On the steady-state turnover of compartments in the ruminant gastrointestinal tract

J. theor. Biol. (1992) 159, 135-145

On the Steady-state Turnover of Compartments in the Ruminant Gastrointestinal Tract P. J. VAN SOEST't, J. FRANCE~§ AND R. C. SIDDONS

t Department of Animal Science, Cornell University, Ithaca, N Y 148534801, U.S.A., ~ AFRC Institute of Grassland and Environmental Research, North Wyke Research Station, Okehampton, Devon EX20 2SB, U.K. (Received on l0 June 1991, Accepted in revised form on 23 March 1992) An analysis of the turnover in steady state of compartments in the digestive tract of the ruminant is presented, with reference to the rumen compartment. Equations are derived governing concentration of a component in the feed to that within and passing out of the rumen. Also, relationships between dietary components having different ruminal turnover times from one another and from total rumen contents are developed, and the metabolic component accounted for. A method of calculating microbial outflow and efficiency based on rumen emptying is proposed, as are graphical procedures for assessing the behaviour of dietary and metabolic components within the rumen.

1. Introduction

Mitchell (1942, 1964) developed a method of nutritional analysis in which the true digestibility of proteins was determined by varying the level of protein in the diet in a series of digestion balances with cattle and sheep. Extrapolation to zero intake of the relationship between faecal excretion and protein intake allowed an estimate of the endogenous and microbial losses (assumed constant), while the slope of the regression (subtracted from unity) represented the true digestibility. Lucas and coworkers (Lucas et al., 1961; Lucas, 1964) extended this approach to other dietary components and converted it into a test for nutritional uniformity (i.e. the seeking of dietary components that behave uniformly in all diets), as a basis for choosing a nutritionally relevant analytical system. The Lucas model for digestion balances involved the division of digestible matter into additive components (digestible amounts) which could be expressed as the digestion coefficient of the component times its amount in the diet (Van Soest, 1967, 1982). In the present paper, the mathematical approach of Lucas and coworkers is extended to the steady-state turnover of compartments in the ruminant gastrointestinal tract, in particular the rumen. One of the problems of the rumen compartment is that it contains more than one pool (e.g. liquid and several solid fractions including microbes and feed material of different particle sizes) with different turnover times from each other and therefore from the total. The relevance of the Lucas analysis to

§ Author to whom reprint requests should be sent. 135 0022-5193/92/220135 + I I $08.00/0

© 1992 AcademicPress Limited

136

P. J. VAN

SOEST

ET AL.

the problem of inhomogenous compartments is that it quantitatively relates components of differing availability and composition to the total balance. It also provides a means of distinguishing biologically uniform from heterogeneous feed components, and accounts for metabolic (endogenous and microbial) matter that arises in the digestion process that was not present in the feed input. The objectives of this paper are therefore three-fold, namely (i) to develop steady-state relationships governing concentration in the feed to that within and passing out of the rumen; (ii) to derive relationships between dietary components having different ruminal turnover times from one another and from total rumen contents, and also to account for the metabolic component and to calculate microbial outflow and efficiency; and (iii) to propose graphical procedures for assessing the behaviour of dietary and metabolic components within the rumen. Much of the mathematics presented is also applicable to other mixing compartments of the gastrointestinal tract. 2. Basic Scheme

Apparent rumen turnover, T (hr), may be calculated as the steady-state content of the compartment, Q (g Dry Matter), divided by the feed intake, F (g DM hr-') : T= Q / F = (Q.r + Q,,)/F= (Or+ Q,,,,e+ Q,,,,b)/F.

(1)

E

~ = _ _

o,

+

0~,°

+

0.,~

----->

p

D FIo. I. Schematic representation of the relationship of feed input (F) to ruminal components and disappearance through digestion (D) and outflow (P). The endogenous influx (E) becomes confounded with feed in the production of microbial matter (Q,,.b), with which the endogenous matter (Q-.e) forms a metabolic component (Q,).

TURNOVER

IN RUMINANT

GASTROINTESTINAL

TRACT

137

Equation (1) indicates that the rumen contents are composed of matter introduced from the feed, QI, plus a metabolic fraction, Q.,, which predominantly comprises rumen micro-organisms, Q.,.b, and endogenous matter, Q.,,e (see Fig. l). In eqn (l), entry into the rumen might logically have been considered to be the sum of feed intake F plus the endogenous influx E (g DM hr-I). However, this has not been followed in view of the historical tradition of ignoring saliva and other endogenous secretions as inputs and regarding digestibility in terms of dietary intake and faecal excretion. Although rumen micro-organisms arise largely from digestion of feed, they cannot be considered as a part of the diet since both rate and extent of digestion of substrate would be confounded by the efficiency with which the digested substrate is used for microbial growth. As the difference between apparent and true digestion is the metabolic amount, comprising microbial and endogenous matter, the greater the microbial efficiency, the greater the difference between apparent and true digestibility. The s a m e effect will apply to the turnover as indicated in eqn (1), causing the apparent turnover time to exceed that of the true turnover time. Relative disappearance rates are the reciprocals of corresponding turnover times, so that rates of disappearance of feed will be underestimated and thus fail to agree with estimated rates of passage and digestion otained by other procedures. Theoretically, the true disappearance rate of feed must equal the sum of the rates of passage and digestion. 3. Relations Between Feed Intake and Rumen Content and Passage

The mathematical symbols used herein are defined in Table 1. Development of the relationships governing concentration of a component in the feed input to that in

TABLE 1

General definition of principal mathematical symbols Symbol

Definition

cx

Concentration of component x in the tureen (g x g-i DM), equals Q.~/Q Concentration of component x in the feed intake (g x g-) DM), equals FJF Concentration of component x in the passage outflow (g x g-l DM), equals Px/P Coefficient of true digestibility in the rumen of the feed dry matter Feed intake (g DM hr -t) Intake of dietary component x ( g x hr -I) Ratio of metabolic matter outflow from the rumen to feed intake (g g-l DM) Rumen passage outflow (g DM hr -l) Passage of component x out of the rumen (g x hr -I) Net quantity in the rumen, i.e. total tureen contents (g DM) Quantity of component x in the tureen (g x) Coel~cent of apparent ruminal indigestibility, equals P/F Coefficient of apparent ruminal indigestibility of component x, equals Px/Fx Apparent turnover in the rumen (hr), equals Q/F Apparent turnover of component x (hr), equals Q.~/F~ Clearance turnover (hr), equals Q/P Clearance turnover of component x (hr), equals Qx/Px

C.~j Cx,o

ol F

F., M P

/,., Q ~2.~ R

R, T

T, 1" l" x

138

P.J.

VAN

SOEST

ET AL.

the rumen in the steady state is parallel to that for digestion balances presented in chapter 4 of Van Soest (1982). The balance between dietary inflow and rumen content is given by eqn (2): (Q/F) . (Qx/a) = (Q:/Fx) . (FJF).

(2)

The proof of this relationship is self-evident, since it reduces to an identity via cancellation. Substituting the algebraic equvalents from Table 1 gives eqn (3): TCx =

TxC,,.,

(3)

which states the relationship between the apparent turnover of component x and that of the total contents. In the corresponding equation for digestion balance in the rumen indigestibility replaces turnover [eqn (4)]: RC~.o = RxC~,,.

(4)

If eqns (3) and (4) are solved for Cx,i, the relationship to outflow concentration is obtained in the resultant equation: Cxa =

TCx/Tx

=

RCx.o/R~.

(5)

Clearance turnover, r (hr), is defined as the ratio of rumen contents Q to passage outflow P: r = Q/P= (Q/F). (F/P) = T/R.

(6)

Rearrangement of eqn (5) indicates the relationship between the clearance turnover of total contents and that of component x: T C J R = T~C,,o/R~

(7)

rC~ = r~C,.o

(8)

i.e.

Clearance turnovers differ from apparent turnovers by the factor of indigestibility [eqn (6)]. In the case of indigestible components, these turnovers are equal since indigestibility is unity. Clearance turnover is the reciprocal of the specific rate of passage and, for components having some but incomplete digestibility, the reciprocal of rx will represent the fraction of these components in the rumen escaping per unit of time. 4. Additivity of Components 4.1. G E N E R A L

CONSIDERATIONS

In the analysis by Lucas et al. (1961), total diet apparent indigestibility comprises the sum of the products of the dietary component concentrations times their partial coefficients of apparent indigestibility [Van Soest, 1982: chapter 4, eqn (V)]. The same additivity principle also applies to the products of the dietary component concentrations and their apparent ruminal turnovers: T = Tx, C ~ u + T=~C~2,~+. . . + T~.C=.,~

(9)

TURNOVER

IN RUMINANT

GASTROINTESTINAL

TRACT

139

where Cxla, Cx2.i, etc., are the respective concentrations of the n components xl, x2 . . . . , x, in the intake and Tx~, Tx2, etc., their respective apparent ruminal turnovers. Provided all individual component concentrations are mutually exclusive and add up to unity, the degree of freedom law applies and the last component is fixed if all others are known. The validity of eqn (9) can be verified by summing eqn (3) over all n components. Practical results using Lucas tests for whole-tract digestion balances (Van Soest, 1967, 1982) indicate the separation of the plant cell wall fraction w from the plant non-cell wall ~ and the attendant metabolic fraction (which may be expressed as the difference between total diet apparent and true digestibility), as summarized in eqn (l 0) : R = R..C.,,i + R.~ C.~,i + M

(1 O)

where R., and R.~ represent true rather than apparent indigestibilities and M denotes the ratio of metabolic matter outflow to feed intake. Thus it is possible that eqn (9) may be reduced to the simplicity of three components : T = T.,C.,,I+ T.~C.~a+ M.

(11)

This division is of importance in the rumen since it is known that cell wall drives rumination, intake limitation and solids turnover. Components within the plant cell wall or non-cell wall can be expected to depend in part upon the overall behaviour of the associated fraction of which they are a part. This particularly applies to nitrogen or protein in the non-cell wall, and lignin and cellulose in the cell wall. From a comparison of eqns (3) and (9) it is apparent that for components with faster turnover than the total rumen contents, ruminal concentrations will be proportionately depleted, and less than the dietary concentration; while components with slower turnover than the total will become proportionally enriched in the rumen. This aspect emphasizes the significance of the ratio of ruminal or compartment concentrations of components to the respective component concentration in the diet, and is indicative of the turnover of any component relative to that of the total. 4.2. M E T A B O L I C C O M P O N E N T

The treatment of the microbial and endogenous component is a special case of the additivity principle as stated in eqns (9) and (11). As noted in eqn (1), the metabolic matter in the rumen causes the apparent turnover time, T, to exceed that for the true feed component, Tf. The difference T - T r is dependent upon the concentration of metabolic matter in the rumen, C,,, and its derivation follows. Substituting for the true feed c o m p o n e n t f for x in eqn (3) gives:

Tcs= TsG,,.

(12)

CI,i, the concentration of true feed in the dietary intake, is unity so eqn (12) simplifies to:

7"~=TG.

(13)

140

P.J.

VAN SOEST ET AL.

Partitioning the concentration of total rumen contents (which is unity) into its dietary and metabolic components gives: CI= l-Cm.

(14)

Tr= T(1-C,.).

(15)

Using eqn (14) in (13) yields:

Rearranging (15), which gives eqn (16), indicates that the incremental effect of the metabolic component on the apparent turnover of total rumen contents is the product of pool concentration times the apparent turnover:

T = T:+ TC,,.

(16)

The metabolic matter cannot have a turnover in the same sense as a dietary component because it has no content in the diet; however, its clearance turnover, r,, (= Q,,/P,,), is an expression of its mean life in the rumen, and is the turnover which should have the most theoretical meaning relative to efficiency of microbial growth and general chemostatic kinetics. An expression for this turnover may be obtained from eqn (7) and eqn (8) as a special case for m:

C,,,,o = TC,,,/(Rr,,).

(17)

TC,,,/r,, = RC,,,o = M.

(18)

Equation (17) gives:

This equation is of interest because it contains all the variables needed for the calculation of microbial efficiency. The efficiency, Y, is the ratio of microbial matter outflow to true ruminally digestible feed intake:

Y = P,.I(D:F) = M / D e

(19)

where DI is the true ruminal digestibility coefficient:

Df=I-RI=I-R+M.

(20)

Note that eqn (19) assumes all metabolic matter leaving the rumen by passage can be regarded as microbial. Using eqn (20) to substitute for DI in eqn (19), dividing the numerator and denominator by M, then substituting for M using eqn (18) gives Y= 1/{1 + [(1 - R)rm/(TC,.)]}.

(21)

The most difficult of these terms to assay are R and r,,, which require estimates of total and microbial outflow from the rumen, respectively (i.e. P and P,,). This has generally meant assay of abomasal or duodenal contents obtained by cannulative sampling. If these two terms could be estimated from rumen turnover kinetics, the experimental problem would be reduced to an analysis of rumen contents. Such estimation procedures are derived in the next section.

TURNOVER IN RUMINANT OASTROINTESTINAL TRACT

141

5. Rumen Escape An equation for the digestion balance in the rumen can be derived by dividing the equation for apparent turnover with the analogous equation for clearance: rxlr. = (GIFx)I(Q,/F~)

= P x l F x = Rx.

(22)

Estimation of the escaping fraction thus requires knowledge of the rumen digestion balance. However, it is desirable to be able to estimate rumen escape from intake and rumen contents. This is possible using an indigestible (therefore fully recoverable) marker y. Substituting y for x in eqn (22) yields:

Ry = Ty/ry = 1.

(23)

It is obvious that Ty=ry (i.e. apparent turnover time of indigestible matter equals its clearance time). The clearance time of undigested matter rx may therefore be estimated from the marker turnover time Ty, provided x and y have the same specific passage rate. Digesting components must associate exclusively with the marker for accuracy, such that marker turnover represents clearance turnover of digesting components. Substitution of Ty for r~ in eqn (22) will yield a form by which digestion balance in the rumen can be obtained from knowledge of intake and its composition, rumen volume and its composition, and marker contents: Rx = Tx/Ty = (Qx/Fx) /(Qy/Fy) = [QCx/( Cx,iF)]/[QCJ( Cy,~F)] =

Gc,,.,/(c,,c~.,).

(24)

Equation (24) is consistent with the escape equation in common use:

Rx = K / ( g p + K~)

(25)

where Kp and Ka (both hr -I) are the specific rates of passage and digestion, respectively, of component x. The sum Kp plus Ka represents relative disappearance of x, the reciprocal of which is the apparent turnover Tx. The reciprocal of Kp is the marker turnover Ty. Although eqn (25) has been commonly applied, the assumptions involved have not always been apparent. These are that component x and the marker are in complete association with one another, and that the marker turnover estimates the clearance of x. Furthermore, x must not be contaminated by microbial interactions in order for accurate estimates of true turnover to be obtained. Application of eqn (24) to whole-rumen turnover will allow an estimate of metabolic outflow from the rumen. Metabolic outflow as a proportion of intake, M, is the difference between apparent and true digestibility (Van Soest, 1982: chapter 4): M = R - R/.

(26)

Using eqn (24) to substitute for R and RI yields:

M = T/Ty- T / G .

(27)

142

P.J. VAN SOEST ET AL.

Again assuming that metabolic outflow from the rumen is all microbial, microbial outflow is obtained from M by multiplying it by the amount of feed intake: P,.= F M = PC, ....

(28)

Microbial efficiency can be determined from eqn (21) using the values obtained for T, Ty and their ratio R in calculating microbial outflow. A value for r .... the clearance time for microbial (i.e. metabolic) matter, is required in eqn (21), and this is given by Tj,. Implicit in eqn (27) is the unlikely assumption that the rumen behaves as a single homogeneous pool, with whole-rumen contents, true feed and marker all having the same specific passage rate. This limitation can be overcome by considering the rumen in terms of its subruminal pools and using markers which associate exclusively with each pool, for example as two pools (e.g. liquid and solids) of sizes Qt and Q2, and using two internal indigestible markers (e.g. a liquid- and a solids-phase marker). Let y, and y2 denote the markers associated with pools 1 and 2, respectively. Assuming first-order kinetics then: P,. = Q,.,/T,., + Q,.2/T,,2

(29)

where Q,,,, and Q,,,z are the respective quantities of microbial matter in pools 1 and 2. Correspondingly, apparent ruminal indigestibility may be determined as: R =

(Q,/Ty, + Q2/Ty2)/F.

(30)

Equations (29) and (30) permit microbial efficiency to be calculated from eqn (21). Theoretically, the approach can readily be extended to three or more pools.

6. Applied Equations Practical equations suitable for conducting Lucas-type tests may be obtained from eqn (31): T.~=

T v + TCx,,/Cxa

(31)

[cf. eqn (16)]. Equation (31) is derived by partitioning component x into its dietary and metabolic subcomponents x: and x,,, respectively, i.e. T.~= (Q.v+ O.~m)/Fx= ax:/F~+ ( Q / F ) ( Q ~ , , / Q ) / ( F x / F ) .

(32)

Multiplication of eqn (31) by Cx.i yields: TxC~.i = T.vC~.;+ TCx,,,.

(33)

TURNOVER I N RUMINANT GASTROINTESTINAL TRACT

143

Equation (33) is analogous to the equation generally used for Lucas tests on digestible

TABLE 2 Equations f o r Lucas tests on component turnovers Linear equation Y=aX+b Form

I li IIi

iv Vt VI Vllt Vlllt

Y

X

a

TxC:<., Q.,

C:,., ~'.,

T.,r

TC.,.,,

T.¢

T.,

I I C.~., I IF.,

TC,,,, Q.,, T.
Q.,m T.x: r.,t

r, (Tx/T)C.,u = C.,, Q.,
C,<.,

F,< I/C.x., I/F,~

b

C,<,,

Q:<,,,IT T..:ilT T.elT

t Ratios of T.~s/T equal R,s-/R for homogenous rumen contents.

components [Van Soest, 1982: chapter 4, eqn (XI)]. It is listed as form I in Table 2. The purpose of the Lucas test on digestible components was to search for and demonstrate components with constant true digestibilities and constant metabolic components across diets. Experience with these analyses has been that metabolic components (expressed as proportions of dietary intake) tend to be constant, while true digestibilities vary. Dietary intake can be expected to have a significant effect on ruminal turnovers, in contrast to whole-tract digestibility which is perturbed to a comparatively minor degree. Furthermore, microbial quantities are likely to vary more in the rumen than in the whole tract. Because of these concerns, other forms of the Lucas test have been derived (Table 2) for assessing the behaviour of metabolic and feed components in the rumen. Another form (form II) is obtained from eqn (33) by multiplication with intake, F : Q,, = 7".,:iF,,+ Qx,,,.

(34)

Two more equations can arise by manipulation of forms I and II. These are obtained by dividing by Cx,; and Fx, respectively, yielding forms III and IV in which the slope represents the metabolic fraction and the intercept the true turnover. These forms are of interest where it is suspected that the metabolic component may vary with diet composition (form III) or intake (form IV). These are shown in Table 2. Another set of equations (Table 2, forms V-VIII) is obtained by dividing forms I-IV by T. This yields terms containing the ratio of T.~s-/T, thus allowing the constancy of the ratio of the turnover of dietary x to total turnover to be tested. In the case of form V, the term (Tx/T)C~.I further reduces to the ruminal concentration C,,, so that plots are between ruminal concentrations and dietary concentrations of the component. If the rumen can be considered to behave as a single homogenous pool with whole-rumen contents and component x having the same rate of passage,

144

P.J.

VAN SOEST

ET AL.

then T:¢/T equals R.~f/R and these tests examine the constancy of the indigestibility of dietary x relative to R:

Txfl T= ( Txsl Tv)I(TI Ty) = RxflR.

(35)

7. Discussion

The present paper proposes a method for the determination of rumen turnover and passage and their separation into metabolic and feed fractions based on rumen emptying. This provides an alternative to traditional methods based on the difficult and disruptive technique of abomasal or duodenal cannulation. The alternative of rumen emptying is simpler and requires fewer samples. However, application and validation of the equations developed in this paper require detailed information on total rumen contents, their compositions (liquid, particulate fractions, microbial matter, etc.) and that of the respective diets. Data on cell wall and non-cell wall fractions and lignin would seem particularly important in view of the demonstrated significance of these fractions in the analysis of whole-tract digestive balances by the methods of Lucas (Van Soest, 1967, 1982). Many rumen emptyings reported in the literature fail to give such information, thus the need for detailed analysis of rumen contents is greater than has hitherto been generally undertaken. It would also be desirable, for comparative purposes, if such measurements were made in conjunction with traditional rumen efficiency and passage studies. The application of turnovers to rumen escape and microbial efficiency will require adequate markers. Whilst it is generally appreciated that markers need to be fully recoverable, the further requirement is that a marker must be indelibly associated with the component that it is intended to mark. There are a number of markers (e.g. ruthenium phenanthroline, rare earths) in which inter-particle migration has been suspected (Faichney, 1975). The chromium mordant (Uden et al., 1980) is the only one which appears to be indelibly associated with the particles to which it was originally attached, but has the danger of increasing the density of these particles (Ehle et al., 1984). Alternatives are internal markers such as lignin and indigestible fibre (Sunvold & Cochran, 1991). However, their recovery needs to be proven relative to the particular method used, and the problem of non-uniform distribution in the rumen solids examined. Liquid markers need to be examined relative to their distribution in water space. It is not known, for example, whether cobalt-EDTA or chromium-EDTA penetrates the water-space of living microbes, though it is unlikely. Also, the uniformity of distribution of liquid markers in hydrated fibre has never been adequately examined. Both absorption and adsorption effects could be problems. The method proposed for estimating microbial efficiency and outflow [eqns (21) and (28)] from rumen-turnover kinetics and thus from analysis of rumen contents, is most likely to be of interest in terms of protein flow since microbes are comprised mainly of protein (approximately 65% of DM) and with most diets account for in excess of 50% of the total protein reaching the duodenum. The method is, however, dependent on the quantity of endogenous protein flowing from the rumen being negligible. Although endogenous proteins are known to enter the rumen (e.g. Siddons

TURNOVER

IN RUMINANT

GASTROINTESTINAL

TRACT

145

et al., 1985), there are no estimates of the amount flowing out. However, they are likely to be soluble and therefore probably rapidly degraded and fermented within the rumen. Endogenous nitrogen flow at the duodenum of sheep is generally assumed to be between 1-2 g per day, but this arises as gastric secretions rather than flow from the rumen (Clarke et al., 1966). The mathematical treatment of rumen-turnover kinetics has allowed the development of several equations for conducting Lucas-type tests (Table 2), which it is hoped will provide additional means of disclosing components which behave uniformly in the rumen. The discovery of which components fulfil this criterion should provide a better understanding of rumen function and for the development of a nutritionally relevant analytical system.

REFERENCES CLARKE, E. M. W., ELLINGER,G. M. & PHILLIPSON,A. T. (1966). The influence of diet on the nitrogenous components passing to the duodenum and through the lower ileum of sheep. Proc. R. Soc. B. 166, 63-79. EHLE, F. R., BAS, F., BARNO, B., MARTIN, R. & LEONE, F. (1984). Particulate rumen turnover rate measurement as influenced by density of passage marker. J. Dairy Sci. 67, 2910-2913. FAICHNEY, G. J. (1975). The use of markers to partition digestion within the gastro-intestinal tract of ruminants. Proceedings of 4th International Symposium on Ruminant Physiology (McDonald, I. W. & Warner, A. C. I., eds) pp. 277-291. Armidale, NSW: University of New England Publishing Unit. LUCAS, H. L., JR., SMART, W. W. G., JR., CWOLLONJ, M. A. & GROSS, H. D. (1961). Relations between digestibility and composition of feeds and foods. S-45 Report, Raleigh, NC: North Carolina State College. LUCAS, H. L. (I 964). Stochastic elements in biological models; their sources and significance. In: Stochastic Models in Medicine and Biology (Gurland, J., ed.) pp. 355-383. Madison, WI: University of Wisconsin Press. MITCHELL, H. H. (1942). The evaluation of feeds on the basis of digestible and metabolizable nutrients. J. Anita. Sci. 1, 159-173. MITCHELL, H. H. (1964). Comparatioe Nutrition of Man and Domestic Animals, Volume II. New York: Academic Press. SIDDONS, R. C., NOLAN, J. V., BEEVER, D. E. & MACRAE, J. C. (1985). Nitrogen digestion and metabolism in sheep consuming diets containing contrasting forms and levels of N. Br. J. Nutr. 54, 175-187. StmVOLD, G. D. & COCHRAN, R. C. (1991). Evaluation of acid detergent lignin, alkaline peroxide lignin, acid insoluble ash, and indigestible acid detergent fiber as internal markers for prediction of alfalfa, bromegrass and prairie hay digestibility by beef steers. J. Anita. Sci. 69, 4951~1955. UDEN, P., COLUCCI, P. E. & VAN SO~T, P. J. (1980). Investigation of chromium, cerium and cobalt as markers in digesta rate of passage studies. J. Sci. Food Agric. 31, 625-632. VAN SO~T, P. J. (1967). Development of a comprehensive system of feed analyses and its application to forages. J. Anita. Sci. 26, 119-128. VAN SOEST, P. J. (1982). Nutritional Ecology of the Ruminant. Corvallis, OR: O & B Books.