation in feed intake and daily MPR

If an accurate estimate of MEI has to be obtained from measurement of the non-ME losses, then an awareness of the sources of variation in methane and energy production and their errors of measurement or prediction is required. The quantity of ME obtained from an ingested feedstuff (Fig. 1) is a function of the digested energy (DE; MJ/day) minus the losses in methane (MPR; MJ/day) and urinary energy (UE; MJ/day) (Armstrong Reference Armstrong1964), where the DE is a function of gross energy intake (GEI; MJ/day) minus faecal energy (FE; MJ/day), i.e. DE=GEI−FE.

Fig. 1. Partitioning of feed energy into FE and DE that are either non-metabolizable [UE and methane energy] or is rendered metabolizable as either products of fermentation (VFA and microbial cells) or products arising from mammalian digestion of the diet.

In animals consuming feed ad libitum, the value of MEI obtained will depend on the duration of measurements. For housed sheep, the coefficient of variation (CV) for daily hay intake is 0·09–0·12 and repeatability of daily intake for animals on a constant diet is 0·59–0·61 (Sheehan et al. Reference Sheehan, Quirke and Hanrahan1985). Lee et al. (Reference Lee, Atkins and Mortimer1995) used alkane capsules to estimate that the CV of DMI for grazing sheep was 0·20–0·27. For beef cattle fully fed on a pellet diet, a period of at least 35 days is desirable to obtain a stable estimate of DMI when estimating residual feed intake (Archer et al. Reference Archer, Arthur, Herd, Parnell and Pitchford1997) and short-term cycles in daily feed intake have been observed (Stroup et al. Reference Stroup, Neilsen and Gosey1987). One implication of large day to day variation in DMI is that estimates of MEI will also require correspondingly long-term data on any predictive parameters. Short-term calorimetric and fermentation studies (e.g. Murray et al. Reference Murray, Bryant and Leng1978; Hegarty et al. Reference Hegarty, Nolan and Leng1994; Wright et al. Reference Wright, Kennedy, O'Neill, Toovey, Popovski, Rea, Pimm and Klein2004) will be inadequate as a basis for estimating the long-term MEI of grazing ruminants.

The influences of diet composition and level of intake on average daily methane production have been extensively reviewed (Blaxter & Clapperton Reference Blaxter and Clapperton1965; Kirchgessner et al. Reference Kirchgessner, Windisch, Muller, von Engelhardt, Leonhard-Marek, Breves and Giesecke1995; Kurihara et al. Reference Kurihara, Shibata, Nishida, Purnomoadi, Terada, Itabashi, Onocera, Sasaki, Ushida and Yano1997; Pelchen & Peters Reference Pelchen and Peters1998). In long-term controlled feeding studies, the CV of methane production across days is approximately 0·072 (Blaxter & Clapperton Reference Blaxter and Clapperton1965). In grazing sheep consuming pasture ad libitum, the CV of methane production over days is 0·13 of the mean (range 0·022–0·426: Ulyatt et al. Reference Ulyatt, Baker, McCrabb and Lassey1999). In dairy cattle, both within-animal (0·069–0·101) and between-animal variation (0·062–0·278) in methane production changed with diet (Vlaming et al. Reference Vlaming, Lopez-Villalobos, Brookes, Hoskin and Clark2008).

Individual animals have been recorded with extremely low MPRs on both grain (Johnson et al. Reference Johnson, Hill, Carmean, Branine, Lodman, Ward, Wenk and Boessinger1991; Goopy & Hegarty Reference Goopy and Hegarty2004) and pasture diets (K. Joblin 2004, personal communication). While the low frequency of these atypical animals is unlikely to cause significant error in estimating the average methane production of a population, it is of concern in obtaining MEI estimates for individual animals. The current paper reports the development and evaluation of models predicting MEI from related traits and tests whether such predictions can be improved by addition of easily collected data on rumen or digestibility characteristics or derived descriptors of rumen fermentation energetics.

MATERIALS AND METHODS

Four models were assessed or developed for prediction of MEI: model 1 used only a published fixed proportional relationship between the non-metabolizable losses of DE (MPR and UE) and MEI; model 2 was developed with the inclusion of the proportion of energy digestibility (EngDig); model 3 was developed with the inclusion of MPR and ruminal factors that influence the stoichiometric relationships between MPR and MEI (VFA proportions and pH) as well as rumen ammonia concentration (NH3; mg N/100 ml) as a possible indicator of UE; and model 4 was developed with the inclusion of the calculated ME arising from rumen fermentation (MEf; MJ/day). Models 2, 3 and 4 were developed using the combined studies of Jentsch et al. (Reference Jentsch, Schiemann, Hoffmann and Wittenburg1972), Osakwe et al. (Reference Osakwe, Steingass and Drochner2004) and Mwenya et al. (Reference Mwenya, Santoso, Sar, Gamo, Kobayashi, Arai and Takahashi2004), respectively. All models were then challenged using the combined data of Itabashi et al. (Reference Itabashi, Takeru and Matsumoto1984), Carulla et al. (Reference Carulla, Kreuzer, Machmüller and Hess2005) and Pinares-Patiño et al. (Reference Pinares-Patiño, Ulyatt, Lassey, Barry and Holmes2003). Data used in both development (models 2–4) and challenge of models (Models 1–4) are summarized in Table 1.

Table 1. Range and mean of input variables used in developing optimized regression predictions of MEI (development data) and data used to challenge models (challenge data). Development data were sourced from Jentsch et al. (Reference Jentsch, Schiemann, Hoffmann and Wittenburg1972), Osakwe et al. (Reference Osakwe, Steingass and Drochner2004) and Mwenya et al. (Reference Mwenya, Santoso, Sar, Gamo, Kobayashi, Arai and Takahashi2004). Challenge data were sourced from Itabashi et al. (Reference Itabashi, Takeru and Matsumoto1984), Carulla et al. (Reference Carulla, Kreuzer, Machmüller and Hess2005) and Pinares-Patiño et al. (Reference Pinares-Patiño, Ulyatt, Lassey, Barry and Holmes2003)

* MEf stands for ME present in VFA and microbial cells as estimated from daily MPR and VFA molar proportions, with a constant microbial growth efficiency.

Model 1

A published fixed proportional relationship between the non-metabolizable losses of DE (MPR and UE) and MEI was used (Eqn 1; SCA 1990). The non-metabolizable losses (Eqn 2) were substituted into Eqn (1) to give Eqn (3) (MEIp1; MJ/day), where the observed values of MPR and UE were used (Table 1) to predict MEIp1.

(1)
{\rm MEI} \equals 0{\cdot}81 \times {\rm DE}
(2)
0{\cdot}19 \times {\rm DE} \equals \lpar {\rm MPR} \plus {\rm UE}\rpar
(3)
{\rm MEI}_{{\rm p\setnum{1}}} \equals 4{\cdot}26 \times \lpar {\rm MPR} \plus {\rm UE}\rpar

Model 2

A nonlinear regression was conducted to predict MEI (MEIp2) from the observed EngDig (Eqn 4).

(4)
{\rm MEI}_{{\rm p}\setnum{2}} \equals \alpha \plus \beta \times \ln \lpar {\rm EngDig} \times 100\rpar \plus {\rm Paper}

Model 3

A nonlinear regression was conducted to predict MEI (MEIp2) from the observed MPR and the observed values of pH and NH3, and the ruminal proportions of acetate, propionate and butyrate (Table 1; Eqn 5).

(5)
\eqalign{{\rm MEI}_{{\rm p}\setnum{3}} \equals \tab \alpha \plus \beta \times \ln \lpar {\rm MPR}\rpar \plus \sum\limits_{i \equals \setnum{1}}^{\setnum{5}} {X_{i} } \cr \tab \plus \sum\limits_{i \equals \setnum{1}}^{\setnum{4}} {\sum\limits_{j \equals i \plus \setnum{1}}^{\setnum{5}} {\gamma _{ij} } X_{i} X_{j} \plus {\rm Paper}}}

Model 4

Potential MEf (MJ/day) was calculated by combining the observed MPR and VFA proportions using stoichiometry to estimate the supply of potential ME (as VFA and microbial cell energy) arising from rumen fermentation. The stoichiometric relationship between the observed ruminal VFA and the observed MPR means that, when MPR and VFA proportions are known, the energy being yielded via VFA can be readily determined (Wolin et al. Reference Wolin, Miller, Stewart, Hobson and Stewart1997). Combined with an assumed microbial growth efficiency, a measure of MPR can be readily used to estimate the yield of energy (MJ/day) arising from rumen fermentation in potentially metabolizable forms (VFA and microbial cells). The stoichiometry of Czerkawski (Reference Czerkawski1986) as modelled by Nolan (Reference Nolan, Reyenga and Howden1998) was used in association with measured MPR and VFA proportions to determine energy of VFA plus cells (MJ) produced/MJ of methane for each data point in the development and challenge data sets. This value was multiplied by the observed MPR to calculate MEf for each data point. In model 4, a nonlinear regression was conducted to predict MEI (MEIp4) from the calculated MEf (Eqn 6).

(6)
{\rm MEI}_{{\rm p}\setnum{4}} \equals \alpha \plus \beta \times {\rm sqrt}\lpar {\rm ME}_{\rm f} \rpar \plus {\rm Paper}

It was assumed that the energy costs of cell synthesis and of cell maintenance were both fixed at 40 mmol ATP/g cells/day, and that energy loss through refermentation of microbial cells in the rumen was assumed to be 30 mmol ATP/g cells in running the model of Nolan (Reference Nolan, Reyenga and Howden1998).

Statistical analysis

Models 2–4 were developed using the PROC MIXED procedure of SAS Inc. An analysis of covariance (ANOVA) was performed on each of the models. The covariates for each of the models were EngDig, MPR and MEf for models 2, 3 and 4, respectively; all two-way interactions and additional covariates for model 3 were evaluated. The intercept–slope, Paper (the subject in the mixed procedure of SAS), EngDig, MPR and MEf were the random-effect terms. Paper was the experimental unit. The Paper effect in the current study was solely an intercept shift; the TYPE=VC statement in the RANDOM statement was removed to achieve the shift in intercept. Terms were included in the model at P<0·05.

All models were evaluated for the assumption of normality and constant variance. A log transformation on DE and MPR was performed and a Shapiro–Wilk test (P<0·05) was performed using the UNIVARIATE procedure of SAS. A Levene's test of the residuals (P<0·05) was used to test the assumption of constant variance. All random-effects models used Restricted Maximum Likelihood (REML) for estimating variance components. The residual (Res) log likelihood is reported for each model. An adjustment was made on the observations (residual added to its corresponding Y predicted value) to take into account the collapsed observations from the multidimensional space into a two-dimensional space (St-Pierre Reference St-Pierre2001). The mean bias and mean square error of prediction (MSEP) were derived for each model and the sources of error decomposed into bias, slope and random error, as a proportion of MSEP, as outlined in a review by Tedeschi (Reference Tedeschi2006). The statistical significance of each mean bias was evaluated using a paired t-test of the mean of the difference between observed and model-predicted values.

RESULTS

Model 1

The challenge to model 1 (MEIp1), where the observed values of MPR and UE were used (Table 1) to predict MEIp1 (Eqn 3), indicated a mean bias and MSEP of 1·16 and 4·08 MJ/day MEI, respectively (Table 2). This error was attributable to substantial bias (underestimation, especially at low MEI; Fig. 2), as well as error associated with the slope of the regression (0·28; Table 2).

Table 2. Mean bias, MSEP and decomposition of errors to bias, slope and random components, as a proportion of MSEP, in models predicting MEI (MJ/day) from: urinary and methane energy (model 1); DE (model 2); methane (model 3); or from energy arising from fermentation as estimated from methane, VFA proportions and stoichiometry (model 4)

* P<0·01, P=0·19, P=0·10, and P<0·05 for models 1, 2, 3 and 4, respectively.

Fig. 2. Prediction (model 1; MEIp1 (MJ/day)) of MEI of sheep plotted against independent data (■, Itabashi et al. Reference Itabashi, Takeru and Matsumoto1984; •, Carulla et al. Reference Carulla, Kreuzer, Machmüller and Hess2005; ▲, Pinares-Patiño et al. Reference Pinares-Patiño, Ulyatt, Lassey, Barry and Holmes2003): (a) observed v. predicted with the line y=x and (b) the difference (observed−predicted) v. predicted with the line y=0.

Model 2

The nonlinear relationship (Fig. 3) of model 2 (MEIp2) indicated that EngDig was a significant factor in the model (P=0·02; Eqn 7). The challenge to model 2 (Fig. 4) showed an improved MSEP relative to model 1 (2·13 v. 4·08 MJ/day MEI; Table 2) There was no substantial bias or error associated with the slope of the regression; the majority of the error was associated with the random component.

(7)
\eqalign{\hskip18{\rm MEI}_{{\rm p}\setnum{2}} \equals \tab \minus 37{\cdot}36\;\lpar 6{\cdot}44\rpar \plus 11{\cdot}26\;\lpar 1.63\rpar \cr \tab\hfill\times \ln \lpar EngDig \times 100\rpar\hfill\cr \tab\hskip-40pt\lpar {\sc {\rm D}}.{\sc {\rm F}}. \equals {\rm 57}\semi {\rm \ residual\ log\ likelihood} \equals 187{\cdot}2\rpar \cr}\hfill

Fig. 3. Plot of adjusted observations of MEI (MJ/day) v. EngDig across studies (□, Jentsch et al. Reference Jentsch, Schiemann, Hoffmann and Wittenburg1972; ○, Osakwe et al. Reference Osakwe, Steingass and Drochner2004; △, Mwenya et al. Reference Mwenya, Santoso, Sar, Gamo, Kobayashi, Arai and Takahashi2004) with the nonlinear prediction (model 2; MEIp2 (MJ/day)).

Fig. 4. Prediction (model 2; MEIp2 (MJ/day)) of MEI of sheep plotted against independent data (■, Itabashi et al. Reference Itabashi, Takeru and Matsumoto1984; •, Carulla et al. Reference Carulla, Kreuzer, Machmüller and Hess2005; ▲, Pinares-Patiño et al. Reference Pinares-Patiño, Ulyatt, Lassey, Barry and Holmes2003): (a) observed v. predicted with the line y=x and (b) the difference (observed−predicted) v. predicted with the line y=0.

Model 3

The nonlinear relationship (Fig. 5) of model 3 (MEIp3) indicated that MPR was a significant factor in the model (P=0·02; Eqn 8). The observed values of pH and NH3, and the ruminal proportions of acetate, propionate and butyrate and their interactions were not significant and were removed from the model. The challenge to model 3 (Fig. 6) showed an improved MSEP relative to model 1 (1·25 v. 4·08 MJ/day MEI; Table 2). There was no substantial bias or error associated with the slope of the regression; the majority of the errors were associated with the random component.

(8)
\eqalign{ {\rm MEI}_{{\rm p\setnum{3}}} \equals \tab 9{\cdot}21\;\lpar 1{\cdot}52\rpar \plus \rm 4{\cdot}72\;\lpar 0{\cdot}59\rpar \times \ln \lpar {\rm MPR}\rpar \cr\tab\hskip-28 \lpar {\sc {\rm D}}.{\sc {\rm F}}. \equals 57\semi {\rm \ residual\ log\ likelihood} \equals 185{\cdot}5\rpar \cr}

Fig. 5. Plot of adjusted observations of MEI (MJ/day) v. MPR (MJ/day) across studies (□, Jentsch et al. Reference Jentsch, Schiemann, Hoffmann and Wittenburg1972; ○, Osakwe et al. Reference Osakwe, Steingass and Drochner2004; △, Mwenya et al. Reference Mwenya, Santoso, Sar, Gamo, Kobayashi, Arai and Takahashi2004 ) with the nonlinear prediction (model 3; MEIp2 (MJ/day)).

Fig. 6. Prediction (model 3; MEIp3 (MJ/day)) of MEI of sheep plotted against independent data (■, Itabashi et al. Reference Itabashi, Takeru and Matsumoto1984; •, Carulla et al. Reference Carulla, Kreuzer, Machmüller and Hess2005; ▲, Pinares-Patiño et al. Reference Pinares-Patiño, Ulyatt, Lassey, Barry and Holmes2003): (a) observed v. predicted with the line y=x and (b) the difference (observed−predicted) v. predicted with the line y=0.

Model 4

The nonlinear relationship (Fig. 7) of model 4 (MEIp4) indicated that MEf contributed significantly to the model (P=0·01; Eqn 9). The challenge to model 4 (Fig. 8) showed a substantial improvement in the MSEP relative to model 1 (0·68 v. 4·08 MJ/day MEI; Table 2). There was no substantial bias or error associated with the slope of the regression; the majority of the error was associated with the random component.

(9)
\eqalign{ {\rm MEI}_{{\rm p\setnum{4}}} \equals \tab 0{\cdot}18\;\lpar 2{\cdot}03\rpar \plus 3{\cdot}42\;\lpar 0{\cdot}36\rpar \times {\rm sqrt\lpar ME}_{\rm f} {\rm \rpar } \cr\tab\hskip-28 \lpar {\sc {\rm D}}.{\sc {\rm F}}. \equals 57\semi {\rm \ residual\ log\ likelihood} \equals 173{\cdot}6\rpar \cr}

Fig. 7. Plot of adjusted observations of MEI (MJ/day) v. MEf (MJ/day) across studies (□, Jentsch et al. Reference Jentsch, Schiemann, Hoffmann and Wittenburg1972; ○, Osakwe et al. Reference Osakwe, Steingass and Drochner2004; △, Mwenya et al. Reference Mwenya, Santoso, Sar, Gamo, Kobayashi, Arai and Takahashi2004) with the nonlinear prediction (model 4; MEIp4 (MJ/day)). MEf was calculated by using the model of Nolan et al. (Reference Nolan, Reyenga and Howden1998).

Fig. 8. Prediction (model 4; MEIp4 (MJ/d)) of MEI of sheep plotted against independent data (■, Itabashi et al. Reference Itabashi, Takeru and Matsumoto1984; •, Carulla et al. Reference Carulla, Kreuzer, Machmüller and Hess2005; ▲, Pinares-Patiño et al. Reference Pinares-Patiño, Ulyatt, Lassey, Barry and Holmes2003) : (a) observed v. predicted with the line y=x and (b) the difference (observed−predicted) v. predicted with the line y=0.

Including MEf (the potential ME in microbial cells and VFA arising from fermentation (MJ/day)) in model 4 (Eqn 9), rather than simply including VFA molar proportions, did improve the MSEP of prediction.

DISCUSSION

The increased use of the SF6 tracer-based ‘emissions from ruminants using a calibrated tracer’ (ERUCT) technique (Johnson et al. Reference Johnson, Huyler, Westberg, Lamb and Zimmerman1994) for measuring the methane production of grazing livestock and increasing use of faecal ‘near infrared reflectance spectroscopy’ (NIRS) to assess diet quality (Coates Reference Coates2000) were the motivation for us to test whether variables measured by such techniques could be used to predict MEI of ruminants accurately. If successful, the approach could provide a way to estimate MEI of grazing ruminants without needing to consider diet selection or pasture sampling and analysis. The nonlinear regression for models 2–4 is in agreement with the study of Mills et al. (Reference Mills, Kebreab, Yates, Crompton, Cammell, Dhanoa, Agnew and France2003), which illustrated a nonlinear trend in the simulation of methane emissions v. MEI.

The average proportion of DE that is non-metabolizable is accepted in the Australian feeding standards as being 0·19×DE at maintenance energy intake (SCA 1990), and this partitioning of energy is relatively consistent within roughage-based diets. In the challenge data, non-metabolizable energy was 0·16×DE, in contrast with the 0·19×DE in the model which would have contributed to the bias in model 1. Armstrong (Reference Armstrong1964) noted a significant positive effect of level of intake (relative to maintenance) on metabolizability of DE so not including an intake effect in model 1 would have contributed to its high MSEP and particularly the proportion of MSEP for slope (0·28; Table 2). The high MSEP of MEIp1 (4·08 MJ/day) associated with using the generic relationship in model 1 to predict MEI suggested that this model was unlikely to give precise predictions for individual animals or group averages. The need to measure UE loss in the field to predict MEI by model 1 further limits the usefulness of this model. UE is not readily measured in grazing animals, and energy in urine is principally present in the nitrogenous compounds (Bristow et al. Reference Bristow, Whitehead and Cockburn1992) and in urea in particular. The possible correlation between rumen ammonia concentration (NH3) and UE was evaluated because up to 0·66 of the urea produced by ruminants is derived from ammonia drained from the digestive tract (Lobley et al. Reference Lobley, Connell, Lomax, Brown, Milne, Calder and Farningham1995). A significant association between UE and NH3 existed in the development data set (R 2=0·61), suggesting that NH3 may provide an easily measured proxy for UE in estimating MEI. However, NH3 did not subsequently explain a significant proportion of variance in model 3 so it was not retained in the model.

Components of nonlinear models

Progression to nonlinear models to predict MEI reduced the mean bias and MSEP of MEI (Table 2). Faecal NIRS is increasingly being developed to describe diet characteristics, including digestibility (Coates Reference Coates2000), especially for rangeland areas where diet selectivity can be high. If the faecal NIRS continues to be developed to predict digestible organic matter intake (Coates Reference Coates2000) it may be able to predict MEI accurately. The lower MSEP when MPR was included in the model (MEIP3v. MEIP2) indicates the value of MPR as a predictor. In a meta-analysis of recent New Zealand data, Machmüller & Clark (Reference Machmüller and Clark2006) found that MPR was strongly correlated with estimated DMI across combined sheep and cattle data (R 2=0·86), but less so within sheep data alone (R 2=0·26–0·42), indicating the need for other physiological predictors to be used in developing predictions of MEI based on MPR. It must also be remembered that these models have been developed and tested using MPR measured in respiration facilities. The precision of MPR measured by the ERUCT technique is lower, with a further between day CV of 0·034 attributable to the method itself (Grainger et al. Reference Grainger, Clark, McGinn, Auldlist, Beauchemin, Hannah, Waghorn, Clark and Eckard2007).

Constraints to prediction of MEI from methane production

MPR in the rumen is the net result of the total energy fermented in the rumen and the partitioning of fermented matter into each of the VFA and microbial cell growth. Consequently, it was expected that estimating the energy captured in VFA and microbial cells synthesized in the rumen from VFA proportions and MPR (by the model of Nolan Reference Nolan, Reyenga and Howden1998) would have improved the ability to predict MEI, relative to that possible from MPR alone. This was the outcome achieved, with model 4 showing a lower MSEP than model 3, although with greater bias (Table 2). Nevertheless, the challenge data of Itabashi et al. (Reference Itabashi, Takeru and Matsumoto1984) illustrate that the prediction of MEI was improved in each of the models: model 2 (Eqn 7; Fig. 4); model 3 (Eqn 8; Fig. 6) and lastly model 4 (Eqn 9; Fig. 8). The independent variables EngDig, MPR and MEf for models 2, 3 and 4, respectively, influence the prediction of MEI and progressively improved the prediction of MEI; that is, fermentation in the rumen had the greatest effect followed by methane and then digestibility.

However, MEI is the sum of both energy released through fermentation (as calculated in MEIf) and energy that is digested in the small intestine, but not by fermentation (Fig. 1). Recognition of these two distinct components of ME obviates two additional sources of error in establishing a highly accurate MPR-based approach to estimating MEI, which are outlined and evaluated below.

  1. 1. How accurately can stoichiometric principles predict ME present in fermentation products, working only from knowledge of MPR and rumen VFA proportions?

  2. 2. How constant is the proportion of ME coming from fermentation relative to ME arising from mammalian digestion? If these proportions do vary, can they be readily predicted?

Adequacy of stoichiometry

The empirical chemical reactions of anaerobic production of the major VFA were summarized by Hungate (Reference Hungate1966). Since then, the ability of some microbes to produce acetate and propionate together has been appreciated and the overall stoichiometry modified (Wolin et al. Reference Wolin, Miller, Stewart, Hobson and Stewart1997). All modelling of fermentation stoichiometry uses the availability of hydrogen (2H; being H2 or protons on reduced cofactors) to link VFA and MPR. MPR is normally assumed to utilize all excess 2H arising from fermentation according to the following reaction: CO2+8H→CH4+2H2O. Conversely, if MPR is known, stoichiometry can be used to calculate the quantity of VFA or of VFA energy produced (Ørskov et al. Reference Ørskov, Flatt and Moe1968).

Recovery of 2H in VFA, methane and cells is typically 0·85–0·95 of that anticipated from stoichiometry in in vitro studies so the stoichiometry itself is a source of error, being an incomplete description of the fermentation process and end-products. Discrepancies in stoichiometry become greater in the hindgut (Demeyer & De Graeve Reference Demeyer and Degraeve1991) and there is a lower methane:VFA yield in the hindgut than in the rumen (Immig Reference Immig1996). Additional issues that could potentially cause stoichiometry to differ from that assumed include variations in microbial growth efficiency, differences between VFA in the relationship between concentration and absorption rate, and failure to include all 2H sinks.

Energy loss through fermentation v. digestion

Even if a revised stoichiometry were developed to allow precise estimation of energy partitioning into VFA, cells and methane, it could only be used to quantify the energy made available in the gut through fermentation. It could not be reasonably expected to predict the energy liberated by mammalian digestion within the abomasum and intestines. There need be no biological or mathematical connections between the magnitude of fermentation and of mammalian digestion in the gut. Information relating to the partitioning of energy release between these two processes is reviewed below.

While there have been few studies on the contributions of mammalian digestion and fermentation to whole tract digestion (Ørskov et al. Reference Ørskov, Flatt and Moe1968), assessments of variance in the proportions of the diet disappearing from the forestomachs relative to the intestines (small and large) abound. Results of these studies are summarized in Table 3, but more exhaustive reviews focusing on starch and protein digestion have been prepared by Merchen et al. (Reference Merchen, Elizalde and Drackley1997) and Wanderley et al. (Reference Wanderley, Theurer and Poore1987). Importantly, the CV across studies is of the order of 0·10 (Table 3), indicating that an assumption of a constant partitioning between forestomach and intestinal digestion is inappropriate in seeking to develop accurate estimates of MEI for individual animals.

Table 3. Variation in the whole tract digestibility of dietary energy and in the proportion of DE fermented in the reticulo-rumen across different diet types

Level of intake of a single species of fresh pasture has little effect on the proportions of organic matter apparently digested proximal to the abomasum; however, there are large differences in site of digestion between pasture species (Beever et al. Reference Beever, Thomson, Ulyatt, Cammell and Spooner1985) and variation due to the maturity of the forage (Beever et al. Reference Beever, Coelho Da Silva, Prescott and Armstrong1972). The existence and magnitude of these sources of variation imply that the proportions of fermented and mammalian-digested energy are likely to vary in grazing animals. To investigate further the between-sheep variance in the proportion of DE fermented on a single fresh forage (ryegrass), the stoichiometric procedures of Ørskov et al. (Reference Ørskov, Flatt and Moe1968) were applied to the data of Armstrong (Reference Armstrong1964). The proportion of DE apparently released through fermentation was highly variable as shown in Fig. 9. The implication of the variation displayed is that while a measure of MPR and stoichiometry using VFA molar proportions may provide accurate prediction of ME arising from fermentation and an approximate prediction of MEI (model 4), it is unrealistic to expect further refining of this approach to provide a quantitative estimate of total DE or MEI, as ME that does not arise from fermentation is an unknown proportion of MEI. Another constraint to accurate prediction of MEI is the variation in daily feed intake as initially reviewed. Since methane production persists for at least 48 h after feeding, MPR as measured will reflect not only DMI on a given day, but also an unknown production of methane from the days before, when intake may have been different.

Fig. 9. Frequency distribution of the proportion of DE fermented and lost from the rumen by individual sheep ingesting a single cultivar of fresh ryegrass. The amount of energy fermented was calculated from the data of Armstrong (Reference Armstrong1964) using the procedure of Ørskov et al. (Reference Ørskov, Flatt and Moe1968) from the mean MPR and the mean VFA proportions for each sheep over three measurement periods.

CONCLUSIONS

Re-assessment of published studies has shown that digestive parameters such as those provided by the new faecal NIRS and ERUCT methods, together with ruminal sampling, can be used to predict MEI from MEf. Realization of this accuracy in field-use will be lower due to the additional error in estimating DM digestibility from faecal NIRS and errors in measuring MPR by ERUCT (Grainger et al. Reference Grainger, Clark, McGinn, Auldlist, Beauchemin, Hannah, Waghorn, Clark and Eckard2007), which were not incurred in animal house and respiration chamber measures used for model development and testing. The value of MPR as a predictive tool for MEI can be increased by measurement of rumen VFA proportions and calculation of ME arising from fermentation (data of Itabashi et al. Reference Itabashi, Takeru and Matsumoto1984) (Figs 4, 6 and 8), but variation in the proportion of MEI obtained from fermentation rather than mammalian digestion will limit the accuracy of this approach. Future efforts to ascertain MEI from measurement of animal parameters may benefit from ongoing improvement in predicting intake from faecal NIRS, and by measurement of CO2 production using the ERUCT technique from which to derive energy expenditure.

We thank Dr M. Derno and Dr W. Jentsch for providing raw data (Jentsch et al. Reference Jentsch, Schiemann, Hoffmann and Wittenburg1972) and Dr C. Pinares-Patiño for data (Pinares-Patiño et al. Reference Pinares-Patiño, Ulyatt, Lassey, Barry and Holmes2003) that were included in development and challenge data sets as described in the text. We also thank an anonymous referee for helpful suggestions.

References

REFERENCES

AFRC (1993). Energy and Protein Requirements of Ruminants. Wallingford, Oxfordshire, UK: CAB International.Google Scholar
Archer, J. A., Arthur, P. F., Herd, R. M., Parnell, P. F. & Pitchford, W. S. (1997). Optimum post-weaning test for measurement of growth rate, feed intake, and feed efficiency in British breed cattle. Animal Science 75, 2024–2032.CrossRefGoogle Scholar
Armstrong, D. G. (1964). Evaluation of artificially dried grass as a source of energy for sheep: No. II. Energy value of cocksfoot timothy and two strains of rye-grass at varying stages of maturity. Journal of Agricultural Science, Cambridge 62, 399–415.CrossRefGoogle Scholar
Beauchemin, K. A., McClelland, L. A., Jones, S. D. & Kozub, G. C. (1995). Effects of crude protein content, protein degradability and energy concentration of the diet on growth and carcass characteristics of market lambs fed high concentrate diets. Canadian Journal of Animal Science 75, 387–395.CrossRefGoogle Scholar
Beever, D. E., Coelho Da Silva, J. F., Prescott, J. H. & Armstrong, D. G. (1972). The effect in sheep of physical form and stage of growth on the sites of digestion of a dried grass. 1. Sites of digestion of organic matter, energy and carbohydrate. British Journal of Nutrition 28, 347–371.CrossRefGoogle ScholarPubMed
Beever, D. E., Terry, R. A., Cammell, S. B. & Wallace, A. S. (1978). The digestion of spring and autumn harvested perennial ryegrass by sheep. Journal of Agricultural Science, Cambridge 90, 463–470.CrossRefGoogle Scholar
Beever, D. E., Thomson, D. J., Ulyatt, M. J., Cammell, S. B. & Spooner, M. C. (1985). The digestion of fresh perennial ryegrass (Lolium perrenne L. cv. Melle) and white clover (Trifolium repens L. cv. Blanca) by growing cattle fed indoors. British Journal of Nutrition 54, 763–775.CrossRefGoogle ScholarPubMed
Blaxter, K. L. & Clapperton, J. L. (1965). Prediction of the amount of methane produced by ruminants. British Journal of Nutrition 19, 511–522.CrossRefGoogle ScholarPubMed
Bristow, A. W., Whitehead, D. C. & Cockburn, J. E. (1992). Nitrogenous constituents in the urine of cattle, sheep and goats. Journal of the Science of Food and Agriculture 59, 387–394.CrossRefGoogle Scholar
Carulla, J. E., Kreuzer, M., Machmüller, A. & Hess, H. D. (2005). Supplementation of Acacia mearnsii tannins decreases methanogenesis and urinary nitrogen in forage-fed sheep. Australian Journal of Agricultural Research 56, 961–970.CrossRefGoogle Scholar
Coates, D. B. (2000). Faecal NIRS – what does it offer today's grazier? Tropical Grasslands 34, 230–239.Google Scholar
Czerkawski, J. W. (1986). An Introduction to Rumen Studies. Oxford, UK: Pergamon Press.Google Scholar
Demeyer, D. I. & Degraeve, K. (1991). Differences in stoichiometry between rumen and hindgut fermentation. Journal of Physiology and Animal Nutrition 22, 50–61.Google Scholar
Dove, H. & Mayes, R. W. (1991). The use of plant wax alkanes as marker substances in studies of the nutrition of herbivores: a review. Australian Journal of Agricultural Research 42, 913–952.CrossRefGoogle Scholar
Goopy, J. P. & Hegarty, R. S. (2004). Repeatability of methane production of cattle fed concentrate and forage diets. Journal of Animal and Feed Sciences 13 (Suppl. 1), 75–78.CrossRefGoogle Scholar
Grainger, C., Clark, T., McGinn, S., Auldlist, M. J., Beauchemin, K. A., Hannah, M. C., Waghorn, G. C., Clark, H. & Eckard, R. J. (2007). Methane emissions from dairy cows measured using the sulfur hexafluoride (SF6) tracer and chamber techniques. Journal of Dairy Science 90, 2755–2766.CrossRefGoogle ScholarPubMed
Hegarty, R. S., Nolan, J. V. & Leng, R. A. (1994). The effects of protozoa and of supplementation with nitrogen and sulphur on digestion and microbial metabolism in the rumen of sheep. Australian Journal of Agricultural Research 45, 1215–1227.CrossRefGoogle Scholar
Hegarty, R. S., Neutze, S. A. & Oddy, H. (1999). Effects of protein and energy supply on the growth and carcass composition of lambs from differing nutritional histories. Journal of Agricultural Science, Cambridge 132, 361–375.CrossRefGoogle Scholar
Hungate, R. E. (1966). The Rumen and its Microbes. New York: Academic Press.Google Scholar
Immig, I. (1996). The rumen and hindgut as source of ruminant methanogenesis. Environmental Monitoring and Assessment 42, 57–72.CrossRefGoogle ScholarPubMed
Itabashi, H., Takeru, K. & Matsumoto, M. (1984). The effects of rumen ciliate protozoa on energy metabolism and some constituents in rumen fluid and blood plasma of goats. Japanese Journal of Zootechnical Science 55, 248–255.Google Scholar
Jentsch, W., Schiemann, R., Hoffmann, L. & Wittenburg, H. (1972). Die energetische Verwertung der Grunfutterstoffe im frischen und getrockneten Zustand durch Wiederkauer. Archiv für Tierernährung 22, 17–40.CrossRefGoogle Scholar
Johnson, D. E., Hill, T. M., Carmean, B. R., Branine, M. E., Lodman, D. W. & Ward, G. (1991). New perspectives on ruminant methane emissions. In Proceedings of the XII Symposium on Energy Metabolism of Farm Animals (Eds Wenk, C. & Boessinger, M.), pp. 376–379. EEAP Publication No. 58.Google Scholar
Johnson, K. A., Huyler, M. T., Westberg, H. H., Lamb, B. K. & Zimmerman, P. (1994). Measurement of methane emissions from ruminant livestock using a sulfur hexafluoride tracer technique. Environmental Science and Technology 28, 359–362.CrossRefGoogle ScholarPubMed
Kirchgessner, M., Windisch, W. & Muller, H. L. (1995). Nutritional factors for the quantification of methane production. In Proceedings of the Eighth International Symposium on Ruminant Physiology (Eds von Engelhardt, W., Leonhard-Marek, S., Breves, G. & Giesecke, D.), pp. 333–347. Stuttgart, Germany: Ferdinand Enke Verlag.Google Scholar
Kurihara, M., Shibata, M., Nishida, T., Purnomoadi, A. & Terada, F. (1997). Methane production and its dietary manipulation in ruminants. In Rumen Microbes and Digestive Physiology in Ruminants. Satellite Symposium of the 8th Animal Science Congress, Kyoto, October 1996 (Eds Itabashi, H., Onocera, R., Sasaki, Y., Ushida, K. & Yano, H.), pp. 199–208. Basel, Switzerland: Karger.Google Scholar
Lee, G. J., Atkins, K. D. & Mortimer, S. I. (1995). Variation between Merino ewes in pasture intake 1. Between flock differences and some environmental sources of variation. Livestock Production Science 41, 133–142.CrossRefGoogle Scholar
Lobley, G. E., Connell, A., Lomax, M. A., Brown, D. S., Milne, E., Calder, A. G. & Farningham, D. A. (1995). Hepatic detoxification of ammonia in the ovine liver: possible consequences for amino acid catabolism. British Journal of Nutrition 73, 667–685.CrossRefGoogle ScholarPubMed
Machmüller, A. & Clark, H. (2006). First results of a meta-analysis of the methane emission data of New Zealand ruminants. International Congress Series 1293, 54–57.CrossRefGoogle Scholar
Merchen, N. R., Elizalde, J. C. & Drackley, J. K. (1997). Current perspective on assessing site of digestion in ruminants. Animal Science 75, 2223–2234.CrossRefGoogle ScholarPubMed
Mills, J. A., Kebreab, E., Yates, C. M., Crompton, L. A., Cammell, S. B., Dhanoa, M. S., Agnew, R. E. & France, J. (2003). Alternative approaches to predicting methane emissions from dairy cows. Journal of Animal Science 81, 3141–3150.CrossRefGoogle ScholarPubMed
Murray, R. M., Bryant, A. M. & Leng, R. A. (1978). Methane production in the rumen and lower gut of sheep given lucerne chaff: effect of level of intake. British Journal of Nutrition 39, 337–345.CrossRefGoogle ScholarPubMed
Mwenya, B., Santoso, B., Sar, C., Gamo, Y., Kobayashi, T., Arai, I. & Takahashi, J. (2004). Effects of including β1–4 galacto-oligosacharides, lactic acid bacteria or yeast culture on methanogenesis as well as energy and nitrogen metabolism in sheep. Animal Feed Science and Technology 115, 313–326.CrossRefGoogle Scholar
Nicholson, J. W. & Sutton, J. D. (1969). The effect of diet composition and level of feeding on digestion in the stomach and intestines of sheep. British Journal of Nutrition 23, 585–601.CrossRefGoogle ScholarPubMed
Nolan, J. V. (1998). Stoichiometry of rumen fermentation and gas production. In Meeting the Kyoto Target: Implications for the Australian Livestock Industries (Eds Reyenga, P. J. & Howden, S. M.), pp. 21–28. Canberra, ACT, Australia: Bureau of Rural Sciences.Google Scholar
Ørskov, E. R., Flatt, W. P. & Moe, P. W. (1968). Fermentation balance approach to estimate extent of fermentation and efficiency of volatile fatty acid formation in ruminants. Journal of Dairy Science 51, 1429–1435.CrossRefGoogle Scholar
Osakwe, I. I., Steingass, H. & Drochner, W. (2004). Effect of dried Elaeis guineense supplementation on nitrogen and energy partitioning of WAD sheep fed a basal hay diet. Animal Feed Science and Technology 117, 75–83.CrossRefGoogle Scholar
Pelchen, A. & Peters, K. J. (1998). Methane emissions from sheep. Small Ruminant Research 27, 137–150.CrossRefGoogle Scholar
Pinares-Patiño, C. S., Ulyatt, M. J., Lassey, K. R., Barry, T. N. & Holmes, C. W. (2003). Rumen function and digestion parameters associated with differences between sheep in methane emissions when fed chaffed lucerne hay. Journal of Agricultural Science, Cambridge 140, 205–214.CrossRefGoogle Scholar
Pinares-Patiño, C. S., D'Hour, P., Jouany, J.-P. & Martin, C. (2007). Effects of stocking rate on methane and carbon dioxide emissions from grazing cattle. Agriculture, Ecosystem and Environment 121, 30–46.CrossRefGoogle Scholar
Standing Committee on Agriculture (SCA) (1990). Feeding Standards for Australian Livestock: Ruminants. Melbourne, VIC, Australia: CSIRO Publications.Google Scholar
Sheehan, W., Quirke, J. E. & Hanrahan, J. P. (1985). Sources of variation in the voluntary intake of hay and silage by 18-month-old wether sheep. Irish Journal of Agricultural Research 24, 171–179.Google Scholar
St-Pierre, N. R. (2001). Invited review: integrating quantitative findings from multiple studies using mixed model methodology. Journal of Dairy Science 84, 741–755.CrossRefGoogle ScholarPubMed
Stroup, W. W., Neilsen, M. K. & Gosey, J. A. (1987). Cyclic variation in cattle feed intake data: characterisation and implications for experimental design. Journal of Animal Science 64, 1638–1647.CrossRefGoogle ScholarPubMed
Tedeschi, L. O. (2006). Assessment of the adequacy of mathematical models. Agricultural Systems 89, 225–247.CrossRefGoogle Scholar
Topps, J. H., Kay, R. N. B. & Goodall, E. D. (1968 a). Digestion of concentrate and of hay diets in the stomach and intestines of ruminants. 1. Sheep. British Journal of Nutrition 22, 261–276.CrossRefGoogle Scholar
Topps, J. H., Kay, R. N. B., Goodall, E. D., Whitelaw, F. G. & Reid, R. S. (1968 b). Digestion of concentrate and of hay diets in the stomach and intestines of ruminants. 2. Young steers. British Journal of Nutrition 22, 281–290.CrossRefGoogle ScholarPubMed
Ulyatt, M. J. & MacRae, J. C. (1971). The sites of digestion of fresh pasture species in the gastro-intestinal tracts of sheep. Proceedings of the New Zealand Society of Animal Production 31, 74–81.Google Scholar
Ulyatt, M. J., Baker, S. K., McCrabb, G. J. & Lassey, K. R. (1999). Accuracy of SF6 tracer technology and alternatives for field measurements. Australian Journal of Agricultural Research 50, 1329–1334.CrossRefGoogle Scholar
Vlaming, J. B., Lopez-Villalobos, N., Brookes, I. M., Hoskin, S. O. & Clark, H. (2008). Within- and between-animal variance in methane emission from non-lactating dairy cows. Australian Journal of Experimental Agriculture 48, 124–127.CrossRefGoogle Scholar
Wanderley, R. C., Theurer, B. & Poore, M. (1987). Duodenal bacterial and non bacterial protein supply in steers fed forage and grain diets. Animal Science 64, 295–302.CrossRefGoogle Scholar
Wolin, E. A., Miller, T. L. & Stewart, C. S. (1997). Microbe: microbe interactions. In The Rumen Microbial Ecosystem, 2nd edn (Eds Hobson, P. N. & Stewart, C. S.), pp. 475–491. London: Blackie Academic and Professional.Google Scholar
Wright, A. D. G., Kennedy, P., O'Neill, C. J., Toovey, A. F., Popovski, S., Rea, S. M., Pimm, C. L. & Klein, L. (2004). Reducing methane emissions in sheep by immunization against rumen methanogens. Vaccine 22, 3976–3985.CrossRefGoogle ScholarPubMed
Figure 0

Fig. 1. Partitioning of feed energy into FE and DE that are either non-metabolizable [UE and methane energy] or is rendered metabolizable as either products of fermentation (VFA and microbial cells) or products arising from mammalian digestion of the diet.

Figure 1

Table 1. Range and mean of input variables used in developing optimized regression predictions of MEI (development data) and data used to challenge models (challenge data). Development data were sourced from Jentsch et al. (1972), Osakwe et al. (2004) and Mwenya et al. (2004). Challenge data were sourced from Itabashi et al. (1984), Carulla et al. (2005) and Pinares-Patiño et al. (2003)

Figure 2

Table 2. Mean bias, MSEP and decomposition of errors to bias, slope and random components, as a proportion of MSEP, in models predicting MEI (MJ/day) from: urinary and methane energy (model 1); DE (model 2); methane (model 3); or from energy arising from fermentation as estimated from methane, VFA proportions and stoichiometry (model 4)

Figure 3

Fig. 2. Prediction (model 1; MEIp1 (MJ/day)) of MEI of sheep plotted against independent data (■, Itabashi et al.1984; •, Carulla et al.2005; ▲, Pinares-Patiño et al.2003): (a) observed v. predicted with the line y=x and (b) the difference (observed−predicted) v. predicted with the line y=0.

Figure 4

Fig. 3. Plot of adjusted observations of MEI (MJ/day) v. EngDig across studies (□, Jentsch et al.1972; ○, Osakwe et al.2004; △, Mwenya et al.2004) with the nonlinear prediction (model 2; MEIp2 (MJ/day)).

Figure 5

Fig. 4. Prediction (model 2; MEIp2 (MJ/day)) of MEI of sheep plotted against independent data (■, Itabashi et al.1984; •, Carulla et al.2005; ▲, Pinares-Patiño et al.2003): (a) observed v. predicted with the line y=x and (b) the difference (observed−predicted) v. predicted with the line y=0.

Figure 6

Fig. 5. Plot of adjusted observations of MEI (MJ/day) v. MPR (MJ/day) across studies (□, Jentsch et al.1972; ○, Osakwe et al.2004; △, Mwenya et al.2004 ) with the nonlinear prediction (model 3; MEIp2 (MJ/day)).

Figure 7

Fig. 6. Prediction (model 3; MEIp3 (MJ/day)) of MEI of sheep plotted against independent data (■, Itabashi et al.1984; •, Carulla et al.2005; ▲, Pinares-Patiño et al.2003): (a) observed v. predicted with the line y=x and (b) the difference (observed−predicted) v. predicted with the line y=0.

Figure 8

Fig. 7. Plot of adjusted observations of MEI (MJ/day) v. MEf (MJ/day) across studies (□, Jentsch et al.1972; ○, Osakwe et al.2004; △, Mwenya et al.2004) with the nonlinear prediction (model 4; MEIp4 (MJ/day)). MEf was calculated by using the model of Nolan et al. (1998).

Figure 9

Fig. 8. Prediction (model 4; MEIp4 (MJ/d)) of MEI of sheep plotted against independent data (■, Itabashi et al.1984; •, Carulla et al.2005; ▲, Pinares-Patiño et al.2003) : (a) observed v. predicted with the line y=x and (b) the difference (observed−predicted) v. predicted with the line y=0.

Figure 10

Table 3. Variation in the whole tract digestibility of dietary energy and in the proportion of DE fermented in the reticulo-rumen across different diet types

Figure 11

Fig. 9. Frequency distribution of the proportion of DE fermented and lost from the rumen by individual sheep ingesting a single cultivar of fresh ryegrass. The amount of energy fermented was calculated from the data of Armstrong (1964) using the procedure of Ørskov et al. (1968) from the mean MPR and the mean VFA proportions for each sheep over three measurement periods.