HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Abstract Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Imamidoost, R. Articles by Cant, J. P. Search for Related Content PubMed PubMed Citation Articles by Imamidoost, R. Articles by Cant, J. P.

Non-steady-state modeling of effects of timing and level of concentrate supplementation on ruminal pH and forage intake in high-producing, grazing ewes¹

Department of Animal and Poultry Science, University of Guelph, Guelph, Ontario, N1G 2W1 Canada

	Abstract

Top Abstract Introduction Experimental Procedures Results and Discussion Implications Literature Cited

 
A computer model was developed to predict responses of lactating ewes to concentrate supplementation, whether on pasture or stall-fed, given concentrate once per day or in multiple feedings, and suckling multiple lambs. The model considers effects of concentrate supplementation on organic acid production, saliva flow, ruminal pH, and forage intake. The user defines ewe BW, feed composition, and concentrate feeding times and amounts. The reference ewe has free access to forage and water. Upon consumption, forages and concentrates enter into lag pools for 2.0 and 0.24 h, respectively. Carbohydrates then enter ruminal pools of degradable fiber, undegradable fiber, or nonstructural carbohydrate, from which they are degraded or pass to the lower gut. Rapid dissociation of organic acids from carbohydrate fermentation and buffers from rumination are simulated to determine ruminal pH according to the Henderson-Hasselbach equation. The pH, in turn, affects fiber degradation rates. Forage intake continues during daylight hours until ruminal NDF exceeds 1.0% of BW, or organic acid concentration exceeds 130 mM. A circadian pattern of organic acid concentrations and pH of rumen contents with multiple concentrate feedings was simulated by the model with root mean square prediction error of 7.7 and 3.0 to 4.0% of the observed mean, respectively. However, ignoring fermentation of dietary protein may have caused an underestimation of organic acid production rates. The model predicted the increase in total DMI and the substitution effect on forage intake of increasing levels of concentrate supplementation. Simulations suggested that a single concentrate meal daily was best fed in the evening to minimize the substitution effect, and that there was no benefit in forage intake to feeding 2 kg/d concentrate in more than two meals per day.

Key Words: Forage Intake • Modeling • Ruminal pH • Sheep

	Introduction

Top Abstract Introduction Experimental Procedures Results and Discussion Implications Literature Cited

 
The NRC (1985) provides nutrient recommendations for ewes suckling up to two lambs, but ewes of highly prolific breeds produce more than two lambs per gestation. To produce enough milk to raise three to four lambs, there is a high demand for dietary nutrients, which is often met by feeding high levels of concentrates. A ewe suckling four lambs would be expected to produce more than 4 kg of milk/d during the first month of lactation (Peart et al., 1975). According to the factorial AFRC (1993) model of energy partitioning, a 75-kg ewe producing 4 kg/d milk containing 6.5% fat requires a daily ME intake of 9.2 Mcal/d. At a DMI of 4% of BW, the required ME content of the diet is 3.07 Mcal/kg. Barley grain itself is reported to have a ME content of 3.11 Mcal/kg (NRC, 1985), which leaves little room for inclusion of forage in the diet. A common practice is to allot 500 g of concentrate/d per lamb suckled, which, when four lambs are suckling, can mean that concentrate makes up more than 80% of the ewe’s intake.

Increasing the level of concentrate in a ewe diet increases milk production (Avondo et al., 1995; Zervas et al., 1999); however, high levels of concentrate feeding can cause low ruminal pH (Mould et al., 1983; Carro et al., 2000), which can decrease forage degradability (Mould et al., 1983; Allen, 1997) and induce clinical ruminal acidosis. The level of concentrate feeding is then a question of optimizing costs and benefits. The acidotic cost of concentrate feeding occurs within hours of each meal of concentrate consumed, and so is dependent on the size and frequency of meals. Ruminal pH can range more than 1 pH unit over the course of a day, and it is the time spent under pH 6.0 or 5.6 that is taken to indicate acidosis (Keunen et al., 2002). To address the need for feeding recommendations for high-producing ewes, a dynamic model was constructed to predict the consequences of timing and level of concentrate intake in lactating ewes. The ewe may be pasture-or stall-fed, given concentrate once per day or in multiple feedings, and may be suckling multiple lambs.

	Experimental Procedures

Top Abstract Introduction Experimental Procedures Results and Discussion Implications Literature Cited

 
The general strategy for modeling the rumen was based on the lag approach of Illius and Gordon (1990), the rumination modeling of Argyle and Baldwin (1988), the concepts of Kohn and Dunlap (1998) for calculating ruminal pH, and the constraints on ad libitum intake from Forbes (1993).

The simulated animal is a grazing, lactating ewe with free access to forage and a restricted level of concentrate feeding during the day. Forage and concentrate composition is defined at the beginning of a model run. The user also may set the number of concentrate meals per day, as well as the time and amount fed in each meal. Feed ingredients are described in terms of their nonstructural carbohydrate (Nc), degradable fiber (Df), and undegradable fiber (Uf) contents. It is assumed the animal has free access to water during the day.

Upon being consumed, forages and concentrates enter lag pools and subsequently become available to the ruminal environment for microbial degradation. Essentially, ruminal pH is calculated from concentrations of organic acids (Oa) produced in fermentation of dietary carbohydrates and of buffers entering from saliva (Figure 1). Ruminal pH affects fiber digestibility. Ruminal fiber content, organic acid concentration, and day length affect forage intake. In turn, forage and concentrate intake and size of the forage lag pool affect buffer production. The user defines concentrate feeding levels, whereas the forage intake is controlled by feedback mechanisms.

View larger version (20K): [in this window] [in a new window]   Figure 1. Diagram of nutrient flows in the model. Boxes represent state variables, and arrows represent flows. Pool sizes and nutrient flows for a ewe consuming 2.0 kg/d of mixed pasture at an instantaneous intake rate of 2.0 kg/d (all other parameters and inputs as in Tables 1 and 2) are shown inside boxes and beside arrows, respectively.

View larger version (9K): [in this window] [in a new window]   Figure 2. Plot of ruminal volume of sheep measured by liquid marker dilution and BW (; from Bergman et al., 1965; Stokes, 1983; Mees and Merchen, 1985; Judkins and Stobart, 1988; Weston, 1988b; Gunter et al., 1990; Charmley et al., 1991; Martin et al., 2001; López et al., 2003). The solid line represents Eq. [1] from the text: ruminal volume = a BWb, where a = 1.3 (approximate SE = 0.7), and b = 0.37 (approximate SE = 0.11); root mean square prediction error = 8.2% of the observed mean volume.

[1]

Lag Pools

According to Illius and Gordon (1990), concentrates and forages each enter a lag pool upon consumption. The feed components are not subject to degradation or passage from the rumen during this time. The differential equations for size, in kilograms, of the lag pools for concentrates (CNlag) and forages (Frlag) are:

[2]

and

[3]

where inCn is the instantaneous concentrate intake rate set at 0 or 30 kg/d depending on concentrate meal times defined by the user, and instantaneous intake of forage (inFr) is calculated in the model as either 0 or 4 kg/d (Table 1) when all conditions for forage intake are met (see below). The user defines concentrate meal times and daily concentrate intake (DMICn), and the model simulates the meals numerically as they occur. The rates of concentrate (UinCn) and forage (UinFr) release to the ruminal environment after the lag period are calculated as a simple delay of intake according to Illius and Gordon (1990):

[4]

and

[5]

where Cnlagtime and Frlagtime are the lag time periods for concentrates and forages, respectively. There is usually a longer lag time for forages than for concentrates due to their higher cell wall contents. Varga and Hoover (1983) reported lag times of 0.24 h for barley grain and 0.9 to 4.3 h for forages. Illius and Gordon (1990) used a 2-h lag in their model for feedstuffs with 30 to 50% cell contents. For the pasture and barley grain inputs for behavioral runs of the model, lag times of 2 and 0.24 h, respectively, were used (Table 1).

Nutrient Pools

After the lag, nutrients become available to microorganisms for degradation and utilization. Feedstuffs are characterized as containing Df, Uf, and Nc. Fiber pools (Df and Uf) are considered for simulation of ruminal fill. In addition, Df and Nc are considered for determining Oa production and ruminal pH (Figure 1). Net Oa production from protein is ignored assuming protein degradation to Oa is balanced by Oa utilization for protein synthesis by microorganisms.

Undegradable fiber is resistant to degradation in the rumen and can be calculated from analytical NDF, NDF-insoluble CP, ADF-insoluble CP, and lignin values according to Weiss et al. (1992). There is no degradation of Uf in the model, so Uf (kg) is calculated from inflow from the delayed lag pool (Eq. [4] and [5]) and passage out of the rumen (UUfpass) as

[6]

where fCnUf and fFrUf are the fractions of Uf in concentrate and forage DM, respectively.

[7]

where kPpass is 40% of the liquid passage rate constant (Table 1).

Degradable fiber is that proportion of NDF that can potentially be degraded by enzymatic activity of microorganisms in the rumen. Thus, Df (kg) is simulated based on input from the delayed lag pools (Eq. [4] and [5]), passage to intestines (UDfpass), and degradation to Oa (UDfDfOa) as

[8]

where fCnDf and fFrDf are fractions of Df, calculated according to Weiss et al. (1992), in concentrate and forage, respectively.

[9]

and

[10]

where the degradation rate constant, kDfOa, ranges from 0 to 100% of the maximum rate constant, depending on ruminal pH. The lower the ruminal pH, the lower the activity of fibrolytic bacteria and rate of fiber degradation (Mouriño et al., 2001). The ruminal pH that is optimal for growth of fibrolytic bacteria is between 6.2 and 6.8 (Mould and Ørskov, 1983), and at pH 5.2, cellulolysis stops (Mouriño et al., 2001). The following equation was parameterized using PROC NLIN of SAS (SAS Inst., Inc., Cary, NC) from the in vitro gas production data of Mouriño et al. (2001) to capture the transition in degradation (Figure 3):

View larger version (9K): [in this window] [in a new window]   Figure 3. Rate constant for cellulose degradation by ruminal microbes in vitro measured at different pH values and expressed as a percentage of the value at pH 6.56 (; from Mouriño et al., 2001). The solid line represents a Eq. [11] from the text: where a = 102% (approximate SE = 2), b = 5.92 (approximate SE = 0.02), and c = 38 (approximate SE = 8); root mean square prediction error = 6.8% of the observed mean rate constant.

[11]

where pH is calculated in Eq. [30]. Values of kDfOa estimated from serial nylon bag incubations of feed-stuffs in situ have ranged from 0.55 to 6.48 d^–1 (Varga and Hoover, 1983; López et al., 1999). For the reference pasture, the value of kDfmax is set at 1.92 d^–1 (Table 1), so that 0 < kDfOa < 1.92 d^–1.

Nonstructural carbohydrate is mainly composed of starch and soluble carbohydrates, which are readily degraded by enzymatic activity of microorganisms. The Nc content of feedstuffs is calculated as the remainder after analyzed NDF, CP, fat, and ash contents have been subtracted from the DM. The differential equation for Nc (kg) is based on inflow from the delayed lag pools (Eq. [4] and [5]), outflow to the intestine (UNcpass), and degradation to Oa (UNcNcOa) as:

[12]

where fCnNc and fFrNc are the fractions of Nc in concentrate and forage DM, respectively, and

[13]

and

[14]

where kNcOa is the degradation rate constant. Starch degradability depends on the feedstuff and the processing applied to it (Theurer, 1986). Degradation rate constants have ranged from 0.58 to 14.0 d^–1 in situ (Offner et al., 2003). A value of 7.2 d^–1, measured for barley, is used for the reference starch degradation rate constant (Table 1).

Organic Acids

The production of Oa that dissociate into conjugate base and H⁺ decreases ruminal pH, which in turn affects the dissociation of Oa. To model the equilibrium between Oa species, two pools were considered for undissociated (OaA) and dissociated (OaD) forms of Oa, respectively.

Organic acid in its undissociated form is produced in the rumen by degrading Df (POaDfOa) and Nc (POaN-cOA) and is removed from the rumen by passage (UOaApass), absorption through the rumen wall (UOaAabs), and dissociation to OaD (UOaAOaD):

[15]

where the fluxes in Eq. [15] are all in moles per day.

[16]

where kpass is the liquid passage rate constant (Table 1). Liquid passage rate from the rumen was 2.30 to 2.69 d^–1 in wether lambs (Judkins and Stobart, 1987) and 2.66 to 2.81 d^–1 in lactating ewes (Weston, 1988b; Gunter et al., 1990). A value of 2.7 d^–1 is used as the reference liquid passage rate constant in the model (Table 1).

For absorption,

[17]

where kOaAabs is 227 d^–1 (Table 1) based on steady-state solutions of the model for inputs from 16 experiments in the literature (see below).

The terms POaNcOa and POaDfOa represent total Oa production from Nc and Df respectively, and are based on total acetate, propionate, butyrate, and valerate productions rates as:

[18]

and

[19]

Each mole of glucose fermented can produce 2 mol of acetate, 2 mol of propionate, 1 mol of butyrate, or 1 mol of valerate (Baldwin, 1995). The proportions produced on a net basis from ruminal fermentation of starch and cellulose were calculated from literature data by Murphy et al. (1982). There were different proportionalities for high-forage and high-concentrate diets. Linear extrapolations of the Murphy et al. (1982) constants are used to predict molar yields (Y) of individual VFA per kilogram of Nc or Df fermented:

[20]

where the molecular weight of glucose in Nc (MwNc) and Df (MwDf) is 0.162 kg/mol. The fractions of forage (fDMFr) and concentrate (fDMCn) in the daily DMI are calculated in Eq. [32].

The production of acetate, propionate, butyrate, and valerate is calculated by applying the yield coefficients to rates of Df and Nc degradation (Eq. [10] and [14]) as:

[21]

The OaD is produced from OaA (UOaAOaD) and removed from the rumen with liquid passage (UOaDpass) and absorption across the ruminal wall (UOaDabs).

[22]

where

[23]

and

[24]

with kOaDabs = 1.41 d^–1 according to steady-state solutions of the model for inputs from 16 experiments in the literature (see below).

Saliva Production and Ruminal pH

Bicarbonate is the most important buffer in saliva. Therefore, for the sake of simplicity, the bicarbonate system is the paradigm for pH buffering in the rumen. The quantity of buffer in the rumen is determined by inflow from the saliva (PBfSaBf) and from the diet (PBfCnBf; in cases where a buffer like sodium bicarbonate is included in the concentrates), outflow from the rumen (UBfpass), and to buffer acid production (UOaAOaD):

[25]

where

[26]

[27]

The term fSaBf is the concentration of buffer in saliva, and PSa is the rate of saliva production. Ruminant saliva contains 126 mEq/L of HCO₃^– and 26 mEq/L of PO₄^2– (McDougall, 1948; Bailey and Balch, 1961) for a fSaBf of 0.15 M (Table 1). According to Meot et al. (1997), 18% of saliva is produced during resting, 36% during eating, and 46% during rumination. Daily saliva production in sheep ranges from 6 to 16 L (Carter et al., 1990). Assuming the parotid glands contribute 50% of total saliva production (Meot et al., 1997), we used the parotid secretion rates reported by Meot et al. (1997) to set instantaneous PSa at 7.2, 16.2, and 19.5 L/d during resting, eating, and ruminating, respectively, following Argyle and Baldwin (1988). Rumination was considered to occur when Frlag > 0.01 kg (Eq. [3]) and the ewe was not eating.

For pH modeling, it was assumed, following Kohn and Dunlap (1998), that dissociation of 1 mol OaA (UOaAOaD) is buffered by 1 mol Bf flowing to CO₂ + H₂O, and that the bicarbonate and Oa systems are always at the equilibrium state described by their respective dissociation constants (KaOa and KaBf), and the CO₂ pressure remains at a constant 0.7 atm due to exchange with the gas phase and eructation.

Accordingly, the equalities

[28]

yield the constraint

[29]

where the leading "c" denotes a concentration in moles per liter.

The value of UOaAOaD in Eq. [15], [22], and [25], for which Eq. [29] holds true, is solved by a Newton-Raphson iteration method. From an initial guess, UOaAOaD is modified in successive iterations until Eq. [29] holds true.

The ruminal pH is then calculated according to the Henderson-Hasselbach equations:

[30]

where pKaBf and pKaOa are the pK_a values for Bf and Oa, respectively. Both equations yield the same pH value.

Forage Intake

Instantaneous intake of forage inFr = 4.0 kg/d when inCn 0 kg/d, cOaA + cOaD 0.13 M, actual ruminal capacity (ARC) 0.8 x maximum ruminal capacity (MRC), and time of day is between dawn and dusk. According to Baile (1975), a typical instantaneous rate of good quality roughage intake from a manger by sheep is 15 kg/d. Intake rate measured over 12 to 15 bites of a pasture sward was 6.2 to 11.5 kg/d. These rates exclude nonbiting and nonchewing times that occur during grazing. Sixty-five-kilogram wethers on a grass sward consumed 1 kg/d DM in 8.9 h of grazing (Thomson et al., 1985), which yields an average rate of 2.7 kg/d. Lactating ewes consumed 2.9 kg/d DMI in 16 h of the heaviest grazing times of the day for a rate of 4.4 kg/d (Bermudez et al., 1989). A value of 4.0 kg/d was chosen for the forage intake rate in the model.

Of NDF weights measured at six time points throughout a day in grazing sheep, the maximum ranged from 0.76 to 1.2% of BW depending on the pasture. Values for MRC of 0.9, 1.2, and 1.38 % of BW have been used in past intake models (Mertens, 1987; Poppi et al., 1994; Chilibroste et al., 1997). The MRC value used here is 1.0% of BW (Table 1). Actual ruminal capacity is calculated as:

[31]

Although forage intake commences when ARC = 0.8 MRC, it continues until ARC MRC or some other condition on inFr is violated.

Organic acid concentration is a controlling factor to terminate feeding in many models (Forbes, 1993; Chilibroste et al., 1997). Forbes (1993) used a threshold of 130 mM Oa, beyond which sheep stop eating. The same concept and parameter value are used in this model.

Day length was considered a limiting factor on total daily intake simulated from instantaneous rates. According to Bermudez et al. (1989), there is lower intake between the hours of 2400 and 0800 compared with the rest of the day. Such a decrease in feeding activity is common among animals that are more active during the day. Sheep typically commence grazing at dawn and continue for 4 h and then have a second grazing bout in the afternoon until dusk (Thomson et al., 1985). Dawn and dusk are inputs to the model and, for the reference state, we simulated a temperate summer day, with dawn at 0500 and dusk at 2100.

Proportions of forage (fDMFr) and concentrate (fDMCn) in the total daily DMI were used in Eq. [20] to calculate proportions of individual Oa produced in microbial fermentation:

[32]

where DMICn is the daily concentrate intake defined by the user (Eq. [2]) and DMIFr is the rolling average inFr over the past day:

[33]

In total,

[34]

Parameters of Oa Absorption

Short-chain fatty acids can be absorbed across the ruminal epithelium in both associated and dissociated forms (Bugaut, 1987; Kramer et al., 1996), although the transport mechanisms are different for the two forms. First-order rate constants for OaA and OaD absorption, kOaAabs (Eq. [16]), and kOaDabs (Eq. [23]) were calculated from 16 measures of BW, nutrient intake, total concentration of Oa in the rumen (cOaT), and ruminal pH (Mees and Merchen, 1985; Judkins and Stobart, 1988; Weston, 1988b; Gunter et al., 1990; Charmley et al., 1991; Chiofalo et al., 1992; Hadjipanayiotou and Photiou, 1995; Carro et al., 2000; Martin et al., 2001; Castro et al., 2002). Differential Eq. [2], [3], [6], [8], [12], [15], [22], and [25] were set to zero to solve the model in steady state for each of the 16 input sets, using the parameter values given in Table 1. Given, from Eq. [30], that cOaA = cOaT/(1 + 10^{pH – pKaOa}), Eq. [15] and [22], respectively, were rearranged to calculate rate constants as

[35]

and

[36]

The value of UOaAOaD at steady state for use in Eq. [35] and [36] was calculated from Eq. [25] as the difference between production (PBfSaBf) and passage (UBf-pass) of Bf.

Model Analysis

Behavior of the model was analyzed by simulating three different concentrate-feeding levels: 1) free grazing with no supplemental concentrate (FR); 2) free grazing with one concentrate meal of 1 kg of barley grain at 2200 daily (CN1); 3) and free grazing with two concentrate meals of 1 kg of barley grain each at 1000 and 2200 daily (CN2). Chemical analyses of mixed-grass–legume pasture and barley grain (Table 2) were obtained from NRC (1996). All parameter values used in the simulations are presented in Table 1. Simulations were run for 11 d, and results from d 11 are presented. Initial values of the state variables have little effect on the d-11 results, but the values used in all simulations were Cnlag₍₀₎ = 0.0 kg, Frlag₍₀₎ = 0.0 kg, Uf₍₀₎ = 0.15 kg, Df₍₀₎ =0.439 kg, Nc₍₀₎ = 0.129 kg, OaA₍₀₎ = 0.001 mol, OaD₍₀₎ =0.062 mol, Bf₍₀₎ = 0.087 mol.

Leng and Leonard (1965) fed twelve 75-g meals of alfalfa chaff hourly to adult sheep from 0800 to 1900 daily, and measured Oa concentration in ruminal fluid samples taken hourly from ruminal fistulas. The experiment was simulated by scheduling forage meals as for concentrate and setting the intake rate to 4.0 kg/d (DM basis). Crude protein content of the alfalfa was 16.4% (DM basis), and all other chemical composition inputs were taken from NRC (1996).

Istasse et al. (1986) investigated the effect of frequency of concentrate feeding on ruminal pH in adult sheep, measured at 2-h intervals throughout a day. The sheep were fed hay ad libitum and a barley-based concentrate at 1.86 times the hay intake in two or four equally spaced meals per day. The value of DMICn was set to 1.02 and 1.09 kg/d for the two treatments, respectively, and DMIFr was predicted by the model. Ash and CP contents of the hay were given in the publication and remaining feed composition inputs were taken from NRC (1996) for mature timothy hay and barley.

Concentrate was fed at 0, 480, and 960 g/d (DM basis) in a single meal at 0900 to 64-kg ewes nursing twins in early lactation and ad libitum intakes from a perennial ryegrass sward were measured by chromic oxide dilution (Milne et al., 1981). The experiment was simulated with chemical composition of ryegrass and barley taken from NRC (1996) to represent the forage and concentrate, respectively.

	Results and Discussion

Top Abstract Introduction Experimental Procedures Results and Discussion Implications Literature Cited

 
Parameterization of Oa Absorption

An important component of pH regulation in the rumen is the absorption of H attached to OaA (Allen, 1997). There has been some question as to the rate of absorption of Oa in the dissociated form, and it has often been called negligible (Dijkstra et al., 1993; Allen, 1997), although Kramer et al. (1996) demonstrated that OaD were absorbed by a system that required Cl^–. At a pH above the pKa for Oa of 4.8, the predominant form of Oa is OaD, and at pH 6.5, the concentration of OaD is 50 times that of OaA. In preliminary modeling, assigning zero absorption to OaD forced a low ruminal pH to obtain realistic Oa absorption rates, and Bf content of saliva was inadequate to maintain Bf presence in the rumen. Accordingly, as in Pitt et al. (1996), first-order rate constants for both OaA and OaD absorption were estimated by solving the model in steady state. Because of the high relative concentration of OaD, values for kOaDabs (–0.7 to 3.22 d^–1) were two orders of magnitude lower than for kOaAabs (82 to 1,460 d^–1), which may account for the tendency to discount OaD absorption. Pitt et al. (1996) reported only three- to ten-fold differences in absorption coefficients for OaA and OaD, but their parameters yield a faster rate of OaD absorption than of OaA absorption, which is not consistent with observations (Ash and Dobson, 1963). According to the steady-state model solutions, on average, 84% of Oa absorbed were in the OaA form and 25% of Oa produced passed out of the rumen with the liquid flow as opposed to being absorbed across the rumen wall. Previous estimates of passage of Oa range from 15 to 40% of net production (Dijkstra et al., 1993; Allen, 1997).

In two cases, a negative number was obtained for kOaDabs. In these cases, the expected rate of OaD production, calculated as the difference between production and passage of Bf (Eq. [25]), was lower than the expected rate of OaD passage, calculated with Eq. [23] from the observed cOaT and pH. Because there is error in prediction of rates of Bf production and liquid passage out of the rumen, kOaDabs values were calculated from many sets of observations and averaged.

There seemed to be an effect of ruminal pH on efficiency of OaA absorption, wherein kOaAabs increased exponentially beyond pH 6.5 (Figure 4). The increase may have been an artifact of the extremely low concentration of OaA relative to OaD at such pH or may have been a consequence of consistent deviations in other parameter values, such as PSa or kpass, at higher pH. Alternatively, some aspect of OaA transport, such as proton donation from the ruminal epithelium (Bugaut, 1987), could be upregulated at high pH. Because the model was constructed to simulate the high-producing ewe experiencing periods of low ruminal pH, Oa absorption parameters used (Table 1) were averages of the nine estimates from pH 6.5 (Figure 4). Means ± SE were 227 ± 27 d^–1 and 1.41 ± 0.38 d^–1 for kOaAabs and kOaDabs, respectively.

View larger version (9K): [in this window] [in a new window]   Figure 4. Plots of first-order rate constants for absorption of associated (kOaAabs) and dissociated organic acids (kOaDabs) across the ruminal wall calculated from steady-state solutions of the model for observations of BW, nutrient intake, total concentration of organic acids in the rumen, and ruminal pH in peer-reviewed publications.

The simulated ewe, with 24-h access to mixed pasture, had two bouts of grazing during the day (Figure 5), as is commonly observed (Thomson et al., 1985). Supplementing concentrate, either at morning or night, decreased the length of the subsequent grazing bout. Actual ruminal capacity increased during each meal and decreased gradually at other times (Figure 6). Forage intake and degradation rates are lower than those of concentrates, so ARC and Oa concentration in the rumen increased more slowly than CN1 and CN2. The first grazing bout of the day on FR was terminated by the ARC limit of 0.70 kg of NDF. The second bout was terminated at dusk at 2100. Grazing commenced at dawn at 0500 and again when ARC = 0.8 x MRC.

View larger version (11K): [in this window] [in a new window]   Figure 5. Simulated intake of forage (inFr; solid line) and concentrate (inCn; dashed line) throughout a day by lactating ewes given ad libitum access to mixed-grass–legume pasture (Table 2) with no supplementary concentration (FR), 1 kg of barley grain at 2200 (CN1), or 1 kg of barley grain at 1,000 and 1 kg at 2200 (CN2). Simulations were run using parameter values given in Table 1.

View larger version (22K): [in this window] [in a new window]   Figure 6. Simulated ruminal fill (ARC), concentrations of organic acids (Oa) and buffer (Bf) in the rumen, and ruminal pH throughout a day in lactating ewes given ad libitum access to mixed-grass–legume pasture (Table 2) with no supplementary concentrate (solid line), 1 kg of barley grain at 2200 (dotted line), or 1 kg of barley grain at 1000 and 1 kg at 2200 (dashed line). Simulations were run using parameter values given in Table 1. The vertical dotted lines indicate concentrate meal times.

The addition of a second concentrate meal at 1000 caused ruminal fill to be higher throughout the day, which led to shorter grazing times and a long break between the two daily bouts (Figure 5). Although daily forage intake was decreased with concentrate supplementation, total DMI and, therefore, ME intake, was increased in CN1 and CN2 ewes (Figure 7).

View larger version (7K): [in this window] [in a new window]   Figure 7. Simulated daily intake of forage (black bars) and concentrate (white bars) by lactating ewes given ad libitum access to mixed-grass–legume pasture (Table 2) with no supplementary concentrate (FR), 1 kg of barley grain at 2200 (CN1), or 1 kg of barley grain at 1000 and 1 kg at 2200 (CN2). Simulations were run using parameter values given in Table 1.

Predicted Oa concentration throughout a day in sheep fed 0.9 kg/d forage followed the same pattern as that observed by Leng and Leonard (1965), but at approximately half the concentration (Figure 8); 98% of the MSPE was due to a mean bias. Daily production of Oa was measured by Leng and Leonard (1965) at 5.4 mol/d, whereas the simulated value was 4.2 mol/d. The simulated volume of the rumen may have been higher than in the sheep of Leng and Leonard (1965); neither volume nor BW was reported. Additionally, rate of liquid passage out of the rumen may have been too high. Increasing DMI of alfalfa chaff from 0.69 to 1.03 kg/d resulted in an increase in the rate constant for liquid passage from 2.30 to 2.82/d (Ulyatt et al., 1984). The value for kpass of 2.7 d^–1 used here was obtained from lactating ewes with an elevated consumption of water and DM (Weston, 1988b; Gunter et al., 1990), so the sheep at maintenance of Leng and Leonard (1965) could reasonably be expected to manifest a slower fractional passage. Setting BW = 50 kg and kpass = 1.2 d^–1 resulted in predictions of Oa concentration similar to those observed (Figure 8; root MSPE = 7.7% of the observed mean) and a net Oa production rate of 5.1 mol/d. In modeling ruminal water dynamics, Argyle and Baldwin (1988), like us, also used a constant fractional liquid passage rate for all simulation conditions. To improve predictions of cOa, the rate constant for liquid passage may need to be the dependent variable in some mathematical function, or the approach of Dijkstra et al. (1996), where kpass was inputted as a diet-specific variable, may be warranted. The model of Dijkstra et al. (1996) predicted nonsteady Oa concentrations in the rumen of dairy cows at the end of grazing and starvation periods in three different experiments with a root MSPE of 32% of the observed mean (Chilibroste et al., 2001).

View larger version (8K): [in this window] [in a new window]   Figure 8. Observed (; from Leng and Leonard, 1965) and predicted (solid line) concentration of organic acids (Oa) in the rumen throughout a day in adult sheep given 0.9 kg/d alfalfa chaff in 12 equally spaced meals between 0800 and 1900. Simulations were run with inFr = 0 at all times, inCn = 0 or 4.0 kg/d depending on meal times, fCnDf = 0.345, fCnUf = 0.120, fCnNc = 0.277, and Eq. [32] was replaced by setting fDmFr = 1.0. All other parameter values and were as given in Table 1. See Tables 1 and 2 for abbreviations. The root mean square prediction error (MSPE) was 50.5% of the mean observed Oa concentration with 98% of the error due to a mean bias. A second simulation (dashed line) was run with BW = 50 kg and kpass = 1.2 d–1, where the root MSPE was 7.7% of the observed mean and 76% of the error was unexplained variance.

Using the parameter values of the reference ewe (Table 1), but setting the daily concentrate intake and meal times equal to those of Istasse et al. (1986) and taking feed composition from NRC (1996), resulted in predictions of a circadian pattern of ruminal pH similar to those observed (Figure 9). Root MSPE were 4.0 and 3.0% of the mean observed pH for the twice and four times daily feeding treatments, with 96 and 79% of the errors, respectively, due to unexplained variance. Predicted DMI for the whole day was 2.07 kg (85.5 g/kg of BW) on both treatments, whereas observed DMI was 67.1 g/kg (Istasse et al., 1986). The overprediction of forage intake may have influenced absolute pH predictions but not the circadian pattern. It has long been recognized that fluctuations in ruminal pH that occur throughout a day can adversely affect intake and well being of the ruminant animal. Continuous pH recording is the current state-of-the-art method in subacute ruminal acidosis diagnosis (Keunen et al., 2002). If analytical techniques have advanced to the point of measuring pH continuously, then there is a need to simulate pH continuously to test hypotheses of pH regulation and its consequences. Previously, Pitt and Pell (1997) simulated identical, sequential periods of pH fluctuation by calculating a steady-state pH empirically from effective NDF content of the diet and the deviation from that mechanistically based on the change in Oa concentrations, a constant saliva concentration, and the stoichiometry of dissociation. Argyle and Baldwin (1988) used an empirical regression equation to relate pH to Oa concentrations that were simulated by solving differential equations numerically. Here, we have presented a first attempt to formulate prediction equations entirely mechanistically according to the rate:state formalism. The approach can be easily incorporated into other models of ruminal digestion that also follow rate:state principles. The approach also allows for simulation of responses to concentrate meals unequally distributed in size and time throughout a day.

View larger version (12K): [in this window] [in a new window]   Figure 9. Observed (; from Istasse et al., 1986) and predicted (solid line) ruminal pH throughout a day in adult sheep given ad libitum access to hay and 1.02 kg/d concentrate in meals at 0900 and 2100 (top panel) or 1.09 kg/d in meals at 0300, 0900, 1500, and 2100 (bottom panel). The black horizontal bars indicate predicted forage intake > 0. Simulations were run with fFrDf = 0.582, fFrUf = 0.124, fFrNc = 0.161, fCnDf = 0.146, fCnUf = 0.027, fCnNc = 0.652, and all other parameter values as given in Table 1. See Tables 1 and 2 for abbreviations. The root mean square prediction errors were 4.0% (top panel) and 3.0% (bottom panel) of the mean observed pH.

Simulation of the so-called substitution effect of concentrate supplementation on forage intake (Figure 7) was a consequence of slower ARC decline at decreased ruminal pH (Figure 6). Freer et al. (1997) predicted substitution by simulating a selective intake behavior, in which grazing sheep consume the feed or herbage components of highest digestibility first, followed by less and less digestible components until MRC or an ME requirement is reached. Using the feedback from low ruminal pH resulted in predicted forage intakes that were within 10% of values observed by Milne et al. (1981) and the magnitude of depression at 0.96 kg/d concentrate was 0.58 kg/d compared with 0.56 kg/d observed (Figure 10). Simulation of results from a single experiment does not constitute a test of intake prediction accuracy of the model. An intake accuracy test would require a larger set of data from several different experiments. The response analysis in Figure 10 merely indicates that the model responds appropriately to the perturbation of concentrate supply and can therefore be used to predict responses in novel situations. Of course, such predictions may not be correct.

View larger version (10K): [in this window] [in a new window]   Figure 10. Observed (black bars; from Milne et al., 1981) and predicted (white bars) daily intakes of forage (DMIFr) in grazing, lactating ewes given 0, 0.48, or 0.96 kg concentrate once daily at 0900. Simulations were run with BW = 64 kg, fFrDf = 0.380, fFrUf = 0.068, fFrNc = 0.187, fCnDf = 0.141, fCnUf = 0.028, fCnNc = 0.551, and all other parameter values as given in Table 1. See Tables 1 and 2 for abbreviations.

View larger version (12K): [in this window] [in a new window]   Figure 11. Simulation of effect on total DMI of time of a single 2-kg concentrate meal (top panel) and effect of frequency of feeding the 2 kg concentrate (bottom panel) without () or with () infusion of 1.63 mol/d of buffer into the rumen. All other parameters and variables were as given in Tables 1 and 2.

	Implications

Top Abstract Introduction Experimental Procedures Results and Discussion Implications Literature Cited

	Footnotes

 
¹ Financial support was provided by the Gartshore Memorial Research Fund, the Ontario Ministry of Agriculture and Food, and NSERC Canada.

² Correspondence—phone: 519-824-4120, ext. 56222; fax: 519-836-9873; e-mail: jcant{at}uoguelph.ca).

Received for publication March 25, 2004. Accepted for publication January 28, 2005.

	Literature Cited

Top Abstract Introduction Experimental Procedures Results and Discussion Implications Literature Cited

 


AFRC. 1993. Energy and Protein Requirements of Ruminants. CAB Int., Wallingford, U.K.

Allen, M. S. 1997. Relationship between fermentation acid production in the rumen and the requirement for physically effective fiber. J. Dairy Sci. 80:1447–1462.[Abstract]

Argyle, J. L., and R. L. Baldwin. 1988. Modeling of rumen water kinetics and effects of rumen pH changes. J. Dairy Sci. 71:1178–1188.

Ash, R. W., and A. Dobson. 1963. The effect of absorption on the acidity of rumen contents. J. Physiol. 169:39–61.

Avondo, M., G. Licitra, M. Bognanno, A. N. Keshtkaran, D. Marletta, and G. D’Urso. 1995. Effects of the type and level of supplementation on grazing behaviour of lactating ewes in a Mediterranean natural pasture. Livest. Prod. Sci. 44:237–244.

Baile, C. A. 1975. Control of feed intake in ruminants. Pages 333–350 in Digestion and Metabolism in the Ruminant. I. W. McDonald and A. C .I. Warner, ed. Univ. of New England Publishing Unit, Armidale, Australia.

Bailey, C. B., and C. C. Balch. 1961. Saliva secretion and its relation to feeding in cattle. 2. The composition and rate of secretion of mixed saliva in the cow during rest. Br. J. Nutr. 15:383–402.[Medline]

Baldwin, R. L. 1995. Modeling Ruminant Digestion and Metabolism. Chapman and Hall, London, U.K.

Bergman, E. N., R. S. Reid, M. G. Murray, J. M. Brockway, and F. G. Whitelaw. 1965. Interconversions and production of volatile fatty acids in the sheep rumen. Biochem. J. 97:53–58.

Bermudez, F. F., J. M. Forbes, and R. Jones. 1989. Feed intake and meal patterns of sheep during pregnancy and lactation, and after weaning. Appetite 13:211–222.[Medline]

Bibby, J., and H. Toutenburg. 1977. Prediction and Improved Estimation in Linear Models. John Wiley & Sons, Chichester, U.K.

Bugaut, M. 1987. Occurrence, absorption and metabolism of short chain fatty acids in the digestive tract of mammals. Comp. Biochem. Physiol. 86B:439–472.

Carro, M. D., C. Valdés, M. J. Ranilla, and J. S. González. 2000. Effect of forage to concentrate ratio in the diet on ruminal fermentation and digesta flow kinetics in sheep offered food at a fixed and restricted level of intake. Anim. Sci 70:127–134.

Carter, R. R., O. B. Allen, and W. L. Grovum. 1990. The effect of feeding frequency and meal size on amounts of total and parotid saliva secreted by sheep. Br. J. Nutr. 63:305–318.[Medline]

Castro, T., T. Manso, A. R. Mantecón, and M. D. Carro. 2002. Effect of either once or twice daily concentrate supplementation of wheat straw on voluntary intake and digestion in sheep. Small Rumin. Res. 46:43–50.

Charmley, E., D. M. Veira, G. Butler, L. Aroeira, and H. C. V. Codagnone. 1991. The effect of frequency of feeding and supplementation with sucrose on ruminal fermentation of alfalfa silage given ad libitum or restricted to sheep. Can. J. Anim. Sci. 71:725–737.

Chestnutt, D. M. B., and A. R. G. Wylie. 1995. The effects of frequency of feeding of supplementary concentrates on performance and metabolite and IGF-1 status of ewes given silage in late pregnancy. Anim. Sci. 61:269–276.

Chilibroste, P., C. Aguilar, and F. García. 1997. Nutritional evaluation of diets. Simulation model of digestion and passage of nutrients through the rumen-reticulum. Anim. Feed Sci. Technol. 68:259–275.

Chilibroste, P., J. Dijkstra, and S. Tamminga. 2001. Design and evaluation of a non-steady state rumen model. Neth. J. Agric. Sci. 49:297–312.

Chiofalo, V., J. P. Dulphy, and R. Baumont. 1992. Influence of the method of forage conservation on feeding behaviour, intake and characteristics of reticulo-rumen content, in sheep fed ad libitum. Reprod. Nutr. Dev. 32:377–392.

Dijkstra, J., H. Boer, J. Van Bruchem, M. Bruining, and S. Tamminga. 1993. Absorption of volatile fatty acids from the rumen of lactating dairy cows as influenced by volatile fatty acid concentration, pH and rumen liquid volume. Br. J. Nutr. 69:385–396.[Medline]

Dijkstra, J., J. France, H. D. St. C. Neal, A. G. Assis, L. J. M. Aroeira, and O. F. Campos. 1996. Simulation of digestion in cattle fed sugarcane: model development. J. Agric. Sci. (Camb.) 127:231–246

Faichney, G. J., C. Poncet, B. Lassalas, J. P. Jouany, L. Millet, J. Doré, and A. G. Brownlee. 1997. Effect of concentrates in a hay diet on the contribution of anaerobic fungi, protozoa and bacteria to nitrogen in rumen and duodenal digesta in sheep. Anim. Feed Sci. Technol. 64:193–213.

Forbes, J. M. 1993. Integrative theories of food intake control. Pages 130–154 in Quantitative Aspects of Ruminant Digestion and Metabolism. J. M. Forbes and J. France, ed. CAB Int., Wallingford, U.K.

Freer, M., A. D. Moore, and J. R. Donnelly. 1997. GRAZPLAN: Decision support systems for Australian grazing enterprises—II. The animal biology model for feed intake, production and reproduction and the GrazFeed DSS. Agric. Syst. 54:77–126.

Gunter, S. A., M. B. Judkins, L. J. Krysl, J. T. Broesder, R. K. Barton, B. R. Rueda, D. M. Hallford, and D. W. Holcombe. 1990. Digesta kinetics, ruminal fermentation characteristics and serum metabolites of pregnant and lactating ewes fed chopped alfalfa hay. J. Anim. Sci. 68:3821–3831.[Abstract]

Hadjipanayiotou, M., and A. Photiou. 1995. The effect of level of inclusion and formaldehyde treatment of soybean meal on the performance of lactating Chios ewes in negative energy balance. Livest. Prod. Sci. 41:207–215.

Illius, A. W., and I. J. Gordon. 1990. Prediction of intake and digestion in ruminants by a model of rumen kinetics integrating animal size and plant characteristics. J. Agric. Sci. (Camb.) 116:145–157.

Istasse, L., R. I. Smart and E. R. Ørskov. 1986. Comparison between two methods of feeding concentrate to sheep given a diet high or low in concentrate with or without buffering substances. Anim. Feed Sci. Technol. 16:37–49.

Ivan, M., S. Mahadevan, and M. de S. Dayrell. 1996. Duodenal flow of microbial and feed nitrogen in sheep fed normal soybean meal or soybean meal treated with modified zein. J. Dairy Sci. 79:121–126.[Abstract]

Judkins, M. B., and R. H. Stobart. 1988. Influence of two levels of enzyme preparation on ruminal fermentation, particle and fluid passage and cell wall digestion in wether lambs consuming either a 10% or 25% grain diet. J. Anim. Sci. 66:1010–1015.

Keunen, J. E., J. C. Plaizier, L. Kyriazakis, T. F. Duffield, T. M. Widowski, M. I. Lindinger, and B. W. McBride. 2002. Effects of a subacute ruminal acidosis model on the diet selection of dairy cows. J. Dairy Sci. 85:3304–3313.[Abstract/Free Full Text]

Kohn, R. A., and T. F. Dunlap. 1998. Calculation of the buffering capacity of bicarbonate in the rumen and in vitro. J. Anim. Sci. 76:1702–1709.[Abstract/Free Full Text]

Kramer, T., T. Michelberger, H. Gürtler and G. Gäbel. 1996. Absorption of short-chain fatty acids across ruminal epithelium of sheep. J. Comp. Physiol. 166:262–269.

Leng, R. A., and G. J. Leonard. 1965. Measurement of the rates of production of acetic, propionic and butyric acids in the rumen of sheep. Br. J. Nutr. 19:469–484.[Medline]

López, S., J. France, M. S. Dhanoa, F. Mould, and J. Dijkstra. 1999. Comparison of mathematical models to describe disappearance curves obtained using the polyester bag technique for incubating feeds in the rumen. J. Anim. Sci. 77:1875–1888.[Abstract/Free Full Text]

López, S., F. D. D. Hovell, J. Dijkstra, and J. France. 2003. Effects of volatile fatty acid supply on their absorption and on water kinetics in the rumen of sheep sustained by intragastric infusions. J. Anim. Sci. 81:2609–2616.[Abstract/Free Full Text]

Martin, C., N. B. Kristensen, and P. Huhtanen. 2001. Comparison of non-tracer and tracer methods for determination of volatile fatty acid production rate in the rumen of sheep fed on two levels of intake. Br. J. Nutr. 86:331–340.[Medline]

McDougall, E. I. 1948. Studies on ruminant saliva. 1. The composition and output of sheep’s saliva. Biochem. J. 43:99–109.

Mees, D. C., and N. R. Merchen. 1985. Effects of sodium bicarbonate additions to wheat straw based diets on rumen turnover rates and nutrient digestibility by sheep. Nutr. Rep. Int. 32:1067–1072.

Meot, F., A. Cirio, and R. Boivin. 1997. Parotid secretion daily patterns and measurement with ultrasonic flow probes in conscious sheep. Exp. Physiol. 82:905–923.[Abstract]

Mertens, D. R. 1987. Predicting intake and digestibility using mathematical models of ruminal function. J. Anim. Sci. 64:1548–1558.

Milne, J. A., T. J. Maxwell, and W. Souter. 1981. Effect of supplementary feeding and herbage mass on the intake and performance of grazing ewes in early lactation. Anim. Prod. 32:185–195.

Mould, F. L., and E. R. Ørskov. 1983. Manipulation of rumen fluid pH and its influence on cellulolysis in sacco, dry matter degradation and the rumen microflora of sheep offered either hay or concentrate. Anim. Feed Sci. Technol. 10:1–14.

Mould, F. L., E. R. Ørskov, and S. O. Mann. 1983. Associative effects of mixed feeds. 1. Effects of type and level of supplementation and the influence of the rumen fluid pH on cellulolysis in vivo and dry matter digestion of various roughages. Anim. Feed Sci. Technol. 10:15–30.

Mouriño, F., R. Akkarawongsa, and P. J. Weimer. 2001. Initial pH as a determinant of cellulose digestion rate by mixed ruminal microorganisms in vitro. J. Dairy Sci. 84:848–859.[Abstract]

Murphy, M. R., R. L. Baldwin, and L. J. Koong. 1982. Estimation of stoichiometric parameters for rumen fermentation of roughage and concentrate diets. J. Anim. Sci. 55:411–421.

NRC. 1985. Nutrient Requirements of Sheep. 6th ed. Natl. Acad. Press, Washington, DC.

NRC. 1996. Nutrient Requirements of Beef Cattle. 7th ed., Natl. Acad. Press, Washington, DC.

Offner, A., A. Bach, and D. Sauvant. 2003. Quantitative review of in situ starch degradation in the rumen. Anim. Feed Sci. Technol. 106:81–93.

Peart, J. N., R. A. Edwards, and E. Donaldson. 1975. The yield and composition of the milk of Finnish Landrace x Blackface ewes. II. Ewes and lambs grazed on pasture. J. Agric. Sci. (Camb.) 85:315–324.

Perez, J. F., J. Balcells, J. A. Guada, and C. Castrillo. 1996. Determination of rumen microbial-nitrogen production in sheep: A comparison of urinary purine excretion with methods using ¹⁵N and purine bases as markers of microbial-nitrogen entering the duodenum. Br. J. Nutr. 75:699–709.[Medline]

Pitt, R. E., and A. N. Pell. 1997. Modeling rumen pH fluctuations: Interactions between meal frequency and digestion rate. J. Dairy Sci. 80:2429–2441.[Abstract]

Pitt, R. E., J. S. Van Kessel, D. G. Fox, A. N. Pell, M. C. Barry, and P. J. Van Soest. 1996. Prediction of ruminal volatile fatty acids and pH within the net carbohydrate and protein system. J. Anim. Sci. 74:226–244.[Abstract]

Poncet, C., and D. Rémond. 2002. Rumen digestion and intestinal nutrient flows in sheep consuming pea seeds: The effect of extrusion or chestnut tannin addition. Anim. Res. 51:201–216.

Poppi, D. P., M. Gill, and J. France. 1994. Integration of theories of intake regulation in growing ruminants. J. Theor. Biol. 167:129–145.

Rogers, M., J. P. Jouay, P. Thivend, and J. P. Fontenot. 1997. The effects of short-term and long-term monensin supplementation, and its subsequent withdrawal on digestion in sheep. Anim. Feed Sci. Technol. 65:113–127.

Stokes, M. R. 1983. Effect of sodium bicarbonate on rumen turnover in frequently fed sheep. Can. J. Anim. Sci. 63:721–725.

Sutton, J. D., W. H. Broster, D. J. Napper, and J. W. Siviter. 1985. Feeding frequency for lactating cows: effects on digestion, milk production and energy utilization. Br. J. Nutr. 53:117–130.[Medline]

Theurer, C. B. 1986. Grain processing effects on starch utilization by ruminants. J. Anim. Sci. 63:1649–1662.

Thomson, B. C., G. J. Cruickshank, D. P. Poppi, and A. R. Sykes. 1985. Diurnal patterns of rumen fill in grazing sheep. Proc. N. Z. Soc. Anim. Prod. 45:117–120.

Ulyatt, M. J., G. C. Waghorn, A. John, C. S. W. Reid, and J. Monro. 1984. Effect of intake and feeding frequency on feeding behaviour and quantitative aspects of digestion in sheep fed chaffed lucerne hay. J. Agric. Sci. (Camb.) 102:645–657.

Varga, G. A., and W. H. Hoover. 1983. Rate and extent of neutral detergent fiber degradation of feedstuffs in situ. J. Dairy Sci. 66:2109–2115.[Abstract/Free Full Text]

Weiss, W. P., H. R. Conrad, and N. R. St. Pierre. 1992. A theoretically-based model for predicting total digestible nutrient values of forages and concentrates. Anim. Feed Sci. Technol. 39:95–110.

Weston, R. H. 1988a. Factors limiting the intake of feed by sheep. X. The effects of concentrate supplements on the voluntary consumption and digestion of a medium quality roughage. Aust. J. Agric. Res. 39:255–271.

Weston, R. H. 1988b. Factors limiting the intake of feed by sheep. XI. The effect of pregnancy and early lactation on the digestion of a medium-quality roughage. Aust. J. Agric. Res. 39:659–669.

Zervas, G., L. Zarkadas, C. Koutsotolis, C. Goulas and A. Mantzios. 1999. The effect of altering the hay to concentrate ratio and concentrate composition on the rumen fermentation of dry sheep and milk production of lactating dairy ewes. Anim. Sci. 69:637–645.

This Article Abstract Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Similar articles in this journal Similar articles in PubMed Alert me to new issues of the journal Download to citation manager Citing Articles Citing Articles via Google Scholar Google Scholar Articles by Imamidoost, R. Articles by Cant, J. P. Search for Related Content PubMed PubMed Citation Articles by Imamidoost, R. Articles by Cant, J. P.