adding the amount of small particles that
would still be in the bag at the same time if
no particle loss had occurred. However,
these corrections are based on the asump-
tion that the particle losses through the bag
pores are representative of the incubated
sample, which is not proven.
In this first-order process of degrada-
tion, the slowly degradable fraction is
assimilated to a homogeneous fraction.
Another way to tackle substrate hetero-
geneity is to consider that the degradation
rate is a continuous variable, assuming the
existence of a gamma distribution of the
degradation rate (see review by Sauvant,
1997). This simple empirical approach
improves the statistical fit of experimental
data; however, it has the drawback of
ignoring the partitioning of substrate into
well-defined subfractions.
In the exponential model including a
lag phase, digestion of the slowly degrad-
able fraction is considered to start only and
instantaneously when factors limiting
digestibility, i.e. hydration, attachment and
colonization, are overcome, i.e. at lag time,
assuming implicitly that the lag phase has
a zero slope. However, because these
limitations can be overcome within certain
microenvironments (e.g. surface of
particles, points of physical damage), it
could be considered that there is partial
substrate availability when describing
digestion. Substrate may thus be digested
as soon as it is placed in the rumen, but at
a very reduced rate. As more substrate is
hydrated and more microorganisms attach,
the rate of disappearance will increase.
Hydration of forage has been shown to
reduce the lag time before in vitrodegrada-
tion, and frequent measurements of in
saccodegradation have shown that there is
actually not a discrete but a progressive lag
phase which can be modelled empirically
or mechanistically (Sauvant, 1997). A
simple approach consists of assuming that
the degradation rate is the outcome of two
basic components, one of accelerating
degradation (i.e. no resistance) and one of
resistance. However, studies are needed to
assess precisely the value of such an
approach for describing in situ kinetics.
Some authors developed more mechanistic
models of the initial lag phase (Sauvant,
1997). These were based on a compart-
mental description, assuming that the sub-
strate is firstly in a pool of matter with a lag
phase prior to degradation. This compart-
ment is transformed progressively, accord-
ing to first-order kinetics, into another
compartment containing the degradable
form of the substrate which is subjected to
digestion with first-order kinetics. This
statement is realistic because processes of
particle hydration and microbial coloniza-
tion are progressive. Compared with the
model with the discrete lag phase, the com-
partmental model reduces the residual
mean squares for predicting the rate of
disappearance.Calculation of parameters
Two main methods are often used for
fitting data to the first-order kinetic model:
logarithmic transformation followed by
linear regression (lnLIN) and non-linear
least square regression (NLIN). The GLM
and NLIN procedures of SAS (Statistical
Analysis Systems, 1985) are often used.
Errors and differences in parameters can
arise according to the method of fitting data
to the kinetic model. This is due to differ-
ences in the statistical error structure
assumed in each model and differences
between sequential and simultaneous
estimation of parameters (reviewed by
Mertens, 1993).
With the lnLIN method, the undegrad-
able fraction is determined using data from
the last incubation time and subtracted
from the residue at each incubation time. A
regression analysis is then conducted on
log-transformed residues according to
incubation time, assuming that error is pro-
portional to the size of the residue for each
observation (Mertens, 1993). The slope of
the relationship corresponds to the con-
stant degradation rate. A curve-peeling
method could be conducted if the presence
of prominent inflexions is detected. The
major disadvantage of the lnLIN approach
is that indigestible residue must be
estimated experimentally using data from
the last incubation time observed. Any242 P. Nozière and B. Michalet-Doreau