Kl

 

APPUCATION OF THE EQUATION OF THE
MW GF DIMINISHING {NCREMENT TO SWINE
NUTRITION

Thesis foe the Dogm of M. S.
MRCHIGAN STATE UNIVERSITY
V‘erl E. Headiay
1960

APPLIGKPIQI CF THE EWM‘IW W THE CURVE
(F DIHIHISHING INCREHENT TO 5m MIG

Val E. Hadley

MW

Sub-uteri to the Cellege of Agriculture
Michigan State University of Agriculture and
lpplied Science in partial fulfillment of
the mural-ate for the degree of
MASTER CF SCIENCE

Dope-taunt. of. Animal Husbandry

1960

ABSTRACI' Verl E. Headley

Two studies were conducted using live weight-feed consumption data
from280babypigs {birthtoueaning) cnasyntheticnilkdietandfrcn
1200 animals (weaning to whet) fed a typical ration of fixed ecu-posi-
timinanattemttcdetermineifthisdataccnfcrmedtotheequatim
of the curve-of diminishing increment and till: Qply all equations
derived from it.

Averages of live weight and feed consunption were calculated at
equalintervalsoftine, thatishdayintervdsforthebabypigsand
2weekintervalsfortheaninalsfronweaningtonarket.

The constants of the equation of the curve of diminishing increment
were calculated and adjusted by the statistical method of least squares.

Its application to the baby pig data on a synthetic milk diet,
though reasonable acctn-acy was obtained, was not found to be practical. .
since the live weight-feed consumticn relationship of the baby pig over
this range (6 weeks) was essentially linear. ‘

bplyingtheequationtoswinedatafromweanixg tomarketwasfound
to conform with a high degree of accuracy. Calculated values of emails-
tive feed comunption were in agreemnt with 11.8.0. standards.

The 1133th efficiency of feed utilisation was equally ids-
tica‘l to the N.R.C. standards to 160 pounds live weight. However, from
160 pounds to 200 pounds live weight the N.R.C. values denote a higher
efficiency than the calculated values in this stub. Calculated instan-
taneous efficiency decreases linearly with increasing live weight.

Maintenance requirements as applied in this study and as defined
by the equation include all feed consumed exclusive of that which is

Verl E. Headley
utilised for protein storage (growth). Cumulative maintenance require-
nents increase exponentially with increasing live weight. Instantaneous
maintenance requirements increase linearly with increasing live weight
when expressed as aspercent of instantaneous feed comunption but expon-
entially when expressed in terms of pounds of feed per day. i

The graphical solution of the live weight at which the pig-plus-feed
cost per pound gain is the least gave a reasonable estimation of the
live weight of the animal at which the madman returns, including weaning
cost of the animal in terms of pounds of feed, is attained for feed
coneueed. ‘

APPLICATION OF THE EQUKPIQV OF THE CURVE
W DIHINISHING INCREHENI TO SWINE NUTRITIQJ

by
Verl E. Headley

A THESIS

Submitted to the College of Agriculture
Michigan State University of Agriculture and
Applied Science in partial fulfillment of
the requirements for the degree of

MASTER OF SCIENCE

Department of Minal Husbandry

1960

ACKNWIEIDMNTS

The author wishes to express his sincere appreciation to Dr. E. R.
Miller, under whose guidance, assistance and encouragement this nami-
script was prepared. ' ’

Thewriteralsowishestoaclmowledgehisindebudnesstom. J. A.
Roofer for his assistance and cooperation in supplying a portion of the
naterial necessary for this study.

Sincere thanks are extended to Dr. D. E.’ Ullrey for his unfailing
interest and encouragenent during the course of this study, and also
to hmda Kay Butcher for typing this manuscript.

Verl.E. Headley
candidate for the degree of

Master of Science

DISSERTATION: Application of the Equation of the Curve of Diminishing
Increment to Swine Nutrition

OUTLINE OF STUDIES:
major subject: Animal Husbandry (Animal Nutrition)
Minor subject: Bio-chemistry'

BIOGRAPHICAL ITEMS:
Born, January 15, 1927, Eden, Ohio

Undergraduate Studies, Tri-State College of Engineering,
1956-1958

Graduate Studies, Michigan State University, 1959-1960

E
a

Ten Sigma.Eta Honorary Engineering Society

TABLE OF CONTENTS

INTRODUCTICN.......................
REVIEWQ‘LII'ERM‘URE...................
History........................
Equationlnprovements.................
acquingIntakeIevelswitthuation.........
CarparingProteinIavelswitthuation........
ConpaflngBreedswitthuation............
ApplyingEquationtoSteers..............
RecentApplications..................
EXPERDENI‘ALPROCEDURE._.................
Derivation of the Equation of Diminishing Increment. .
Derivation of Equations for Application. . . . . . . .

Solving for Constants A and k by Method of Least
sqmaeeeeeeeeeeeeeeeeeeeeeeee

Method of Feeding and Mmagenent of Baby Pig on
smwetumnmetOOOOOOOOOOOOOOOOOO

Composition of Synthetic Milk Diet . . . . . . . . . .
Observed Data of Baby Pig on Synthetic Milk Diet . . .

Calculations and Adjustments of Constants A and k for
Babypignataeeeeeeeeeeeeeeeeeeeee

Method of Feeding and Management of Pigs Weaning to

Mketeeeeeeeeeeeeeeeeeeeeeeee
Coaposition of Typical Ration Used . . . . . . . . . .
mutaofPingnWeaningtoMarket. .. .. .

Calculations and Adjustment of Constants A and k for
Pigsweaning‘toOMBrketeeeeeeeeeeeeeeee

Page

‘ONIO‘UIMMH

21

25
26
27

29

36
37

Lo

Page

Rasmsmmscussxm.................. 1,7
BabyPigCalculations................. 1,7
WeaningtoMarketCalculations............ 56
smxmcmcmsxons.................. 69
BIBLIGRAPHY....................... 71

TABIE or ILLUSTRM‘IONS
Page

Figure l - General Relationship of Live Weight to Feed
Consqution'Conforuingto Curve of Diminishing Increment 114

Figure 2 - weerved Cunulative Efficiency of Feed
Utilisation (go) Versus Live Height (w). . . . . . . . 28

Figure 3 - weerved thulative Efficiency of Feed
Utilization (go) VON“. u” Weight (')e e e e e e e e 39

Figure I; - Live ht (w) Versus mserved Cumulative Feed
Consuaption (fo and Calculated leative Feed
muon(tc)seeeeeeeeeeeeeeeeee 50

Figure 5 - Instantaneous Efficiency of Feed Utilisation
(Ei)vmuamwwaight(w)eeeeeeeeeeeeee, 51

Figure 6 - Ooserved Cumulative Efficiency of Feed
Utilisation (go) and Calculated Cumulative Efficiency
of Feed Utilization (13c) Versus Live weight (w). . . . 52

Figure 7 - live weight (w) Versus Cumulative Maintenance
W<M¢)eeeeeeeeeeeeeeeeeee 53

Figure 8 - Live Height (w) Versus Cumlative Feed
0013th (re) and Cumulative Maintenance
Requiremt(fic)................... 5h

Figure9-Instantaneous MaintenanceRequirenent(M1)
as Percent of Instantaneous Feed Consumtion Versus
unweight(')eeeeeeeeeeeeeeeeeeee 55

Figure 10 - Live Height (w) Versus Observed Cumlative
Feed Gonennption (to) and Calculated Culmletive Feed

Won(tc)eeeeeeee.eeeeeeeeeee 61

Figure 1.1. - Comparison of Calculated Cumlative Feed
muon(f¢)mdN.R.C.Vdues..eeoeeee. 62

Figure 12 - Comarison of Calculated Instantaneous
Efficiency of Feed Utilisation (E1) and N.R.C. Values. 63

Figure 13 - (beerved Cmmlative Efficiency of Feed
Utilisation (g2) and Calculated Cumulative Efficiency
of Feed Utili tion (5c) Versus Live weight (w). . . . , 6!:

Figm-e 1h - Live Weight (w) Versus Cmuilative Maintenance
W(MO)OOOOOOOOOOOOOOOOOOOa65

Page

Figure 15 - Live Weight (w) Versus Omnilative Feed
Consmption (fc) and Cumulative Maintenmce -
W(Mc)eeeeeeeeeeeeeeeeeee “

Figure lé-Instantaneous Maintenance Requirement (”1)
as Percent of Instantaneous Feed Consumption Versus
M"Wt(w)eeeeeeeeeeeeeeeeeeee 6?

Figurel'l- calMethodofmtdningtheDesii-ed
Value of (w in Equation (20) for each Value of (u)
”mmMeeeeeeeeeeeeeeeeeee &

INTRODUCTIOI

Workers in animal nutrition have long felt the need for some satis-
factory meane of expressing mathematically the relation between growth
of an animal and feed consumtion. likewise the med for a simle but
accm'ete method of measurim and cowering the efficiency with which
animals utilise feed. for growth has long been recognised by nutritionists.

Titus _e_t__g,_,, for a umber of years have shown that the equation of
the curve of diminishizg increment, w - L-(Aawik'k‘, accurately describes
therelationbetweenlive weight of anmimal andfeed consumtionona
diet of fixed cosposition.

In a recent publication Titus (1959) applied the equation of the
curve of diminishing increment (andgequations derived from it) to
poultry. '

The objective of the present study was to apply the equation of the
curve of diminishing increment to swim. That is to deter-ins whether
or not the live weight-feed consumtion data for 280 baby pige (birth.
to weaning) on a synthetic milk diet and the live weight-feed consumtion
data for 1200 animals (weaning to market) on a fixed ration did accurately
conform to the equation of the curve of diminishing increment, and if so
apply the equation and all equations derived from it.

.2-
LITERM'URE REVIEW
new:

The term "law of diminishingreturns' is a cannon one in the
literature of ecmomics as well as in agriculture.

The mathematical expressions of the above law were discovered
independently by Dr. E. A. uiteoherlieh, of the K3ningsberg (Germany)
kperiment Station, mid by Dr. H. J. SpiJJman of the United States
Department of Ag'iculture. Dr. Mitscherlich's discovery ante-dated
Dr. Spillman's by several years. However, in Germany this law was
very prOperly called Mitscherlich's law, while Dr. Hitscherlich himself
’ called it the Law of Physiological Relations. Dr. Spillman adopted the
name, Law of the Diminishing Increment for it since it applied quite
generally to natural phenomena, both biological and physical. Dr. Lang
of Bonn University, Ger-w, suggested the same name as did Dr. Spinner).

Ir. SpilJman was born in 1863. His original home was in Lawrence
county, Missouri. He spent a great deal of his lifetime in service
with the United States Department of Agriculture. From 1902 to l918
he was in charge of grass and forage plmt investigation in the Agri-
culture Department. He left the department for a few years in 1918.
During this time he held several positions one of which was in an
cecutive position with the Farm Journal and another as a professor at
Georgetown University. Later he rejoined the United States anartmait
of Agriculture where he remained until his death in 1931.

Dr. Spillman ie credited with being the discoverer of the nethe-
maticalfomofthelawofthediminishingincrenent, whileDr. Lang
is associated as co-author of the same law.

'3-

The ten "law ofdiminishing returns" is more or less loosely
applied to several types of phenomena all of which involve a gradual
decrease in the per unit effect of some factor as the quantity of the
factor acting increases.

Dr. Spill-en's first observance of the possibility of such an effect
wasinAugustl920, inanarticleoftheCoimtryGentleman. Inthis
article, J. 8. Gates gave the resulting increases in the yield of
eottonononeoftheencperinentalterneintheuorthCerolinenepert-
ment of Agriculture. Gates gave the increase in yield for each two
hundred pounds of additional fertiliser applied. The increments applied
weretwohmdredtptoonethousandpomdsperacre. This decreaseof
net increase in yield is shown in the second colt-n of the following

 

 

table. .

I II III IV
meet y erved et ie et srence
Fertilizer lbs Increase Diff. ”field Increase

200 102.5 103.9 _ 1.1:
1:00 85.0 80.0 -3.6
600 62.5 61.8 4A.}
800 15.0 h9.h 0.1
1,000 ‘ 32.5 313.9 2.5

 

In studying the data at the time of its publication it occlirred to
Dr. Spillman that possibly the figures in the second colusli tend to
constitute the tens of a decreasing geometric series 3 that is if the
second figure was 72 percent of the first, then the third was 72 percent
ofthesecond, thefourthfigure72peroentofthethird, etc. He

.1...
calculated the geometric series agreeing most nearly with this series
of increments in yield, the calculated series being shown in the third
colum of the table.

Dr. Spillman found that the agremt between the two series,
while far from perfect, seemed to be sufficiently close as indicated
in column four. In view of the reasonably small variability of less .
than 2 percent of the calculated from the observed values, In. Spillmm
pursued the matter further.

‘ with further observations Dr. Spillman (1921) found the following
trenbi -' . _

(a) The increase of an application of a second unit of fertiliser
didnotproduceasgreatanincreeseinyieldaccordingasthefiret
unit of fertilizer.

(b) then increasing the inches of irrigation water applied per acre,
thenetincreaseinbushels ofpotatoes per acrewas less than that for
the preceeding water application.

(c) The second increasing unit of feed consumed by an animal pro-
ducedlese increaseinliveweightaccordingasthefirstunit offeed
consumed. _ . .

In practically all cases Dr. Spill-an found only a slight deviation
of the values calculated by the equation for a decreasing geometric
series freer actual observed values. 7

Dr. Lang (Germany) pointed out in 1923 in his part of. the book

written in eondmction with Dr. Spill-an that when the mute or feed
consumed were plotted as the abscisses and tin live weight as the

ordinates, successive increments in weight corresponding to successive

-5-
equal increments in feed consumed would tend to constitute the terns of
a decreasing geometric series.

The observations led Dr. Spillnan to the derivation and application
of the equation of the diminishing increment. Since his first applica-
tion in the early 1920's a considerable effort has been made to inprove
the equation, its application, and the formulas derived from it. Most
of the work with the equation has been done in poultry nutrition in the
past thirty years, with small amounts in other fields, and will be
illustrated in the remainder of the literature review.

Titus 931$: (1928) showed that theegrowth of Pekin ducklings
could be described by the equation very well. They found the equation
to be a fairly accurate means of expressing the live weight of growing
ducklings as a function of feed consthion. Beymd this they pointed
out the fact that each successive gain in live weight for an acquired
increment of feed intake seemed to bear a constant ratio to the gain in
11” weight illnediately preceding .

ion rovenents

Titus. $.93; (1931) suggested a more accurate method of interpreting
the results of feeding experiments by means of the equation. Up until
this time the most rapid and accurate method of deteming the values
' of the constants of the equation was by arithlog plotting. However, it
was found to be very difficult to judge with accm'acy the values of the
comtmte because of the fluctuation of the data from a straight line .

These men tried a nethod of approximating the values of the con-
stants which appeared to give more accurate results than the method of
arithlog plotting. They found that by differentiating the equation,

.6.
w - i-se-ki', and through manipulation the following differential equa-
tion was obtained, dw/df - G -kw. From observing the form of this dif- .
ferential equation it was seen to be that of a straight line of the form
y I m: + b. Furthermre, since the differential equation was now in the
form of a straight line the nethod of least squares could easily be
applied. The values of the constantsgandgcouldbe foundandadjusted
by the sons method.

Intheirpoultry experiment Titusgtgggfomd that the chief
someofinaccuracyintheprevious rapid-ethodwasduetothefluct-
nation in the data between intervals, while the advantage of using the
differential equation and method of least squares was the elimination
oftheerrorofjudgnentastowheretodrawthelineonthegraphfor
determiningtheconstantsgandk', (c-u).

In levels th tion

Hendricks Le}; (1931) studied the requirements for growth of
chickens rising from different nutritional levels . These nutritional
levels were: ad libitun, 87.5, 75.0, 62.5, 50.0, 37.5 and 25.0 percent
levels of the amount a chicken would be expected to consume ad libitun.
Theequationofthedininishing incrementwas appliedinthis studyas
wellastoestablishthe reqtdmentforgrowth. Itwasundertakento
deterunne whether or not Q of the equation, which represents the maxi-
um instantaneous efficiency of feed utilization for growth that would
be observed if no feed'me required for maintenance, was influenced by
the level of nutrition on which the chicken was reared.

The results showed the equation of the diminishing increment to be
01' value in determining the suitability of a given feed mixture for

-7-
growth. The degree of utilisation of that fraction of the feed intake,
which remains for growth after the other requirements of the body have
been met, Qpeared to be independent of the level of nutrition at which
the diet was fed if the level of the diet were held at Qproxinately a:
constant percentage of ordinary ad libitm feed consumtion . The nati-
nun live weight,A, atdnable as found by the equation was seen to be
roughly directly proportional to the level of nutrition on which the
the chickens were reared.

Titus gm; (1931;) ran comparative feeding experiments on groups
of chickens fed at a level of intake to 70 percent of an idealized value
aswellas adlibitun. This unperinentwaerunrorszmeksetwhichtine
average live weights were plotted against cumlative feed consumtion.
The limited fed chickens showed the 25 percent protein diet to be the
most efficient while ad libitm showed the 21 percent diet as giving the
the largest live weight. Likewise the lots fed on the 70 percent limited
diet showed the 17 percent protein diet to be slightly more efficient
in utilisation of protein than lots fed the 15 percent protein diets.
W

Hammad g_t_._a_l_. (1938) performed a comrehensive study on the rela—
tionship between the level of protein intake aid live weight, feed
utilization, and protein utilization of crossbred male chickens from

.8.
Rhode Island Red males md Barred Plymouth Rock females. The diets
ranged from 13 to 25 percent crude protein md were so arrmged to
increase in protein by 2 percent increments. Data were collected for
52 weeks 31d from these the stmdarden‘or of the mean was calculated
for live weights as well as the statistical significmce of the diff-
erences between the means. Applying the equation of the diminishing
increment the proper values established were as follows: the modicum
live weight obtainable, the efficiency of the diet when there is no
maintenance requirement, maocimma gain obtainable, and the Spillman
ratio.

The results of the equation indicated on the basis of feed comuned
that the 21 percent protein diet was the most efficient of the lots fed
ad libitum , aid those on the 25 percent protein diet were the most
efficient of the limited fed lots. Also with chickens on the 70 percent
normal intake diets, the Spillnan ratio decreased as the level of protein
increased.

Hendricks M. (1933) found by use of the equation that as the
age of chickens increased, efficiency of feed utilization decreased and
that as the protein content of the diet increased efficiency of feed
utilization increased, but in chickens of the same age the efficiency
of protein utilization decreased.

Harmond 31;]; (1939) measured the feed efficiency and growth
rate by varying the level of protein intake in the diet of turkeys. It
was observed that the efficiency data of feed utilization in turkeys

-9-
would fit very close to a straight line when plotted against live weight.
Therefore, the equation of the diminishing incessant was applied and the
constants detemined by the method of least squares with similar effi-
ciency results as found in chickens.
Capturing Breeds with Equation

Hess 333;. (191d) used the equation and method of least squares
in testing the efficiency of feed utilisation of Barred Plymouth Rock
broilers and crossbred broilers (crossbred between Barred Plymouth Rocks
and New Hampshire pullsts). The results showed that in most instances
the crossbred chickens of a given sire were more efficient thn the pure-
brads of the suns sire.

Glazener 93.5.1; ( 19w) studied efficiency of feed utilisation in
two strains of New Hamshires md Barred Plymouth Rocks aid found that
the progeny of the long shenked strains tend to grow faster and utilise
feed more efficiently th- the progeny of the short shanked strains.
Growth was calculated as a function of feed consumtioa and all data
were malysed by the method of least squares as well as the equation
conforming to that of the diminishing incremnt.

Jull £41911?) selected two strains free New Hampshire poultry.
The two strdns that were selected were those that differed significantly
in body weight at four weeks of age. The progeniee of these strains were
placed under uperinantation. The emerinental results were found through

the application of the equation and nethod of least squares.

~10-
ihs results showed differences between progenies as to the rate of gain
and efficiency of feed utilisation although efficiencies approached each
other toward the end of the ten week period. However, evidence brought
forth by the equation indicated some heritability of efficiency of food
utilisation. _

Hess 313.; (19th) made a study of the inheritance of feed utili-
sation efficiency in the growing domestic fowl using both crossbred
stock (Barred Plymouth Rocks and New Hallpshires) and purebred stock.
Solution by use of the equation and method of least squares showed a
definite inheritance of differences in feed utilisation between indiv-
iduals. These differences were as follows:

(a) The male chickens were slightly more efficient than the females.

(b) The .15 values in males are somewhat lower than for females indi-
cating either a lower naintenance requirement for sales or a more rapid
decrease in efficiency in females due to a lower mature weight.

(c) Crossbrsd chickens were more efficient in feed utilisation than
purebreds sired by the e... male.

(d) Inbreeding had a detrimental. effect on efficiency of reed
utilisation.

(3) New Hewehirss were more efficient in feed utilisation than the
strains of Barred Plymouth Rocks.

Fox 2.2.2.1.: (1953) used the equation in establishing the ehperinental
results with four breeds of poultry (New Hmnpshires, Dark Cornish, Purdue
Dominant whites, and South Carolina white leghorns) as to feed efficiency
along breeds of chickens and its relationship to growth rate.

.11..

The analysis of data calculated by use of the equation showed the
New Harpshires yielding the overall highest efficiency of gain. The
male chickens gave higher efficiency than females, and there was also
a decrease in efficiency with an increase in live weight.
32m much to Steers

anp at}; (19%) selected steers because they were equal in
gross efficiency. They observed the steers with the largest initial
live weight made the higher daily gain, ate lore but were slightly less
efficient than those of a lighter weight. But when the equation of the
dinnishing increment was applied by the method sinlar to that of
Hanldns and Titus (1939) the heavier steers were more efficient than
those of the lighter initial weight. The correlation between daily
gain and corrected efficiencies of gain was found to be 0.83.

They then concluded from their previous error that selection of
animals on gross efficiency in time constant feeding periods is generally
(misleaditu and even erroneous.
hcent lications

Titus (1959) applied the equation of the dimnishing increment and
equations derived from it to poultry feed consumption as conpared to
live weight in obtaining estimations of the following:

(a) The live weight that is attained as the result of the consum-
tion of any specified quantity of feed (within range over which data
had been acquired). I

(b) The quantity of feed required to attain any specified live
weight (within range ..........).

.12-

(c) The instantaneous efficiency of feed utilisation at any
specified live weight (within range ...........)

(d) The cumlative efficiency of feed utilisation to any specified
live weight (within range ...........)

(e).The cumulative maintenance requirement to any specified live
weight (within range ..........).

(f) The maintenance requirement between any two live weights
(within range ..........).

(g) The percentage of feed being used at any live weight (within
range ..........) for maintenance. .

(h) The live weight (within range .........) at which the "animal-

plus-feed" cost is the least.

~13-
EIPERINENTAL PROCEDURE
Derivation of the mtion of Diminism Increment

Dr. Spillman indicated the curve of diminishing increments by
illustration of figure I.

The abscissas :1, :2, :3, etc. represent the quantities of feed .
eonsmeed by an minal. The ordinates n. 12, y3, etc. represent the
increases in the live weight. Dr. Spinner: pointed out that the ratio
ofarwinoreaseinliveweighttoitspreceding valuewouldtendto
yield a constant ratio, less than one (and in this example equal to 0.8.

These types of observations led to the application of the formula
for a decreasing geometric series and derivation of the equation of the
diminishing increuent which was derived as follows:

The formla for the sun of a decreasing geometric series is described by

l. S - “la-Rn}
1-8
Where

§_isthesun oftheincreaseofgtemsintheseries.
gistheflrstterwintheseries.
gistheflerofternsintheseries.
.R_ is a constant ratio and is less than unity.
Uhengbecouesinfinite
2.3- a

Letgrepresentths sun of the seriesasgbeoones infinite orthe
Iain poseibleincreass.

Reva-iting (1) in a more algebraic form

3. y - Ian-m)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2°°° F T T.
1 3 ::
* E
y '- 3(1-8‘) :
' 1'8
I 105
1500 76 fi
75 f - 131
§ s - 16h
‘ 71; ”iii
no i . was
T. --
c 1- 256
E a ....-
é ; 3
- b - 320 i
500 .43.- ...JL. % ,.. ..___.|
11 -
s - hOO a:
I
§
0 4 ——l———H———i
I0 *1 12 X3 214 :5 16 1=7 18
1.c
Figm'e 1

General Relationship of Live weight to Feed conexnption cantons-dag to
Curve of Diminishing Increment.

.15.

It embeshownthatgcanbe replacedbyet'k
Proof:
If ya, ynfl, ya... 2, represent the sums of increases, then the ratio
of the differences of any two consecutive increases must equal e'k if it
is to replace 5.

yn - 8(1-e'h)

ya i» 1- 3(l-e-k(x*1))
yn + 2- B(l-e’k("‘2))
Taking the ratio

13% - 7n . 3(1-9’1‘1‘2“) - 8(1-s’h'k) . 3.1;

Ml " In '0' "
Ravi-tins (3)
h. I " 3(1-e'h)
Transforming (h) to show actual values instead of the increase of values.
Let‘ y-f-I, and 3-4.1,
where

Tie the actual observed value

_!,i is the initial observed value.

_A_ is the marina possible.

(A-n) is equal to g which was previously defined.
By substitution in (h) and simlification

1-11 - (As-Ii) (l-s'h)
5. I O A - (A-Yfle'h
Replacing symbols in (5) by those pertaining to feeding observations.
6. *w - AAA-Iii)?“
*Equatiou of the curve of the diminishing increment.

-16-
Where:
1 is the live weight after any quantity of feed, g, has been con-
smiled.
A is the maximum live weight attainable as a result of growth, but
not as a result of fattening.
a is the. initial live weight, or the weight at which feeding is
begun. I
g is the base or the natural systm of logarithms.
.1; is a constant which determines the decrease in the efficiency of
feed utilization as the live weight increases .
g is the quantity or feed that is required for any live weight g.
_B_ is the total gain, (A411), possible as the result of growth.
Derivation of tions for lication
Solving (6) for _f_ as a function of g and sinplifying.

I ' A -(A-N1)e'kf

°'kf'%

Takingsthe logarithms of both sides of the equation

(4:2) (in e) 'ln{_A;-w;)_y
i
f- -; lnéhvwz
1‘ i
Rearrangement of equation to eliminate minus sign

7. 1"th '12. l M
e m1 a was“ the

Note: Replace-ant of. the natural logarithm to the base 3 may be made
by loglo, since 2.3025851 logy, - lna

.17.
Differentiating equation (6) to obtain instantaneous efficiency of feed
utilisation. I
. w - A - (Hh'fl
dw'O'tkU-wfle'kfdf-O
dw/df " “Av-111%”
Substituting for e-kf, the equation becomes
dv/dr - led-u)
Since dw/df is the instantaneous efficiency, it will be replaced by the
synbol 31. ‘
8. E; - knew) or 81 - 0 do:
Since equation (8) is that of astraightlineofthe foray-n+b,
then it is evident that if E; is at its naxinun, 3 essentially goes to
zero. Therefore c - kA represents the headlam- instantaneous efficiency
of feed utilisation for growth that would be observed if no food were
required for maintenance. . i
This being true then ; is the quantity of feed required to obtain live
weight A. k
Also:

cumulative efficiency '- gain in live mm;
feed consulted

9.1.0.2? . ting}

1

 

Similarly, the reciprocal of E1 is the instantaneous feed conversion
efficiency, as is the reciprocal of fig equal to the cmlative feed

conversion efficiency.

.18 a

10. Fi-éi- 1

11. P'], .111"
c ‘E; _Effli§w;
"1

The equation fer cumulative maintenance requirement can be written as

 

follows:

12. H5 - f -§w~w32

Where:
£Lis the total feed consumed
Eigi'ia the feed required to bring about the gain in live weight,

(wuwi), providing no feed is used fer maintenance.
By substitution '

“vi-hat '15—'41

Likewise, between any two live weights

11.4353: - rz-ri- w-nfin

k E u

k E:
An accurate estimate of the percentage of the feed that is being used
fer maintenance at any instant can be obtained.by'differentiation of

mu (12)e

He - f - gw'-'w32

nd-df- hide-o

.19..
$1 " 1 " it“
Now dw/df - Kin-w) from equation (8).
By substitution and simlification

$4" -kA- flaw I'w
"'13€EL“" ‘I

Expressdngasapercentage

16. %-M1(as%offeed)-vllxloo

Similarly, equation (16) may be used for estimating the percentage of
feedthatis usedbetween anytwo live weights that arenot greatly
different.

[M] :1 -Sn+322%xloo
17. [gig -Sg+m2x50
'1

The relationship described by the curve of the diminishing increment may
be used for determining the minim 'animal-plus-feed' cost per pound of
gain in live weight, as follows:
Ietg-themlmberofpoundsoffeedthatisequalinvaluetothe
cost of one animal, and
rm; - the animal-plus -feed cumulative feed conversion

Equation is:

180?“- £+u
{w-wfl

Differentiating equation (18) .

an“) - gu - wfldf - Sf + uzdu
w .. w1

-20-
Dividing both sides of the equation by g;

dSFEfl I w- dfdw- f+u
aw-wflz

By substitution for instantaneous feed conversion dfldw

19. dwfifl - gs - 312455“; - gr + uz

v - vi .
than 53%;) - O.
Thieisthapointvhenl'wrbasitsninimvalnsoritis the valueat
which aninal-plns-feed costs are the least per unit gain in live weight.
Therefore, setting the right hand side of equation (19) equal to zero

and siaplifying results in the following:

w- Aw-f'tu '0
w-w1

(w - WinU-N) - (r + u) - o
Placing over cannon denominator and simlifying
(w - w1)-k(f + u) (As-w) ' 0
Substituting equation (7) for f

(w-vi)-l:ku+ln*m{| (A—s) -0
20. (w-w1)-(A-w) ku+lnéfi§l

The value oftheliveweightgforanyspecifiedvalue ofgcanbe
obtained graphically as follows:
Plot

a) w vs. (w-w1)

b) w ve.(1~v) Eu'tlnfiflgl

-21-
The point at which the straight line and curves intersect (one for each
value of 2) will be the live weight g which satisfies the equation md
likewise will be the live weight at which d(Fu+f)/dw - 0, which will be
the live weight of the animal at which "mind-plus-feed“ cost per pound
of gain is the least.
Solving for the Constants A and k by the Method of Least Squares.

 

 

Note:
The method of least squares gives the most probable values of the

unknowns that render the sun of the squares of the differences a mini-
aua, where the most probable values of the unknowns are those that most
nearly satisfy the observation equations.

The basic equation for the sin of the squares of the differences is:
21. z -Ze2 - Zip-w; -c)"’

Note: .. ..
E has replaced (4:) inequation (21) togiveBi-k'wi- c, the

equationofastraight line ofthe formyfnx+b, the formto fit any
general case whether _lg', the slope of the straight line, be positive or
negative. .
Thedesiredvaluesarethoseofgandy whichrenderthefunctiona
Mailman. This is obtained by equating to zero the derivative of the
function with respect to that variable. That is to say it is desired
to have as follows:

d_Z_-0 and _d_Z_-O
dc dk'

By differentiation of (21) with respect to g and y
g_z_- 2X(-E'1-k' 3-0) -dc
%- 2:51-» w-c) (.1)

.22-
Also
dz -2Z(E-k' w-c) -;dk'
a: 2’3“ ‘ ' °’ "

Setting dz/dc - o and dZ/dk' - o and simplifying
22.8%: ; -c) (-l) - o *
23.233» 3 -c) (3) - o

It can be pointed out that in each case each observation which
renders the function with respect to g a minimum is multiplied by the
coefficient of g, and likewise each observation which renders the
function with respect to .1; a minimum is multiplied by the coefficient
of .15.

Therefore, for any number of observations we can write 5 equations
with respect to Q and sumate (using equation 22) yielding one normal
equation. Idleewise one can write 3 equations with respect to g and
sunsets (using equation 23) yielding another nonnal equation. Now there
are two normal equations and two unknowns which can be solved simultaneously
for Q and k, and since 2 I In, A can be easily calculated.

The follfndng derivation is based on any mmber of observations, and since
the coefficient of Q is one, a will equal the sum of the coefficients of Q.
Equation (22) become

XE - k'Z; - nc - 0

Likewise equation (23) for g observations~ becomes
{353' - k'XE'2a-cZ? -- o

-23-
Solving simultaneously for y
a) began? - nk'Z? moi; - o
)ZE Zw -k'q.)2- nCZwI
n w-E -27} «amaze2 + 16(23):: - 0
mg: n)2 - {:3 I211! - {Ii '
21:. k‘ IZweE - {32.3.
i. D
zw _ gig?

n

 

Note:
In the derivation of equation (2].), 5 can replace 5' man using

the proper signs of the coefficients for the equation (8) E I a; + c,
that is the coefficients are aid?) for g and that of El. plus one.
For em of derivation these signs could be neglected since as indicated
by equation (23) and (21:) both are negative.
Similarly constant 9 can be calculated as follows:

ZE-ktzw-nc -o
25. g - ~k'z-w- +212;

n n

Since the values of _A_ and 5 previously calculated may not be the
west accln'ate values for equation. (9), it is necessary to adjust than
insuchawayastoreduceto aminiuuinthe suuof the squares of the
differences between the observed values of E0 and the calculated
values Ed.

The adjustment equation is:
26. '15,, (5:1,)2 - e
C £ + c B
T lib-1'17 (AI!)

 

.2)”.
Where:
CKCfis the correction to be made to 5;
Q is the correction to be made to _A_
e - E0 .. E,
c c
cx:‘and G3 are calculated by the method of least squares
Each set of adjustment values 0C and e , which are calculated,
are added to or subtracted fromeLand'§;depending upon whether the sign
is positive or negative. Taking the newly adjusted values of g and .15.,
one again.applies them to the adjustment equation and new correction
values chd B are obtained. This is continued until the adjustment
valuestlc:and G3 are very small in comparison.toԤ,and A, The corrected
values of 5 and A are now the most stable, and can be used in the .

application of all previously derived equations.

p 25‘
Method of Ffl and Management of Baby Pg on 82thetic Milk Diet
In this study of the baby pig on a synthetic milk diet the live

 

weight and feed consqution (dry basis) data were observed and recorad.
Data of this. type from approximately 280 animals were used. The animals
were selected at 3 days of age and placed in the Michigan State University
Hutrition Barn where all studies were made. There, another 14 days on the
synthetic milk diet was allowed prior to collection as an adjustment
period. The data in this study are therefore recorded at b day intervals,
thatisfronthetinetheaniaalwas7daysofageuntilh7daysofage.

As to the method of feeding md aanagenent the general procedure
was as follows:

1. Pigs were fed on the average I; to S tines daily.

2. Tenperature of synthetic milk fed to pigs was 80 to 100° F. for

‘ the first week and so to 70° F. thereafter.
3. The environ-ental temperature «a: . 70° 1“. plus infrared lamps to
give proper teaperature for the pig .

h. All animals were individually fed throughout the entire study.

The observed data were obtained. by taking the average of all live
weights and feed consmption data at 1; day intervals for the 280 animals.
These averages were entered in the table as average live weight and
feed consuletion. ‘

The observed cumulative feed consmption was obtained by emanation
of the feed consumtion for all previous intervals. Likewise the
observed efficiency for the interval (E '2':- - :11; and cumulative
efficiency (Kc-w L111) were calculated by the use of these averages

for live weight and0 feed consumtion.

-26-
The live weight and feed consusption data handled in this manner
were used in the application of the equation of the dininishing incre-

sent and equations derived from it.

Composition of Synthetic Milk nietl

 

 

Constituents kaount (S dry basis)
NIHC 1.5
Casein, Labco 30.0
Lard 10.0
Cerelose 52-5
Mineral nurture 6.0
A, C, D, E, K and B-conplax vitamins +
Vituins (amt. per kg. milk) Minerals
Thiamine 0.65 ng. Cali? 3&0
Riboflavin 0.65 118.01 ).01S KI) 120
Niacin 2.50 ' KzflPOh 260
Pyridoxine 0.65 Ga lactate 230
Calcium pantothenate 3.00 HgSOhJIzO 35
‘ Para-aninobensoic acid 2.60 “011,320 1
1310811901 26.00 ZnSOhJ'IzO h
Choline 260.00 0601,5320 0.5
Biotin 0.01 00012.6820 0.5
Pteroylglutanic acid , 0.052 FeSO],.7320 8.5
Ascorbic acid 16.00 Cerelose 0.5
Alpha-tooopherol acetate 1.00
2-nethyl-l, h-napthoquinene 0. 28
Vitamin A 2,000 1.0.
Vitamin D 200 LU.
W

 

J"Twenty percent solids in water. _
2NaHCO3 supplied to aid in suspension of casein in water.

Cbserved Date of Baby Pig on Synthetic Milk Diet

-27-

A_

 

Age Average Av. Feed Av. Feed Efficiency. Efficiency
(days) Live wt. Consumd Consumed Cbserved, E Observed E.
(lbs.) Period (lbs.) Oun.(lbs.) Period Cu-ulativi

7 5.13 0.00 0.00 0.000 0.0000000
11 6.00 0.72 0.72 1.210 1.2083333
15 7.00 1.02 1.7h 0.980 1.07h7126
19 8.10 1.28 3.02 0.859 0.983hh37
23 9.50 1.59 14.61 0.881 0.9109393
27 11.15 2.02 6.63 0.817 0.9079939
31 13.20 2.h3 9.06 0.8hh 0.8907285
35 15.h0 2.7h 11.80 0.803 0.8703389
39 17.50 3.23 15.03 0.650 0.8230206
1:3 20.30 3.70 18.73 0.757 0.8099306
b? 23.80 b.26 22.99 0.822 0.8120922

 

-28-

1.5 F

1.2 "'

“J”

0.9 b

L 1 l I

o 5 lo 15 20 25

 

‘ w (lbs.

Figure 2. )

Observed Cumulative Efficiency of Feed Utilisation (E0) Versus Live
Weight (w) °

-29-
flgglations and Adjustments of Constants A and k for Baby PiLData
Fron the observed data given previously the estimates and adjust.
acute to constants A and k can be obtained. .
The first step is to obtain estimates of the constants C and k in
the equation,
Bi-c-kw..................(8)
And since equation (8) is that of a straight line, it my also be I
written as

E-C-kSg+gz or E-C-kw

Where E and .1; as calculated as follows:

7;, the average weight1 E, the average efficiency?

 

5.57 1.210
6.50 00980
7.55 0.859
8.80 0.881
10.33 0.817
12.18 0.8“.
1h.30 0.803
16.15 0.650
18.90 0. 757
22.05 0.822

1 G is the average weight for each four day period.

2 E is the averaged observed efficiency for each four day period.

This urical values of C and k are then obtained by the method

.30-

of least squares, illustrated in the derivation fron equation (21)

through (25) and applied as follows:

 

 

 

a b 1 8 hi) b]. be
4' E

1 - 5057 10210 - 303w 31.02119 - 6e7397 1807152
1 I- 6.50 0e980 " 11.520 112.2500 " 6.3700 29.380)
1 - 7.55 0.859 - 5.691 57.0025 - 6.b855 112.9670
1 - 8.80 0.881 - 6.919 77.18.00 - 7.7528 60.8872
1 “me 0e81,} .10e3& 11880352" - 9091,85 126e2s78
1 '1he30 0e803 .12 .119 7 206‘s hm -1.1.h829 178 e 7071
1 .16ehs 0e650 -1’.1.8m 270ew25 .10e692h 2113.116“)
l -18.90 0.757 -17.1h3 357.2100 -1h.3073 328.0027
1 -22.05 0.822 -20.228 h86.2025 «48.1251 “16.02711
0 - , 3 , 3 .10) .03 , z , .3 a. 0'0 0*” .,

01‘ 01‘ 01' or 01' 01‘ or
(«)1 (ab); (al)1 (ash (bb)1 (bl)1 (bs)1
Check:

(as); + (ab); * (a1)1 - («)1

10 - 122.63 ‘0' 8.593 ' 1011.03?

(abh + (bb); + (b1)1 - (be);
-122.63 + 1, 781.2837 - 100.3099 - 1558.31.38

Calculations tor the first estimate of k, c and 11.:

k-(b1)2 ,c--§ab;] k+éalgg 3a-C/k
2 .1‘11 .“"1,

(bb)2 " (bb)1 - ab ab 3
(“)1

1The equation used here for calculating k and c are identical to previously
derived equations (21.) and (25), for sample (bl)1 is equal to £3.35.

(b1), - (bl); - (ab? (a1);
. a 1

-31-
(bb)2 - 1,781.2837 - (4.22.6322 - 277.h720
10

(bl)2 --100.3099 - 9122.6;5 (8,523) - 5.0661

1: ' .0661 ' 0.018258058

C . - .122e6 ) 0.01.82 0 ) + 8.52: . 1.0831981}?
10

A $88-$86

The first estinates of A and I: have now been calculated. The next

" 59327111143

step is to adjust the values of these constants A and k in such way as

to reduce to a minimum the sun of the squares of the differences between

the observed cumlative efficiency and the calculated cumulative effi-

ciency. This is done through application of the method of least squares

again when applied to correction equation (26) by the following procedure:
Calculations for f:

for w1 - 5.13, A - 59.3271hh3, k - 0.018258058, (A-wi) - 514.1%th

 

 

 

w (M) fiat-a) log iA-wiz f - log (lg!
- w A - w c 1
’ 01329 k
5.13 5h.197u;h3 1.0000000 0.000000000 0.0000000
6.00 533271183 1.0163th 0.007025187 0.8859700
7.00 52. 327111143 1.0357367 0.0152m82 1.922h950
8.10 51.227lhh3 1.0579771 0.02hh80369 3.0873016
9.50 1.9.8271th3 ’ 1.0877032 0.036511276 8.6015597
11.15 1.8.177JJ4h3 1.1210555 0.051133093 6.1885661
13.20 1.6.1271hh3 1.1710512 0.0700219h8 8.8307031
15.1.0 1.3.92711813 1.2337962 0.0911h6636 11.h9h8085
17.50 n.82mu3 1.2957109 0.112521926 1h.19°5180
20.30 39.027117173 1.3887038 0.11.2608181 17.98h7960
, 23.80 35.5271115 1.5255136 0.181.13827 23.13093h0 -

 

 

He distiiguish fitween t5 observecFfiues o? f and the calculate-d values
of f, the observed values will be written as f. and the calculated values
will be written as fc, both ef which represent cumulative feed comunption.

.32-

Calculations for go, Ec and <§° - 13c) as follows:

 

 

 

w I f (w-Iwi) - Eo- 9-( - )

o c 5° Lian). c ilfl go EC
SelB 0.“) OQW Com m
6.00 0.72 0.8859700 0.87 1.2083333 0.9819716 +0.2263588
7.00 1.71. 1.9221050 1.87 1.07b7126 0.9726913 -0.1020183
8.10 3.02 3.0873016 2.97 0.983hh37 0.9620051 -0.021b386
9.50 h.6l h.60b5597 8.37 0.9h79393 0.9h90593 -0.0011199
11.15 6.63 6.hh85661 6.02 0.90799h0 0.9335h09 -0.0255h69
13.20 9.06 8.8307031 8.07 0.8907285 0.9138570 .0.0231285
15.h0 11.80 11.h9h8085 10.27 0.8703390 0.893hh68 -0.0231078
17.50 15.03 H.1905180 12.37 0.8230206 0.8717088 -0.0h86882
20.30 18.73 17.98h7960 15.17 0.8099306 0.8838902 -0.0335596
23.80 22.99 234309310 18.67 0.8120922 0.80m +0.00h9b80

 

With the right hand side of the adjustment equation (26) now cal-
culated the next step toward the adjustment of the constants A and k is
to calculatethe values for the left hand side of equation (26).

Calculations for lgc/k and (1392/ lea-n) (A-w)

 

 

 

2
5.}. 03..)2 mag) (A...) (gs) /k(A-w1) (A...)

53.78 30753 0.961.27398 52.7690558 0.018273h7h
53.27h7956 0.9h613h26 51.7795212 0.018272361.
52.68931875 0.9258538? 50.6910331 0.018256757
51.98029h3 0.900713% 89.30568176 0.0182679b3
51.1303h69 0.871h985h h7.6729525 0.018280775 ,
50.0522558 0.83513h6b 1.5.61.1.th 0.018296538 -
189310823 0.7982h720 h3.h67b303 0.018 361.260
h7.7h37863 0.75987630 bl.389h076 0.018359197
h6.h526669 0.711147579 38.6187106 0.018h23085
11113075609 0.651h8181 35.159391. 0.018531518

 

 

 

 

-33-

anodes-Hon on» .«o

.eeaseos scene are ounces eflssa near: unease wuss-see an asset as one use
fund a on outflow-on so: one ens-.3. 6333-0 one: Auden-acouuv 933.30 scene one 0.33 33» :HH

 

 

 

ans :3 :3 :3 :3
ho Ho “0 .no .no
sensmnemoo.o meccoemmoo.o oeae~a~4.as nonessea.e nsmre.so~.m~
omen-mooco.o+ oasflamamooo.o mamnpmam.o + Humnmmam.o H::m0m.4mma empamsoo.o+ mamammmao.o moem~o~.aa
Nsmmnaeooo.cu eooflsenmooo.o swmmcmmm.a - msaonmmo.o «esomm.ama~ meemmnno.ou mmonmsmao.o aeewms.es
secmmmmooo.ou maoeoammooo.o amemmswn.m . «mammepm.o oche4.m-~ «momemso.oa sesamneao.o newsmse.ps
Nwmmsmsooo.o. monswpnnooo.o emce~0ma.a . nsnsermr.o Hhcmpm.smn~ nocoanmo.on oemsemoao.o nwonsme.es
mwssmwsooo.o- unmeasmmooo.o commesm-.- - Nonesmae.o Hame-.m0m~ smesflmwo.on enmeeweao.o emmmmmo.om
assesesooo.o- assessmmooo.o eeHNNeom.H . ammo-snm.o s»m~nm.sae~ omesmmmo.o. masomumao.o mnemonfl.sm
mmmeo~oooo.o. nae-anmmooo.o Hecamemo.o . comamesm.o emmomQ.Ho- memaaaoo.ou maeaemnao.o mammooe.am
meemasmooo.o. aseomnnnooo.o swarmewa.s . mmemedem.o s~o~ea.e-~ smrmsaso.o+ amsemmmne.o mesmeee.~m
amasseesoo.o+ emmaemnnooo.o Hesoomns.m + esemenem.o esmmo~.emom HmmHoNoH.o. som-~mao.o emm~s-.nm
asemenasoo.o+ neeflcnnnooo.o emu-wsafl.ma. memonmem.o meflmfle.wme~ owemne-.o+ scsnsueao.o mmnOmes.mm
its aura a .uw.
enemy em
.3 as do he as H n e

 

8305c“ on Hoops-.8» serum no venues on»

he vol-«Hoodoo on son 50 Q ~3on no need-b Hecate-5a on» «send-.50 so: nos-Her Eamon-on 23 5a:

-31,-
Calculations for the correction values 0C and e

"' b1 . -é‘bel +
e bb 2 3 DC as 1 e (“)1
(bb) - (bb) - (:1sz § b2] 3 (b1) - (b1) - (ab); (a1);
2 1 a i 2 1 u 1
(bb) 0.00 609095 - 68 08 2
2 33 2% 2'0' E£3£3

+ 0.000025780870

0.003635731414 - .168 108 11.) 1261
52" 2%,")."20 .683i3

- 0.000 188 08 - - 20.12619350
B 4- W70
0C . .. (2.168g_7%08% 920926123522 + W
2 ,2 . 3 3 2 ’20 e 3 3

Therefore, since 6 is the correction for A and {is the correction

‘

(bl)2

for k, the first adjusted values for A and I: become as follows:
59.327813 ' 0.018258058

Adjusted A 39.2009 Adjusted k .02 3231

Using these adjusted values of A and 1:, new values were calculated
for fc, E0, and (13° - gc) and the same procedure was used for making the‘
second adjustment (an adjustment of the previously adjusted values of A
and k) . These adjustments were continued until the correction values of
8 _andaneresnall in coaparison to A and k.

Upon adjusting the values of A and k for the baby pig data, three

adjustments were made. Adjustment results were as follows:

-35..

1
First estinate 59.327114143
After first adjustment 39.2009508
After second adjustment 39.h565826
After third adjustment 39.25317h1

Spillnan ratio, e--k - 0.9691800?

_g_
0.018258058
dampng
0.031127115

0.031329h37

-36-

Method of Fflg and Mggement of Pigs Wgagigg to Market
In this study of the pig from weaning to market all live weights

 

and feed consumption data were observed and recorded. Data of this
type ure collected from 1950 to 1960 with a total of approximately 1200
animals being selected over this period. Animals which gained normally
(minim overall average gain of 1.115 pounds per day) were the ones
selected for this study.

The animals selected were weaned at from 6 to 8 weeks of age and
reared in the Michigan State University Swine Research Barn.

The live weight and feed consumption data were collected Ct 2 Wk
intervals, that is, from the time the animals were weaned (6 weeks) 7 8
until marketed (211 weeks).

As to the method of feeding and management the general procedure
was as follows:

1. Animls were all fed ad libitum (self-fed).

2. Animals were group fed throughout the entire study (from 5 to

10 animals per lot).

3. All animals had free access to water at all times.

The observed data were obtained by taking the average of all live
weights and feed comunption data at two week intervals for 1200 animals.
These averages were entered in the table as average live weight and feed
consunption. I

The observed cumulative feed consumtion was obtained by sumation
of the feed consuaption for all previous intervals. Also the observed

efficiency for the two week intervals (E - (w2‘- n) ) and cumulative
(£2 — £1)

-37-
efficiencies (gc - (w'-‘wj) were calculated.by use of these averages
for live weight and feed consumption.
The live weight and feed consumption data handled in this manner
were used in the application of the equation of the diminishing incre-

ment and equations derived from it.

Eggposition.of’szical Ration QE9d

 

 

Ingredientsl Fed to pigs Fed.to pigs
under 125 lbs.2 over 125 lbs.
Ground corn 768.1 855.9
Soybean meal (W) 180.0 92.2
Fishmsal (60%) 20.0 20.0
mm. meal (17%) 20.0 20.0
Limestone 3.h 3.h .
Dicalciun phosphate 2. 0 2 . 0
'Traee mineral salt (0.8% Zn.) 5.0 5.0
B vitamin mix, 0.5 0.5
Vitamin 312 0.5 0.5
Aurofac 10 A 0.5 0.5
Vitamin.A.and D mix _ 0.25 0.25

 

1Amount of an ingredient used is based on 1,000 lbs. of the total
ration. '

2The 16.5% protein ration was fed to pigs under 125 pounds and the
13% ration to those from 125 pounds to market weight.

Observed Data of’Pig from weaning to market

 

 

 

 

Age Average ' Av. Feed Av. Feed Etticiency;, Efficiency'
(wks) Live wt. Consumed Consumed Observed, E Observed, Eo
(1bs.) Period(1bs.) Cum.(1bs.) Period Cumulativec
6 26.6 00.00 00.00.. ~°
8 38.6 29.9 29.9 0.b01 0.h013378
10 55.0 h2.3 72.2 0.387 0.3933518
12 75.9 63.6 135.8 0.329 0.3630339
n. 98.5 71.9 207.7 0.311. 0.3h6172h
16 122.h 8h.5 292.2 0.283 0.3278576
18 1h5.8 95.2 387.h 0.2b6 0.3076923
20 169.6 100.? 1.88.1 0.236 0.2929728
22 191.8 100.8 588.9 0.220 p 0.2805230.
2h 213.7 10h.9 693.8 0.211 0.26967h3

 

-33-

mserved Data of Pig from Weaning to Market

 

 

 

Age Average ' Av. Feed Av. Feed Etticiency_ Efficiency
(wks) Live wt. Consumed Consumed Observed, E Observed, Ea
(lbs . ) Period( lbs . ) Cum. (lbs . ) Period Cumulativec
6 26.6 00.00 00.00. . mm“
8 38.6 29.9 29.9 0.101 0.8013378
10 55.0 112.3 72.2 0. 387 0. 3933518
12 75.9 63.6 135.8 0.329 0.3630339
lb 98.5 71.9 207.7 0.31h 0.3h61728
16 122.1: 8h.5 292.2 0.283 0. 3278576
18 1hs.8 95.2 387.h 0.2h6 0.3076923
20 169.6 100.7 h88.1 0.236 0.2929728
22 191.8 100.8 588 . 9 0.220 0. 2805230
2!. 213.7 10h.9 693.8 0.211 0.2696783

 

-39-

 

 

0.5 F
0.h *-
E 0. '
co 3
0.2 ‘
0.1 P
O 1 1 _n l I
50 100 150 200 250
w'(lbs.)

Figure 3. Observed Cumulative Efficiency'of Feed Utilisation (Bo) Versus
Live Weight (1:).

4:0-

Calculations and Adjustments of Constants A and k for Pigs Weaning to
Market '

From the observed data given previously the estimates and adjust-
ments to constants A and k can be obtained.

Similarly as previously illustrated, the first step is to obtain
estimates of the constants c and k for the equation,

Ei-c-kw....................(8)
And since this equation for "instantmecms' efficiency of feed utilisa-
tion, El, is that of a straight line it may also be written as

E-c-k(g+322 or E-c-k'u'

Where E and S are calculated as follows:

 

 

‘G, the average weight1 E, the average efficiency?
W ' *1 + I2 E - w2 - u
2 I2 " 21
32.6 0.1.01
’46. 0.387
65.5 0.329
87.2 0.3114
110.5 0.283
13(401 0.21:6
157.7 0.236
180.7 0.220
202.8 0.211

 

1 7 is the average weight for each two week period.

2 E is the average observed efficiency for each two week period.

~171-

The num erical values of C and k are then obtained by the method

 

 

 

    
        

 

“u
2 .unucz2sb Ru 2 m
( 78 98u2w9
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W R1233 la
M m mm
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1 ohm Ru7{umw 1 . A”
b n )

m emhmmnnne 3.0. 1. ... .1 me
n 1’ 7. QZDOML . {\ )1 r
O
u enmemeeei m m A m cm
a u e a. ( . .m
(up I. 7 Ir .. ’
fi .

so \. Rake x romMm mmzef

a m: 553.». $5 EMMMAWSDEE

39.233; Fr 3 _ o

E. .3.wa
HZfiMWFwa>w< FODZ aflfiunm

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00 40C IOFU >20 3>< 8M moxno€ flow firo<Oe m.m. >0.mn..

Imbcrmws Gem. K.m& ammmmm .000

Dvfirnn>4~oz ow 43m.moc>a~oz on Him chfim om UHZHz~mx~2n ”ZGQMEMZA
fio mfiwzm ZCfideHOZ. Zuommm>z mfl>fim CZ~1MJw~d<.

20% 4mm.
Dadan LMZZ< X2>CHI\HO

vcaucm C rum

.mzn arr no _ . .
newecm : rum , , .
NZU

 

-h1-
The num.erical values of C and k are then Obtained by the method
of least squares, illustrated in the derivation from equations (21)

through (25) and applied as follows:

 

 

 

a b 1‘ s bb b1 be
'5' ‘fi'

1 - 32e6 Oehol - 31e199 1&076 .1300726 1°17em7h
1 - 6e8 Defi? " hSeh-IB 2190e2h 4.8.1116 2125.328);
1 "' 65e5 0e329 " 615.171 (429er; -21.Sh9h h203e2m5
l - 87. 0.31h - 85.886 7603.8h -27.3808 7&89.2592
l e13h.1 0.2h6 -132.85h 17982.81 -32.9886 17815.721h
1 -157.7 0.236 456.1161. 28869.29 -37.2172 2h67h.3728
1 -180.7 0.220 479.880 32652.1.9 -39.7Sho 32h32.0360
1 -202.8 0.211 -201.589 81127.5h ~h2.7908 39368.2h92

- e e " e2 3 e "' 0 3 0 3
or 01‘ 01‘ or 01‘ 02‘ 01‘
(“)1 (ab)1 (81h (”)1 (bb)1 (bl)1 (bs)1
Check:

(aa)1 + (ab)1 * (al)1 ' (as)1

9 - 1017.9 +' 2.627 - ' 1006.27

(ml + (bb)1 + (bl); - (ten

-1017.9 + 110989.77 - 268.1366 - 11727073331.
Calculations for the first estimate of k, c, and 11.

k-ébl)“ 016w}; k+§algls 1-0/1:
2 ‘3 l as 1
(bb) - (0b) - ah ab 3 (b1) - (b1) - (ab)1 (a1)
2 1 1.3.3:); 2 1 7.2534

1The equationsused here-for calculating k and C are identical to the
previous dgrived equations (2b) and (25), for example (b1)1 is
m to “Es '

~172-

(bb)2 - 110,989.77 - 11,911,221 - + 28,865.28
9

(bl-)2 '-26h.1366 - 5-1017e23 S2e6272 . + 32e9771
ga,§§;e58

C -{.1017.9)_(0.0011h211h8§) + 2.627 - 0.1:2109982
9 9

A " 0. 1 82 " 3&.S9h092
$132388 '

The first estimates of A and l: have now been calculated. The next
step is to adjust the values of these constants A and k in such a way
as to reduce to a minimum the sum of the squares of the differences
between the observed cumulative efficiency and the calculated cumulative
efficiency. This is done exactly as shown on the baby pig data previously,
that is through the application of the method of least squares Qplied
to equation (26) by the following procedure:

Calculations for fc

for wi - 26.6, A - 368.59h092, k - 0.0011112171186, (m1) - 31.1.998092

w w (m) ((1331 108%. £°-1081(A—§:
' 9 k

 

 

 

m
26.6 3141391092 1.0000000 0.000000000 ‘ 0.000000
38.6 329.99h092 1.0363613 0.015513006 31.266190
55.0 313.591.092 1.0905629 0.0370091 75.881966
75.9 292.69h092 1.1688352 0.067601021. ' 136.21.8673
98.5 270.09h092 1.2662035 0.102501225 2065891112

122. 21.6.1911092 1.3891239 ~ 0.1h2738h09 7 287.6867748
11.5.8 222-.7911092 1.5350232 04861161796 3754111518
169.6 198.9914092 1.7186113 0.235179718 h7h.000577
191.8 176. 798092 1.930201: 0.28655sz8 577.51.11.90
213.7 15113917092 2.2079221 0.31.39811120 693.291.537

Calculations for go, go: and (5° -.§c) as follows:

-1.3-

 

 

 

 

 

 

 

 

 

 

' I. to H1 Ea.“ c. 0-(EO-Ec)
c -551' g 27:1 c c
26.6 00.0 00.000000 00.0 M
38.6 29.9 31.266190 12.0 0.1.013378 0.3838012 0.0175366
55.0 72.2 75.881966 28.1. 0.3933518 0.3782655 0.0190863
75.9 135-8 136.21.8673 119.3 0.3630339 0.3618 3814 0.0011955
98.5 207.7 206.5891112 71.9 0.31.61721. 0.31.80333 0.0018609
122.1. 292.2 287.6867h8 95.8 0.3278576 0.3330011 0.0051135
11.5.8 387.1. 375.111.518 119.2 0.3076923 0.3177670 0.0100717
169.6 1.88.1 h71..000577 11.3.0 0.2929728“ 0.3016871. 0.0087116
191.8 588.9 577.51.11.90 165.2 0.2805230 0.28601400 0.0055170
213.7 693.8 693.29h537 187.1 0.2696713 0.2698709‘ 0.000196h
Calculations for gc/k and (Ec)2/k(lfifli)(lev)

8.x]. (8.)2 we.) (1...) (892

° ° WHYUHJ
335.91.61.30 0.111730336 128.932216 0.001111211868
327599809 0.11.007h66 122.521.561 .0.00111.32371.
316.721809 0.13092703 111..358707 0.00111.1.8803
301.301.9111 0.12112718 105.52861.6 0.0011178133
291.1.801119 0.11088973 96.190661 0.0011528118
278.11.55115 0.1009758? 87.01.8031 0.0011600017
261..070861. 0.09101529 77.71.9117 0.0011706279
250.371.1193 . 0.08181888 69.075310 0.001181.1.B75
236.2211172 0.07283033 60.518776

0.001203h336

 

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63»an 0.33 Agdoolmv usages moons on» sand» mane dHH

 

n

 

 

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ammonuoooooo.ou ommwmeaaooooo.o oaaneao.o. emeawam~.o mmcmmm.oommm semaooo.ou enmamomaoo.o ~a4-~.om~.
mawammoooooo.o. aoaomoeaooooo.o Heamamn.a. pamemeem.o msaewm.ame~6 cadmmoo.o. macaeoaaoo.o neaeam.om~
ammeomoaoooo.o. meemo~maooooo.o o-~aon.~- mammaaom.o 4H~H~4.mmaae eaaamoo.o. mameoaaaoo.o accoao.ae~
aseaaaaooooo.o. amoememaooooo.o mummwom.~- onmaemwm.o momqaa.aemaa aeaooao.o- aaooooaaoo.o mammaa.ma~
megawamooooo.on omamommaooooo.o Hemmmea.au chamoemm.o Howaae.oomam mnaamoo.o. magnumaaoo.o assom:.em~
oommmamooooo.on mmaeaamaooooo.o eaamaom.on camaaman.o awmeoo.aommm moccaoo.on mnemaeaaoo.o asunoa.aon
42838686. 82328686 8.826. $86806 832.38H mmad86. 8844286 «8.856%
«anemmamoooo.o+ aaaaeomaooooo.o ooeo~m~.6+ ammwmaam.o aaamam.fl~maon neaoaao.o+ samwnaaaoo.o eoemem.-m
ammmmoomoooo.o+ meawmomaooooo.o mmmmamm.m+ noaammon.o aemmom.ammwaa oenmaao.o+ momawaaeoo.o omaeaa.mnn

n31<~ws=1<~x 1m:

o
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.3 ab .7 as ea H p e

 

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on... he eopegoaee on see m ens Us we need; 83.35.: 05. 605.396 so: needs» Scenes: 05 and»

4:5-
Gslculations for the correction values 0C and Q

9 '(b1)23 0C- 4.»); e + (a);
“1 . (

(uh); I 7 “51
(bb)2 - (bb)1 - gab}; (a); 3 (01)2 - (01h - (ebh (:1);
as 1 an 1 ‘

(bb)2 - 0.000012136705 .. S250l25629222 - 0.000000202591
7 ,007. 991 2

(01);, - 0.000006511726 - g3,0%%E%;2 éfizggoan
’ e

--0.000009000162h

8 - - gwm?!‘ - - hu.u25282 ~
0C ' W ” W
,00 . 991 2 , . 172
. 0.00018071766 I
Since 8 is the correction for A. and etc is the correction for k,
the first adjusted values for A end 1: then calculated as follows:
368591092 0.001lb2hh86
Adjusted A 32 .1 1 Adjusted k - . 13231 3
Using these adjusted values of A and 1:, new velues were calculated
for :6, 13c, and (go - EC) end the same procedure was used for making the
second adjustment (en adJustnent of the previously adjusted values of A
and 1:). These adjustments were continued until the correction values
of e endoC were small in comparison to A and 1:.
Three adjustments were required for A and k on the data pertaining
to the pig from weaning to nerket. Adjustment results were as follows:

First estimate

After first adjustnent
After second adjustment
After third adjustment

Spillnsn ratio,

4:6-

...é...
368 . 5911092
326.168810
331.814th0

331.678085

e'k - 0.99868273

k
0.0011h2hh86h
0.00132316630
0.00131h95825

0.0013151377h

.-h7-

RESULTS AND DISCUSSIGJ

Babz Pig Calculations _

In reference to Table I the calculated cumulative feed comuaption
(fc) of the baby pig on a synthetic nilk diet conforms with fair accuracy
to the observed values (see Figure 1;). The instantaneous efficiency of
feed utilization (E1) decreases linearly with increasing live weight
(see Figure 5). The, instantaneous feed conversion (F1) increases with
increasing live weight. Cumlative efficiency of feed utilisation
decreases linearly with increasing live weight (see Figure 6) and the
reciprocal of (gc) or cumulative efficiency of feed conversion (13¢) as
would be expected showed more feed consumed per pound gain as live
weight increased.

In reference to Table II the cumulative maintenance requirement
(Me) was found to increase exponentially with increasing live weight
(see Figures 7 and 8). The maintenance requirement between any two
live weights was shown to have an increasing effect as live weight of
the baby pig increased. Also the instantaneous maintenance requirement
(M1) expressed as a percent of instantaneous feed consumption was found
to increase linearly with increasing live weight (see Figure 9).

Note:

As previously illustrated, maintenance requirements as applied in
this study and as defined by the equation include all feed consumed
exclusive of that which is utilized for protein storage (growth).

-h8-

l‘lll

 

 

$53386 .. a Seamuem .. 3

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moa-a~n.a o~m4m4m~.o «Hammmom.a memoumom.o caumpw.m~ oo.m~

$283.4 Sfiofle6 endgame; oflmfioed 383.3 8.8

$334 Seaweed «canine; sanded 423.2 8.:

Sign; . 9329.86 omemmnemé $533.6 8286 8::

5.39884 3.8436 enigma; 803386 8886 84a

ommacpsm.o mm:~mm~o.a bmmmmauo.a mmaaamvm.o mmoaom.~ oo.o
amnoemme6 «88864 888.8 aim

LEI on

on Ari: 3...; 3-4:
I 0.0% I 0m I HM I H.” ’

 

 

encapesuo ee>wnen noun noanne>cco seem new honoaoauue obaaeassso ene.nsoonwanuneeH

.aa scum neaanon uncapdsuo henna new Hanoaeuona madnnacasao on» we convenes one no naaneem

83 ea: one-sedan .- do and .33 23 e0 33 3 83.5 30323 we 398m

H Danna

hnamundmod a a

3888.8 .. «a

 

 

888.8 888.8 4888.“ 288:8. 883.8 8.88
4.88.5 888.8 33988 84856 388.8 8.8
888.8 888.3 28084 8888...” 3838.2 . 8.3
888.8 888.8 888.24 28.8.... mS8o.a 8;:
888.8 388.8 «882.6 «.3884 8886 85
0., 538.3 888 .8 38846 38346 , 8888 86
.w Isis... 5886.2 68886 88866 688.8 mum
8a a d .. N ,
. nlllb. . LP 3. w 388.39
was”. 8” e .. 8%an .. :1: 3... ea E
IN mad
I H 3

Gene «0 a new WOO 800m no a 9: «z .. man-Hem .. o:

 

incoapesvo enhance scnu 3558.300." cognac: 333350 was 3853.33

83 can eeeefihnm . do 5 Pan 33 no 33 3 sundae 3333 we 33
HH 0.3:.

-50.

 

 

 

25 "
20
w (leo)
15
10
S
o 5 ' 10 15 20 25

f0 and {C (3)8.)

Figure 1;. Live Weight (1:) Versus Observed Cumulative'Fecd Consumption
(f0) and Calculated Cumulative Feed Conannption (to). ,

-51.

1.2 f

1.0 F

0.8 ‘

0.1: #-

0.2 F

 

l l

 

0 5L i0 15 20
W (use)

Figure 5. Instantaneous Efficiency of Feed Utilization (E1) Versus
Live Weight (w).

.52..

1.2 [

1.0 '

dE
13°“cc

0.6 ‘"

ooh F'

0.2 F

 

i I 4

AL
0 5 10 15 20

w (1ba.)

Figuro 6. Oosemd melativn Efficimcy of Food Utilization (Eo)lnd

Calculated Cumulative Efficiancy of Food nunzauon°(sc)
Versus Live Weight (1:) .

 

-53-

 

25 -
20 -
W (1138.)
15 —
10 L.
S
o 2 h 6 5 173

 

4 “c (1138.)
Figure 7. Live Weight (w) Versus Cumulative Maintenance Requirement (Me) .

-51..

 

 

 

 

25 F
N
C re
20 -
V (1138.)
15 -
10 ’
5
0 S 10 15 20 25

to and MC (1be.)
Figure 8. Live Weight (17) Versus Cumulative Feed Consumption (re) and
Cumulative Maintenance Raduiremnt (Me) .

-55-

ho e
Mi (as X 01 feed)

30-

20...

 

 

l l L l J

o 5 ‘ 10 15 20 25
w (lbae)

Figure 9. Instantaneoue Maintenance Requirement (M1) as Percent of
Inetantaneeua Feed Consumption Verena Live Weight (3).

-56.
Nagging to Market Calculations

In reference to Table III the calculated cunnflative feed consuqation
(fc) of swine from weaning to market conforms with a high degree of accuracy
to the observed values (see Figure 10). likewise, the calculated cumula-
tive feed commtion (fc) conforms with accm'acy to National Research
Council (N.R.C.) standards (Beeson £93, 1959) as shown in Figure ll.
The instantaneous efficiency of feed utilisation (31) decreases linearly
with increasing live weight and conpares to N.R.C. standards to approxi-
mately 160 pounds live weight. Figure 12 indicates that swine from 160
to 200 pounds live weight may not be as efficient as N.R.C. standards
designate. The instantaneous feed conversion (F1) increases with in-
creasing live weight. Cumulative efficiency of feed utilization decreases
linearly with increasing live weight (see Figure 13) and the reciprocal
of (13c) or cumulative efficiency of feed conversion (13c) showed more feed
consumed per pound gain. as live weight increased.

In reference to Table IV the cumulative maintenance requirement (Me)
was found to increase exponentially with increasing live weight (see
Figures. 11; and 15). The maintenance requirement between any two live
weights was shown to increase as the live weight of the animal increased.
Also instantaneous maintenance requirement (Mi) expressed as a percent
of the instantaneous feed consmption was found to increase linearly
with increasing live weight (see Figure 16).

In reference to Table v the calculated daily feed consunption
conpares very well with N.R.c. standards. The instantaneous daily main-
tenance requirements indicate that the pounds of feed required for daily

maintenance increases with increasing live weight. It should be pointed

-57-

out that the instantaneous daily food consumtion and maintenance
requirements were obtained by the tangential method from the curves of
cumulative feed consumption(fc) versus days of age and cumulative main-
tenance requirements versus days of . age at points corresponding to spec-
ified live weights.

The pounds of feed available for growth were obtained by the diff-
erence between daily feed consunption and daily maintenance requirement.
It should also be pointed out that calculations indicate the ratio between
daily gain and pounds of feed per day available for growth bears a reason-
ably constant relationship.

Plotting as in Figure 17 yields the graphical solution of the live
weight at which pig-plus-feed costs per pound live weight gain are the
least. This gave a reasonable estimation of the live weight of the animal
at which madame returns, including weaning cost of the animal in terms of

pounds of feed, were attained for feed consumed.

-53.

5.888686 .. s

. member—Hm a 1n

 

 

 

 

88.386 28.3.6.6 8.3.5.6 85.856 3486.80 . 6.86.
38336 4.35686 8.88%.: 88886 masheom 6.3.6
88836 88886 636886 88686.6 888.48 0.86
6.84386 088686 28836 383.66 9886.86 8mm."
68836 6838m6 8888.8 88386 48:88... o.§
«$68.96 683686 638686 488886 868.8." o5.
83886 33886 863636 _ 984.886 «868.8 0.8
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5.2.5285 .. x

 

 

 

883.3 838.8 388.2. _ amamé... . 3.38.5 0.86
888.3 6862.6.“ 386.8 3.6363 mfiaohéom o5."
$88.3 9.38.3 «6.8.9.3 2.5:...3 8825mm o6?
888.2 4.58.: 423.8 8382. 8886.86 0.66
933.8 3.36.8 88.3.8 288.2 32.3.86 0.86
48893 866.366 8.38.3 8.38.8 86862 0.2.
38% :3 538.3 538;. $2.84. 358.8 0.8
. .6836 0880.8 888.8 08898 0.8
an A a
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«3.3x 3 manna: 38m 83 mo 38 3. 835 30333 no 398m
B 3.3 .

Tabla V

Calculated Daily Feed Consunption Compared to N.R.C. Standards and
Estimates of the Daily Feed Intake Required for Maintenance
and That Which Is Available for Growth

 

 

It Calculated N. R. C. Instantaneous Lbs. of feed
live wt. lbs. of feed lbs. of feed maintenance per day
(lbs . ) per day per day requirements available
lbs. feed/day for growth
50 3.131; 3.20 0.52 2.92
75 h.67 0.25 1.05 3.62
100 5.28 5.30 1.59 3.69
125 6.20 6.05 2.35 3.85
150 6.80 6.80 3.07 3.73
175 7.22 7.10 3.80 3.1.2
200 8.50 8.00 5.12 3.38

 

.61..

21.0

220 ..
fO

..I ,2
200 If“ fc

180

160

w (1138.)
11:0

120
100

80

ho

 

20

 

1

o 70 11.0 210 280 350 1.20 1.90 5:0 630 700 720
fom£c(1bao)

Figure 10 Live Wei h
' 8 t (V) Versus Observed Cumula vs
ti 1“
(£0) and Calculated Cumulative Feed Constantia: Ezg‘mtion

.62..

2140 F

220 L

N.R.C.
200

180

160
U (1b8.)

11:0
120
100
80
60

1.0

 

20

 

L

0 70 11.0 210 280 350 1.20 1.90 560 630 700
1c and 11.3.0. (lbe.)

J; l I

Figure ll. Conpsrison 0! Calculated Cumulative Feed Consumticn (to)
and N. R. 0. Values.

-63-

0.5 F

0.1; ‘3

 

0.3 t

0.2 r-

 

001 b

 

1 1 L i l

0 to 80 ' 120 160 200
I (We)

Figure 1.2. Conuison of Calculated Instantaneous Efficiency of Feed
Utilisation (E1) and 11.8.0. Values.

0.1; b

 

0.1 "

 

A 1 J L J l L 1 a j

0 25 50 75 100 125 150 175 200 225 250
w (109.)

Figure 13. wserved Cumulative Efficiency of Feed Utilization (£0) and
Calculated Cumulative Efficiency of Feed Utilization (Ec)

Versus Live Weight (:0.

.65.

21.0 ..
220 r

200

180

160
1: (lbs e )
11.0
120
100

80

60

to

 

 

L a 1* 1 1 J L l i l

0 25 50 75 100 125 150 175 200 225 250
new...)

Figure 11;. Live Height (1:) Versus Cumulative Maintenance Requireurrt (Me).

 

2110 F
220 b
200 - c
1.80 r

160 P
W (1b8e)

1110 -

1201-

lOOr-

 

110

20

l l l L I l l l l I

0 70 11.0 210 280 350 1.20 1190 560 630 700
1‘,ch (lbe.)

Figure 15. Ian Weight ' (1:) Versus Cumulative Feed Consumption (2c) and
Cumulative Maintenance Requirement (He)

.67-

 

65 r
60 _
55 -
so _
145 "
ho L
35 L
141 (as S or road)
30 _
25 1-
20 -
15 1-
10 r
5 .

 

o ‘20 ho 60 80 100 120 110 160 180 200
v (1128.)

Figure 16. Instantaneous Maintenance Requirmt (H1) as Percent of
Instantaneous Feed Consumption Versus Live Weight (11) .

2110
220
r—1 200
i
J!
«a: 150
§ 160
2%
a A 11°
«= ‘3
+ 8. 120
5 a
’3 3 100
I
ca? .0
1w .0
i’.‘
I
3 to
20
Figurel'l.

.68-

EA - emu + 2.3025851 1081211)

 

 

 

 

 

 

 

 

 

 

 

(A - I
F
.- /‘500
u ' 1100
1- n I 3m
11 I' 200
1.
r u l v I
- 200 170 .
1. 300 192
" 1.00 201.
1—
500 216
L
l 1 L 1 J_ J L J A
0 25 50 75 100 125 150 175 200 225 250
1' (lbs.)
Graphical Method of Obtaining the Desired Value of (w) in

Equation (20) for each Value of (u) as Shown in Chart

-69-
SUHHARY MD WOLUSIONS

Bab: Pg

(1) Though reasonable accuracy was obtained, the baby pig data donot
conform to the equation of the curve of diminishing increment as well as
one would desire.

(2) The major reason was that the plot of live weight versus feed con-
suaption of the baby pig from birth to weaning was essentially a straight
line relationship.

(3) The fluctuation of observed efficiencies of the baby pig on a syn-
thetic milk diet due to considerable scouring from time to tine also con-f .
tributed to deviation in its application.

' (1.) Therefore, it can be concluded that in the case of the baby pig
since the equation was applied to data taken over a relatively short
time range and during a period of relatively rapid growth, the value of
its application to the baby pig is questionable.

Pigs 11ng to hornet ‘

(l) The live weight-feed consumption data of the pig from weaning to
market conforms to the equation of the curve of diminishing increment
with a considerable degree of accuracy.

(2) The calculated cumulative feed consumtion and observed cumulative
feed consumtion were found to be almost identical.

(3) The calculated cumulative feed consumtion compares very well to
3.3.0. standards.

(1.) The calculated instantaneous efficiency of feed utilisation (E1)
comma to 11.3.0. to approximately 160 pounds live weight from which
point the calculated instantaneous efficiency of feed utilisation shows
a lower efficiency to 200 pomds live weight than does N.R.C.

--70-

(5) The instantaneous maintenance requirement as a percent of feed
consumed (Mi) is shown to be a linear relationship in comparison to live
weight.

(6) Therefore, as the result of these findings the following conclusions
can be made:

(a) The equation of the curve of diminishing increment and equations
derived free it are applicable to swine from weaning to whet.

(b) The equation shows an instantaneous efficiency of feed utilisa-
tion decreasing linearly with increasing live weight, indicating that
swine from 160 pounds live weight to 200 pounds live weight may not be
as efficient as 14.3.0. standards designate. '

(c) Cumlative maintenance requirements (he) in terms of pounds of
feed increases exponentially with increasing live weight and age of the
animal.

(d) The plots. in .- Figure 17 indicate the live weights at which
the initial cost of the weaning pig in terms of pounds of feed plus
feed consumption (lbs.) per pound of live weight gain is the least.
This indicates a possible marketing weight for maximum net returns for
feed consumed. V

1.

2.

3.

h.

5.

9.

10.

13.

-n-
BIBLICBRAPHY

Beeson, W. 11., E. U. Cramton, T. J. Cunha, N. R. Ellis, and R. W.
Luecke. 1959. Nutrient Requirements of Swine. National Research

Council Publication 91,8 .

Brow, Samuel. 1927. Growth and develqment. Missouri 533;. at.
Sta. Res. Bull. No. 2].

Dixon, Wilfred, Jr. and Frank J. Massey, Jr. 1957. Introduction to
Statistical Aggie. McGraw Hill, New York

For, T. w. and B. B. Bohren. 19511. An analysis of feed efficiency
amongbreeds of chickens and its relationship to rate of growth.

Pauitg Sci. 33: 5149-561.

Glascner, E. N. and M. A. Jull. 19116. Feed utilization in growing
chickens in relation to shank length. Poultq Sci. 213355-3611.

Harmond, J. C., W. A. Hendricks and H. W. Titus. 1938. Effect of
percentage protein in the diet on growth and feed utilization of
male chickens. J. 551. Res. 56: 791—810.

Hammad, J. C. and S. J. Harsden. 1939. The effect of the level of
protein intake on growth and feed utilisation of the turkey.

P011122 Sc 0 18:11.19e

Hanldses, 0. G. and H. N. Titus. 1939. Growth, fattening and meat
production. Yearbook of Agriculture. U.S. Gov. Printing Office,

Washington, DT'E.

Hendricks, W. A., M. A. Jull and H. W. Titus. 1931. A possible
physiological interpretation of the law of diminishing increment.
§______cience 73311274429.

Hendricks, W. A. 1931. Fitting the curve of the diminishing incre-e
neat to the feed consumption-live weight curves. Science 711: 290-
291.

Hendricks, W. A., H. A. Jull and H. W. Titus. 1932. The utilization
of feed by chickens. Poultg Sci. 112711-77.

Hess, C. W., T. C. Byerly and M. A. Jull. 19111. The efficiency of
feed utilization by Barred Plymouth Rocks and crossbred broilers.

Pauly Sci. 20: 210-216.

Hess, C. W. and M. A. Jull. 19118. A study of the inheritance of
feed utilization efficiency in the growing domestic fowl.

Poulm Sci. 27: 214-39.

-72-

111. Jull, H. A. and H. H. Titus. 1928. Growth of chickens in relation
to feed conception. J. BE. Res, 36:5111-550.

15. Jull, M. A. and H. G. McCartney. 19117. Efficiency of feed utilisa-
tion in New Hamshires to ten ween. Poultiz Sci. 25:17-23.

16. Knapp, B., Jr. and A. L. Baker. 191111. Correlation between rate and
efficiency gain in steers. J, Animal Sci. 3: 219-223.

17. Leland, H. 0. 1921. Practical Least ems. McGraw-Hill, New York.

18. Mansfield, Merriam. 1907. The Method of Least Squares. John Wiley
and Sons, New York. .

19. Nelson, A. I... K. w. Folley and M. Coral. 1952. Differential
Mica. Heath and Company, Boston, Mass.

20. Spillnan, W. J. ‘ 1923. The law of diminishing returns. Farm Mange-
m. Orange‘Judd Publishing 00., New York.

21. Spinnan, w. J. and E. Lang. 1921.. The Law of 13mm.
World Book Coqany, Chicago, Illinois.

22. Snedecor, G. W. 19110. Statist Methods lied to crime

in m culture and Biolegz. owe te Co ge ss, Amos.

23. Titus, H. U. 1928. Growth and the relationship between live weight
and feed mticn in the case of White Pekin ducklings.

P011122 Sale 7: 2511-262e

211. Titus, H. 11., M. A. Jull and W. A. Hendricks. 19311. Growth of
chickens as a function of feed consumption. J. egg. Res.
1183817-835.

25. Titus, H. w. 1955. Utilisation of feed. The Scientific Feggihng
, ef Chickens., Interstate Printers and Pub rs ., Danville, Ill.

26. Titus, H. H. 1959. Some lications of the Equation of the Curve
ef Diminis Increnen utrit on. tons roducts

r on 0 rice, on, ew ersey.

 

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