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MICROCOPY RESOLUTION TEST CHART
LEGAL NOTICE
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Government sponsored work. Neither the
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!
e
AM
Kiwango
ORNL-P_1339
CVE-650709-1
WUN 2 4 1965
PROBABILISTIC ESTIMATES OF RANGE FORAGE INTAKE
G. M. Van Dyne?
Radiation Ecology Section, Oak Ridge National Laboratory
Oak Ridge, Tennessee
Forage intake 18 never measured directly in grazing studies, but
estimates of mean forage int&ke are obtained indirectly by lignin ratio,
chromogen ratio, fecal nitrogen index, or microdigestion techniques.
Estimates of dietary composicion are usually obtained from a group of
esophageal or ruminal fistulated animals and estimates of quantity and
composition of fecal output are obtained from a separate group of animals.
No measure of precision is obtained with these techniques, however, be-
cause estimates of forage intake obtained thereby apply to the group
rather than to individual animals. In addition to an estimate of the
mean forage intake, it is desirable to have a knowledge of the distribu-
tion about that mean.
A method is described in this paper for generating a population of
forage intake values about the mean value of forage intake so that the
nature of the distribution may be examined. . The method is applied to
data from range nutrition studies ir: which microdigestion techniques were
used to calculate mean forage intake.
METHODS
Daily forage intake (F) may be calculated by the equation
F = (100 •E•E.) / (100.F -F.M).
(1)
Waere E is the quantity of feces produced per day, e lo the porcent cell-
ulose content of the feces, Fc 18 the percent cellul3se content of the
diet, and Mc 18 the percent microdigestion of dietary cellulose (Van Dyne
and Meyer, 1964a,b). In these experiments E, Ec, and Mc were measured
with one group of animala and F. was measured with a second group of
animals grazing with the first group. Estimates of the means and standard
deviations of these four variates and the simple linear correlations
among E, Ec, and Mc were obtained with esophageal and ruminal fistulated
steers and sheep in three grazing experiments. All data aro on organic
matter basis. It was assumed that these four variates follow a normal
distribution. .
Values of F were generated by equation (1) from generated values of
B, Ec, Moe and F. Values for E, EC, and Mc were selected independently
in the first set of computer experiments. In a second series of experi-
ments these values were selected at random from a trivariate normal popo
ulation. The method used for selecting variates is an extension of that
Research sponsored by the U. 8. Atonic Energy Commission under
contract with the Union Carbide · Corporation.
L. R. Shenton is ac knowledged for his suggestions for a method to
select random deviator from trivariate normal populations.
LXXVII-1
PATENT CLEARANCE OBTAINED. RELEASE TO.
THE PUBLIC IS APPROVED. PROCEDURES
ARE ON FILE IN THE RECEIVING SECTION.
described by Meller et al. (1955) for generating randon deviates from
the bivariate normal population.
Random deviates wore obtained by using random number generators to
select u, V; and w as mutually independent standard norngi deviates with
means of zero and variances of one. Values for x, y, and 2 were then
selected so that they were standard deviates from a trivariate normal
population. His was done by first lotting x equal u and generating y
us follows:
(2) yur, ou + &•v whore r, 1. the measured correlation between E
and E. . The value for a was derived as follows:
(3) variance of y-i.*+ 8? which lead to
(4) yorguu+(1-2).9.v.
Having selected x and y, then z vus selected so that
(5) 2* •4 + bov + cow subject to
(6) variance of solra +6C + c where a equals r. (the correla.
tion between E and Mc) and b was calculatod from ra (the Eorrelation
between me and Me) by (
19. 3. *0f3-)=7703f1-4).
t bo i o
bdi.
solving for d gave
By substituting the nalues of a
talood u
Loto (6) the wlwo for o vus ob-
19
..(*
)
Hou waing these wives for a, b, and c and substituting into equation
(5) the ya lue for u was detenuined so that x, y, and 2 were random
dorsator from a trivariate normal distribution.
the standard normal deviates x, y, and %, whether selected inde.
pendently or from a trivariato normal population were then scaled by
equations (10)
(10)
LOVII-2
.
.
.
whore ogg , and on vere the measured standard deviations and 3, ...
and were the mousure: moans.
Values for F. vore selected similarly at random using the nown and
standard deviation for forage collulose (respectively wad sy ). Po
was selected independently from E, Ec, and Me and then equationc(1) was
used to calculate values of F. The nature of the distribution of i was
examined by conventional statistical techniques.
RESULTS AND DISCURSION
Repeatability of procedures.--To check the reliability of the avoro
procedures for generating random normal deviatos, arbitrary nalunu verd
selected of means and standard deviations of I, E., Mae and Pi. Tasso
values weru wod to gonorate 2000 values of fin six fwi assuming no
intorcorrelation among the variates. The resulting mean values of F,
with seven significant digits for comparative purposes only, were as
follows:
956.4872
954.0356
952.2196
953.4908
957.6038
954.9436 :
the slight variability wrong those means for p shows the range in masvers
that might be expected due to different sets of computer gonerated randon
aumber. The closeness of those betinatos of F led to the use of only
1000 gonorated values in succeeding experiments.
Bsperimental nluas for I, C. M, and E. --Means, standard dort.
ations, and numbers of an Iman on which these statistics are based on
given in Table 1. The animals were grazed on an annual grass-open oak
voodland mange throughout the summor. The unpunt of bertato available,
la metric tons por hectare, was 1.67 in Period I (early July), 1.37 la
Period II (early August), and 0.47 in Period III (early September).
Table 1. Basic data from six range experiments with cattle and sboep.
Soccretion and forage data are expressed on organic matter basis.
Data are mean I standard deviations.
· Shear
Cattle
Huriod: ::
Vurdable
Pocos, 8 3931123 4601104 3914106 22801206 287&t297 32961532
. Noon
cellulose,$ 35+1:3 3743.0 3634.3 34+1.7 3413.7 3481.3
Cellulose
mbarodi.
gestion, $ 5212.5 . 56t2.1 5214.7 6473.
9 5206.7 5015.8
forage
cellulose, % 37+2.4 4111.3 4051.6 4081.1 43+1.2 1241.0.
lountity of scoreta, focal collulose, and cellulose microdigestion data
won menoured with 9 riminal fistulatod wether and stoon. Forge collu.
Lore data are based on results for 7 and 5 csophageal fistulated sheep and
stmersrespoctively (Van Dime und Meyer, 19640; Van Dime and Heady, 1963).
LOVII-3
win-
+
Iride pendent vs. dependent variates.--Average results for F from
several computer experiments are given in Table 2 for runs in which E,
Ec, and Mn wero selected independently (r4y = 0) or where they were
selected from trivariate normal population (rello). When the variables
measured with the riminul fistulated animals were not assumed indo pondent,
there were slightly higher extimates of forage intake than 11 they vore
assumed independent. The greatest variations occurred for sheop in
middle and late summer. These latter two differences are significant in
a statistical, but not a practical sense. Most of the measured corre-
lations, however, were small as shown in the following table :
Period
Sheen
Cattle
I
E:E.
Sheon Cattle
..18 .04
.62 .24
. .60 ..35
E:M
Sheen Cattle
.0 .66
.05 .25
...25 . .36
.0)
.02
.25
.31
II
III
.240
.04
It it noteworthy that the only instance where F for independently se-
lected variates was greater than F for dependently selected variator was
for cattie in period III when there was a high correlation between E.
and Mc.
Table 2. Comparisons of means and standard deviations for generated
values of forage intake with and without intercorrelations of
varistes.
Class
Period
*13*0
-------grams organic mattor-------
787 1 247
785 $ 250
8houp
945 + 226
970 1 287
738 • 242
761 t 273
5444 1 841
5475 : 1040
Cattle
4862 1017
4852 1186
ILI
5392 1 1163
5386 1 2090
1 Bach mean 18 based on 1000 generated values.
Normality of distribution of F.--The distributions of the generated
values were examined by O plotting normal curves, generated from the
data in Table 2, on histograms for ten class intervals and (b) by plot-
ting the cumulative distributions on a probability scale. Por both
species, but especially for cattle, there was a tendency for the observad
distributions to be skewed slightly to the left when compared with the
normal curve. This phenomena was equally prominent for independent and
dependently selected values of I, Ic, and Ma. The greatest single
deviation from normality occurred, .bowever, for sheep in period III when
the variator were selected dependently. The data suggest that, for all
LOVII-4
practical purposes, the distribution of coon be regarded as approaching
the normal distribution. Logarithmic trunsfur:nations of the data did
not produce "neuror norioul" distributiu!e.
Precizion of estimates of ".--lhe inagnitudes of the coefficients of
variation may be used as an estimate of the precision of estinates of
i'oruge intake. Iliesc val.123, 111 percolt, were as follows:
Sre::108
Periori
114
10130
· Sheep
II
ano
III
Cattle
TI
III
The above data suggest (a) estimates of t'orage intake for sheep are
significantly less precise than those for cattle, (b) estimates of for-
age intake assuming interdependence of Ei, Ec, anů M, are slightly less
precise than assuming independence of these vario.coš, und (c) estimates
of forage intake, averaged over both species and methods, were slightly
less precise in late sumner than in early summer. The average coef-
ficients of variation for the summer respectively for E, EC, Mc, and F.
for sheep were 30, 8, 6, and 6 and for cattle were 11, 7, 20, and 3.
Thus, for sheep the precieion of the estimule of l'orage Intake 10 similar
to that for total fecal output, but for cattle total fecal output is
measured with greater precision than 18 forage intake.
SUMMARY
Forage intake is never measured directly in grazing stu: les. Daily
forage intake (F) may be calculated by the equation
·
--
-
F = (100•E. •E) / (100.F. - FM)
where E 18 the amount of feces produced per day, E. 1s the percent cell-
ulose content of the feces, F. 1s the percent cellulose content of the
diet, and M is the percent microdigestion of the dietary cellulose.
The means and standard deviations of these four variables are obtained
by sampling and these values are assumed to be normally distributed.
Correlations between E, and E, E. and Me, and E and Mc may be evaluated
because estimates of these three variables are obtained concommitantly
from & given group of animals. Estimates of F.are usually obtained
from a second group of animals which graze with the first group.
The mean and distribution of estimates of the forage intake may be
obtained by generating values of f calculated with the above equation
from independently or dependently selected values of E., E, and M and
Independently selected values of Fc. This technique was applied to
data from range nutrition experiments with cattle and sheep to determine
the nature of the distribution about F.
LXXVII-5

.
1
*
Although generated populations of i were slightly skewed to the
leit in some instances, especially for cattle, for all practical pur.
poses they can be regarded as approximately normuse I distributions
whether generated from independently or dependently selected values of
E, E., and Mc The precision of estimator of forage intake for cattle
were greater than for sheep. Estimates of forage intake for either
species were less precise than the corresponding estimates of F., Moe
and E. For sheep, but not for cattle, the precision of estimates of
were of the same magnitud as those for F.
this procedure offers a means of assessing the precision of esti-
mates of Porage intake in studies with grazing animals, whereas by con-
ventional procedures there 18 no measure of precision.
LITERATURE CITED
Poller, £. C., T. Lewis, and F. 8. Pearson. 1955. Tracts for college
putors: XXVI. Correlated random normal deviates. Cambridge U.
Press. XV + O pp.
Van Dyne, G. M. and H. F, Heady. 1965. Dietary chemical composition
of cattle arid sheep grazing in common on a dry annual range. J.
Range Mangt. 18:78-86.
Van Dyne, G. M. and J. H. Meyer. 1964a. A method for measurement
. of forage intake of grazing livestock using microdigestion
techniques. J. Range Mangt. 17:204-209.
Van Dyne, G. M. and J. H. Meyer.
sheep on a dry annual range.
19646. Porage iptake by cattle and
J. Animal Sci. 23:1108-1115.
.
.
LXVII-6
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81 / 30/ 165
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