blaxter1978

Prévia do material em texto

J. agric. Sci., Gamb. (1978), 90, 47-68 4 7
With 6 text-figures
Printed in Great Britain
The estimation of the nutritive value of feeds as energy sources for
ruminants and the derivation of feeding systems
B Y K. L. BLAXTER AND A. W. BOYNE
Rowett Research Institute, Bucksburn, Aberdeen AB2 9SB
{Received 17 May 1977)
SUMMARY
The results of 80 calorimetric experiments with sheep and cattle, mostly conducted
in Scotland, were analysed using a generalization of the Mitscherlich equation
R = B(l-exp(-pG))-l,
where R is daily energy retention and G daily gross energy intake, both scaled by
dividing by the fasting metabolism. The relations between gross energy and metaboli-
zable energy were also examined. Methods of fitting the Mitscherlich equation and the
errors associated with it are presented.
I t is shown that the gross energy of the organic matter of feed can be estimated from
proximate principles with an error of ± 2-3 % (coefficient of variation) and that provided
different classes of feed are distinguished, the metabolizable energy of organic matter
can be estimated from gross energy and crude fibre content with an error of ±6-9%.
Parameters of the primary equation made with cattle agreed with those made with
sheep and there was no evidence of non-proportionality of responses on substitution of
feeds in mixtures.
The efficiency of utilization of gross energy for maintenance and for body gain of
energy was related to the metabolizability of gross energy and, in addition, to fibre or
to protein content. Prediction equations are presented which describe these relation-
ships.
It is shown that the primary equation can be manipulated to express a number of
biological concepts and that its two parameters B and p can be simply derived from
estimates of the two efficiency terms for maintenance and production.
The results are discussed in relation to the design of feeding systems for ruminant
animals and to the derivation of optima in their feeding.
TNTTt ODTTPTTOW energy for maintenance, km, varied with the quality
J.1M l H W U ^ l l U a o f ^ ^ d . e t from a b o u t Q 6 Q t Q Q ^g T h e g l o p e o f t h e
The relationship between the rate of feed intake equation above maintenance, called the efficiency
by a growing or fattening ruminant and the rate at of utilization of metabolizable energy for fattening,
which it retains energy in its body is curvilinear. kf, varied more with quality of the diet than did
Successive increments of daily intake result in km, ranging from O2 to 0-6.
progressively smaller increments in daily energy In an attempt to devise a feeding system based on
retention. Blaxter & Graham (1955) showed that these relationships Blaxter (1962) had to introduce
this relationship could be described by a simple a component to accommodate the decline in pro-
exponential equation and during the next few years portional retention of the gross energy of the feed
it was shown that no great error was involved if the as the amount ingested each day was increased. This
relationship between daily rate of energy retention term, the feeding level correction, in effect intro-
and rate of feed intake expressed as metabolizable duced a curvilinearity to the system above main-
energy was approximated by two straight lines tenance and it then approximated closely to the
intersecting at zero energy retention, that is at underlying continuous curvilinear function. This
energy maintenance (Blaxter & Wainman, 1961). system, usually called the metabolizable energy
The slope ofthe linear equation below maintenance, system, was adopted by the Agricultural Research
called the efficiency of utilization of metabolizable Council's Working Party on the Nutrient Require-
48 K. L. BLAXTER AND A. W. BOYNE
ments of Ruminants and included in its 1965
publication (ARC, 1965).
It was later adopted in principle in a slightly
modified form by the Agricultural Departments of
the United Kingdom (MAFF, DAFS & DANI,
1975) and replaced the older starch equivalent
system which was shown to be less precise in
estimating animal needs (Alderman, Morgan &
Lessells, 1970).
Even so, the system, although capable of accom-
modating new findings, is cumbersome to use and
probably leads to difficulty on extrapolation to high
levels of production. Several attempts have been
made to simplify the computation of rations by
algebraic manipulation of the ARC System as
exemplified in the Agricultural Departments'
publication (MAFF et al. 1975), without taking into
account that the system was an approximation to a
continuous relationship. For these reasons, and in an
attempt to provide a simple and firm basis for the
development of feeding systems, we have under-
taken a reassessment of the basic calorimetric data
on feed evaluation for ruminants. A progress report
has been published on this work based on fewer
experiments than are now included (Blaxter &
Boyne, 1970) and an account of some of the conclu-
sions arising from preliminary calculations has been
given (Blaxter, 1974).
MATERIALS AND METHODS
The Appendix Table lists details of the 80 experi-
ments which were analysed. Most of these were
carried out at the Hannah Dairy Research Institute,
Ayr and at the Rowett Research Institute, Aberdeen
and we are grateful to our colleagues for access to
unpublished details. Fourteen experiments made in
America, Australia or Japan were recorded in
sufficient detail to permit their inclusion. The
experiments comprise sets of determinations of
energy retention when each animal was given
various amounts of the same diet and also when it
was starved to provide an estimate of its fasting
metabolism. The methods used are described in the
references to the Appendix Table.
In 70 of the experiments the diets had been
analysed chemically to give values for ash, N, crude
fibre and ether extract contents and in 34 of these
lignin content had been determined. The heat of
combustion of each diet was also known. These
diets were classified as shown in the Appendix
Table into six classes:
(1) Pelleted diets: mainly pelleted roughages
including pelleted mixtures of roughages and
cereals (13 diets).
(2) First harvests of grasses: artificially dried
herbages including not only very young spring grass
but also more mature herbage which would normally
have been made into hay rather than artificially
dried (15 diets).
(3) Begrowths of grasses: second and subsequent
harvests of grasses which had all been artificially
dried (11 diets).
(4) Hays: both legumes and grasses distinguished
from 2 above only because of the method of drying
(10 diets).
(5) Cereal mixtures: mixed diets of cereals and
hay or dried herbage; the lowest cereal inclusion
was 20% (24 diets).
(6) Other mixtures: roughages together with oil-
seed cakes and meals, animal products and some
cereals (6 diets).
This classification into six groups was found to be
too fine; classes 5 and 6 were combined to give a
group of 30 diets and classes 2 and 4 combined to
give a group of 25 diets. One experiment, No. 61,
was omitted from the analysis since it gave com-
pletely anomalous results compared with the
remainder.
The results of analysing these data are presented
in two parts. In the first a simple mathematical
model is developed which describes the relationship
between rate of energy retention and rate of energy
intake; the estimation of the parameters of the
model is described and aspects of the parameters
themselves discussed. The algebraic derivation of
efficiency terms is presented and their relation to
the ARC (1965) system described. In the second
part these efficiency terms are then related to
attributes of the diet to provide prediction equa-
tions. Finally further simplification of the approach
is presented.
RESULTS
Development
The basic descriptive equations relating energy reten-
tion to feed energy intake
The Mitscherlich equation, which describes a
system to which the law of diminishing returns
applies, was first used by Wiegner & Ghoneim (1930)
to analyse the two calorimetricexperiments made
with cattle which had been carried out at the time.
Brody (1945) re-analysed these same experiments
and a third using the same form of the equation and
Blaxter & Graham (1955) followed a similar approach
to analyse the results of two experiments they had
made with sheep. The present treatment derives
from these approaches but is more general; its
derivation is given in full:
LetB' = the rate of energy retention of an animal
(kj/day) and G' the rate at which it ingests feed
energy (kJ/day).
Then — = p'(A-R'),
where A is the maximal attainable rate of energy
Nutritive value of feeds as energy sources 49
retention and p' is a constant. On integration this
gives
R'= A-B'(exp(-p'G')), (1)
where B'is a constant of integration. When G' = 0,
R' = A-B' =-Hb,
where 2?» is the rate of fasting metabolism. Sub-
stituting for A = B' — Hb in equation (1) and divid-
ing throughout by Hb gives
.„ G'\\ Hh
(2)
which may be written
R = B{l-exp(-pG))-l,
where R, B and G are scaled as multiples of fasting
metabolism. B— 1 is equal to the scaled asymptote
of equation (1), namely A\Hb.
The relationship expressed by equation (2) is
general in form. We have applied it to sealed energy
retention and sealed gross energy intake. Our
reason for choosing gross energy instead of meta-
bolizable energy is that each estimate of energy
retention depends on the same measurements of
energy lost as methane and in faeces and urine as
does the corresponding estimate of metabolizable
energy; thus errors in both estimates are correlated,
a situation which gives spurious information on the
relationship between them.
Examination of the relationship between scaled
gross energy intake (G) and the scaled metabolizable
energy (M) showed that in any one experiment the
two were closely associated by an equation of the
form
M = c + bG. (3)
Equation (2) can be written as
R = B{l-exp(-p(M-c)lb)-l, (4)
where retention is expressed in terms of metaboli-
zable energy. The asymptotic energy retention
remains B — 1, unaffected by the way in which the
energy of the feed intake is described.
Metabolizability, q, of the diet is the ratio of meta-
bolizable to gross energy, i.e. q = ME\GE = M\G =
b + cjG.
In particular metabolizability at maintenance,
It will be noted that if c in equation (3) is zero, q
does not vary with feed intake; if c is positive, q falls
as feed intake increases. Finally, the device of
dividing energy intake and retention by fasting
metabolism enables observations on more than one
animal on the same diet to be combined for esti-
mation of the parameters B, p, c and 6.
The regression of scaled metabolizable energy intake,
M, on scaled gross energy intake, G
Appendix Table 1 lists the slopes (6) and inter-
cepts (c) of equation (3). All the regressions were
highly significant statistically and the proportion of
the total sum of squares accounted for by the re-
gression averaged 0-988 with a standard deviation of
± 0-063. Clearly a linear regression provided a very
satisfactory fit to the data. The 80 experiments can
be grouped according to the number of animals used
in each and the residual standard deviation from the
regressions calculated for each group. Table 2
(column 5) shows a tendency for the residual
standard deviation to increase with increasing
number of animals used in an experiment. Even so,
the standard deviations were very small, about 2 %
of the mean value.
The slopes and intercepts of the individual equa-
tions were negatively correlated and both appeared
to be related to the crude fibre content, F, of those
diets for which chemical data were available. This
Table 1. Within-experiment dependence of M, the scaled metabolizable energy and of q, the metabolizability,
upon G, the scaled gross energy. The standard error of each regression coefficient is given below it
Class of diet
Pelleted (1)
First harvests (2 and 4)
Regrowths (3)
Mixed diets (5 and 6)
Change in M with unit
change in G
(i.e. 6 in regression equation
M = c + bG)
0-661 -O-OOORF*
+ 0-025 + 0-0001
0-976- 0-0016F*
+ 0023 ±00001
0-928 -0-0015.F*
0-054 + 0-0002
0-803-0-0012^*
±0-015 + 0-0001
Change in q with unit
change in O
(i.e. 6 in regression equation
q = c + bG)
-0-0067
±0-0014
0-0187-0-000079.F*
±0-0058 ±0-000022
-0-0057
±00017
0-0627-0-000322^*
+ 0-0136 + 0-000087
• Where change in M or q is of the form d, —&2.F, then the effect of unit change in 0 is smaller in diets of high
crude fibre content than in diets with little crude fibre in them,
ACS 90
50 K. L. BLAXTBR AND A. W. BOYNE
Table 2. Residual standard deviations of the scaled metabolizable energy from
equation (3) and of scaled energy retention from equation (2)f
Residual standard deviations (+)
No. of animals
used in the
experiments
One
Two
Three
Four
Six
All
No. of
experiments
5
6
42
18
6
79
Mean no. of
observations
per animal
6-8
3 1
2-8
1-9
1-5
,
D.F.J
24
25
272
102
41
510
Scaled
metabolizable
energy (M) from
equation (3)
0046
0054
0067
0-067
0-057
0-063
Scaled energy-
retention (B)
from equation (2)
0060
0-084
0096
0097
0-109
0093
t Equation (2) R = B ( l - exp ( - p G ) ) - 1 ,
Equation (3) M = c + bG.
I Two degrees of freedom deducted for constants.
was examined further by carrying out, for each of the
four main groups of diets, a within-experiment re-
gression analysis of M on Q and GxF, where F was
expressed as g crude fibre per kg of organic matter.
The regression coefficients are given in Table 1. The
relationship between M and G, which accounted for
0-99 of the variability in M, clearly depended upon
F in that the yield of metabolizable energy for each
unit increment of gross energy intake fell as the
crude fibre in the diet increased.
From these expressions the intercepts were cal-
culated for each experiment and no relationship was
found between them and crude fibre. For each of the
groups, the mean intercept, its standard deviation
and the number of experiments are given below:
Diet class
Pelleted diets (1)
1st harvests (2, 4)
Regrowths (3)
Mixtures (5, 6)
Intercept
0142
0085
0025
0-016
S.D. (±)
0-113
0-163
0-056
0136
No. of
expts
25
12
11
22
Thus for most of the diets the intercept was + ve,
indicating that metabolizability usually fell as in-
take increased. This effect of intake on metaboliza-
bility was examined directly via the relationship
between q, G and GxF.
The regression coefficients are also presented in
Table 1. These show that for pelleted diets and re-
growths, metabolizability fell as intake (G) in-
creased, whereas for first harvests and mixtures the
effect of intake was conditional upon the crude fibre
content of the diet; for first harvests q fell with
intake if crude fibre content was greater than
238 g/kg organic matter (OM), and for mixtures the
corresponding fibre value was 196 g/kg OM.
Fitting the exponential relationship between scaled
energy retention, R, and scaled gross energy intake, G
An iterative calculation method, similar to that
outlined by Williams (1959), was used to fit equation
(2) to each data set. The method was devised to give
approximate estimates of error variability and is
described below.
Fitting the equation R = B{1 — exp (— pG)) — 1,
or R = f(B, p, G) was accomplished by making pre-
liminary estimates Bo and p0 of the parameters and
making adjustments to them SB and 8p. R was then
estimated by
where the partial derivatives are evaluated at
Bg, p0. The procedure was repeated at ad j usted values
of B and p until the magnitude of the adjustments
in B and p and the change in the residual mean
square became negligible.
Appendix Table 1 lists for all experiments the
values of B and p together with the residual mean
squares. In Fig. 1 the best estimates of B and p in
the equation R = B(l — exp (— pG)) — 1 are plotted
against one another. It seemed possible at first that
the relationship between these two parameters
might be so close as to enable one to be expressed in
terms of the other. If this had been so then estima-
tion of one parameter wouldhave been enough to
describe the relationship between energy retention
and intake. This, however, did not prove possible,
largely because of the nature of the correlation be-
tween estimates of B andp for any one experiment.
In Fig. 2 for two experiments, 46 and 52, the best
estimates of B andp are plotted along with contours
of values of B and p for which the residual mean
square in retention are respectively twice and four
Nutritive value of feeds as energy sources 51
a
o
_ A A • • O l
0°
«52
#46
o . s
• °n o 4 "
0-2 0-3 0-4
Pig. 1. Scatter diagram of best estimates of B and p for all 79 experiments. A, Hays; • , hay-cereal;
D, hay-cereal-protein; A, pelleted; O» 1st cut grass; • , 3rd cut grass. # 46 and # 52 are the best
estimates for Expts 46 and 52, respectively.
times the residual associated with the best estimates.
The contours for these two experiments do not inter-
sect anywhere indicating that no point-pair of B, p
can satisfactorily fit the data from both experiments.
The best estimates of Expts 46 and 52 are indicated
on Fig. 1, showing that these are by no means the
least compatible experiments in the series.
It can also be seen from Fig. 2 that a large change
in B may be accompanied by a compensatory change
in p with little effect on the goodness of fit. To illus-
trate and amplify this, estimates of B and p for
Expt 52 were used corresponding to x, the best fit,
and to (1), (2), (3) and (4), 'corners' of the contour
corresponding to twice the minimal residual mean
square. The resulting values of 0*, EG, m and
Eg, t (vide infra for their definition) are given in
Table 3 where it can be seen that although values of
B and p may differ from the best estimate by as
much as 40%, the differences in O*, EQ m and
EG. t are no greater than 9%. There is, however,
4-2
52 K. L. BLAXTER AND A. W. BOYNE
010 0-15 0-20 0-25 0-30 0-35
Fig. 2. Envelopes for Expts 46 and 52 enclosing values of B and j> for which residual mean square
does not exceed twice and four times minimum.
Table 3. Estimates of O*, EGt n and EG,ffor Expt
52, derived from the best estimates of B and p, and
from estimates corresponding to each 'corner' of the
contour in Fig. 2 at which the residual mean square is
twice the minimum.
Point
X
(1)
(2)
(3)
(4)
B
3-38
4-78
2-68
3-43
3-32
P
0193
0122
0-280
0-199
0-188
G*
1-82
1 92
1-67
1-73
1-91
E0,m
0-55
0-52
0-60
0-58
0-52
Eg, t
0-39
0-41
0-38
0-41
0-37
no doubt, as was shown by Blaxter & Graham
(1955), that a curvilinear relationship more closely
describes the results of energy metabolism studies
in which different amounts of the same diet are
given than does a linear equation. Estimates of
retention of energy within the effective range are
little affected by the inability to predict B and p
precisely.
Studies made with both cattle and sheep (Schie-
mann, 1958;Blaxter, 1967) suggest that the error of
a single estimate of scaled energy retention is likely
to be about ± 0-07 kJ /kJ fasting metabolism, the
precise value depending largely on the duration of
the experiment. As shown in Table 2, the residual
standard deviation from equation (2) was on
average ± 0-093, which is slightly greater than the
error of a single trial. There was a tendency, as with
the estimation of scaled metabolizable energy, for
the precision of the estimated scaled retention to
worsen as the number of animals included in the
experiment increased. In our opinion the increase in
residual variability is more than compensated for by
the facility that equation (2) provides for combining
the results from a number of animals.
Algebraic definition of biological terms
Manipulation of the two basic equations (2) and
(3) provides expressions for a number of the more
commonly accepted measures of energy exchange
such as maintenance, level of feeding and efficiency
of energy utilization. These are developed below,
extending the approach used by Blaxter & Graham
(1955).
The gross energy required for maintenance is the
Nutritive value of feeds as energy sources 53
amount of feed energy which results in zero energy-
retention and from equation (2) is
ln
p B—l
(5)
and, from equation (3), the metabolizable energy
required for maintenance is
Mm = M* = c + bG*.
The metabolizability of the gross energy of the
diet measured precisely at maintenance is
q* = M*\Q*. (6)
The level of feeding of an animal is defined in
terms of multiples of the amount of feed required for
maintenance. The gross energy concentration of
feed is independent of level, so
L = GIG*. (7)
The efficiency with which the gross energy of feed
is used for maintenance is
1
E°. - = G* (8)
because in the scaled equations the fasting meta-
bolism is axiomatically unity. Similarly, the effi-
ciency with which the metabolizable energy is used
for maintenance is
E M, m = j£i = km (9)
The shape of the relationship between energy reten-
tion and feed intake dictates that the efficiency with
which feed energy is used to promote retention
above maintenance declines with increasing intake.
To obtain comparable estimates of the efficiencies
with which different feeds are used above main-
tenance, the points between which such efficiencies
are measured must be standardized. We measure
efficiency for production between maintenance and
a feeding level precisely 2 x maintenance.
The gross energy retained by an animal at any
feeding level, L, is from equations (2), (5) and (7)
from which B2 =
B-l
B '
The efficiency of utilization of gross energy for
production measured between maintenance and
2 x maintenance is thus
EG,t =
B-l
BG* '
(10)
If the metabolizability of the gross energy is
taken to be that at maintenance, then at 2G*, the
efficiency of utilization of metabolizable energy for
production is
(11)
This is the definition we have used. The terms derived
algebraically above are for the most part
formally equivalent to those currently adopted in
describing the energy metabolism of animals. Thus
EM. m is identical to km, the efficiency of utilization
of metabolizable energy for maintenance in the ARC
(1965) system, and L, the feeding level, is also pre-
cisely the same. The efficiency of utilization of
metabolizable energy for production, EM /, is very
closely analogous to kf, the ARC coefficient of
efficiency of utilization for fattening. It is not pre-
cisely the same, because it is calculated over a de-
fined range and also because it refers to a constant
metabolizability of gross energy. In the ARC (1965)
scheme hf was obtained directly from the observed
metabolizable energy intakes above maintenance
and any decline in the proportional retention with
increase in feeding level was dealt with separately.
These quantities EG, m and EG, f are simply related
to B andp of equation (2). Thus from equation (10)
it follows that
B = EG,mj(EG_n-EG,t), (12)
and from this result and equation (5)
p = EG,m]n(EG.mIEG.f). (13)
(From these it is simple to derive the equations re-
lating B andp to EM, m and EM, /•)
Knowledge of the two efficiencies enables energy
retention to be predicted at any level of intake, and
not solely at maintenance and 2 x maintenance.
When, additionally, EG, m and EG, f are found to be
related to composition of diets in terms of their
proximate constituents, it becomes possible to pre-
dict for a diet the energy retention at any level of
feeding from its proximate composition.
Table 4 summarizes the mean values and coeffi-
cients of variation of these biological terms as de-
fined above together with the mean chemical com-
positions of the feeds. Figure 3 gives frequency
distributions of the proximate chemical constituents.
In each distribution the abscissae are in units of
50 g/kg. These feeds varied considerably in quality;
metabolizability of gross energy varied from 0-38 to
0-83, crude fibre from 20 to 390 g/kg, and crude pro-
tein from 54 to 256 g/kg. The efficiency terms also
varied considerably, especially when expressed in
terms of gross energy.
54 K. L. BLAXTER AND A. W. BOYNE
Table 4. The variationpresent in the 70 experiments for which chemical data were available. Mean values and
coefficients of variation of the estimates derived from the equations and for chemical constituents. The results for
all 79 experiments are given in brackets^
Symbol
6*
E(3,m
EO. 1
M*
EJI, m
•^if, /
9*
Name
Gross energy for maintenance
Efficiency of utilization of gross
energy for maintenance
Efficiency of utilization of gross
energy for production
Metabolizable energy (ME) for
maintenance
Efficiency of utilization of ME
for maintenance
Efficiency of utilization of ME
for production
Ash, g/kg dry matter
N x 6-25, g/kg organic matter
Ether extractives, g/kg
organic matter
Crude fibre, g/kg organic
matter
N-free extractives, g/kg
organic matter
Heat of combustion, MJ/kg
organic matter
Metabolizability of gross
energy at maintenance
Mean value
2-59
(2-55)
0-405
(0-409)
0-262
(0-267)
1-45
(1-43)
0-696
(0-705)
0-443
(0-453)
68
147
28
244
582
20-2
0-578
(0-571)
Standard
deviation (+)
0-60
(0-57)
0-087
(0-084)
0094
(0091)
0 1 5
(0-15)
0-070
(0-074)
0118
(0-117)
24
55
14
92
104
0-80
0-086
(0-082)
Coefficient of
variation (%)
23-0
(22-4)
21-5
(20-5)
36-0
(34-0)
10-3
(10-7)
10-1
(10-4)
26-5
(25-7)
35-4
37-6
49-8
37-7
17-8
4-0
14-9
(14-2)
"f In any one experiment the efficiencies for maintenance are the reciprocals of the amounts of scaled energy
required for maintenance. The reciprocals of the means of a series of estimates of efficiencies are unlikely to be the
same as the means of a series of amounts.
Analysis
The relationship between the gross energy and the
metabolizable energy of feed and its chemical com-
position
The heat of combustion of the organic matter of
the wide range of feeds was subject to little varia-
tion, the mean value being 20-17 MJ/kg with a
standard deviation of ±0-80, corresponding to a
coefficient of variation of ±4-0%. The distribution
is shown in Fig. 3. Eegression of the heat of combus-
tion on chemical composition was undertaken to
provide estimates of the heats of combustion of
crude protein, ether extractives, crude fibre and
nitrogen-free extractives which together sum to give
the organic matter. The results are given in Table 5
where they are compared with those derived by
Schiemann et al. (1971) from calorimetric studies in
East Germany. The only major discrepancy relates
to the low heat of combustion of ether extractives.
Triacylglycerols have heats of combustion of about
38kJ/g; other ether-soluble constituents, notably
carotenoids and chlorophyl, have lower ones. In any
event, the error caused by the use of the coefficients
given in Table 5 is not likely to be great since ether
extractives in ruminant diets rarely exceed 60 g/kg.
The residual standard deviation which results from
use of the regression equation was + 0-47 MJ/kg,
corresponding to a coefficient of variation of only
2-3 %. There were no significant differences between
classes of feeds.
A similar analysis was made of the relationship
between the metabolizable energy/kg organic
matter, measured at the maintenance level of nutri-
tion, and chemical composition. The overall rela-
tionship gave the coefficients shown in Table 5 which
includes a set derived by MAFFetal. (1975) from the
work of Schiemann et al. (1971) based on assumed
digestibility coefficients for the individual nutrients.
They permit the estimation of metabolizable energy
of feeds from their crude chemical composition with
an error of + 1-09 MJ/kg. The factors derived in the
present analysis give higher values for most rumi-
nant feeds than do the factors of MAFF et al. (1975)
64
60
24
20
51 16
I
Nutritive value of feeds as energy sources
201-
55
16
12
0 100
Ether extract
(g/kg OM)
100 200
Fibre
(g/kg OM)
300 400 19 20 21 22 23
Gross energy (MJ/kg OM)
20
16
<U 82
100 200
Protein
(g/kgOM)
= 1 f =
300 400 500 600 700
NFE
(g/kgOM)
900
Fig. 3. Histograms representing the frequency distributions of the proximate chemical constituents
(g/kg) and of the gross energy (MJ/kg) of the organic matter of the experimental diets.
Table 5. The gross energy and metabolizable energy of crude protein, ether extractives,
crude fibre and N-free extractives estimated by regression methods (MJjkg)
Crude protein (N x 6-25)
Ether extractives
Crude fibre
N-free extractives
BSD
Coefficient of variation
Gross energy
1
Estimated
26-8
27-2
21-8
17-4
±0-47
±2-3
Schiemann et al.
(1971)
22-6
40-7
19-2
17-7
—
—
Metabohzable energy
Estimated
161
33-7
8'6
13-9
±l'O9
+ 9-4
MAFF et al.
(1975)
12
31
5
14
—
1
for which no great precision has been claimed. A
number of other possibilities of estimating meta-
bolizable energy/kg organic matter were explored.
The best estimate was given by the equation
tion (MJ/kg), x is the gross energy of the organic
matter (MJ/kg), F is the crude fibre content of the
organic matter (g/kg) and c is the intercept which
varies from class to class of diet:
y = 0-412a;-0-0205.F + (14)
where y is the metabolizable energy of the organic
matter measured at the maintenance level of nut ri-
Diet class
Pelleted (1)
First harvests (2 and 4)
Regrowths (3)
Mixed diets (5 and 6)
Intercept
7-57
9-29
8-79
7-44
56 K. L. BLAXTER AND A. W. BOYNE
This equation has a residual standard deviation of
+ 0-80 corresponding to a coefficient of variation of
± 6-9 % of the mean value.
It will be noted that either the coefficients in
Table 5 or the equation above enable the metaboliza-
bility of gross energy at the maintenance level to be
derived from crude chemical composition alone with
relatively little error.
Agreement of estimates of parameters made with sheep
and cattle
Seven experiments were duplicated with sheep
and cattle (Blaxter & Wainman, 1961) and Table 6
summarizes the mean values of the parameters ob-
tained with each species. The seven diets covered a
wide range of diets as exemplified by the metaboliza-
bility of the gross energy which ranged from 0-5 to
0-8. The table shows that there were no differences
attributable to species. It can be concluded, there-
fore, that the device of scaling by the fasting meta-
bolism equates for the wide differences in body size
of different ruminant species. The coefficient of
variation in the final column refers to an individual
determination of the parameter based on these
replicated trials.
Additivity of dietary characteristics
If two diets of different nutritive values are mixed
in a given proportion, it is important to know
whether their nutritive values combine additively to
give the nutritive value of the mixture, or whether
there is evidence of synergism. Three experiments to
test this were carried out by Blaxter & Wainman
(1961) and by Blaxter, Wainman & Smith (1970).
The characteristics examined were the metaboliza-
bility at maintenance, q*, the gross energy required
for maintenance, G*, and EG, f, the efficiency of
utilization of gross energy for production. Each
experiment contained six mixtures, and there was
no evidence of non-additivity of q* or of EG, /. In
only one experiment, in which cattle were given
mixtures of hay and maize, was there evidence of
eynergism in G*, significant at the 5 % level, but in
that experiment there was a small residual mean
square, and the departure from linearity was
negligible.
Recent work carried out by the Feed Evaluation
Unit at the Rowett Institute (DAFS, 1976) also
shows that there is linearity of substitution of grains
for long roughages or of grains for silages in the
determination of q*. It can be concluded from this
limited evidence that no error is likely to accrue if
linearity of substitution of feeds is assumed in terms
of metabolizable energy.
The prediction of the utilization of the energy of feed
In the preliminary analysis of the data, EM, m and
EM. f, the efficiencies of utilization of metabolizable
energy for maintenance and fattening, had been
related to attributes of the feed (see Blaxter, 1974).
A more direct analysis is now preferred on logical
grounds. Itwas pointed out earlier that the relation-
ship between energy retention and gross energy is
preferred, to that between energy retention and
metabolizable energy since measurements of faecal,
urinary and methane energy are common to meta-
bolizable energy and energy retention. The same
preference applies to efficiency measurements; they
are less open to bias when based on relationships
between retention and gross energy. Accordingly,
the efficiencies related to attributes of the feed were
EG, m and EG. /, which are defined by equations (8)
and (10). The corresponding equations in terms of
metabolizable energy may be derived from the
relationship
= EG, Jq*,
EM. t = EG, ,\q*.
Maintenance
Analysis of all 79 experiments showed that there
was a statistically highly significant regression
(P < 0-001) of the efficiency of utilization of gross
energy for maintenance on metabolizability of
energy measured at the maintenance level of nutri-
tion. The slope of the relationship was common to
all feeds but intercepts differed. The equation was
Eo. m = 0-817g* + c,
Table 6. Comparison of the values of parameters determined with both cattle and sheep.
Results of seven experiments in which the two species were given tlie same diets
Parameter
Metabolizability of gross energy
measured at maintenance
Scaled amount of gross energy required
for maintenance (kJ/kJ fasting metabolism)
Efficiency of utilization of gross energy for
production measured between maintenance
and 2 x maintenance
Mean
Sheep
0-625
2-32
0-288
values
Cattle
0-621
2-21
0-287
Difference and S.E.
of difference
0-004 + 0-007
0-11 + 0-06
0-001 ±00076
Coefficient
of variation
20
4-6
7-1
Nutritive value of feeds as energy sources 57
where the intercept, c, had the following values:
Diet class
Pelleted (1)
Forages (2, 3 and 4)
Mixed diets (5 and 6)
Intercept
-0069
-0-078
- 0 0 4 0
The residual standard deviation was + 0-037 which
is ± 9 % of the mean value.
Further analysis was made of the 70 experiments
for which compositional data were available in
which metabolizability and the content of proxi-
mate principles in the organic matter were tested as
predictors, separately and in combination. For the
70 feeds, the simple relationship with q* was again
highly significant and very similar to that obtained
with the complete data; again there were differences
between classes of feed. It was found, however, that
these differences were removed by inclusion in the
equation of either crude fibre or crude protein along
with metabolizability. No other combination elimi-
nated class differences or gave lower residual mean
squares. These equations were:
EG.m = 0-838g*- 0-00012.F -0-050, (15)
USD = + 00353, CV = ± 9%,
EG m = 0-947g*-0-00010P-0-128, (16)
RSD = ± 0-0354, CV = ± 9%,
where F is the content of crude fibre in the organic
matter (g/kg) and P is the content of crude protein
in the organic matter (g/kg).
Values of Eg, m predicted from these two equations
are given in Tables 7 and 8 together with the derived
values of EM_ m.
Analyses in which only the proximate principles
were regarded as independent variables singly and
in combination showed that the regression on crude
fibre gave the lowest residual standard deviation
Table 7. Prediction of the efficiency of utilization
from the metabolizability of gross energy and
Metabolizability
of gross energy
(«•)
0-40
0-50
0-60
0-70
0-80
0-40
0-50
0-60
0-70
0-80
of gross energy and metabolizable energy for maintenance
the crude fibre content of the organic matter
Crude fibre, g/kg organic mattei
50 100 200
Efficiency of utilization of gross energy, EOt „
— —
— 0-441
0-531 0-525
0-614 0-608
Efficiency of utilization
— —
— —
— 0-735
0-759 0-750
0-766 0-761
0-345
0-429
0-512
—
i of metabolizable energy, i
—
0-690
0-715
0-731
•(F)
300
0-249
0-333
0-417
—
—
'11, m
0-623
0-666
0-695
—
of the feed
400
0-237
0-321
—
—
—
0-592
0-642
—
—
Table 8. Prediction of the efficiency of utilization of gross energy and metabolizable energy for maintenance
from the metabolizability of the gross energy and the crude protein content of the organic matter of the feed
Metabolizability
of gross energy
(?*)
0-40
0-50
0-60
0-70
0-80
0-40
0-50
0-60
0-70
0-80
Crude protein, g/kg organic matter (P)
50 100 150 200 250
Efficiency of utilization of gross energy, EQi m
0-246 0-241 0-236 — —
0-340 0-336 0-330 0-326 —
0-435 0-430 0-425 0-420 0-415
0-530 0-525 0-520 0-515 —
0-625 0-620 — — —
Efficiency of utilization of metabolizable energy, EM: m
0-615 0-602 0-590 — —
0-680 0-670 0-660 0-650 —
0-725 0-717 0-708 0-700 0-692
0-757 0-750 0-743 0-736 —
0-781 0-775 — — —
58 K. L. BLAXTER AND A. W. BOYNE
and no other combination reduced it. Class dif-
ferences were, however, apparent and the equation
was
Ea.m = c - 0-000862*'
RSD = ±0-0505, CV = 12-5%,
where the intercept, c, had the following values:
Diet class Intercept
Pelleted (1) -0-573
First harvests (2 and 4) -0-644
Regrowths (3) -0-609
Mixed diets (5 and 6) -0-604
It will be noted from comparison of the residual
standard deviations that there is distinct advantage
in using metabolizability in the prediction.
Growth and fattening
Analysis of 79 experiments showed highly signifi-
cant regressions of the efficiency of utilization of
gross energy for production on its metabolizabiiity.
The regressions varied from class to class of diet
and these differences were statistically significant
(P = 0-014). These regression equations are given
in Table 9.
Further analysis was undertaken with the 70
experiments for which chemical data were available.
When crude fibre and metabolizability were in-
cluded in the analysis, it was found that for pellets
fibre had no effect and that all other diets could be
described by the same regression coefficients. For
first harvested material, however, the intercept term
was 0-06 greater than for the remainder. The equa-
tion was
EG., = 0-6002*-0000622^ + 0, (17)
where F is the crude fibre content of organic matter
(g/kg) and the intercept, c, was 0-036 for classes 3, 5
and 6 (regrowths and mixed diets) and for first
harvests and hays (classes 2 and 4) it was 0-096. The
residual standard deviation from this regression was
± 0-0353. Values predicted from the equation are
given in Table 10.
Hoffmann, Schiemann & Nehring (1962) gave
pure starch to oxen in a number of experiments and
found it to have a mean metabolizability of 0-868
and that its metabolizable energy was utilized with
an efficiency of 0-641 ± 0-017 for fattening. For a
fibre-free diet with a metabolizability of 0-868 the
above equation predicts an efficiency of 0 • 641, which
is precisely the same.
A similar analysis was undertaken with crude
Table 9. Relation between
Class of feed
Pellets
First harvests and
Aftermaths
Mixed diets
All diets
and the
hays
. the efficiency of utilization of gross energy for production Eg ,
metabolizability of the gross energy of feed q*
No. in class Equation
12 Eg , = 0-494g*-0-008
25 Eg , = M15g*-0-380
11 Eg, = 0-874J*-0-299
30 Eg[, = 0-774g*-0-157
78 Eg., = 0-899g*- 0-251
Residual standard
deviation( +)
0-015
0-048
0023
0046
0-052
Table 10. Values of EG, , and EMi , predicted from the metabolizability at maintenance of the
9*
0-40
0-50
0-60
0-70
0-80
0-40
0-50
0-60
0-70
0-80
gross energy, q*
PftllRtfiH rHfit<3
. t UA1«31/UvL Lliv 09
(Class 1)
0-186
0-236
0-285
0-335
0-385
0-465
0-472
0-475
0-478
0-481
, and the
50
—
—
—
0-425
0-485
crude fibre content, F, of the organic matter <
Regrowths and mixed diets (Classes 3, 5 and
Crude fibre, g/kg organic matter (F)
100 200 300
Efficiency of utilization of gross energy, Eo.
— — 0089
— 0-212 0-149
0-334 0-272 0-209
0-394 0-332 —
0-454 — —
Efficiency of utilization of metabolizable energy,
—
—
—
0-607
0-606
— — 0-222
— 0-424 0-298
0-556 0-453 0-348
0-563 0-474 —
0-567 — —
of the diet (g\kg)
6) Addition for
first harvests
400 and 4)
0027 0-06
0087 0-06
— 0-06
— 006
— 006
Eu t
0070 0-150
0-174 0-120
— 0-100
— 0-086
— 0-075Nutritive value of feeds as energy sources 59
Table 11. Values of EG, t and Em, t predicted from q*, the metabolizability of gross energy at maintenance,
and the crude protein content, P, of the organic matter (gfhg) for diets other than Glass 1 (pelleted diets)
First harvests and mixed diets (Classes 2, 4, 5 and 6)
9*
0-40
0-50
0-60
0-70
0-80
0-40
0-50
0-60
0-70
0-80
50
0-158
0-254
0-348
0-444
Crude protein, g/kg organic matter (P)
100
A
150 200
Efficiency of utilization of gross energy, EBi f
0081
0-177
0-272
0-367
0-462
0-100
0196
0-290
0-386
—
—
0-214
0-309
0-404
—
Efficiency of utilization of metabolizable energy, Eu
0-319
0-423
0-497
0-555
0-203
0-354
0-453
0-524
0-578
0-250
0-392
0-483
0-551
0-428
0-515
0-577
250
—
—
0-328
—
—
r, /
—
—
0-547
—
Adjustment
for regrowths
(Class 3)
-0070
-0-070
-0-070
-0-070
-0-070
-0-175
-0-140
-0117
-0-100
-0-088
protein replacing crude fibre. Its inclusion did not
improve the prediction of Eg, / for pelleted diets.
For all other diets the inclusion of crude protein
significantly reduced residual error and between
feed classes there were no differences in the regression
coefficients. The intercept was, however, signifi-
cantly greater for regrowths of herbage (class 3) than
for the remainder. The equation was
EG, , = 0-951g*+ 0-00037P + C,
where P is crude protein content of organic matter
(g/kg) and the intercept, c, was — 0-336 for all diets
other than regrowths for which it was —0-406.
The residual standard deviation was +0-0349.
Values estimated from the equation are given in
Table 11.
DISCUSSION
The effect of crude fibre
It is unfortunate that the feedingstuffs had been
described chemically in terms of the Weende
methods of analysis; more modern ones based on the
use of detergents and enzymes (see Clancy & Wilson,
1966; MacRae & Armstrong, 1968; van Soest &
Wine, 1967) would have been more meaningful. Of
the other proximate constituents, only crude protein
appears to be as useful as crude fibre for predicting
nutritive value, and an examination of their values
in the 70 diets shows that, apart from mixed diets,
crude protein and crude fibre are negatively corre-
lated. It is possible that more precisely defined
attributes of the carbohydrate fraction of the feeds
would have been of even greater value. It has been
shown that metabolizable energy/g of organic matter
of feed can be predicted from the heat of combustion
of the feed and its crude fibre content with a residual
error of only + 6-9 % of the mean value. Inclusion
of crude fibre as a variable in regressions of efficiency
on metabolizability abolishes class differences be-
tween feeds for maintenance, and for production
enables a separation of feeds into two classes,
pellets and other feeds, to be made, again removing
class differences and reducing residual variability.
Increase in the fibre content of the organic matter
of a diet markedly reduces its metabolizability:
irrespective of the class of diet an increase of 1 g/kg
in its crude fibre content causes a fall of 0-0010 +
0-00008 in q*, the metabolizability at maintenance.
In equations (15) and (17), however, fibre content
contributes along with metabolizability to estima-
tion of EQ_ m and EG f. This suggests that crude
fibre, however poorly it describes the fibrous con-
stituents of diets, has relevance to the nutritive
value over and above that accounted for by its part
in determining metabolizability.
Feeding systems
The attributes of a feeding system which are
important in practice are that it should enable
calculation of the performance of an animal knowing
the amount and quality of the feed consumed, the
amount of feed of a given quality necessary to
support a particular performance, and the amount of
a feed of one particular quality which substitutes for
another of different quality in a diet without af-
fecting the performance of the animal. The per-
formance of growing and fattening animals with
which this analysis has been concerned is repre-
sented practically by a gain or loss in body weight.
Any system designed to meet the energy needs of
animals implies that these gains or losses of body
weight can be expressed in terms of a rate of energy
60 K. L. BLAXTER AND A. W. BOYNE
retention. For example, the loss of body weight on
fasting an animal represents a loss from the body of
energy equivalent to fasting heat production, while
a gain in body weight represents a retention of energy.
The use of the descriptive equation (2) requires
that measures of body weight gain should be con-
vertible into rates of energy retention. This entails
a tabulation of fasting heat production according
to breed, size, sex and other attributes and of the
energy retentions associated with gains in body
weight.
Given such a tabulation the model enables most
of the computations required of a feeding system to
be undertaken. If the metabolizability of a feed and
its protein content are known, the efficiencies of
utilization of gross energy for maintenance and
production can be estimated and the constants of
the basic equation derived. For example, for a diet
with a metabolizability of 0-6 and a protein content
of the organic matter of 150 g/kg, EG, m = 0-425
(Table 8) and .EG. , = 0-290 (Table 11). insertion of
these efficiencies in equations (12) and (13) yields
the constants, B and p, of equation (2), thus:
B =
EG 0-425
EG_m-EGit 0-425-0-290
= 315,
= 0 - 4 2 5 1 ^ = 0-162.
For any value of scaled gross energy intake, G,
1-6
1-4
1-2
10
0-8
0-6
0-4
0-2
0
-0-2
-0-4
-0-6
-0-8
-10
."8
0 1 2 -3 4 5 6 7 8 9 10 11 12
Scaled gross energy intake
Fig. 4. Energy retentions, R, corresponding to energy
intakes, O, of pelleted diets of differing metabolizabi-
lities. (The corresponding metabolizable energy intakes,
M, are also indicated.)
scaled energy retention B can then be estimated
from equation (2):
B = 3-15(l-exp(-0-162G))-l.
Conversely for any desired energy retention, B, the
gross energy intake is:
B
In this example,
O = • I n
315
0162 3 -15 - .R -1 '
Figures 4 and 5 show the corresponding scaled
gross energy intakes and retentions for diets with
different metabolizability. Figure 4 refers to pelleted
diets and Fig. 5 to diet classes 2, 4, 5 and 6 with a
constant protein content of 100 g/kg organic matter.
Similar graphs can be constructed for feeds with
different attributes.
Using tabulations of fasting metabolic rates these
scaled values can be converted to absolute gross
energy intakes and retentions for any given animal.
Absolute retentions can be expressed as changes in
body weight and absolute gross energy intakes as
amounts of organic matter either on the assumption
of constancy of the heat of combustion of organic
matter or more precisely if the composition of the
diet is known. The basic relationship thus enables
1-6
1-4
1-2
10
0-8
0-6
0-4
0-2
0
-0-2
-0-4
co
1 >e
u
-0-6
-0-8
- 1 0
0-4
0 2 4 6 8
Scaled gross energy intake
10
Fig. 5. Energy retentions, E, corresponding to gross
energy intakes, 0, of first harvests of forage crops and
of mixed diets (classes 2, 4, 5 and 6) all containing 100
g crude protein/kg organic matter but differing in
metabolizability. (The corresponding metabolizable
energy intakes, M, are also indicated.)
Nutritive value of feeds as energy sources 61
either performance of animals to be predicted from
their feed intake or vice versa more simply than by
the methods proposed in the ARC (1965) system.
The computation of the relative value of feeds as
components of diets is more difficult since replace-
ment value is not constant but depends on the level
of performance. Evidence is accumulating in support
of the hypothesis that metabolizability is an additive
attribute of feeds; the metabolizable energy of a
mixture is thus the sum of the products of the weight
of each feed present and its metabolizable energy per
unit weight. Replacement value of feeds on a weight
basis is not, however, proportional to metaboliza-
bility since energy retention is not directly propor-tional to the amount of metabolizable energy
supplied, but varies with the metabolizability of the
mixture as a whole, and also with fibre or protein
content.
It is evident that there is no unique replacement
value of one feed for another, either as complete
diets or as constituents. It depends upon feeding
level and upon the metabolizability and protein or
fibre content of each of the feeds involved in an
iterative way which precludes solution by single
algebraic expressions. Nevertheless, provided a
statement can be made of the context in which
replacement value is to be measured, it is not diffi-
cult to devise numerical or graphical solutions.
Table 12. Maximal efficiencies of utilization of the gross energy of feed (RjO)^^, and the feed intakes at which
these maxima occur (0^^ for diets of classes 2, 4, 5 and 6
Protein content of organic matter (g/kg)
Efficiency when intake is
optimal (B/G)m0I
Scaled feed intakes at which
efficiency is maximal (?mu
Metabolizability
of gross energy
0-4
0-5
0-6
0-7
0-8
0-4
0-5
0-6
0-7
0-8
,
50
0031
0081
0135
0-192
0-254
7-91
6-87
6-08
5-46
500
100
0041
0092
0-149
0-208
0-270
8-66
7-42
6-52
5-85
5-35
. —*
150
0-051
0-105
0162
0-225
—
9-54
8-10
7-07
6-34
200
0118
0-180
0-244
—
8-88
7-75
6-94
—
250
—
0-200
—
—
—
8-68
—
—
12
10
3
~ \
1 I
— — 2G*
G'
1
0-4 0-5 0-6 0-7
Metabolizability of gross energy, q
0-8
Pig. 6. Scaled gross energy intake at which maximal efficiency of utilization occurs (<?mox)> the intakes
at nutritional levels of 1, 2 and 3 x maintenance, and estimated maximal intake plotted against meta-
bolizability of gross energy, q, for diets of classes 2, 4, 5 and 6 with protein content of 100 g/kg OM.
62 K. L. BLAXTER AND A. W. BOYNE
Some derivations from the primary equation
Equation (2) can be manipulated algebraically to
define optimal amounts of feed to be given to an
animal. Since the primary descriptive equation
relates rate of energy retention to rate of feed intake
so also do the solutions, which describe optimal
amounts of feed to be given on a single day rather
than over weeks or months.
First, equation (2) can be used to define gross
efficiency, the ratio of retention to intake, viz.
which on maximizing shows that overall production
is maximal when
Differentiating this equation and equating to zero
shows that a maximum occurs when
dG'
From the efficiencies of utilization of gross energy
for maintenance and production given in Tables 8
and 11, values of B and p were derived by means of
equations (12) and (13) for classes 2, 4, 5 and 6.
Maximal efficiency of feed utilization was then
estimated for each pair of values of B and p by the
use of iterative methods to solve the equation
above. The results are given in Table 12 and plotted
in Fig. 6 for diets with protein content of 100 g/kg
OM. They show that irrespective of feed quality
intakes for maximal efficiency lie between twice and
slightly in excess of three and a half times main-
tenance . From the Figu re it may be seen that only for
diets with metabolizability in excess of 0-65 is there
evidence that the intakes necessary for maximal
efficiency can be achieved (on the basis of voluntary
intake estimated from Blaxter's (1964) relationship
for sheep and a fasting energy loss of 230 kj/kg
PP°'7S). This agrees with a conclusion reached by
Blaxter & Graham (1955). The relationship between
efficiency and scaled feed intake, however, is rather
flat around the optimum. Thus for a diet with 100 g
crude protein/kg organic matter and a metaboliza-
bility of 0- 7 a 20 % reduction in feed intake from the
optimal of 5-85 to 4-68 changes efficiency by only
3%, from 0-208 to 0-202. This suggests that animals
can gain at widely different rates in the region of
maximal efficiency without much change in their
overall efficiency. In the above instance the 20%
reduction in feed intake from that which gave maxi-
mal efficiency reduced gain by 23 %.
An analogous problem relates to the allocation of
a fixed resource of feed to animals. Denoting the
total feed by T and the number of animals as n the
problem can be formulated
/ / T\\
Z = nR = nJBll-expl -p-\\-n,
\ \ n)J
n d(Tjn)'
which is equivalent to
dG
and identical to the expression for maximal effi-
ciency in the individual. Thus, there is no advantage
to be gained by feeding animals other than at maxi-
mal efficiency.
Maximal profit is estimated by maximizing the
difference between the price of output and the cost
of inputs. If a is the price ascribed to output (R) and
y is the cost ascribed to input (G)
Profit, Z = aR-yG = ot(B- l-B(exp(-pG)))
— yG, which on maximizing gives the exact solution
= - ln-
PL 7
and this occurs when
1_dR
<x~ dG'
that is when the inverse price ratio is equal to the
first differential of the relationship between output
and input.
Proportional profit, that is profit as a proportion
of input can be formulated as
which is maximal when
«-§•
This solution is identical to that for optimal effi-
ciency of feed utilization.
All the above relationships deal with rates of
energy intake and retention, scaled as multiples of
fasting metabolism. If, however, equation (2) ia
supplemented by two additional relationships, the
first to convert energy retention into weight gain,
and the second relating fasting metabolism to body
weight, it is then possible to formulate a model
describing body weight gain over a period of weeks
or months.
Nutritive value of feeds as energy sources 63
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CORBETT, J . L., LANGLANDS, J . P . , MCDONALD, I . &
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FORBES, E. B., BRAMAN, W. W. & KRISS, M. (1928).
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64 K. L. BLAXTER AND A. W. BOYNE
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MITCHELL, H. H., HAMILTON, T. S., MCCLTTRE, F. J.,
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A
P
P
E
N
D
IX
 
T
A
B
L
E
 1
R
ef
er
en
ce
no
. 2 30 33 46 47 48 59 60 68 71 73 80 82 3 4 5 6 27 42 43 44 64
N
o.
 a
nd
sp
ec
ie
s 
of
an
im
al
IS 6S 8S 6S 6S 2S 4S 4S 3
S
4
S 4S 3S 4S 3S 3S 3S 3S IS 4S 4S 4S 3S
N
o.
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f
ob
se
rv
at
io
ns
in
 a
dd
it
io
n
to
 f
as
ti
ng 7 11 16 6
|
6 ;;} 9 12 8 1 7 8) 12 f 12) 8 CD 00 00 00
6
5 66
3S 3S
P
la
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of
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xp
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R
an
do
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 a
ll
oc
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2 
am
ou
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s 
of
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ac
h 
di
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gi
ve
n 
in
 a
 f
or
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eq
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1 
m
ai
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 1
di
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am
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S
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sh
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cr
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 a
m
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nt
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of
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M
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1 
ad
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11 11 12 19 19 23 24 25 22
^ S TO 05 s O5 Ox
A
P
P
E
N
D
IX
 T
A
B
L
E
 
1 
(c
on
t.)
O
5
er
en
ci
n
o
.
39 40 4
1 7 1 8 9 10 11
N
o.
 a
nd
B 
sp
ec
ie
s 
of
an
im
al
4S 4S 4S 4
S IS 3S 3
S
3
S 3S
N
o.
 o
f
ob
se
rv
at
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ns
in
 a
dd
it
io
n
to
 f
as
ti
ng 00 00 00 8 51 9
/
9 1 9 9J
28 29 45 67 72 74 1
2 13 14 15 16 31
IS 6S 6S 3S 4S 3S 2S 2S 2S 3S 3C 6S
12 6 9 8 6J 12
C
on
st
an
ts
 o
f 
th
e 
en
er
gy
 e
qu
at
io
ns
F
or
 e
st
im
at
in
g 
en
er
gy
re
te
nt
io
n 
fro
m
 g
ro
ss
en
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gy
 i
nt
ak
e
F
or
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st
im
at
in
g 
m
et
ab
ol
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ab
le
en
er
gy
 f
ro
m
 g
ro
ss
en
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M
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ia
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d
S.
37
 c
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fo
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 d
ri
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, 
1s
t 
cu
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B 6
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62
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83
S.
24
 r
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gr
as
s 
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ie
d 
1s
t 
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4-
54
P
la
n 
of
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xp
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t
P
ai
re
d 
ob
se
rv
at
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ns
 w
it
h
ea
ch
 a
ni
m
al
P
ai
re
d 
ob
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at
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ns
R
an
do
m
 a
ll
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at
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n
L
at
in
 s
qu
ar
es
 i
n 
w
hi
ch
ea
ch
 a
ni
m
al
 r
ec
ei
ve
d
3 
am
ou
nt
s 
of
 f
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d
R
an
do
m
 a
ll
oc
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n
2 
am
ou
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s 
of
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ac
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di
et
 
F
es
cu
e 
ha
y 
fe
d 
as
 c
ha
ff
gi
ve
n 
in
 a
 f
or
m
al
 s
eq
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nc
e
L
on
g 
dr
ie
d 
gr
as
s 
(f
es
cu
e)
3r
d 
cu
t 
pa
st
ur
e 
gr
as
s,
2 
cw
t 
N
 f
er
til
iz
er
3r
d 
cu
t 
pa
st
ur
e 
gr
as
s,
3 
cw
t 
N
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er
til
iz
er
3r
d 
cu
t 
pa
st
ur
e 
gr
as
s,
4 
cw
t 
N
 f
er
til
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er
3r
d 
cu
t 
pa
st
ur
e 
gr
as
s,
5 
cw
t 
N
 f
er
til
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er
A
ut
um
n 
cu
t 
fr
ee
ze
-d
ri
ed
S
ep
ar
at
e 
sh
ee
p 
gi
ve
n
di
ff
er
en
t 
am
ou
nt
s
L
at
in
 s
qu
ar
e
2 
am
ou
nt
s,
 1
 a
d 
li
bi
tu
m
L
at
in
 s
qu
ar
e
P
ai
re
d 
ob
se
rv
at
io
ns
 w
it
h
ea
ch
 s
he
ep
E
ac
h 
an
im
al
 r
ec
ei
ve
d 
a
m
ai
nt
en
an
ce
 a
m
ou
nt
 o
f
fe
ed
 a
nd
 a
n 
am
ou
nt
do
ub
le
 t
hi
s 
in
 a
 r
un
do
w
n
al
lo
ca
ti
on
 s
ch
em
e
2 
am
ou
nt
s 
of
 e
ac
h 
di
et
gi
ve
n 
in
 a
 f
or
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A
P
P
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N
D
IX
 T
A
B
L
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1 
(c
o
n
t.
)
C
on
st
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ts
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f 
th
e 
en
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gy
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qu
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io
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R
ef
er
en
ce
n
o
.
62 63 3
2 81 17 18 19 20 21 22 2
3 24 25 26 34 3
5 36 37 38 4
9 50 51 5
7
N
o.
 a
n
d
sp
ec
ie
s 
of
an
im
al
3S 3S 3
S
4S 3S 3C 3S 3C 3S 3C 3
S 3C 3S 3C 3C 3C 3C 3C 3C 3C 3
S 2C 2C
N
o.
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f
ob
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ns
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 a
dd
it
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to
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as
ti
ng
12
 (
4)
"j
12
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4
)/
9 \ 8j 6' 6 6 6 6 6 6 6 6 6 9
]
9 9 1 15 17 11 8
P
la
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M
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h 
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im
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%
 
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M
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ra
ss
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d 
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at
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L
it
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at
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re
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e
21 21 8 5 5 5 5 5 5 5 5 5 5 1
0 10 10 10 10 13 13 14 17
< i" TO | 'feeds a 03 s 2 i
O
S
0
0
A
P
P
E
N
D
IX
 
T
A
B
L
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1 
(c
on
*.
)
N
o.
 a
nd
N
o.
 o
f
ob
se
rv
at
io
ns
R
ef
er
en
ce
 
sp
ec
ie
s 
of
 
in
 a
dd
it
io
n
to
 f
as
ti
ng 9 9 9 9
75 76 77 78 79 52 53 54 55 56 58
an
im
al
3S 3S 3S 3S 3S 1C 4C 4C 4C 4C 7S
P
la
n 
of
 e
xp
er
im
en
t
L
at
in
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qu
ar
es
S
eq
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nt
ia
l 
fe
ed
in
g
T
w
o 
am
ou
nt
s 
of
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ee
d 
fo
r
ea
ch
 a
ni
m
al
34
 
W
it
h 
on
e 
ex
ce
pt
io
n 
ea
ch
sh
ee
p 
gi
ve
n 
5 
am
ou
nt
s
8
\
C
on
st
an
ts
 o
f 
th
e 
en
er
gy
 e
qu
at
io
ns
F
or
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st
im
at
in
g 
en
er
gy
re
te
nt
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n 
fro
m
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ro
ss
en
er
gy
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nt
ak
e
F
or
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st
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at
in
g 
m
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ab
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le
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er
gy
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ro
m
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ro
ss
en
er
gy
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nt
ak
e
M
at
er
ia
l 
fe
d
20
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ba
rl
ey
 
E
x
p
t 
6/
R
R
I
40
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np
ro
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E
x
p
t 
6/
R
R
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60
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ce
ss
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x
p
t 
6/
R
R
I
80
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E
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p
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6/
R
R
I
A
ll 
ba
rl
ey
 
E
x
p
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6/
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22
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6
1
6
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R
M
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2
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63
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5
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0-
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97
9
M
ix
ed
 d
ie
ts
; h
ay
, 
ce
re
al
, p
ro
te
in
 c
on
ce
nt
ra
te
:
0-
16
49
6 
0-
57
65
 
00
00
97
3-
38
 
0-
19
32
 
00
04
43
73
 %
 m
ai
ze
, 
24
 %
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ay
,
2-
0 
%
 l
in
se
ed
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il 
m
ea
l
30
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uc
er
ne
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ay
, 
40
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m
ai
ze
, 
30
 %
 l
in
se
ed
 m
ea
l
30
 %
 t
im
ot
hy
 h
ay
, 
50
 %
ba
rl
ey
, 
20
 %
 m
ea
t 
sc
ra
ps
1
5
%
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ed
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lo
ve
r 
ha
y,
 6
0
%
 
2-
72
 
01
65
9 
00
02
03
 
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0
5
6
3
6
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ts
, 
25
 %
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ot
to
ns
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d
20
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at
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tr
aw
, 
45
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w
he
at
, 
20
 %
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oy
a-
be
an
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ea
l
P
el
le
ts
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f 
50
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he
at
, 
40
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3
0
2
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ce
rn
e 
ha
y,
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0
%
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ol
as
se
s
7-
82
 
00
61
9 
00
08
23
 
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0
2
2
6
7
5-
63
 
0-
08
47
 
00
05
02
 
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1
3
0
6
8
2-
67
 
0-
16
93
 
00
08
89
 
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0
7
4
6
5
0-
22
05
 
00
07
39
 
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5
7
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4
0-
64
44
 
00
00
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0-
65
97
 
00
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0-
55
60
 
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58
80
 
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72
98
 
0-
00
27
6
L
it
er
at
ur
e
re
fe
re
nc
e
26 26 26 26 26 1
5 16 16 16 16 18
R
ef
er
en
ce
s:
 1
. B
la
xt
er
 &
 G
ra
ha
m
 (
19
55
);
 2
. A
rm
st
ro
ng
 (
19
64
);
 3
. B
la
xt
er
, W
ai
nm
an
, D
ew
ey
, D
av
id
so
n,
 D
en
er
le
y 
&
 G
un
n 
(1
97
1)
; 4
. B
la
xt
er
 &
 W
ils
on
 (
19
63
);
 5
. B
la
xt
er
&
 W
ai
nm
an
 (
19
64
);
 6
. 
C
or
be
tt
, 
L
an
gl
an
ds
, 
M
cD
on
al
d 
&
 P
ul
la
r 
(1
96
6)
; 
7.
 K
. 
L
. B
la
xt
er
 &
 N
. M
cC
. G
ra
ha
m
 (
19
57
 E
xp
t,
 u
np
ub
li
sh
ed
);
 8
. B
at
em
an
 &
 B
la
xt
er
 (
19
64
);
9.
 K
. 
L
. 
B
la
xt
er
 &
 J
. 
L
. 
C
la
pp
er
to
n 
(1
96
6,
 u
np
ub
li
sh
ed
) 
an
d 
B
la
xt
er
 (
19
68
);
 9
a.
 B
la
xt
er
 (
19
68
);
 1
0.
 B
la
xt
er
, 
C
la
pp
er
to
n 
&
 W
ai
nm
an
 (
19
66
);
 1
1.
 B
la
xt
er
 &
 G
ra
ha
m
(1
95
6)
; 
12
. G
ra
ha
m
, 
W
ai
nm
an
, 
B
la
xt
er
 &
 A
rm
st
ro
ng
 (
19
59
);
 1
3.
 B
la
xt
er
 &
 W
ai
nm
an
 (
19
61
);
 1
4.
 F
or
be
s,
 B
ra
m
an
, K
ri
ss
, S
w
if
t, 
F
re
nc
h,
 S
m
yt
he
, W
il
li
am
s 
&
 W
ill
ia
m
s
(1
93
0)
; 
15
. M
it
ch
el
l, 
H
am
il
to
n,
 M
cC
lu
re
, 
H
ai
ne
s,
 B
ea
dl
es
 &
 M
or
ri
s 
(1
93
2)
; 
16
. M
itc
he
ll 
&
 H
am
il
to
n 
(1
94
1)
; 
17
. F
or
be
s,
 B
ra
m
an
 &
 K
ri
ss
 (
19
28
);
 1
8.
 M
ar
st
on
 (
19
48
);
19
. G
ra
ha
m
 (
19
67
);
 *
20
. H
as
hi
zu
m
e,
 K
ai
sh
io
, A
m
bo
, M
or
im
ot
o,
 M
as
ab
uc
hi
, A
be
, H
or
ii
, T
an
ak
a,
 H
am
ad
a 
&
 T
ak
ah
as
hi
 (
19
62
);
 2
1.
 G
ra
ha
m
 (
19
64
);
 2
2.
 F
. W
. 
W
ai
nm
an
&
 K
. 
L
. 
B
la
xt
er
 (
19
69
, u
np
ub
li
sh
ed
);
 2
3.
 B
la
xt
er
, W
ai
nm
an
 &
 S
m
it
h 
(1
97
0)
; 2
4.
 W
ai
nm
an
, B
la
xt
er
 &
 P
ul
la
r 
(1
97
0)
; 2
5.
 W
ai
nm
an
, B
la
xt
er
 &
 S
m
it
h 
(1
97
2)
; 2
6.
 W
ai
nm
an
&
 B
la
xt
er
 (
19
72
).
* 
T
he
 c
on
st
an
ts
 f
or
 t
hi
s 
Ja
pa
ne
se
 e
xp
er
im
en
t 
ar
e 
no
t 
in
cl
ud
ed
 i
n 
th
e 
ta
bl
e.
 A
s 
m
en
ti
on
ed
 i
n 
th
e 
te
xt
, 
th
e 
re
su
lts
 w
er
e 
an
om
al
ou
s.
w > w o