Agriculture Reference
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this relationship is used to estimate the op-
timal response to varying nutrient levels of
a population of animals showing some de-
gree of heterogeneity. In contrast, the fac-
torial method estimates, for a unique animal
at one specific growing state, the requirement
for expressing the full growth potential.
Thus, when the factorial method is used to
estimate the requirements of a given popu-
lation, the chosen individual should be
the best representative of the population
(Pomar
et al
., 2003; Hauschild
et al
., 2010).
The empirical method estimates optimal
nutrient allowances from a population per-
spective, whereas the factorial method ad-
dresses the needs of one reference animal
during a very short period, normally 1 day.
The relationship between the empirical
and factorial methods is difficult to estab-
lish and is affected by many factors related
to the animal, the growth state and popula-
tion heterogeneity. For instance, Hauschild
et al
. (2010) found that maximum ADG was
reached in
25-
50 kg BW pigs with a Lys:NE
ratio 12% higher than the requirement of
the average pig estimated by the factorial
method
(Fig. 12.1
)
. This estimation corres-
ponded to an animal whose requirement
for this nutrient was in the 82nd percentile
of the population. For the FCR, however,
the empirical estimates corresponded to
those for a pig in the 58th percentile of the
population
(Fig. 12.2
)
. These results can-
not, however, be generalized, as the diffe-
rence between the factorial method and the
empirical method can be expected to in-
crease with the level of heterogeneity of
the population (Pomar
et al
., 2003).
One of the problems in evaluating the
empirical and the factorial requirements for
optimizing population responses lies in the
difficulty of integrating the main factors
implicated in animal responses. Variation
among animals, which is an important fac-
tor modulating population responses, is rarely
taken into account. The importance of
considering variability among animals in
evaluations of biological responses and in
nutritional programmes has been demon-
strated in recent years (Pomar
et al
., 2003;
Main
et al
., 2008; Brossard
et al
., 2009; Vau-
tier
et al
., 2013). Between-animal variation
shapes population responses and, therefore,
the overall efficiency of nutrient utilization
(Pomar
et al
., 2003) and optimal nutrient levels
(Leclercq and Beaumont, 2000; Pomar
et al
.,
2003; Brossard
et al
., 2009).
Mechanistic mathematical models that
implement the factorial approach are proposed
in an attempt to represent the complexity of
1150
2.90
1.09 g/MJ
1030
2.63
910
2.35
790
2.08
670
0.99
g/MJ
550
0.43
1.80
0.51
0.60
0.69
0.78
0.87
1.05
Lys:NE (g/MJ)
0.96
1.14
1.23
1.32
1.40
1.49
Fig. 12.1.
The effect of different lysine:net energy (Lys:NE) ratios (g/MJ) on ADG and FCR and maximum
response of pigs fed between
26
to 53 kg (
ADG, • FCR), standard error of the mean and curve estimated
by the quadratic equation (
—
ADG, —FCR). (From Hauschild
et al
., 2010.)
