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E. Kebreab, J. Dijkstra, A. Bannink and J. France
Recent advances in modeling nutrient utilization in ruminants
doi: 10.2527/jas.2008-1313 originally published online Sep 26, 2008;
2009.87:E111-E122. J Anim Sci
http://jas.fass.org/cgi/content/full/87/14_suppl/E111
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ABSTRACT: Mathematical modeling techniques
have been applied to study various aspects of the rumi-
nant, such as rumen function, postabsorptive metabo-
lism, and product composition. This review focuses on
advances made in modeling rumen fermentation and its
associated rumen disorders, and energy and nutrient
utilization and excretion with respect to environmental
issues. Accurate prediction of fermentation stoichiom-
etry has an impact on estimating the type of energy-
yielding substrate available to the animal, and the ratio
of lipogenic to glucogenic VFA is an important determi-
nant of methanogenesis. Recent advances in modeling
VFA stoichiometry offer ways for dietary manipulation
to shift the fermentation in favor of glucogenic VFA.
Increasing energy to the animal by supplementing
with starch can lead to health problems such as sub-
acute rumen acidosis caused by rumen pH depression.
Mathematical models have been developed to describe
changes in rumen pH and rumen fermentation. Models
that relate rumen temperature to rumen pH have also
been developed and have the potential to aid in the
diagnosis of subacute rumen acidosis. The effect of pH
has been studied mechanistically, and in such models,
fractional passage rate has a large impact on substrate
degradation and microbial efficiency in the rumen and
should be an important theme in future studies. The
efficiency with which energy is utilized by ruminants
has been updated in recent studies. Mechanistic models
of N utilization indicate that reducing dietary protein
concentration, matching protein degradability to the
microbial requirement, and increasing the energy sta-
tus of the animal will reduce the output of N as waste.
Recent mechanistic P models calculate the P require-
ment by taking into account P recycled through saliva
and endogenous losses. Mechanistic P models suggest
reducing current P amounts for lactating dairy cattle
to at least 0.35% P in the diet, with a potential reduc-
tion of up to 1.3 kt/yr. A model that integrates nutri-
ent utilization and health has great potential benefit
for ruminant nutrition research. Finally, whole-animal
or farm level models are discussed. An example that
used a multiple-criteria decision-making framework is
reviewed, and the approach is considered to be appro-
priate in dealing with the multidimensional nature of
agricultural systems and can be applied to assist the
decision process in cattle operations.
Key words: modeling, nutrient utilization, ruminant
©2009 American Society of Animal Science. All rights reserved. J. Anim. Sci. 2009. 87(E. Suppl.):E111–E122
doi:10.2527/jas.2008-1313
INTRODUCTION
Ruminants account for almost all of the milk and
one-third of the meat production worldwide (FAO,
2007). The widespread application of advanced breed-
ing and feeding technologies had a major effect on the
improved production of ruminants. Additionally, data
are being generated at a rapidly increasing rate because
of advances in technology, computing, and engineer-
ing. As qualitative knowledge increased, it became pos-
sible to develop quantitative approaches to further our
understanding of biological systems and to integrate
various aspects of nutrient utilization. Initially, this was
achieved by complex statistical analyses, but in recent
years, dynamic mathematical models have been used
not only to summarize existing data, but also to show
where gaps in knowledge exist and where further re-
Recent advances in modeling nutrient utilization in ruminants1
E. Kebreab,*2 J. Dijkstra,† A. Bannink,‡ and J. France§
*Department of Animal Science, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada;
†Wageningen Institute of Animal Sciences, Animal Nutrition Group, Wageningen University, Marijkeweg 40,
6709 PG Wageningen, the Netherlands; ‡Animal Sciences Group, Division Animal Production,
Wageningen University and Research Centre, PO Box 65, 8200 AB Lelystad, the Netherlands;
§Centre for Nutrition Modelling, Department of Animal and Poultry Science,
University of Guelph, Guelph, Ontario N1G 2W1, Canada
1
Supported in part by the Canada Research Chairs Program (Ot-
tawa, Ontario, Canada). Presented at the Early Career Achievement
Awards during the joint annual meeting of the American Society of
Animal Science and American Dairy Science Association in India-
napolis, IN, July 7 to 11, 2008.
2
Corresponding author: kebreabe@cc.umanitoba.ca
Received July 21, 2008.
Accepted September 6, 2008.
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search should focus (Dijkstra et al., 2005a). A search
of all manuscripts published in the Journal of Animal
Science with the key word of “modeling” revealed that
nearly 50% of the 616 papers were published after the
year 2000. No modeling manuscripts were found before
1970, and the proportion of total modeling papers to
date increased from 3.2% in the 1970s to 17.0% in the
1980s and to 31.5% in the 1990s.
Various modeling approaches have been applied to
study nutrient utilization in ruminants. These range
from statistics, and in particular, meta-analysis, to op-
erational research for the study of complex decision-
making problems concerned with the best utilization
of limited resources, and to applied mathematics us-
ing theories of mass conservation and thermodynamics
(France and Kebreab, 2008). The primary objective of
this review is to summarize advances made through
mathematical methods in understanding the underly-
ing concepts of ruminant nutrient utilization at various
levels of organization. Advances in rumen fermentation,
including rumen health issues, and in energy and nutri-
ent utilization and excretion in ruminants using studies
that have utilized empirical and mechanistic approach-
es are discussed.
RUMEN FERMENTATION
Fermentation of Substrates for Energy
Carbohydrate and protein digestion in the rumen,
and starch and fat digestion in the intestine deliver most
of the energy used by the ruminant. Dietary carbohy-
drates, such as cellulose, hemicelluloses, pectin, starch,
and soluble sugars, are the main sources of energy and
are degraded in the rumen by microorganisms to hexo-
ses and pentoses before being fermented to VFA. In
ruminants, VFA can contribute up to 70% of the caloric
requirement (Bergman, 1990). Acetate, propionate, and
butyrate account for more than 95% of VFA produced,
and the molar proportions of these VFA have implica-
tions for energy utilization. Therefore, the fermentation
stoichiometry of distinct substrates must be known.
Murphy et al. (1982) made an important attempt to
derive the coefficients that describe this stoichiometry
by using a modeling approach. These coefficient values
were considered generally applicable (Baldwin, 1995)
and have been used in several mechanistic rumen mod-
els (Baldwin et al., 1987; Dijkstra et al., 1992). Howev-
er, it has been shown that the prediction of VFA molar
proportions in rumen fluid of high-yielding dairy cows
by these models is inaccurate (Bannink et al., 1997c).
Subsequent simulation studies (Bannink et al., 1997b)
demonstrated that this inaccuracy is most likely caused
by an inadequate representation of the stoichiometry
of VFA production or the rate of VFA absorption. In
an attempt to improve predictability, Bannink et al.
(2006) used meta-analysis of data from lactating cows
only to determine coefficient values that define the con-
version of a specific substrate to a specific VFA. Such
statistical models consider the fermentation pattern as
affected by the composition of the microbial popula-
tion, which is largely determined by the basal diet and
by the rate of depolymerization of available substrate
indirectly. Bannink (2008b) has shown that rumen pH
has an effect on the VFA profile produced from rapidly
fermentable carbohydrates (Figure 1). Alternative rep-
resentations to predict VFA in the rumen have been
discussed recently by Dijkstra et al. (2008b). The au-
thors concluded that although inclusion by Bannink et
al. (2008b) of pH as an explanatory factor has improved
VFA prediction, further developments are still needed,
preferably based on mechanisms that also include the
protozoal contributions to VFA formation.
Methanogenesis
The ratio of lipogenic (mainly acetate and butyrate)
and glucogenic (mainly propionate) VFA is an im-
portant determinant of methanogenesis in the rumen
and hindgut. The largest biogenic source of methane
(CH4), a greenhouse gas that has up to 21 times more
global warming potential than carbon dioxide, is enteric
fermentation from ruminant animals (US EPA, 2006).
Methane production by ruminants not only is an envi-
ronmental concern, but also is a loss of productivity,
because CH4 represents a loss of carbon, and therefore
an unproductive use of dietary energy. Johnson and
Johnson (1995) estimated that 2 to 12% of GE intake
will be lost as CH4 energy. However, CH4 formation is
essential in the rumen ecosystem because it keeps the
hydrogen pressure low, favoring the growth and activity
of many microorganisms.
Measurement of CH4 production in animals requires
complex and often expensive equipment; therefore, pre-
Figure 1. Fitted effect of rumen pH on the fraction of individual
types of VFA (Ac = acetate; Pr = propionate; Bu = butyrate) pro-
duced from rapidly fermentable carbohydrates (Sc = soluble carbohy-
drates; St = starch). Adapted from Bannink et al. (2008b).
Kebreab et al.
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diction equations are widely used to estimate CH4 emis-
sions. Some models have been developed specifically to
predict CH4 emissions from animals (Blaxter and Clap-
perton, 1965; Moe and Tyrrell, 1979; Mills et al., 2003;
Ellis et al., 2007) and others have been either modified
or adapted to estimate CH4 emission from rumen fer-
mentation (Dijkstra et al., 1992; Baldwin, 1995). At
present, mathematical models are used to estimate CH4
emissions from enteric fermentation at a national and
global level (see review by Kebreab et al., 2006a). The
Intergovernmental Panel on Climate Change publishes
guidelines (IPCC, 2006) that are used for official esti-
mates of CH4 emissions. However, the accuracy of these
models has been challenged (Kebreab et al., 2006b).
Using the rumen model of Dijkstra et al. (1992), Mills
et al. (2001) added a mechanistic model of methanogen-
esis that also included CH4 emissions from the hindgut.
A comparison of models performed by Kebreab et al.
(2008a) showed that mechanistic models were better
than empirical ones in predicting CH4 emissions from
US cattle and were more suited to assessing the effec-
tiveness of mitigation options implemented at a farm
or national level. Bannink et al. (2005) developed an
adapted version of the model of Mills et al. (2001) and
evaluated the impact of rumen fermentation conditions
(i.e., pH) on type of VFA and amount of CH4 produced
in the rumen of lactating cows. This version of the
model has been used for estimating CH4 emissions from
dairy cows in the Dutch Inventory Report since the year
1990 (Van der Maas et al., 2008). Empirical models are
applicable only within the range in which they were
developed; therefore, further advances in modeling CH4
emissions will probably result from a deepening of the
mechanistic description of the underlying fermentation
biology in the gastrointestinal tract of ruminants. To
this end, Ellis et al. (2008) have reviewed and identified
key aspects of rumen microbiology that could be incor-
porated or that could improve representation within a
model of ruminant digestion and environmental emis-
sions. Descriptions of rumen pH dynamics (discussed
subsequently) and of protozoal dynamics are the main
key elements, but explicit representation of protozoa in
rumen models is scarce (Dijkstra, 1994).
Acid Load in the Rumen
Rumen models (and experiments) have shown that
feeding starch instead of structural carbohydrates fa-
vors the production of glucogenic VFA and reduces
CH4 emissions. However, overfeeding of starchy sub-
strates, such as corn or wheat grains, to meet increased
energy demands (e.g., during early lactation) may lead
to a digestive disorder that affects health and produc-
tivity, commonly known as subacute ruminal acidosis
(SARA). Various authors (e.g., Garrett et al., 1999)
have described SARA as the accumulation of organic
acids within the rumen, causing depressed ruminal pH
below a critical range (i.e., pH 5.0 to 5.8) for several
hours.
Empirical Modeling of Rumen Acid Load.
AlZahal et al. (2007) used meta-analysis to evaluate
various equations to describe pH curves collected from
different experiments that used continuous rumen pH
measurement. The authors reported that the logistic
equation (Eq. 1) described curves constructed from pH
data:
y x yy
yyy
f
f
kx
() ,=
+-
()
é
ë
êù
û
ú
-
0
00
e
[1]
where y(x) is the time spent below cutoff point x (min/d);
x is pH −5; and y0, yf, and k (all >0) are parameters
that define the scale and shape of the curve. AlZahal
et al. (2007) suggested that the degree of decline in pH
can be described by a shift of the pH curve position to-
ward the decreased pH range, hence, by greater values
of the predicted time and area below most critical pH
cutoff points. The authors also suggested that the shift
can be identified by a decrease in the curve inflection
point (x*, y*) and curve slope, calculated as follows:
xk
yy
y
y y
f
f
*ln,
*.
=-
æ
è
ç
ç
ç
ç
ç
ö
ø
÷
÷
÷
÷
÷
÷
=
1
1
2
0
0
[2]
AlZahal et al. (2007) compared 3 concentrations of
nonfiber carbohydrate in the diet (low, <37%; moder-
ate, 37 to 39%; and high, ≥40% of DM). The authors
reported that the inflection points for moderate and
low nonfiber carbohydrate concentrations in the diet
were 16 and 27% greater, respectively, compared with
the diet with high concentrations of nonfiber carbo-
hydrate. The authors argue that the approach allows
comparison of pH data across studies and helps quanti-
fy dietary effects on rumen pH. Similarly, using a meta-
analysis, Zebeli et al. (2008) showed that an increase
in physically effective NDF (peNDF) up to 31.2% of
dairy cattle dietary DM increased rumen pH to a pla-
teau value of 6.27, after which no further increase in
pH was achieved. However, the concentration of peNDF
required to stabilize rumen pH and maintain milk fat
content without compromising milk energy efficiency
varied. The required peNDF increased quadratically
with increases in concentration of rumen degradable
starch from grains and with increases of DMI.
Subsequently, AlZahal et al. (2008) developed a
predictive equation that might aid in the diagnosis of
SARA by investigating the relationship between rumen
pH and rumen temperature. Rumen pH and tempera-
ture were linearly associated within the range of 39
to 41°C, but the authors expected it to be nonlinear
over extreme ranges of temperature and pH. The linear
equation developed was
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pH = 16.9 − 0.29 temperature,
r2 = 0.77, n = 22, P = 0.002. [3]
Although rumen temperature can predict minimum
rumen pH and has the potential to be developed into a
noninvasive diagnostic technique, its use in field situa-
tions depends on future development of a practical and
cost-effective intraruminal wireless telemetry tempera-
ture-sensing device compared with pH sensors.
Mechanistic Modeling of Rumen Acid Load.
Bannink (2007) and Bannink et al. (2008b) developed
a mechanistic model that represents the mechanisms
involved with the formation of VFA in the lumen of the
reticulorumen, absorption of VFA across the reticulo-
rumen wall, and the intraepithelial metabolism of VFA
by reticulorumen epithelia. The effects of pH on VFA
yields from some substrates, including starch, were in-
cluded in the model and were based on in vivo rumen
observations. The model assesses the effect of nutri-
tional strategies on VFA metabolism and acid load of
the rumen. Simulations showed that a reduction of pH
from 6.3 to 5.7 had moderate effects on the absorption
rates of VFA from the rumen and that the relative con-
tribution of facilitated transport of VFA was reduced
drastically with reduced pH. Bannink et al. (2008b)
considered the rumen wall to play a key regulatory role
by reacting to exposure of the rumen epithelia to acid
load. A dynamic model was constructed that combines
the representation of the absorption of VFA by the ru-
men wall and rumen wall adaptation to feeding strat-
egy. They hypothesized that epithelial adaptation is
evoked by the integration of the history of epithelia ex-
posure to rumen VFA load. This memory function and
the goal-directed adaptation of rumen epithelial tissue
were represented by a dynamic modeling approach and
a mechanism of negative feedback control. Simulations
showed that a doubling of VFA production rate from 65
to 130 mol of VFA/d within 11 d postpartum resulted
in 0 and 12% increases of rumen VFA concentrations
after 10 and 20 d postpartum, respectively, similar to
observed values. They concluded that the role of the
rumen wall in preventing rumen contents from becom-
ing too acidic during early lactation was more impor-
tant than rumen pH in affecting VFA clearance. With
respect to investigating the functionality of the rumen
wall, Bannink et al. (2008a) recommended the use of
genomics techniques in collecting more specific infor-
mation on the genetic control and limits of the molecu-
lar mechanisms involved with epithelial adaptation and
function. They argued that a systems biology approach
is needed to analyze the meaning of such data and to
identify the precise mechanisms involved with rumen
adaptation. Such an effort should include a representa-
tion of changes in the rumen wall in response to nutri-
tional strategies and the physiological state of the cow,
as well as a representation of the intraluminal fermen-
tation processes and conditions.
The pH of rumen fluid is an important indicator of
rumen fermentation conditions. Simulating the effects
of rumen pH on the diverse microbial groups present
in the rumen remains a challenge, but perhaps an even
greater task is to model adequately the diurnal fluctua-
tions in pH itself. This would require the representation
of all causal factors, which include all relevant buffer-
ing mechanisms such as VFA production with microbial
growth, VFA clearance with fluid outflow and absorp-
tion by the rumen wall (passive and facilitated trans-
port), and saliva production.
Rumen Feed Degradability
Feed evaluation systems and mechanistic rumen mod-
els rely on degradation and passage kinetics. Therefore,
accurate estimates of variables that drive degradation
and passage are required. Several in vitro and in situ
techniques have been developed to estimate the degrad-
ability of feedstuffs in the rumen and their digestion in
the whole gastrointestinal tract, including batch culture
digestibility with rumen microbial inocula or added en-
zymes and in situ methods. Regression equations are
applied to predict in vivo digestibility from these in
vitro or in situ methods (Dijkstra et al., 2005b). Fathi
Nasri et al. (2006) evaluated linear, negative exponen-
tial, and inverse polynomial models to describe DM and
CP degradation kinetics. The authors reported that al-
though there was no significant difference in predict-
ing the extent of degradation, the linear and negative
exponential models fit the data better when describing
degradation kinetics. Lopez et al. (1999) showed that
for analyzing in situ disappearance curves, sigmoidal-
type models provided useful alternatives to the most
commonly used negative exponential model. These sig-
moidal models have the advantage of being versatile
and able to cope with the changing shapes of disap-
pearance profiles. They also represent the biological
process in a more rational way than do nonsigmoidal
models. However, the predicted extent of degradation
was very similar among all models evaluated by Lopez
et al. (1999). Thus, in choice of the model, the ability to
obtain good estimates of degradation parameters and
the feasibility of each model of being incorporated into
the feeding system of choice are likely more important
than the accuracy of fitting.
More recently, rate of degradation of feeds has been
studied by using gas production profiles obtained from
manual or automated systems of in vitro fermentation
of feeds, and their application to ruminant feed eval-
uation systems has been discussed by Dijkstra et al.
(2005b). Dhanoa et al. (2004) proposed a combination
of statistical and mechanistic models to determine ru-
minal feed degradation based on a degradation profile
using feces as the inoculum. France et al. (2005) devel-
oped a 3-pool general compartmental model for inter-
preting gas production profiles. The equations in the
model permit the extent of ruminal degradation, and
Kebreab et al.
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the supply of microbial protein to the duodenum, to
be evaluated, thereby linking the gas production tech-
nique to animal production. Evaluation of the extent
of degradation and the microbial protein supply relies
on assumptions regarding fractional passage rate and
microbial efficiency per unit of fermented substrate.
These factors are unlikely to be constant, and calcula-
tions suffer from the same drawbacks as empirical sys-
tems. The equations are derived from first principles,
and the potentially degradable feed fraction, undegrad-
able feed fraction, and accumulated gases represent the
underlying pools. In most cases, the models derived
assume that substrate degradation follows first-order
kinetics, resulting in nonlinear functions representing
either diminishing returns (constant fractional degra-
dation rate) or sigmoidal (fractional degradation rate
that varies with time) behavior (France et al., 2005).
Lopez et al. (2007) derived an alternative approach as-
suming that degradation can follow zero-order kinetics,
and evaluated the resulting piecewise linear model with
other nonlinear models. Although the model showed
acceptable behavior, nonlinear models showed some su-
periority in terms of statistical goodness-of-fit, and the
authors questioned the validity of the assumption of
a constant degradation rate implied in the zero-order
kinetics model. Ellis et al. (2005) considered various
models for describing ruminal digestion of NDF based
on the gamma distribution. The 2-pool, age-dependent,
and gamma-distributed models were inferred to be su-
perior when quality data were available, and the gam-
ma-distributed age-constant model was superior when
data quality was limited. However, gamma-distributed
events can themselves be interpreted as simple com-
partmental schemes, as demonstrated by France et al.
(1985).
Much less recent attention has been given to modeling
passage kinetics, although issues still remain, such as the
nonavailability of models capable of resolving bimodal
fecal marker excretion patterns (S. Lopez, University of
Leon, Spain, personal communication). Experimental
data on ruminal retention times are relatively scarce,
yet accounting for retention time is a prerequisite for
many feed evaluation systems (e.g., AFRC, 1993; NRC,
2001; Thomas, 2004), and fractional passage rates are
also key parameters in mechanistic models of rumen
fermentation (e.g., Dijkstra et al., 1992). Moreover, the
fractional passage rate is a major determinant of mi-
crobial protein efficiency, as indicated by the classical
microbial growth equations derived by Pirt (1975) and
observed experimentally (e.g., Oba and Allen, 2003).
Fractional rate of growth of microbes is related to their
fractional passage rate. A greater fractional rate of
growth decreases the relative amount of substrate for
maintenance purposes and increases efficiency. Even
though the partitioning of energy into microbial growth
and nongrowth functions has been mathematically
well established, these are applied surprisingly little in
empirical protein evaluation systems. Often external
markers are used to estimate the passage dynamics of
feed particles. However, external markers may restrict
the digestibility of the particles they are linked to, they
may bind preferentially to small particles, and they
may migrate to rumen fluid. Internal markers based on
stable isotopes do not suffer from these disadvantages
(Dijkstra et al., 2007). Fecal excretion of both external
and internal markers can be described by using vari-
ous models. Of these, the multicompartmental model
of Dhanoa et al. (1985) has often been applied, and
the results of this model based on fecal excretion pat-
terns will yield estimates of the fractional passage rate
from the slowest and second-slowest compartments.
Fractional passage rates as applied in rumen models
are usually based on estimates from regression equa-
tions, in which DMI and proportion of concentrate or
roughage of the diet are independent variables. Recent-
ly, Seo et al. (2007) developed a mechanistic model to
describe the physiological aspects of liquid dynamics in
the rumen and to predict liquid flow out of the rumen
quantitatively. These authors assumed the liquid flow
through the reticuloomasal orifice to be coordinated
with the frequency, duration, and amplitude of reticu-
lar contractions during eating, ruminating, or resting.
Such a model helps to understand the factors that af-
fect the liquid outflow dynamics. Given the impact of
passage on ruminal degradation and microbial growth,
quantitative knowledge of rates of nutrient passage out
of the rumen should be an important theme in future
research.
ENERGY AND NUTRIENT UTILIZATION
AND EXCRETION
Energy Utilization
Determination of energy requirements in ruminants
and the efficiency with which energy is utilized have
traditionally been described by the NE and ME sys-
tems in North America and the United Kingdom, re-
spectively (AFRC, 1993; NRC 2000, 2001). The values
of the key parameters in the NE and ME systems were
determined largely by using linear regression methods
to analyze energy balance data from calorimetry ex-
periments. Kebreab et al. (2003) analyzed an exten-
sive data set by using a meta-analytical approach and
nonlinear regression modeling. Based on the best fit
models, the average efficiencies of utilization of ME in-
take for milk production, BW gain, efficiency of uti-
lization of tissue energy for milk production, and the
maintenance energy requirement were 0.55, 0.83, 0.66,
and 0.59 MJ/(kg0.75∙d) compared with 0.64, 0.75, 0.82,
and 0.51 MJ/(kg0.75∙d) in the NE system (NRC, 2001)
and 0.62, 0.60, 0.84, and 0.49 MJ/(kg0.75∙d) in the ME
system, assuming the diet contains an ME:GE value
of 0.6 (AFRC, 1993). The results of the analysis now
make up the core values for the Feed into Milk system
in the United Kingdom (Thomas, 2004). However, in
an independent evaluation of various energy evaluation
systems in grass-based diets fed to dairy cattle, the
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Feed into Milk system, like the Agricultural and Food
Research Council system, still predicted energy require-
ments for maintenance and milk production to be con-
sistently less than actual energy supply (Dijkstra et al.,
2008a). A mechanistic model based on those of Dijkstra
et al. (1992, 1996a,b) predicted glucogenic nutrients to
limit the performance of dairy cattle on grass-based di-
ets. The mechanistic model proved to be more accurate
and precise than the energy systems evaluated.
Current NE and ME systems do not consider the fact
that animals have a certain requirement for particular
nutrients per se, rather than just a requirement for their
energetic potential. If diets are balanced for the same
amount of ME or NE but the supply of glucogenic, ami-
nogenic, or lipogenic nutrients differs, the response of
the animal can vary. In a series of studies, Van Knegsel
et al. (2007a,c) evaluated the effect of isocaloric (NE
basis, Dutch VEM system) diets with different concen-
trations of glucogenic or ketogenic nutrients in early-
lactating dairy cattle (1 to 9 wk postpartum) by using
indirect calorimetry in climate-respiration chambers.
Cows fed the lipogenic diet had a greater milk fat pro-
duction, and thus partitioned more energy to milk, than
cows fed the glucogenic diet. Energy mobilized from
body fat tended to be greater in the lipogenic group.
In the glucogenic group, energy retention of body fat
was positive from wk 8 postpartum, whereas in the li-
pogenic group energy retention of body fat was still
negative at wk 9 postpartum. Cows fed the lipogenic
diet had greater plasma NEFA and decreased insulin
concentrations than cows fed the glucogenic diet. The
effects of isocaloric lipogenic or glucogenic diets on milk
yield, milk composition, and plasma concentrations
were confirmed in a large-scale trial (i.e., 114 cows; Van
Knegsel et al., 2007b). Thus, cows fed the glucogenic
diets evaluated have a reduced risk of metabolic disor-
ders compared with cows fed lipogenic diets, although
NE intake does not differ. Such results highlight vari-
ous weaknesses of the current feed evaluation systems.
Current energy and protein systems do not predict how
production level and product composition will change
in response to deliberate changes in feeding strategy.
The amount of aggregation of these systems hampers
the inclusion of new concepts and data that arise from
experiments conducted at the organ, tissue, or cellular
levels. To improve on current prediction schemes, new
feeding systems need to be based on mechanisms that
govern the response of animals to nutrients, by quan-
titatively describing metabolite supply in more detail
than the current aggregated components (Dijkstra et
al., 2007).
N Utilization and Excretion
Nutritionists aim to maximize protein output in ani-
mal products, such as milk and meat. The overall ef-
ficiency of utilization of dietary N varied from 13 to
31% in various experiments measured by Kebreab et al.
(2001b), but 40 to 45% efficiency values are theoretical-
ly possible (Hvelplund and Madsen, 1995). Increasing
the efficiency of use of protein N by ruminants, leading
to less N excretion, is becoming an environmental im-
perative in many countries (Castillo et al., 2001). There
have been several attempts to formulate mathematical
models to predict N utilization from cattle. The models
can be classified into 2 principal groups: empirical (sta-
tistical) models that relate protein intake to N output
directly and mechanistic models that attempt to simu-
late N utilization based on a mathematical description
of rumen and postrumen fermentation and digestion
biochemistry.
Castillo et al. (2000) collated data from the literature
and, through regression analysis, described the relation-
ships between N intake and output in feces, urine, and
milk. The authors reported that 72% of dietary N is ex-
creted in manure. Kebreab et al. (2001b) further stud-
ied the relationship between N intake and the form in
which N is excreted because urinary N has been shown
to be a much more important determinant of ammonia
and N2O emissions and of nitrate leaching than fecal N.
The authors reported a nonlinear correlation between
N intake and urinary N, and the model predicted that
approximately 80% of dietary N consumed above 500
g of N/d would be excreted in urine. The efficiency of
N utilization for milk protein synthesis decreased from
31.5% at 400 g of N/d to 26.1% at 550 g of N/d for a
600-kg lactating dairy cow.
Nitrogen utilization is affected by many factors, such
as dietary N concentration, degradability, microbial
community, and their interaction with other nutrients
(Firkins and Reynolds, 2005). Therefore, a mechanistic
approach is necessary to improve the prediction of N
utilization in cattle. Kebreab et al. (2002) developed
a dynamic, process-based model that can predict the
amount and form of N excreted by dairy cattle under
various nutritional strategies, and they fitted predic-
tions to observed values (Figure 2). The 4-pool model
took into account several variables that determine N
utilization, and they reported that urine N was sig-
nificantly affected by protein degradability and energy
status of the animal. The authors showed that increas-
ing the energy concentration from 8 to 11 MJ of fer-
mentable ME/kg of DM could potentially reduce urine
N excretion and, by extension, ammonia emissions by
up to 25%. Similarly, the authors argued that reducing
dietary protein concentration from 19% of DM to ap-
proximately 16% of DM could reduce ammonia emis-
sions by 20% and reducing the degradability of protein
to match the microbial requirement by 19%. Kebreab
et al. (2004) went further by incorporating an N utili-
zation module into the rumen model of Dijkstra et al.
(1992). The integrated model was able to take advan-
tage of detailed microbial representation in the rumen,
which improved the prediction of N utilization by a
lactating dairy cow. This representation allowed the as-
sessment of diet manipulation to improve N utilization
and, as a consequence, to reduce environmental pollu-
tion caused by ammonia emissions and excess N excre-
Kebreab et al.
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tion. Improvements in the area of N recycling, rumen
and postrumen absorption processes, and AA-based
N transformations with intermediary metabolism and
productive functions of the animal would further ad-
vance the understanding and prediction of N utilization
in ruminants.
P Utilization and Excretion
Phosphorus is an essential nutrient that has received
attention for environmental reasons, such as depletion
of finite inorganic P sources (e.g., dicalcium phosphate)
and pollution of ponds and streams causing eutrophica-
tion. Therefore, optimizing P intake and understanding
the factors affecting P utilization have environmental
and economic benefits.
Quantitative aspects of P utilization in ruminants
have been reviewed by Kebreab and Vitti (2005) and
Kebreab et al. (2008c). Empirical and mechanistic ap-
proaches have been used to model P utilization in rumi-
nants. Kebreab et al. (2005) reported a positive linear
relationship between P intake and excretion in feces.
However, the slope of the linear relationship was a func-
tion of the energy status of the animal. Tracer-based
mechanistic modeling, also referred to as kinetic model-
ing, has been an important method of understanding P
metabolism in ruminants because a significant amount
of P recycling (especially through saliva) occurs, which
makes it difficult to determine P excretion from di-
etary sources without P labeling. Vitti et al. (2000)
identified 4 pools that regulate P homeostasis in rumi-
nants, and they numerically solved equations based on
experimental data obtained using radiolabeled isotope
tracer techniques. At low P intakes, bone and tissue
mobilization represented a vital process to maintain P
concentrations in blood. The model was also used to
identify the minimum endogenous loss of P from the
animal and the amount of P needed to be supplied to
meet the requirement. Dias et al. (2006) revised the
model of Vitti et al. (2000) and extended its use to
study Ca flows in growing sheep. Investigations based
on the model showed that Ca and P metabolism are
closely related and imbalance of the minerals results
in impaired P utilization (Dias et al., 2008). The au-
thors argued that the model developed for small ru-
minants could be extended to cattle because it would
be costly to conduct tracer-based experiments in large
ruminants. The derivation of values for maintenance P
requirement and minimum endogenous P losses when
using empirical models is possible only by extrapolating
linear relationships, which are subject to error because
of the lack of accountability for differences in the effi-
Figure 2. The relationship between N intake and output in feces (○), milk (▵), and urine (□), and total N in feces plus urine (◊). Symbols
represent observed values, and solid lines are model predictions. Adapted from Kebreab et al. (2002).
Modeling nutrient utilization E117
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ciency of utilization of P fed at low concentrations and
the availability of other nutrients and energy.
Mechanistic models of P utilization have been either
developed as a stand-alone (Hill et al., 2008) or in-
corporated into a larger model (Kebreab et al., 2004).
The latter researchers developed a model containing
10 state variables representing P pools in the rumen,
small intestine, large intestine, blood, and saliva, and
incorporated it into the rumen model of Dijkstra et
al. (1992). Comparison of model predictions with mea-
sured values showed that mean fecal P excretion was
within 8.7% of the observed mean. Inclusion of Ca me-
tabolism and its interaction with P might increase the
accuracy of prediction. Kebreab et al. (2008b) used the
integrated model to assess the environmental and eco-
nomic implications of reducing P pollution from dairy
cows in Canada. Using the mechanistic model, the au-
thors showed that producers could save up to CAN
$20/cow per year by feeding 0.35% P, which, in many
cases, means not supplementing the diet with inorganic
P sources.
In constructing a dynamic, mechanistic model of
P digestion and metabolism, Hill et al. (2008) took a
slightly different approach to the model of Kebreab
et al. (2004) because of different objectives. Hill et al.
(2008) designed a model to investigate the composition
of P in excreta, in particular the amounts of organic,
inorganic, and phytate P. The model contained 5 state
variables and 4 compartments, and a comparison of
predicted against measured values showed that model
prediction errors were within 20% of observed values.
The authors indicated the need for additional data to
derive parameters associated with the regulation of P
absorption and bone P turnover because absorption ap-
peared to be an important site of regulation. Repre-
sentation of active and passive P transport across the
intestinal wall would also advance understanding and
prediction of P utilization.
Nutrient Utilization at the Animal
and Whole-Farm Levels
Thornley and France (2007) described different levels
of organization in representing biological systems. Ad-
vances in whole-animal or farm level modeling include
addition of methanogenesis, N, and P transactions into
the mechanistic model of rumen function by Dijkstra et
al. (1992), which has been described earlier (Kebreab
et al., 2004). Usually, models of fermentation and diges-
tion assume a constant feed intake. However, cows do
not eat continuously but in discrete bouts, both dur-
ing grazing (e.g., Taweel et al., 2004) and in stable-fed
situations (e.g., Abrahamse et al., 2008). This intake
behavior may have pronounced effects on the fermen-
tation of substrates in the rumen. Among the major
effects of a meal is the instantaneous decline in ru-
men pH, in particular if the diet is rich in rapidly fer-
mentable carbohydrates. Baldwin (1995) integrated the
physical concept of particle dynamics with the chemical
transactions in his rumen model. He assumed that large
particles are not subject to degradation or passage and
are subject only to comminution. Thus, this represen-
tation will greatly affect the diurnal pattern of rumen
pool sizes and flows to the duodenum, but its effect on
the simulated average extent of degradation compared
with continuous feed intake is likely to be small (Ban-
nink et al., 1997a). Collao-Saenz et al. (2005) adopted
this representation as developed by Baldwin (1995) but
included a representation of increased microbial death
rate when substrate availability was decreased several
hours after feeding. Moreover, rumen volume was as-
sumed to be related to size of the meals and DM con-
tent. Chilibroste et al. (2008) included a representation
of effect of chewing efficiency on the release rate of
intracellular constituents in their rumen model. This
release rate appears to be an important determinant of
instantaneous substrate availability to rumen microor-
ganisms, and therefore also determines the rumen pH
and VFA diurnal patterns. However, quantitative data
on release rates are scarce. Moreover, insufficient quan-
titative information on variation in fractional passage
rates in meal-fed animals hampers further development
of these models.
Nutrient digestion and utilization models for tropi-
cal cattle have been developed and adapted for region-
specific nutrient availability. Dijkstra et al. (1996a,b)
constructed a model to predict nutrient supply to the
animal from predefined dietary inputs, as a means of
indicating pre-experimentally which combination of lo-
cally available ingredients was most likely to enhance
animal performance. The mechanistic model comprised
11 state variables representing N-containing, carbohy-
drate, fatty acid, and microbial fractions, and 4 zero
pools representing the nutrients available for absorp-
tion. The model was optimized for cattle fed sugarcane-
based diets, and Kebreab et al. (2001a) compared mod-
el simulations with data observed in feeding trials. The
authors were satisfied that the model predictions were
close to observed values and, based on simulations, rec-
ommended supplementing the basal diet with Leucaena
and rice bran to increase milk production. Subsequent-
ly, Chilibroste et al. (2001) and Rodrigues et al. (2002)
adapted the model to evaluate supplements to enhance
the nutrient supply and milk production of cattle fed
diets based on ryegrass and elephant grass, respectively.
Behera et al. (2005) also used the model to simulate
milk production by dairy cows fed sugarcane top-based
diets and other local supplements in India. Assis et al.
(2008) reviewed advances in modeling sugarcane utili-
zation by dairy cows in the tropics, describing the ad-
dition of a submodel to represent endogenous protein N
and large intestine digestion, discontinuous feed intake,
and extension to other forage diets.
Various linear programming (LP) approaches were
used to develop a whole-farm level model to optimize
resource utilization in small-scale dairy operations in
several stages. First, Val-Arreola et al. (2004c) used LP
and partial budgeting methods to optimize land use
Kebreab et al.
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for forage production and nutrient availability, and to
evaluate the economic impact of such changes in small-
scale dairy systems. The model provided a solution for
a better nutrient supply and for maintaining a greater
stocking rate than the traditional strategy, and includ-
ed utilizing a combination of forages such as alfalfa hay,
corn silage, fresh ryegrass, and oat hay. Second, LP and
Markov chain components were built to study the effect
of calving interval on calving pattern and herd structure
(Val-Arreola et al., 2004b). The Markov chain model
suggested adopting different reproduction strategies
according to period of the year in which the cow was
expected to calve. Third, they conducted an analysis of
feeding strategies for small-scale dairy systems by using
LP (Val-Arreola et al., 2005). The study recommended
an improvement in forage quality to increase efficiency,
rather than increasing concentrate supplementation, as
a viable strategy.
As part of optimizing nutrient utilization in the cow,
Val-Arreola et al. (2004a) also considered 5 equations
to describe the lactation curve. The authors used an
extensive data set that was divided into small-scale and
intensive systems and first, second, and third or greater
parity to fit the equations. The equations described by
Dijkstra et al. (1997; Eq. 4) consistently gave better
predictions and because of its more mechanistic nature,
the parameters lend themselves to physiological inter-
pretations. Therefore, differences between systems and
parity could be explained by variations in theoretical
initial milk production at parturition (a), specific rates
of secretory cell proliferation (b) and death (d), and
specific rate of decay (c):
Ya bcdt
ct
=--
-
exp[ ()/],1e
[4]
where Y is milk yield (kg/d) and t is time of lactation
(d).
Finally, a multiple-criteria decision-making frame-
work was considered to be appropriate in dealing with
the multidimensional nature of agricultural systems
and was applied to assist the decision process in small-
scale dairy farms (Val-Arreola et al., 2006). Goal pro-
gramming and compromise programming were used to
examine whether a single optimal solution or a set of
nearly optimal solutions could better achieve the ob-
jectives. Both models provided information concerning
how a forage shortage might be alleviated by modi-
fying the calving period to match nutrient availabil-
ity with requirements at each lactation stage, with a
minimum reduction in milk production. The use of a
multiple-criteria decision-making framework and dy-
namic programming techniques does allow more realis-
tic representations than ordinary LP and offers better
prediction in simulating whole-farm model interactions.
Recommendations of management options or an evalu-
ation of nutritional strategies under specific farming
conditions requires realistic coefficients that are derived
in an integrated manner.
SUMMARY AND CONCLUSIONS
In conclusion, empirical and mechanistic models
have important applications in understanding rumen
fermentation, and energy and nutrient utilization and
excretion. In describing the relationships between nu-
trient intake and excretion, empirical models can be
useful, particularly if input data are limited. However,
as Dijkstra et al. (2007) pointed out, empirical models
lack the biological basis necessary to evaluate mitiga-
tion strategies to reduce the excretion of waste, in-
cluding N, P, and CH4, in an integrated manner. Such
models may have little predictive value when compar-
ing various feeding strategies. Examples include the
Intergovernmental Panel on Climate Change (IPCC,
2006) Tier II models to quantify CH4 emissions and
the current protein evaluation systems to evaluate low-
protein diets to reduce N losses to the environment.
Nutrient-based mechanistic models can address such
issues (e.g., the Tier III model used by Van der Maas
et al., 2008). These models still need to be extended to
include prediction of rumen health issues such as SARA
and to predict and understand the effects of nutritional
strategy on pH and, subsequently, on rumen function.
Finally, as advances in mathematical and computing
techniques offer powerful data-processing capabilities,
construction of mechanistic models to understand and
predict biological phenomena at the organ, animal, and
farm levels should be actively encouraged.
LITERATURE CITED
Abrahamse, P. A., B. Vlaeminck, S. Tamminga, and J. Dijkstra.
2008. The effect of silage and concentrate type on intake behav-
ior, rumen function and milk production in dairy cows in early
and late lactation. J. Dairy Sci. 91:4778–4792.
Agricultural and Food Research Council (AFRC). 1993. Energy and
Protein Requirements of Ruminants. CAB International, Wall-
ingford, United Kingdom.
AlZahal, O., E. Kebreab, J. France, M. Froetschel, and B. W.
McBride. 2008. Ruminal temperature may aid in the detection
of subacute ruminal acidosis. J. Dairy Sci. 91:202–207.
AlZahal, O., E. Kebreab, J. France, and B. W. McBride. 2007. A
mathematical approach to predict biological values from rumen
pH measurements. J. Dairy Sci. 90:3777–3785.
Assis, A. G., O. F. Campos, J. Dijkstra, E. Kebreab, and J. France.
2008. Modelling sugarcane utilization by dairy cows in the
tropics. Pages 526–543 in Mathematical Modelling in Animal
Nutrition. J. France and E. Kebreab, ed. CAB International,
Wallingford, UK.
Baldwin, R. L. 1995. Modeling Ruminant Digestion and Metabo-
lism. Chapman and Hall, London, UK.
Baldwin, R. L., J. H. M. Thornley, and D. E. Beever. 1987. Me-
tabolism of the lactating dairy cow. II. Digestive elements of a
mechanistic model. J. Dairy Res. 54:107–131.
Bannink, A. 2007. Modelling volatile fatty acid dynamics and ru-
men function in lactating cows. PhD Diss. Wageningen Univ.,
Wageningen, the Netherlands.
Bannink, A., H. De Visser, J. Dijkstra, and J. France. 1997a. Impact
of diet-specific input parameters on simulated rumen function.
J. Theor. Biol. 184:371–384.
Bannink, A., H. De Visser, A. Klop, J. Dijkstra, and J. France.
1997b. Causes of inaccurate prediction of volatile fatty acids
Modeling nutrient utilization E119
by Ermias Kebreab on April 4, 2009. jas.fass.orgDownloaded from
by simulation models of rumen function in lactating cows. J.
Theor. Biol. 189:353–366.
Bannink, A., H. De Visser, and A. M. Van Vuuren. 1997c. Compari-
son and evaluation of mechanistic rumen models. Br. J. Nutr.
78:563–581.
Bannink, A., J. Dijkstra, J. A. N. Mills, E. Kebreab, and J. France.
2005. Nutritional strategies to reduce enteric methane forma-
tion in dairy cows. Pages 367–376 in Emissions from European
Agriculture. T. Kuczynski, U. Dämmgen, J. Webb, and A. My-
czko, ed. Wageningen Academic Publishers, Wageningen, the
Netherlands.
Bannink, A., J. France, E. Kebreab, and J. Dijkstra. 2008a. Model-
ling rumen wall functionality and potential for a systems biol-
ogy approach. Can. J. Anim. Sci. In press.
Bannink, A., J. France, S. Lopez, W. J. J. Gerrits, E. Kebreab, S.
Tamminga, and J. Dijkstra. 2008b. Modelling the implications
of feeding strategy on rumen fermentation and functioning of
the rumen wall. Anim. Feed Sci. Technol. 143:3–26.
Bannink, A., J. Kogut, J. Dijkstra, J. France, E. Kebreab, A. M.
Van Vuuren, and S. Tamminga. 2006. Estimation of the stoichi-
ometry of volatile fatty acid production in the rumen of lactat-
ing cows. J. Theor. Biol. 238:36–51.
Behera, U. K., E. Kebreab, J. Dijkstra, A. G. Assis, and J. France.
2005. Simulation of milk production in dairy cows fed sugar-
cane top based diets with locally available supplements under
Indian conditions. J. Agric. Sci. 143:217–229.
Bergman, E. N. 1990. Energy contributions of volatile fatty acids
from the gastrointestinal tract in various species. Physiol. Rev.
70:567–590.
Blaxter, K. L., and J. L. Clapperton. 1965. Prediction of the amount
of methane produced by ruminants. Br. J. Nutr. 19:511–522.
Castillo, A. R., E. Kebreab, D. E. Beever, J. H. Barbi, J. D. Sutton,
H. C. Kirby, and J. France. 2001. The effect of energy supple-
mentation on nitrogen utilization in lactating dairy cows fed
grass silage diets. J. Anim. Sci. 79:240–246.
Castillo, A. R., E. Kebreab, D. E. Beever, and J. France. 2000. A
review of efficiency of nitrogen utilisation in dairy cows and
its relationship with environmental pollution. J. Anim. Feed
Sci. 9:1–32.
Chilibroste, P., J. Dijkstra, P. H. Robinson, and S. Tamminga. 2008.
A simulation model “CTR Dairy” to predict the supply of nu-
trients in dairy cows managed under discontinuous feeding pat-
terns. Anim. Feed Sci. Technol. 143:148–173.
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.
Collao-Saenz, E. A., J. Dijkstra, P. C. Aguiar Paiva, A. Bannink, P.
B. Arcuri, J. C. Teixera, J. R. O. Perez, and F. M. David. 2005.
Simulation model for particle dynamics in rumen of cattle fed
sugarcane diet. Sci. Agric. 62:102–110.
Dhanoa, M. S., J. France, L. A. Crompton, R. M. Mauricio, E. Ke-
breab, J. A. N. Mills, R. Sanderson, J. Dijkstra, and S. Lopez.
2004. A proposed method to determine the extent of degrada-
tion of a feed in the rumen from the degradation profile ob-
tained with the in vitro gas production technique using feces as
the inoculum. J. Anim. Sci. 82:733–746.
Dhanoa, M. S., R. C. Siddons, J. France, and D. L. Gale. 1985. A
multi-compartmental model to describe marker excretion pat-
terns in ruminant faeces. Br. J. Nutr. 53:663–671.
Dias, R. S., E. Kebreab, D. M. S. S. Vitti, A. P. Roque, I. C. S.
Bueno, and J. France. 2006. A revised model for studying phos-
phorus and calcium kinetics in growing sheep. J. Anim. Sci.
84:2787–2794.
Dias, R. S., E. Kebreab, D. M. S. S. Vitti, A. P. Roque, and J.
France. 2008. Application and comparison of two models to
study the effects of calcium sources in sheep. Anim. Feed Sci.
Technol. 143:89–103.
Dijkstra, J. 1994. Simulation of the dynamics of protozoa in the ru-
men. Br. J. Nutr. 72:679–699.
Dijkstra, J., J. M. Forbes, and J. France. 2005a. Quantitative As-
pects of Ruminant Digestion and Metabolism. 2nd ed. CAB
International, Wallingford, UK.
Dijkstra, J., J. France, A. G. Assis, H. D. Neal, O. F. Campos, and L.
J. M. Aroeira. 1996a. Simulation of digestion in cattle fed sugar
cane: Prediction of nutrient supply for milk production with lo-
cally available supplements. J. Agric. Sci. 127:247–260.
Dijkstra, J., J. France, M. S. Dhanoa, J. A. Maas, M. D. Hanigan,
A. J. Rook, and D. E. Beever. 1997. A model to describe growth
patterns of the mammary gland during pregnancy and lacta-
tion. J. Dairy Sci. 80:2340–2354.
Dijkstra, J., J. France, H. D. St. C. Neal, A. G. Assis, L. J. M.
Aroeira, and O. F. Campos. 1996b. Simulation of digestion
in cattle fed sugarcane: Model development. J. Agric. Sci.
127:231–246.
Dijkstra, J., E. Kebreab, A. Bannink, L. A. Crompton, S. López,
P. A. Abrahamse, P. Chilibroste, J. A. N. Mills, and J. France.
2008a. Comparison of energy evaluation systems and a mecha-
nistic model for milk production by dairy cattle offered fresh
grass-based diets. Anim. Feed Sci. Technol. 143:203–219.
Dijkstra, J., E. Kebreab, A. Bannink, J. France, and S. López.
2005b. Application of the gas production technique in feed
evaluation systems for ruminants. Anim. Feed Sci. Technol.
123–124:561–578.
Dijkstra, J., E. Kebreab, J. France, and A. Bannink. 2008b. Model-
ling protozoal metabolism and volatile fatty acid production
in the rumen. Pages 170–188 in Mathematical Modelling in
Animal Nutrition. J. France and E. Kebreab, ed. CAB Interna-
tional, Wallingford, UK.
Dijkstra, J., E. Kebreab, J. A. N. Mills, W. F. Pellikaan, S. Lopez,
A. Bannink, and J. France. 2007. Predicting the profile of nutri-
ents available for absorption: From nutrient requirement to ani-
mal response and environmental impact. Animal 1:99–111.
Dijkstra, J., H. D. St. C. Neal, D. E. Beever, and J. France. 1992.
Simulation of nutrient digestion, absorption and outflow in the
rumen: Model description. J. Nutr. 122:2239–2256.
Ellis, J. L., J. Dijkstra, E. Kebreab, A. Bannink, N. E. Odongo, B.
W. McBride, and J. France. 2008. Aspects of rumen microbiol-
ogy central to mechanistic modelling of methane production in
cattle. J. Agric. Sci. 146:213–233.
Ellis, J. L., E. Kebreab, N. E. Odongo, B. W. McBride, E. K. Okine,
and J. France. 2007. Prediction of methane production from
dairy and beef cattle. J. Dairy Sci. 90:3456–3467.
Ellis, W. C., M. Mahlooji, and J. H. Matis. 2005. Models for esti-
mating parameters of neutral detergent fiber digestion by rumi-
nal microorganisms. J. Anim. Sci. 83:1591–1601.
Fathi Nasri, M. H., M. Danesh Mesgaran, J. France, J. P. Cant, and
E. Kebreab. 2006. Evaluation of models to describe ruminal
degradation kinetics from in situ ruminal incubation of whole
soybeans. J. Dairy Sci. 89:3087–3095.
Firkins, J. L., and C. K. Reynolds. 2005. Whole animal nitrogen
balance in cattle. Pages 167–185 in Nitrogen and Phosphorus
Nutrition of Cattle and Environment. E. Pfeffer and A. Hristov,
ed. CAB International, Cambridge, MA.
Food and Agriculture Organization of the United Nations (FAO).
2007. The State of Food and Agriculture. FAO, Rome, Italy.
France, J., and E. Kebreab. 2008. Mathematical Modelling in Ani-
mal Nutrition. CAB International, Wallingford, UK.
France, J., S. López, E. Kebreab, A. Bannink, M. S. Dhanoa, and J.
Dijkstra. 2005. A general compartmental model for interpret-
ing gas production profiles. Anim. Feed Sci. Technol. 123–
124:473–485.
France, J., J. H. M. Thornley, M. S. Dhanoa, and R. C. Siddons.
1985. On the mathematics of digesta flow kinetics. J. Theor.
Biol. 113:743–758.
Garrett, E. F., M. N. Pereira, K. V. Nordlund, L. E. Armentano, W.
J. Goodger, and G. R. Oetzel. 1999. Diagnostic methods for the
detection of subacute ruminal acidosis in dairy cows. J. Dairy
Sci. 82:1170–1178.
Kebreab et al.
E120
by Ermias Kebreab on April 4, 2009. jas.fass.orgDownloaded from
Hill, S. R., K. F. Knowlton, E. Kebreab, J. France, and M. D. Hani-
gan. 2008. A model of phosphorus digestion and metabolism in
the lactating dairy cow. J. Dairy Sci. 91:2021–2032.
Hvelplund, T., and J. Madsen. 1995. Protein utilization in rumi-
nants. Pages 83–89 in Proc. 7th Int. Symp. Protein Metabolism
and Nutrition. A. F. Nunes, A. V. Portugal, J. P. Costa, and
J. R. Ribeiro ed. Estacoa Zootechnia National Santerem, Valde
Santare, Portugal.
Intergovernmental Panel on Climate Change (IPCC). 2006. 2006
IPCC Guidelines for National Greenhouse Gas Inventories.
IGES, Hayama, Kanagawa, Japan. http://www.ipcc-nggip.iges.
or.jp. Accessed Jan. 20, 2008.
Johnson, K. A., and D. E. Johnson. 1995. Methane emissions from
cattle. J. Anim. Sci. 73:2483–2492.
Kebreab, E., A. G. Assis, J. Dijkstra, and J. France. 2001a. Evalu-
ating sugarcane diets for dairy cows using a digestion model.
Trop. Anim. Health Prod. 33:127–139.
Kebreab, E., K. Clarke, C. Wagner-Riddle, and J. France. 2006a.
Methane and nitrous oxide emissions from Canadian animal
agriculture—A review. Can. J. Anim. Sci. 86:135–158.
Kebreab, E., J. France, R. E. Agnew, T. Yan, M. S. Dhanoa, J.
Dijkstra, D. E. Beever, and C. K. Reynolds. 2003. Alternatives
to linear analysis of energy balance data from lactating dairy
cows. J. Dairy Sci. 86:2904–2913.
Kebreab, E., J. France, D. E. Beever, and A. R. Castillo. 2001b. Ni-
trogen pollution by dairy cows and its mitigation. Nutr. Cycl.
Agroecosyst. 60:275–285.
Kebreab, E., J. France, B. W. McBride, N. E. Odongo, A. Bannink,
J. A. N. Mills, and J. Dijkstra. 2006b. Evaluation of models to
predict methane emissions from enteric fermentation in North
American dairy cattle. Pages 299–313 in Nutrient Utilization in
Farm Animals: Modelling Approach. E. Kebreab, J. Dijkstra,
W. J. J. Gerrits, A. Bannink, and J. France, ed. CAB Interna-
tional, Wallingford, UK.
Kebreab, E., J. France, J. A. N. Mills, R. Allison, and J. Dijkstra.
2002. A dynamic model of N metabolism in the lactating dairy
cow and an assessment of impact of N excretion on the environ-
ment. J. Anim. Sci. 80:248–259.
Kebreab, E., J. France, J. D. Sutton, L. A. Crompton, and D. E.
Beever. 2005. Effect of energy and protein supplementation on
phosphorus utilization in lactating dairy cows. J. Anim. Feed
Sci. 14:63–77.
Kebreab, E., K. A. Johnson, S. L. Archibeque, D. Pape, and T.
Wirth. 2008a. Model for estimating enteric methane emissions
from US cattle. J. Anim. Sci. 86:2738–2748.
Kebreab, E., J. A. N. Mills, L. A. Crompton, A. Bannink, J. Di-
jkstra, W. J. J. Gerrits, and J. France. 2004. An integrated
mathematical model to evaluate nutrient partition in dairy
cattle between the animal and its environment. Anim. Feed
Sci. Technol. 112:131–154.
Kebreab, E., N. E. Odongo, B. W. McBride, M. D. Hanigan, and J.
France. 2008b. Phosphorus utilization and environmental and
economic implications of reducing phosphorus pollution from
Ontario dairy cows. J. Dairy Sci. 91:241–246.
Kebreab, E., and D. M. S. S. Vitti. 2005. Mineral metabolism. Pages
469–486 in Quantitative Aspects of Ruminant Digestion and
Metabolism. J. Dijkstra, J. M. Forbes, and J. France, ed. CAB
International, Wallingford, UK.
Kebreab, E., D. M. S. S. Vitti, N. E. Odongo, L. A. Crompton,
and J. France. 2008c. Modelling phosphorus metabolism. Pages
353–369 in Mathematical Modelling in Animal Nutrition. J.
France and E. Kebreab, ed. CAB International, Wallingford,
UK.
Lopez, S., M. S. Dhanoa, J. Dijkstra, A. Bannink, E. Kebreab, and
J. France. 2007. Some methodological and analytical consider-
ations regarding application of the gas production technique.
Anim. Feed Sci. Technol. 135:139–156.
Lopez, 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 incubat-
ing feeds in the rumen. J. Anim. Sci. 77:1875–1888.
Mills, J. A. N., J. Dijkstra, A. Bannink, S. B. Cammell, E. Ke-
breab, and J. France. 2001. A mechanistic model of whole-
tract digestion and methanogenesis in the lactating dairy cow:
Model development, evaluation, and application. J. Anim. Sci.
79:1584–1597.
Mills, J. A. N., E. Kebreab, C. Yates, L. A. Crompton, S. B. Cam-
mell, M. S. Dhanoa, R. E. Agnew, and J. France. 2003. Alter-
native approaches to predicting methane emissions from dairy
cows. J. Anim. Sci. 81:3141–3150.
Moe, P. W., and H. F. Tyrrell. 1979. Methane production in dairy
cows. J. Dairy Sci. 62:1583–1586.
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. 55:279–296.
NRC. 2000. Nutrient Requirements of Beef Cattle. 7th rev. ed. Up-
date 2000. Natl. Acad. Press., Washington, DC.
NRC. 2001. Nutrient Requirements of Dairy Cattle. 7th rev. ed.
Natl. Acad. Press., Washington, DC.
Oba, M., and M. S. Allen. 2003. Effect of diet fermentability on effi-
ciency of microbial nitrogen production in lactating dairy cows.
J. Dairy Sci. 86:195–207.
Pirt, S. J. 1975. Principles of Microbe and Cell Cultivation. Black-
well Scientific Publication, Oxford, UK.
Rodrigues, S. I. F. C, J. Dijkstra, A. G. Assis, J. France, and S.
Tamminga. 2002. Evaluation of supplements to enhance nutri-
ent supply and milk production of cattle fed diets based on
elephant grass (Pennisetum purpureum) using a mathematical
model. Livest. Prod. Sci. 77:273–286.
Seo, S., C. Lanzas, L. O. Tedeschi, and D. G. Fox. 2007. Develop-
ment of a mechanistic model to represent the dynamics of liquid
flow out of the rumen and to predict the rate of passage of
liquid in dairy cattle. J. Dairy Sci. 90:840–855.
Taweel, H. Z., B. M. Tas, J. Dijkstra, and S. Tamminga. 2004. Intake
regulation and grazing behavior of dairy cows under continuous
stocking. J. Dairy Sci. 87:3417–3427.
Thomas, C. 2004. Feed into Milk: A New Applied Feeding System for
Dairy Cows. Nottingham University Press, Nottingham, UK.
Thornley, J. H. M., and J. France. 2007. Mathematical Models in
Agriculture: A Quantitative Approach to Problems in Agricul-
ture and Related Sciences. 2nd ed. CAB International, Wall-
ingford, UK.
US Environmental Protection Agency (US EPA). 2006. Global An-
thropogenic Non-CO2 Greenhouse Gas Emissions: 1990–2020.
EPA Report 430-R-06-003, June 2006. http://www.epa.gov/
methane/pdfs/GreenhouseGasReport.pdf Accessed Jun. 3,
2008.
Val-Arreola, D., E. Kebreab, J. Dijkstra, and J. France. 2004a. Study
of the lactation curve in dairy cattle on farms in central Mexico.
J. Dairy Sci. 87:3789–3799.
Val-Arreola, D., E. Kebreab, and J. France. 2006. Modeling small-
scale dairy farms in central Mexico using multi criteria pro-
gramming. J. Dairy Sci. 89:1662–1672.
Val-Arreola, D., E. Kebreab, J. A. N. Mills, and J. France. 2004b.
Analysis of the calving pattern of herds in small-scale dairy
systems in central Mexico. J. Anim. Feed Sci. 13:557–574.
Val-Arreola, D., E. Kebreab, J. A. N. Mills, and J. France. 2005.
Analysis of feeding strategies for small-scale dairy systems in
central Mexico using linear programming. J. Anim. Feed Sci.
14:607–624.
Val-Arreola, D., E. Kebreab, S. L. Wiggins, and J. France. 2004c.
A study of forage production and nutrient availability in small-
scale production systems in central Mexico. Nutr. Cycl. Agro-
ecosyst. 69:191–201.
Van der Maas, C. W. M., P. W. H. G. Coenen, P. G. Ruyssenaars,
H. H. J. Vreuls, L. J. Brandes, K. Baas, G. van den Berghe,
G. J. van den Born, B. Guis, A. Hoen, R. te Molder, D. S.
Nijdam, J. G. J. Olivier, C. J. Peek, and M. W. van Schijn-
del. 2008. Greenhouse Gas Emissions in the Netherlands 1990–
2006. National Inventory Report 2008. MNP report 500080009.
Netherlands Environmental Assessment Agency, Bilthoven, the
Netherlands.
Modeling nutrient utilization E121
by Ermias Kebreab on April 4, 2009. jas.fass.orgDownloaded from
Van Knegsel, A. T. M., H. Van den Brand, J. Dijkstra, W. M. Van
Straalen, M. J. W. Heetkamp, S. Tamminga, and B. Kemp.
2007a. Dietary energy source in dairy cows in early lacta-
tion: Energy partitioning and milk composition. J. Dairy Sci.
90:1467–1476.
Van Knegsel, A. T. M., H. Van den Brand, J. Dijkstra, W. M. Van
Straalen, R. Jorritsma, S. Tamminga, and B. Kemp. 2007b. Ef-
fect of glucogenic vs. lipogenic diets on energy balance, blood
metabolites, and reproduction in primiparous and multiparous
dairy cows in early lactation. J. Dairy Sci. 90:3397–3409.
Van Knegsel, A. T. M., H. Van den Brand, E. A. M. Graat, J. Dijk-
stra, R. Jorritsma, E. Decuypere, S. Tamminga, and B. Kemp.
2007c. Dietary energy source in dairy cows in early lactation:
Metabolites and metabolic hormones. J. Dairy Sci. 90:1477–
1485.
Vitti, D. M. S. S., E. Kebreab, J. B. Lopes, A. L. Abdalla, F. F.
R. De Carvalho, K. T. De Resende, L. A. Crompton, and J.
France. 2000. A kinetic model of phosphorus metabolism in
growing goats. J. Anim. Sci. 78:2706–2712.
Zebeli, Q., J. Dijkstra, M. Tafaj, H. Steingass, B. N. Ametaj, and W.
Drochner. 2008. Modeling the adequacy of dietary fiber in dairy
cows based on the responses of ruminal pH and milk fat produc-
tion to composition of the diet. J. Dairy Sci. 91:2046–2066.
Kebreab et al.
E122
by Ermias Kebreab on April 4, 2009. jas.fass.orgDownloaded from
