Agriculture Reference
In-Depth Information
statistical description of the model to be de-
veloped later (Curnow, 1973).
Thus mechanistic ideas have played a
part in applied poultry science for a long
time and yet the main thrust of both the ex-
perimental approach used and of thinking
has remained rooted in empiricism and in
trials with small groups of birds. Why this
has happened is outside the scope of this
overview, but a consideration of the issue
must be central to the further development
of modelling in support of the poultry in-
dustry. As a simple example of how ideas
have been developed, some of the follow-up
to Heuser's statements can be reviewed.
The statement that 'the requirement
(for protein) is for the various amino acids'
is not at all controversial and is fully em-
bedded in future developments. After a
long controversial period of trying to deal
with individual amino acids and inter-
actions between them (e.g. D'Mello, 1994)
it is interesting that the emphasis for prac-
tical nutrition is now being given to the
idea of the profile of amino acid require-
ments and the response to 'balanced' pro-
tein (Lemme, 2003). In a general sense this
is a return to a systems approach after the
failure to resolve practical issues using a re-
ductionist approach.
Heuser's recognition that 'in practice it
is necessary to meet the requirements of as
many of the individuals as we can econom-
ically' draws attention to the need to con-
sider stochastic elements in nutritional
modelling and also to the idea that nutri-
tional requirements are economic concepts.
In modelling, biological determinants or
mechanisms must be conceived and defined
at the level of the individual animal, while
the observed population response is simply
the mean of the responses of contributing
individuals.
The statement 'the actual need is prob-
ably on the basis of certain amounts of
amino acids per unit weight of maintenance
plus definite additional quantities for pro-
ductive increases such as units of growth
and quantity of eggs' reflects the develop-
ment and use of the factorial approach in
nutrition. This was well established at the
time of Heuser's work and has continued to
play a large part in nutritional science. The
idea of nutrient requirements being seen as
rates of nutrient utilization for different bio-
logical functions has been at the root of
mechanistic nutritional modelling and this
seems likely to continue.
In the 1960s several authors were propos-
ing simple factorial equations as a guide to
feeding chicks (e.g. Combs, 1967) and laying
hens (e.g. Combs, 1960). Thus Combs (1960)
proposed that the methionine requirement of
a hen could be represented by the equation:
MET
= 5.0
E
+ 0.05
W
± 6.2∆
W
. Where
MET
=
requirement for methionine (mg/day),
E
= egg
output (g/day),
W
= body weight (g), ∆
W
=
change in body weight (g/day).
The linear nature of such expressions
was obviously at variance with the observa-
tion of diminishing response curves seen in
experiments and elsewhere. Combs intro-
duced some iterative procedures to deal
with this problem. Fisher
et al
. (1973) pro-
posed that such expressions of nutrient util-
ization could only be applied at the level of
the individual animal and that the non-linear
population response was a reflection of the
variation in output characteristics (
E
,
W
and
∆
W
) amongst individual animals. The work
of Curnow (1973) in formalizing this idea
makes it possible to estimate the coefficients
of the assumed underlying linear model
from non-linear observations of populations
(e.g. Morris and Blackburn, 1982) given as-
sumptions about the variance-covariance
structure of the underlying population
(Curnow and Torenbeek, 1996).
Continuing work has concentrated on
both of the issues raised by such factorial
equations; first, on the definition of suitable
output characteristics, and second, on the
determination of nutrient utilization coeffi-
cients. A third question about how the equa-
tion elements should be scaled has received
less attention although it is important, espe-
cially for maintenance. The description of
growth has been discussed briefly above
and also concerns the level of biological or-
ganization that is used in the system being
modelled. Mathematical models of growing
birds have used growth of the whole body
(King, 2001), growth of feather-free body
protein (Emmans, 1981) and protein and
