ESTIMATES O F HUB IT ABII4TY OF BIBTH WEIGHT
AND WEANING WEIGHT OF LAMBS

By
GANAPATHY VEHKATACHAIAM

A THESIS
Subm itted to the School of G raduate Studies of Michigan
S tate C ollege of A griculture and Applied Science
in p a rtia l fulfillm ent of the req u irem en ts
fo r the degree of
DOCTOit OF PHILOSOPHY

D epartm ent of Anim al Husbandry
1949

ProQuest Number: 10008474

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AC KNQ W3LEDGMENT

The w rite r wishes to e x p ress his sin cere thanks to Dr* Ronald H*
N elson, P ro fe sso r of A nim al B reedingfor h is m ajor help and suggestions,
and to P ro fe sso r George A, Brown, Head of the D epartm ent of A nim al
H usbandry fo r a ll the fa c ilitie s he provided in the departm ent during the
p rep aratio n of this th esis.

A word of appreciation is extended to the men of le tte rs of the
guidance com m ittee, and to D r. W illiam D. Baten, R esearch P ro fe sso r
of S tatistics fo r his help in sta tistic a l procedures.

TABLE OF CONTENTS

Page
ACKNOWLEDGMENT
INTRODUCTION

....................... * * .....................

1

D efinition of H er liability . . , * .......................................................... 1
Why E stim a te H er liab ility ? . * . . , .....................................................2
REVIEW O F LITERATURE

*'*,«.«.<** *

4

D ifferent Methods of E stim ating H eritability

4

H eritability E stim a te s for V arious T ra its in S h e e p ...............

9

ANALYSIS OF DATA

............„ , ♦ * * * . ..............

13

Source of Data

.

13

F lock Survey

»

...................................................................... 13

Sex R atios

15

B irth Weight and C onversion F a c to rs

*.

22

C alculation of H eritability of B irth Weight

2?

Weaning Weight and Influence of Environm ental F a c to rs . . .

43

C alculation of H eritability of Weaning W e ig h t

4?

*. , , .

............................

61

Sources of E r r o r s ,« * , . * * » « * . » * * * » * « • * * * * » * * » * .

62

.................... * ............................

63

DISCUSSION OF RESULTS

P ra c tic a l A pplications

SUM M ARY..............................................................

66

LITERATURE CITED

67

............... . . . . . . . . .....................

INTRODUCTION
Both h ered ity and environm ent play an im portant ro le in the ultim ate
m ake-up of a c h a ra c te ris tic in an individual. The question of w hether
h ered ity o r environm ent is the m ore im portant one fo r th at p a rtic u la r
tr a it in a p a rtic u la r population m ay be answ ered by the estim ates of
h e rita b ility of that tra it.
Definition of B erltab illty
The h eritab ility of a tra it may be defined as the ra tio of the amount
of genetic v ariatio n to the to tal variation observed in the population. In
o th er w ords, it is that p a rt of the v ariab ility which would be lo st if a ll
the individuals of a population had one and the sam e genotype.
Lush (1940) defines h eritab ility a s the fractio n of the observed
v arian ce which was caused by differences in heredity. This fractio n
is a sta tistic d escribing a p a rtic u la r population.
2
Let S__
* that p a rt of the v arian ce caused by differences in the

h ered ity which different individuals have
2 * that p art of the variance caused by differences in the
SB
environm ents under which different individuals developed
2

S* +

2

* T otal v ariance observed.
2
Then, the fractio n
SH
is the portion of the observed v arian ce
fo r which differences

H

KE in heredity a re responsible. When this

fractio n is la rg e , the c h a ra c te ristic is said to be highly h ered itary ! when
it is sm all, then the c h a ra c te ristic is said to be slightly h e re d ita ry o r
larg ely environm ental.

2

*fTh© n arro w est definition includes a s h e re d ita ry only the additively
genetic v a ria n c e . The b ro a d est definition of h eritab ility includes a s
h e re d ita ry the differen ces caused by ep istatic and dominance deviations
and even by the joint n o n -lin ear interactions of heredity and environm ent/*
Lush (1940).
Why E stim a te H eritab ility ?
The r a te of im provem ent of the fu tu re generations of livestock over the
p resen t generation that can be brought about through selection depends on
the extent to which the v ariatio n s in the c h a ra c te ris tic s concerned a r e tr a n s ­
m issib le fro m parent to offspring. Thus, an estim ate of h e rita b ility of a
tr a it is im portant and useful to the b re ed er a s it indicates the am ount of
im provem ent which w ill, on the av erag e, be tran sm itted to the off spring of
selected p aren ts, and a lso , it estim ates the probable genetic im provem ent
which is perm anent a s against the p ro g re ss through environm ent. (Lush. 1935)*
In addition, estim ates of heritab ility a re e sse n tia l in planning efficient
breeding sy stem s. A breeding program successful fo r c h a ra c te rs w here
v aria b ility is larg ely genetic, m ay be unsuccessful if m ost of the v ariab ility
is environm ental (W right. 1939). While choosing an efficient breeding
sy stem , an estim ate of h eritab ility of the econom ically m ost Im portant
tr a its is the f ir s t thing a b re e d e r needs to know a fte r he has decided upon
his goal. If the d e sire d tr a its a re highly h ered ita ry the b est method will

he m ass selection (phenotypic selection), paying little attention to pedigree,
re la tiv e s , progeny te s t o r inbreeding. If h eritab ility is low. but th e re is
not m uch ep istatic v a ria n c e , then considerable use of pedigree, progeny
te s ts and selection on a fam ily b asis would be a b e tte r plan.

3

If th e re is much of ep istatic variance a considerable am ount of
inbreeding m ay be practiced in o rd e r to c re a te new lines distinct fro m
each other (Lush, 1940).
F in ally , a knowledge of h eritab ility is useful in setting up a c cu rate
c r ite r ia fo r the selection indexes and also, in determ ining the re la tiv e
em phasis due each of se v e ra l tra its when breeding anim als a re selected
(Hazel, 1943).
The purpose of the p resen t study was to estim ate the heritab ility
of b irth weight and weaning weight of lam bs of different breed s ra ise d
in the M ichigan State C ollege flock.

4

REVIEW OF LITERATURE
D ifferent Methods of E stim ating H eritability
Lush (1940) has given various ways of estim ating h eritab ility . All
m ethods of estim ating h eritab ility a re fundam entally based on the
relatio n sh ip between the individuals. Since re la te d anim als a r e m ore
likely to have received som e of the sam e genes from common an c esto rs
they m ay be expected to be m ore alike in th eir h ered ita ry tra its than
a r e the unrelated individuals. The methods r e s t on m easuring how much
m ore clo sely anim als with sim ila r genotypes resem b le each other than
do the le s s closely re la te d anim als. R elatives such a s parents and
offspring* fu ll-sib s and h alf-sib s a re m ost useful fo r this purpose.
The method used depends on the m a te ria l one has to w ork with, that
is , w hether genetically pure lines a re available; the m ating sy stem s,
such a s inbreeding, which m ay have been practiced; or the nature of
the data which has alread y been collected fo r other purposes and from
which you m ust make your estim ate. If it is a tr a it which has not
previously been investigated sev e ral m ethods o r sev eral so u rces fo r
sep arate estim ates would be d esirab le in o rd e r to have a check on the
fig u re since sam pling e r r o r s m ay have quite a la rg e effect on a single
estim ate that is based on a sm all volume of data.
Isogenic Line Method
V ariation within isogenic lines is wholly environm ental. If genetically
pure (homozygous) individuals o r lines (identical twins if at a ll th ere a re
any in fa rm anim als) a re available the method of isogenic lines is a

5

m ethod likely to m easu re a ll the genetic v arian ce due to e p is ta s is ,
dom inance and additive effects. The pro ced u re is sim ila r to the in tra c la s s c o rre la tio n method of com paring the observed variance between
isogenic lines with the v arian ce in the population being studied and thus,
d eriv e a d ire c t e stim ate of h eritab ility . Since the relationship between
two individuals having the sam e genotype# o r between the identical twins is
100 p er cent the calculated ra tio of the variance o r the c o rrelatio n coefficient
is the estim ate of h eritab ility.
The disadvantages of this method a re (1) th e re may be a tendency
fo r the individuals within the isogenic line to re ceiv e a m ore uniform
environm ent than those in the population, as a whole. This might re s u lt
in an o v e r-e stim a te of h eritability; and P ) in livestock, isogenic lines
a r e usually unavailable. Identical twins a re one source of such isogenic
lin es but they a r e v ery r a r e and hard to identify. In the co u rse of this
p ap e r, s ta tis tic a l evidence will be presented to show that identical
tw ins in sheep a r e r a r e if they exist at a ll. It would probably be possible
to produce inbred lin es homosygous enough to be used but it would take
a long tim e to get them inbred enough to m ake the method practicable.
Selection E xperim ent Method
This method m ay be used if the data w ere collected fro m the parents
selected fo r a p a rtic u la r tra it fo r which a h eritab ility estim ate is d e sire d .
In o rd e r to get the e stim a te , the difference between the average of the
offspring of the selected p aren ts and the average of the generation in which
the selected p aren ts w ere b o rn is divided by the difference between the

6

average off the selected parents and the average of the generation in which
they w ere horn. The resu lt m ultiplied by

%

gives the estim ate of heritability.

If selectio n continues fo r m o re than one generation, then the
rep lacem en ts m ust com e fro m within each line itself, hi o ther w ords,
th e re should be no interchange of individuals between the two lin e s. A
disadvantage of th is method is that the individuals m ay not have been
selec te d s tric tly fo r ju st one c h a ra c te r. F urther* fo r adequate control
of environm ent it is usually n e c e ssa ry that selection hi the opposite
d irectio n sh all be practiced in a contem porary control line. T his method
is not often available to the breeder* since he can r a re ly afford to select
in the undesired d irectio n ju s t to get inform ation on h eritab ility .
I n tr a - s ir e B aughter -Dam C o rrelatio n o r Eegres&ion Method
Sewail W right (1921, 1034) illu stra te s the p rinciples of th is m ethod in
his w orks. It was by the method of path coefficients that W right proved that
the co rrelatio n betw een the p arent and offspring was half of the estim ate of
h e rita b ility <rpo » 1/2 h2). T h erefo re, we m ultiply the co rrelatio n betw een
p aren t and offspring by 3 to get the m easu re of h eritab ility . The m ain
b a sis of the following in tr a - s ir e re g re ssio n o r c o rrelatio n method is the
th eo ry of path coefficients.
This is the m ost frequently used method fo r m ost data available in the
field of anim al husbandry because of c e rta in distin ct advantages in estim ating
h e rita b ility by com puting the c o rre la tio n o r re g re ssio n of offspring on dam
within groups of offspring by the sam e s ire . T his is essen tially a p aren t offspring resem b lan ce but computing it on an in tra - s ir e b asis red u ces m o st

7

of the environm ental d ifferences and any p e c u lia ritie s of the m ating
sy stem (L.ush, 1940).

The in tr a - s ir e re g re s s io n dodges m ost of the

environm ental c o rre la tio n s because (1) the daughters and m ates of
a s ir e a r e n e a rly alw ays kept in the sam e h erd and th ere fo re, the
effects of heterogeneity of m anagem ent from h erd to herd would be
left hi the differences between s ire s , and (2) the offspring of one
s ir e a re usually n ea rly contem porary.

Selection of the dam s will

tend to low er the c o rre la tio n coefficient but w ill not b ias the re g re ssio n
of offspring on dam .

Since som e selection of dam© is usually practiced

in m o st flocks th© re g re s sio n method is p referab le to correlation*
The c o rre la tio n and re g re ssio n fig u res a r e obtained fro m the
an aly sis of covariance of th© data grouped on an in tr a - s ir e b asis.
T hese fig u re s a r e m ultiplied by 2 to get the estim ates of h eritab ility
because the relatio n sh ip between parent and offspring is fifty p er
cent a s a limit*

In o th er w ords, each parent contributes, on the

av erag e, only half of th© inheritance to the offspring.
H alf-sib C o rrelatio n Method
T his method of p atern al h alf-sib o r m atern a l h alf-sib r e la ­
tionship is usually not a s ac cu rate a s the previous method of
p aren t-o ffsp rin g relatio n sh ip .

However, when the data a r e analysed

by the an aly sis of v arian ce, the in tra -c la s s c o rre la tio n a s o u t­
lined by Snedecor (1948), gives th© req u ired sta tistic which, on
m ultiplying by 4 gives an estim ate
we m ultiply the sta tistic

of heritability*

H ere,

by 4 because the relationship between

8

h a lf-sib s Is 25 p e r cent* Even a smaU e r r o r when m ultiplied by 4
ap p ears to be la rg e and hence, the method is often inaccurate. In the case
of the fu ll-sib c o rre la tio n m ethod, the sta tistic is m ultiplied by 2*
Mid-parent«*Offspring C o rrelatio n o r R egression Method
T his method is the sam e a s the parent -offspring relationship method
except that in th e place of on© parent you take the average of both p a re n ts.
T h ere is not m uch lite ra tu re on th is method to review since m ost of the
studies of h eritab ility w ere concerned with c h a ra c te rs which could be
d ire c tly m easu red in one p aren t only. However, th is mid -parent -off spring
method m ay be used if the tr a it can be m easu red in both p aren ts; fo r
exam ple, fleece weight. By this method, the sta tis tic is m ultiplied by
1,41 to get the estim ate of h eritab ility fo r the following reaso n .
The c o rre la tio n between the offspring and erne of its p aren ts is 0.5 fo r
c h a ra c te rs which a r e com pletely h ered itary . Squaring this c o rre la tio n
gives 0*25 as the degree of determ ination of the offspring by one of its
p a re n ts, by th© th eo ry of path coefficients. Thus, the inheritance of the
individual is 25 p er cent determ ined by each parent; and the degree of
determ ination of the offspring by both parents is 50 per cent. The square
root of 0,5 gives 0.707 a s the co rrelatio n between the parental average
(m id-parent) and the offspring fo r tra its which a re com pletely h ered ita ry .
C onsequently, the co rrelatio n (or the re g ressio n ) between the offspring
and the m id -p aren t would be m ultiplied by 1.0/0.707 o r 1*41 in place of
l.o/G .5 o r 2 used fo r the c o rrelatio n between the offspring and only one
of its p aren ts (Nelson, 1941).

9

Of th ese m ethods, only the following ones w ere chosen a s the best
fo r the s e t of data available fo r th is study,
1, P a te rn a l H alf-sib C o rrelatio n Method,
2, I n tr a - s ir e R egression of D aughter on Dam Method, and
3 , In tra-sir© D aughter -Dam C o rrelatio n Method.
U ltim ately, to a rriv e a t the b e st estim ate, the weighted av erag e of th ese
th re e m ethods, the weighted av erag e of five b re ed s and the weighted
av erag e of th re e m ethods and five breeds have been calculated. This
w ill be d escrib ed to the co u rse of toe p ap er,
H eritab ility E stim ates fo r V arious T ra its to Sheep
The review on th is topic is well condensed by the table published
by P h illips (1943-1947). H ence, the table has been reproduced h ere;
to th is study, toe tra its fo r which toe h eritab ility estim a te s found a r e the
b irth weight and toe weaning weight of tom bs,
TABLE 1, ESTIMATES OF HEKXTABIUTY FOE VARIOUS CHARACTERS
IN SHEEP (After P hillips)

C h a ra c te r

H er lia ­
bility Method used
(p e r­ to d eterm ine
heritab ility
cent)

R eference

B irth weight

30

P atern a l half Chapman and l*u$h (1932)
sib

Y earling staple
length

30

Xntrasire
re g re ssio n

T e r r ill and B asel (1943)

Y earling weight of
clean wool

38
28

Xntrasire
re g re s sio n

T e r r ill and H azel (1943)
T e r r ill and H azel (1943)

Y earling body weight

40

Xntrasire
re g re ssio n

T e r r ill and H azel (1943)

10

TABLE I. (Continued)
H*H erita bility Method used
C h a ra c te r
(p e r­ to determ ine
h eritab ility
cent)

R eference

Y earling body sco re

12

In tra s ire
re g re ssio n

T e r r ill and H azel (1943)

F ace covering

32

In tra s ire
re g re ssio n

T e r r ill and H azel (1943)

Neck folds

26

In tra sire
re g re ssio n

T e r r ill and Hazel (1943)

Body folds

37

In tra sire
re g re ssio n

T e r r ill and Hazel (1943)

Weaning weight

26.9

P aternal
half sib

H azel and T e r r ill (1945)

f 17.0 A verage 3

Staple length at
weaning

b re e d s, 2
methods
33.9 In tra sire
re g re ssio n
Weighted
30
average of 2
methods
P atern al
\ 41
half sib
38.7 In tra sire
re g re ssio n
40
Weighted
average of 2
methods
\4 3 .0 Average 3
b re ed s, 2
methods

/ 15.2 P atern al

Type sco re at
weaning

half sib
6.8 In tra s ire
re g re ssio n
/ 13.0 Weighted
average of 2
methods
1 7.0 A verage 3
b re ed s, 2
methods

H azel and T e r r ill (1946a)
Hazel and T e r r ill (1945)
H azel and T e r rill (1945)
Hazel and T e r r ill (1945)
H azel and T e r rill (1945)
H azel and T e r rill (1945)
H azel and T e r rill (1946a)

H azel and T e r r ill (1946)
Hazel and T e r rill (1946)
H azel and T e r r ill (1946)
H azel and T e r rill (1946a)

11

TABLE I. (Continued)

C h ara cter

H e rita ­
bility Method used
(p e r­ to determ ine
h eritab ility
cent)

f

Condition sco re
at weaning

P atern a l
half sib
1 13.8 In tra s ire
re g re ssio n
Weighted
av erag e of 2
I *
methods
2.4

( 45.8 A verage of
Skin folds

4 methods
51.2 A verage of
\
4 m ethods,
within y ear

f 36.2 P atern a l
45.1
Neck folds

\ 39

L

8

half sib
In tra sire
re g re ssio n
Weighted
av erage of 2
methods
A verage 3
b r e e d s ,2
methods

f 51.0 P atern al
half sib
In tra s ire
re g re ssio n
J 56
Weighted
average of 2
m ethods
I 4 6 , 0 A verage 3
b re ed s, 2
m ethods
80.3

F ace covering

N um ber of nipples

14.4 In tra sire
co rrelatio n
r*26

N um ber of
functional nipples

(22

In tra sire
co rrelatio n
In tra s ire
re g re ssio n

R eference

H azel and T e r r ill (1946)
Hazel and T e r rill (1946)
H azel and T e r r ill (1946)

Jones et al. (1946)
Jones et al. (1946)

T e r r ill and Hazel (1946)
T e r r ill and Hazel (1946)
T e r rill and Hazel (1946)
Hazel and T e r r ill (1946a]

T e r r ill and Hazel (1946)
T e r r ill and Hazel (1946)
T e r r ill and H azel (1946)
H azel and T e r rill (1946a]

P hillips, et al. (1945)
P hillips, et al. (1945)
P h illip s, et al. (1945)

12

The v ariatio n s in the e stim a te s of h eritab ility of various c h a ra c te rs
a r e due to sam pling e r r o r s and environm ental differences; and in some
of the e a rly stu d ie s, the sy stem of m ating has not been taken into
consid eratio n . R eference to the original paper of Chapman and Lush
(1932) showed that 30 p er cent of h eritab ility of b irth weight of lam bs
was obtained by the h alf-sib method from the re c o rd s of 361 sets of
tw ins born fro m 1915 to 1930 inclusive. The data collected over a long
period of y e a rs a r e likely to contain m ost of the environm ental v ariatio n s
due to changes in feed and m anagem ent. If the estim ates w ere m ade on
the adjusted data it is probable that the re a l h eritab ility of b irth weight
of lam bs would be m ore than 30 per cent.
H azel and T e r rill (1945) estim ated that the h eritab ility of weaning
weight of lam bs was 0.269 1' .05 by the h alf-sib method and 0.339 t .08
by the in tr a - s ir e re g re ssio n method; and 0.30 i .04 by the weighted
av erag e of the two m ethods. He found that about 50 per cent of the
v arian ce in weaning weight was due to environm ental fa cto rs such as sex#
age of dam# type of birth# age at weaning and p er cent inbreeding for
which p ro p er c o rrectio n s w ere made before the calculation of h eritab ility .
The rev iew of lite ra tu re on sex ra tio s and the environm ental fa c to rs
that affect the b irth weight and weaning weight of lam bs is d iscu ssed in
the co u rse of the analysis of data.

13

ANALYSIS OF DATA
Source of D ata
The data used in th is study w ere taken fro m the Michigan State
C ollege flock of sheep, which contained the following b re ed s: S hropshire,
H am p shire, Oxford, R am bouillet, Southdown, Cotswold, and B lack Top
D elaine, T h ere w ere a lso som e grades and c ro ssb re d s. The re c o rd s date
back to 1930, A to tal of 4470 lam bs of th ese d ifferen t b reed s and c ro ss b re d s
was available fo r the p re lim in ary study of sex ra tio s . A total of 3484
lam bs out of 2305 pregnancies was used fo r estim ating the percentages
of different types of b irth s at different ages of ew es. Some of these
re c o rd s w ere taken fro m the sheep flock at the Kellogg F a rm , a branch
station of Michigan State C ollege, Since the num bers in some breed s
w ere ex trem ely sm all fo r a thorough and detailed study it was decided
to include only those b reed s which had re lia b le and com plete inform ations.
F o r the study of the estim ates Of h eritab ility of b irth weight and weaning
weight of lam b s, only the re c o rd s of the five b reed s in the M ichigan State
College flock fo r the period fro m 1845 through 1948 w ere used, The b reeds
w ere H am pshire, Oxford, R am bouillet, S hropshire and Southdown.
F lock Survey
A g en eral su rv ey of the flock was m ade m ainly to find out th©
p ercentages of different types of b irth s a t different ages of ewes in each
breed and then in th© e n tire flock. F o r th is, a table was set up fo r
tw o -y ear-o ld ew es and m ature ewes each with th re e types of b irth s , v iz .,
sin g les, tw ins and trip le ts . The re c o rd s of the yearling ewes w ere

14

excluded fro m th is study* In o th er w ords, the ewe had to s ta r t h e r f ir s t
lam bing when two y e a rs old* A ll ewes o v er two y e a rs of age w ere grouped
under m a tu re ewes* T he re c o rd s which did not contain the date of b irth
of the ewe w ere a ls o excluded* An attem pt was m ade to Include only
th o se ew es which had a t le a s t two lam bing records*
Table 2 shows the num ber of lam bs based on the age of ewe and the
type of b irth in different breeds*
TABt,E 2* NUMBER O F BIRTHS ACCORDING TO THE AGE OF EWE
AND THE TYPE OF BIRTH IN VARIOUS BREEDS
T w o -year-old Ewes

M ature Ewes

Twins

Twins

T rip le ts

B reed
Singles

T rip lets Singles

H am pshire

83

70

2

IS©

107

14

Oxford

32

33

2

51

49

©

Ram bouillet

41

10

0

61

88

©

S hropshire

158

50

2

34©

283

12

Southdown

at

25

1

36

57

2

Cots wold

10

14

0

29

36

0

C ro ssb red

100

37

0

140

1S2

4

Total

474

245

7

707

824

4©

s--------------------------

Table 3 gives the p ercentages of different types of b irth a t different
ages of ew es in the e n tire flock* Out of a total of 2305 pregnancies in a ll
b re e d s, about 51 p e r cent w ere single b irth s and about 48 p er cent m ultiple
b irth s of which 2*4 p e r cen t w ere triplets* It is in terestin g to note that
the two -y e a r -old ewes drop, on the av e rag e, m ore singles than twins*

15

M ost of th m twins and tr ip le ts a r e born to the m atu re ew es, T hese
re s u lts a g re e with the previous works of Jones (1920). She re p o rte d
th at 4 p e r cent trip le ts and 54 per cent twins w ere born out of a total of
1194 b irth s . The p ercentage of twin and trip le t b irth s in creased with the
age of the ewe, The la rg e s t percentages of single and m ultiple b irth s
w ere produced resp ectiv ely by tw o-year-old and m atu re ew es.
TABLE 3* PERCENTAGES OF DIFFERENT TYPES OF BIRTHS AT
D IFFERENT AGES OF EWES
Type
Of
B irth

T w o-year-old Ewes

M ature Ewes

Total

Num ber of

Per
cent

N um ber of

Per
cent

Num ber of
P regnancies

Per
cent

Singles

474

95,5

707

44,3

1131

51.2

Twins

245

53.7

324

32.2

1059

46.4

7

1,0

43

3.0

55

2.4

T rip le ts
Sex R atios

The sex ra tio in a sp ecies of anim als may be expressed a s the
p ercen tag e of m ales at b irth . F o r a m atter of convenience* the sex ra tio s
could be con sid ered at th ree different stages in die life h isto ry of anim als*
namely* at conception* b irth and m aturity. Sex ra tio s a t these stag es a r e
usually spoken of a s p rim a ry ,

s e c o n d a ry

and tertiary * resp ectiv ely . The

ra tio s re p o rted in th is study a re based on the num ber of offspring born
(including s till b irth s), that is , the secondary sex ra tio which w ill b e,
h e re a fte r, re fe rre d to m e re ly a s the sex ra tio .
The lam bing re c o rd s of a ll the available ewes w ere used without any
d iscrim in atio n fo r the study of the sex ra tio In the flock. The num ber of
ra m lam bs and ewe lam bs is given in table 4,

16

TABLE 4. NUMBER OF MALES AND FEMALES IN DIFFERENT TYPES
OF BIRTHS
T otal
P regnancies

P regnancies
with Sex
R ecorded

Singles

1087

1876

856

820

Twins

1333

1316

1298

1334

58

54

73

89

3078

3046

2227

2243

Type of B irth

T rip le ts
T otal

M ales

F em ales

It i© considered that the lam bing re c o rd s a re the m ost re lia b le source
of d ata fo r the study of sex ra tio and that the data obtained fro m herd books
and b re e d e rs ’ re p lie s do not p o ssess the n e c e ssa ry accuracy fo r a study
of sex ra tio s and frequency of sex com binations in m ultiple b irth s. F ro m
a total of 4470 lambs* a m ale percentage of 49.8 i 0.75 % as obtained in
th is flock. T his shows a slightly le s s num ber of males* which a g re e s with
previous re p o rts . Henning (1939) rep o rted a m ale percentage of 48.96 1
0.14 on a to tal of 127587 lam bs from various so u rces.
Twin Sex Ratio
Twinning in sheep is of considerable im portance to both sheep men
and sc ie n tists from the point of view of economy and re s e a rc h , resp ectiv ely .
However, the la tte r is m uch in terested in the identical (monozygotic) twins
^Stan d ard e r r o r of the percentage was calculated by using the form ula
yPQ /N . In terp retatio n of the standard e r r o r : Male 49.8% ± 0.75 m eans
th at if we re p e a t the study using a num ber of sam p les, we would expect
the percentage of m ale in approxim ately tw o-thirds of the re s u lts to fall
in the ran g e fro m (49.8 - 0,75) * 49.05% to (49.8 + 0.75) * 50.55%.

17

in fa rm an im als, which a re v ery r a r e and difficult to identify if, at a ll,
th e re a r e any. The sheep seem s to be interm ediate between uniparous
and m u ltiparous m am m als. That it is b e tte r adapted to m ultiple
b irth s than the cow is shown by a low er ra te of p re m a tu re b irth s and
a low er postnatal m o rtality as a re s u lt of m ultiparity, In c a ttle , m ultiple
b irth s a r e considered as disadvantageous but in m utton breeds of sheep,
they a r e v ery d esira b le fro m an economic point of view (Johansson,
1932),
It is a well-known fact that twinning m ay occur as the re su lt of
eith e r of two d istinct p ro c e sse s, (1) Monozygotic twins resu ltin g fro m
the splitting of a single fe rtiliz e d ovum. Twins of this type a re called
id en tical tw ins, since they have the sam e genotype. Hence, the variance
observed within the sets of identical twins is wholly environm ental,
(2) Dizygotic twins o r fra te rn a l twins re su lt fro m the fe rtilizatio n of
two ova; and they a r e the sam e a s ordinary full sibs in genetic v ariab ility .
L>ush (1937) is of the opinion that the diagnosis of identical
(monozygotic) twins r e s ts on the sim ila rity in a long se rie s of c h a ra c te r­
is tic s , each of which is determ ined to a considerable extent by heredity.
F ra te rn a l (dizygotic) twins m ight, of co u rse, happen to be as like each
other as identicals in one o r a few c h a ra c te ris tic s but as the num ber of
c h a ra c te ris tic s is in creased it becom es m ore and m ore im probable that
fra te rn a l twins would happen to be alike in a ll the genes involved,
w hereas that is to be expected of twins a risin g fro m a single fe rtiliz e d
egg. K ronacher (1936) tr ie s to show how one can be su re that a p a rtic u la r
p air of twins a re in fact identical and not fra te rn a l. The methods that

18

he used to identify identical tw ins in cattle w ere the sim ila rity quotients,
the p o st-m o rtem m easu rem ents of sta tu re , and the analysis of blood and
horm one c h a ra c te ris tic s .
An attem pt has been m ade in this study to p re se n t sta tistic a l evidence
to show that, in sheep, we a re dealing alm ost exclusively with fra te rn a l
tw ins. A study of the sex com binations in twins m ay be used to estim ate
the frequency of identical tw ins. A ssum ing the sex ra tio to be equal,
the ra tio s of the th re e possible sex com binations would be approxim ately
1 ^ : 2 ^ : ^ ,

derived fro m the binom ial distribution form ula (a + b)2

w here a is the proportion of m ales and b, the proportion of fem ales. One
p o ssib le cause of deviation from this ra tio would be the frequent o ccu rren ce
of identical twins which would in crease the proportion of like-sexed twins.
Twin sex com binations w ere tabulated fo r different b reed s separately.
D espite the sm all sam ple num bers in m ost b reed s it is interesting to
note that the twin sex combination ra tio 1 : 2 : 1 consistently holds tru e
in each ca se. Table 5 shows the twin sex ra tio s in various b reed s.

19

TABLE 5. TWIN SEX RATIOS IN DIFFERENT BREEDS OF SHEEP
Twin Com binations
B reed

Ram and Ewe

Both Ewes

d g

99

5

12

6

C ots wold

10

20

9

Southdown

18

41

23

Oxford

23

39

18

R am bouillet

19

60

23

H am pshire

81

145

69

S h ropshire

97

239

119

C ro ssb re d s and
G rades

55

126

59

308

682

326

B lack Top D elaine

Total

Both Ram s

T able 6 shows the observed num bers of twins of each sex com bination
and the corresponding num bers expected on the b asis (1) of the sex ra tio
among these tw ins, (2) of the sex ra tio in this whole flock and (3) of
assum ed equal sex ra tio in sheep. The sex ra tio fro m 1316 twins is
49,3 t 0.97, The expected num bers of twins w ere calculated a s follows:
L et a * % of m ale
(1) Sex ra tio from twins ==49.3 * a
(2) Sex ra tio fro m the flock = 49.8 = a
(3) A ssum ed equal sex ra tio * 50.0 - a

20

Value
of
a

<?<f

.493

c f9

99

2 a (l-a )

( l- a ) 2

.243

.50

.257

.498

.248

.50

.252

.500

.250

.50

.250

M ultiply the ra tio s in the table by the total num ber of twins (1316) to
get th© expected num ber in each c la ss.
TABUS 6. ACTUAL* AND EXPECTED NUMBERS OF TWINS OF
DIFFERENT SEX COMBINATIONS
Expected Num bers
Type of Twin

O bserved
Number

F ro m
Sex Ratio
in Twins

F ro m
Sex Ratio
in Flock

F ro m
Assum ed Equal
Sex R atio

Both R am s

308

320

326

329

Ram and Ewe

682

658

858

658

Both Ewes

326

338

332

329

Since the proportion of the unlike-sexed twins is in excess it is
concluded that identical twins in sheep m ust be a r a r e and odd phenomenon.
T h is, how ever, does not ru le out the possibility of identical twins in sheep
since Henning (1937) produced a strong evidence in favor of am onovular
origin of two fetu ses by finding a single corpus luteum , where the fetu ses
w ere of like sex and they w ere v ery sim ila r in other re sp e c ts. The twin
sex ra tio in this flock was 308
a ra tio of 129

: 273 dcj> : 121

6 8 2 : 326^^ . C lark (1931) re p o rted
. Chapman and Lush (1932) observed a

ra tio of 87 <4d*: 184 c&j>: 90 <x> . Johansson (1932) observed 1164
2685 do : 1239 £ £ .

22

BIKTH WEIGHT AND CONVERSION FACTORS
B irth Weight
The growth of lam bs m ay be said to co n sist of an in tra -u te rin e phase
and an e x tra -u te rin e phase. The fo rm er could be m easured by the b irth
weight and the la tte r, by the weaning weight. The data on b irth weight
included those lam bs which w ere born alive as w ell as dead; but the dead
ones included only the s till b irth s c a rrie d full tim e and not the p re m a tu re
b irth s, The b irth weights w ere taken within about 24 hours a fte r partu ritio n .
It is hoped that the b ias in the weight of the wet lam b im m ediately a fte r
b irth w ill com pensate fo r the d ry lam b weighed a fte r a few hours of
grow th in v itro . The m ean and standard deviation of the b irth weight of
the five b reed s a r e given in table 7 a s a prelim in ary routine study.
TABLE 7. MEAN AND STANDARD DEVIATION OF THE TJNCORRECTED
BIRTH WEIGHT OF LAMBS OF FIVE BREEDS (1945-1948)
Num ber
of Lambs

Mean + Standard
Weight ~ E rro r

Standard , Standard
D eviation ~ E r r o r

137

9,38 t 0.19

2.24 + 0.14

Oxford

89

9.01 t 0.28

2.44 t 0.18

R am bouillet

51

8.69 ± 0.19

1.38 + 0.14

S hropshire

170

7.61 t 0.12

1.61 ± 0.09

Southdown

51

7.52 + 0,20

1.46 ± 0.14

B reed
H am pshire

The av erag e standard deviation of the b irth weights for the
com bination of a ll the b reed s was 2,09 pounds, and it - will; be used
la te r fo r estim ating the expected in crease in b irth weight per generation,

23

with c e rta in in ten sities of selection. The values fro m table 7 w ere taken
fo r the following calculation of the standard deviation.
Standard deviation of the com bined s e ts of d ata fo r the u n co rrected
b irth weight i

• 1 /4 9 8 jl3 7 (2 .2 4 2 + 8.38*) + 89(3.442 + f . o t 8) + 81(1.38* + 8.80*)
+ 170(1.61* + 7,81*) + 51(1.46* + 7.52*)1 - (42 0 7 .8 8 /4 8 8 )*

* 4.372
S* * / O W * 2.03
C onversion F a c to r
The question of conversion fa c to r a ro s e because c e rta in environm ental
fa c to rs conceal the actu al genetic m e rit of the individuals, thereby
confusing the b re e d e r in h is selection of anim als. F o r exam ple, two
an im als which have the sam e genotype o r equal breeding value m ay differ
co n sid erab ly in th e ir phenotype because of the effect of the differences in
age of darn, type of b irth and sea . In o rd e r to elim inate o r control som e of
th ese environm ental v aria tio n s, ait adjustm ent fa c to r was deem ed desirable*
which would place a ll an im als on a com parable b a s is . The co rrectio n
fa c to r applies to the group a s a whole and not to the individuals within the
heterogeneous group. Sex* age of dam and type of b irth w ere the fa c to rs
adjusted fo r in th is study of b irth weight of lam bs. A ll the y e a rs w ere
throw n to g eth er a s th e re was no significant y ea r difference.

24

The b irth weights of lam bs w ere grouped under tw o-year-old ewes
and m atu re ewes which, in tu rn , w ere su b -classed into singles and
m ultiples* m ales and fem ales since the object was to bring the weight
of a ll lam bs to an equivalent b a sis of ewe lamb* single b irth and m ature
dam . On the av erag e the m ales outweighed the fem ales consistently
in each b reed , Lam bs b o m a s singles w ere heavier than the individuals
in tw ins and trip le ts . M ature ewes dropped heav ier lam bs than the
tw o -y ear-o ld ew es. T hese differences w ere observed in a ll breeds*
but th e re was no significant difference in the average weights fro m y ea r
to y e a r. In o rd e r to get a common conversion fa c to r for a ll the breeds
it was decided to com bine the average differences and adopt the
m ultiplicative method instead of the additive method of c o rrectio n . By
the m ultiplicative method* the heavy b reed s and the light b re ed s a r e
equally adjusted in proportion to the size of the lam b.
The com bined average b irth weight of ra m lam bs w as 0.5 lb, m ore than
that of ewe lam bs; the m ultiple b irth s weighed 1,62 lbs, les s than the singles*
and the lam bs fro m m ature ewes averaged 0,53 lb, m ore than those of the
tw o -y ear-o ld ew es. The conversion fa cto rs fo r the m ultiplicative method
w ere obtained by figuring the average differences a s follows:
Sex
The av erag e b irth weight of a ll fem ale lam bs fro m m ature dam s
divided by that of a ll m ale lam bs fro m m ature dam s is 8,63/9,23 3
0,935,

The av erag e b irth weight of a ll fem ale lam bs fro m tw o -y ear-

old dam s divided by that of a ll m ale lam bs fro m tw o-year-old dam s

25

is 8,19/8,55 » 0*998, The av erag e of these two values is 0.847, which is
the co n version fa c to r fo r sex.
Age of Ha m
The av erag e b irth weight of a ll single lam bs fro m the m a tu re dam s
divided by th at of a ll sin g les fro m the tw o-year-old dam s is 10,231/9.381 *
1,889. The av erag e b irth weight of a ll twins and trip le ts fro m the m ature
dam s divided by that of a ll m ultiples from the tw o-year-old dam s is
8,474/7,588 « 1.115, The average of these two values is 1,102 which is
the conversion facto r fo r age of dam .
Type of B irth
T he av erag e b irth weight of a ll singles fro m tw o-year-old dam s
divided by that of a ll m u ltip les fro m tw o-year-old dam s is 9,391/7.596 »
1.236, The av erag e b irth weight of a ll singles fro m m atu re dam s divided
by th at of a ll m ultiples fro m m ature dam s is 10,231/8,474 * i,2&7> The
av erag e of th ese two valu es is 1.822, which is the conversion facto r fo r
type of b irth .
C onversion fo r Sex * -9,3 p e r cent
C onversion fo r Age of B am * 10.2 p e r cent
C onversion fo r Type of B irth * 22,2 p er cent
T hese p ercen tag es of adjustm ent fo r the environm ental differences in
b irth weight w ere consisten t in a ll the b re ed s, and w ere used fo r adjusting
the d ata. F o r exam ple, the b irth weights of m ales w ere reduced by
5,3 p e r cent to b rin g them to the fem ale b a sis. A ra m lam b weighing
10 lbs* would be converted to 10 x 0,847 * 9,47 lb s. to place it on a

26

com parable b a sis with ewe lam bs. Likew ise, lam bs fro m m ultiple b irth s
will be in cre ased by 22.2 p er cent, that is , a twin lam b weighing 10 lbs.
will be ra is e d to 10 x 1.222 « 12.22 lbs. to bring it to a single lam b b asis.
The weight of lam bs fro m tw o-year-old ewes w ill be increased by 10.2
p er cent. A single lam b fro m a tw o-year-old ewe, weighing 10 lbs. will
be c o rre c te d to 10 x 1.102 = 11.02 lbs. to bring it to the m ature ewe
b a s is . Thus, a m ale twin lam b fro m a tw o-year-old ewe, weighing 10
lb s. was adjusted to 10 x 1.271 * 12.71 lbs. on a fem ale, single and m ature
ewe b a sis.

27

CALCULATION O F HBRXTABILITY OF BIRTH WEIGHT
The calculations fo r the h alf-sib method* and the in tr a - s ir e re g re ssio n
and c o rre la tio n m ethods w ere c a rrie d out fro m the values in the tables of
an aly sis of covariance* F o r this* the co rre c te d b irth weight of dam s was
tre a te d a s one variable* X, and that of th eir offspring as the other
variable* If* The b irth weight of the dam which had m ore than one offspring
was re p eated fo r each offspring fo r the analysis* Thus, some of the
X -v a riab les w ere repeated* The weights w ere grouped on an in tr a - s ir e
basis* Then, the usual an aly sis of covariance was run between the X - and
Y -v a ria b le s a s outlined by Snedecor (1946), T h eir sums* sum s of squares
and pro d u cts a r e given in table 8a. F o r a detailed explanation of the
procedures* one breed* nam ely, Oxford* was chosen at random . The
com pleted an aly sis of covariance fo r Oxfords is given in table 8b,
TABLE 8a. FREUM m A RY BATA FOR THE STATISTICS OF BIRTH
WEIGHT O F OXFORDS
Num ber
©f F a irs
S ire of Dam
O ffspring

Sum
of X

Sum of
S quares of X

Sum
of Y

Sum of
P roducts
Sum of
of
Squares of Y
X and Y

I

34

320.6

3188.84

327.6

3453.80

3198.57

H

26

277.3

3010.83

276,8

3089,98

2925.45

III

27

286,1

3118.25

300,3

3432,53

3209.64

IV

4

384

383.05

46.1

537.23

439.87

Total

81

8224

9661,77

950.6

10513.54

9773.53

28

C alculation P ro ced u res:
C o rre c tio n fo r X « (922,1)2/91 * 8343*61
C o rre c tio n fo r T * (950*6)^/81 58 9930*11
C o rre c tio n fo r XY « (922*i)(990.6)/91 * 9632,40
T o tal
Sum of S quares fo r X * 9661*77 ** co rrectio n * 318.16
Sum Of S quares fo r Y * 10513.54 * co rrectio n « 383.43
Sum of P roducts fo r XY * 8773*53 *• c o rre c tio n * 141*13
Between S ire s
Sum of S quares fo r X * (320*6)2/3 4 +

+ (38*l)2/4 - co rre c tio n * 31*47

Sum of S quares fo r Y » (327,8)2/8 4 *

+ (4©.l)2/4 - co rrectio n » 40.31

Sum of P ro d u cts fo r XY * <329*©){327,0)/34 + —- + (38*l)(48*l)/4 * c o rre c tio n
» 27,88
TABLE 8b. ANALYSIS OF COVARIANCE OF BIRTH WEIGHT OF BAMS
AND THEIR OFFSPRING FOE OXFOEBS
Source of
V ariatio n
T otal
Between S ire s
Within S ire s
(or E rr o r)

Sums of Squares and P roducts

D egrees
of Freedom

Sx2

Sxy

Sy2

90

318,1©

141*13

583.43

3

31*47

27,88

40*31

87

286.69

113.25

543,12

29

TABUS 8c. ANALYSIS OF VARIANCE OF BIRTH WEIGHT OF BAMS
(X) IN OXFORDS
Source of
V ariatio n
T o tal
Betw een S ires
W ithin S ire s
(or E r r o r )

D eg rees
of F reed o m

Sum of
Squares

90

318.16

8

m

Mean
Square

F -v alu e

31*4?

10,49

3,19s*

286.69

3.29

* Signifies probability of chance o ccu rren ce a t le s s than 8% level*
TABLE 8d, ANALYSIS OF VARIANCE OF BIRTH WEIGHT O F OFFSPRING
(Y) IN OXFORDS
Source of
V ariatio n
T otal
Between S ire s
W ithin S ire s
(or E rr o r)

D eg rees
of F reedom

Sum of
Squares

00

883,43

3
8?

Mean
Square

F -v alu e

40,31

13,44

2*18

543.12

8.24

F ro m the d ata of the an alysis of covariance tab le 8b, a p relim in ary
a n a ly sis of v aria n ce of the b irth weight of dam s (X) was m ade a s shown
in tab le 8c. The F -v alu e between s ir e s was significant a t 5 p e r cent
lev el indicating that the av erag e b irth weight of one group of dam s was
significantly different fro m that of the o th er groups of dam s m ated to
d ifferen t s ir e s . The calculation of c o rre la tio n s and re g re ssio n s on an
i n tr a - s ir e b a sis which m in im ises the v arian ce due to different groups of
dam s is thus justified* L ikew ise, the analysis of v arian ce of the b irth
weight of offspring (Y) w as m ade a s shown in table 8d. H ere, the F -te s t
did not show any significant difference in the average b irth weights

30

of d ifferen t groups of offspring sire d by different r a m s , indicating th at
th e re was no significant y e a r to y e a r difference in the average b irth
w eights of d ifferen t groups of offspring.
TAB IM 3e. CORRELATION AND REGRESSION BATA FOE THE FOUR
0 E F 0 R D SIRES (B.Wt.)
Sums of
S quares and P roducts

D egrees
of
F reed o m

Sx2

$xy

Sy2

1

38

146,37

108,50

207,28

0,5246

0.7470

H

as

53.32

-24,59

147,38

-0,2774

-0,4611

HI

28

86.65

27*87

92,53

0,3081

0.3181

IV

3

0.15

0,77

5.93

0,8164

5.1333

at

286,69

113,28

843*12

0,2870

0,3950

sir®

T o tal

C o rrelatio n
C oefficient

R eg ressio n
Coefficient

The c o rre la tio n and re g re ssio n data w ere calculated sep arately for
each s ir e group and en tered in table Be. The notable fe atu res of this
tab le are? (1) the to tals in the th ree colum ns Sx2, Sxy and Sy2 a r e the
sam e as the values fo r the within s ire s te rm in the an aly sis of covariance
tab le 8b, This checks the calculations in both tab les. Also* the within
s ir e s re g re s s io n of table 8b is an average of the four s ire group re g re ssio n s
of tab le Be. The values of e ith e r of these tables w ere used fo r the
following calculation of the re q u ired statistic*
C o rre la tio n C oefficient = r * S x y //sx 2*Sy2 = 1 1 3 .2 5 //(280;89){543.12) 0.2870
Standard e r r o r of the c o rre la tio n coefficient was calculated by using the
form ula! Sr - 1 - r 2/ / n ^ i * 1 -

(0.287)2//9 1 - 2 « 0.9176//89 * 0.0972

31

The h e r liab ility estim a te is obtained by m ultiplying th is c o rre la tio n
coefficient by 2* which Is equal to 2 x 0.287Q * 0.5740. The standard
e r r o r of h e r liab ility is , likew ise, obtained by m ultiplying the standard
e r r o r of c o rre la tio n coefficient by 2, which Is equal to 2 x 0.0872 *
0.1944. T hus, the h er it ab ility of b irth weight of Oxford lam bs by the
in tr a - s ir e c o rre la tio n m ethod is 0,5740

t

0.1944.

E e g ressio n of offspring on dam is the re q u ire d re g re s s io n coefficient.
R eg ressio n Coefficient » b *» Sxy/Sx2 « 113,25/286*8® * 0,3950
Standard e r r o r of the re g re s sio n coefficient was calculated as follow s:
s - s.
2 ^Standard e r r o r of estim ate of the e r r o r te rm /n -2
b *
^--r—
Sy2 * (Sxy}2/S x 2 543,12 * (113,25)2/286.69
n -2
91 - 2
5.599
-------- _-g------------------ 5 I T O ”
Sb * \Zo7oT553 * 0.1397
The above re g re ssio n coefficient when m ultiplied by 2 gives the
e stim a te of h e rita b iiity , which is equal to 2 x 0.395 ® 0,790, S im ilarly,
the stan d ard e r r o r of the re g re ssio n was m ultiplied by 2 to get the standard
e r r o r of h e r liability, which is 2 x 0.1387 * 0,2794. Thus, the h eritab ility of
b irth weight of Oxford lam bs by the in tr a - s ir e re g re s s io n method is
0,790 £ 0,2794.
H alf-sib Method
The in tra c la s s c o rre la tio n was calculated fro m the data in table 8d,
A nalysis of V ariance of B irth Weight of O ffspring (Y). In tra c la ss c o rre la tio n
2 -2
2
2
» r i * S /(S +S ) w here S * the m ean square of the e r r o r te rm ,
m
m

32

2
Mean sq u are between s ir e s * Mean sq u are of e r r o r term
m *
X verage num ber in each s ire group
F i r s t , calcu late the av erag e num ber as follows:
K0 * (1 / n -l)(S k - Sk^/Sk) w here n K num ber of s ir e groups, and k = num ber
in each s ir e group.
Kg » (1 / 4-l)(91 - 342+262+272+42/91) = 20.89
Now, substituting in the in tra c la ss co rrelatio n form ula, we get the h alf-sib
c o rre la tio n : $2 « 6.24
2

13.44-6.24

sm " - T E W"

* °'3447

» 0.3447^.24+0.3447)= 0.0523
Standard e r r o r of this c o rre la tio n was calculated by the previous form ula
a s shown below:
Sr i = ( l - r i 2)/VnT2 = (l-0 .5 2 3 2 )/,/9 rT = 0.9973/9.434 = 0.1057
The h a lf-sib c o rre la tio n 0.0523 was m ultiplied by 4 to get the
e stim a te of h e r liability, which is equal to 0.2092. Likew ise, the standard
e r r o r of h eritab ility was obtained by m ultiplying the standard e r r o r of
h a lf-sib c o rre la tio n by 4, which was equal to 4 x 0.1057 * 0.4228. Thus,
the h e rita b ility of b irth weight of Oxford lam bs by the paternal h alf-sib
c o rre la tio n m ethod is 0.2092 t 0.4228.
The calculations fo r the other four breed s w ere identically the sam e
a s d escrib ed above fo r Oxford. Hence, only the data of p relim in ary
calcu latio n s, the analysis of covariance and the c o rre la tio n and re g re ssio n
values a re given in the succeeding tables. T ables 9a, b and c p ertain to
H am pshire; tab les 10a, b and c to Bambouillet; tables 11a, b and c to
S hro p sh ire; and tables 12a, b and c to Southdown,

33

TABLE 9a. PRELIMINARY DATA FOR THE STATISTICS OF BIRTH
WEIGHT O F HAMPSHIRE

S ire

Num ber
Sum of
of P a irs
Sum of
Sum of
of Dam Sum of X S quares of X Sum of Y S quares of Y P roducts
of X and Y
O ffspring

I

60

635,1

6937.73

644.7

7346.55

6930.66

II

9

101,8

1159.30

101.2

1213.06

1180.35

HI

40

449.8

5141.62

448.2

5177.10

5068.59

IV

6

61.9

644.31

60.6

619.68

623.08

V

11

118,6

1315.30

113.1

1186.71

1239.39

VI

8

93.1

1104.69

90.0

1019.32

1047.62

VII

3

32.6

357.66

34,4

396.66

371.09

137

1492.9

16860.61

1492.2

16959.08

16440.18

T otal

TABLE 9b. ANALYSIS O F COVARIANCE OF BIRTH WEIGHT OF DAMS
AND THEIR OFFSPRING OF HAMPSHIRE
Source of
V ariatio n
T otal
Between S ires
Within S ires

D egrees
of F reedom

Sums of Squares and Products
Sx2

Sxy

Sy2

136

392.36

179.56

706.08

6

18.77

14.00

16.20

130

373.59

165.56

689.88

34

TABLE 9c. CORRELATION AND REGRESSION DATA FOR THE SEVEN
HAMPSHIRE SIRES (B.Wt.)

S ire s

D eg rees
of
F reed o m

Sums of
Squar*as and Products
Sx2

Sxy

Sy2

C o rrelatio n
Coefficient

R egression
C oefficient

I

59

215.20

105.91

419.25

0.3526

0.4921

II

8

7.83

15.67

75.12

0.8461

2.0012

III

39

83.62

28.59

155.02

0.2511

0.3419

IV

5

5.71

-2*11

7.62

-0.3199

-0.3695

V

10

36.58

19.97

23.84

0.8763

0.5459

VI

7

21.24

0.25

6.82

0.0208

0.0112

VII

2

3.41

-2.72

2.21

-0.9905

-0.7976

130

373.59

165.5 6

889.83

0.3261

0.4431

T otal

TABLE 10a. PRELIMINARY DATA FOR THE STATISTICS OF BIRTH
WEIGHT OF RAMBQILLET

j

Sum of
Products
Sum of
of
Squares of Y
X and Y

S ire

Num ber
of P a irs
of Dam
O ffspring

Sum
of X

I

32

331.7

3499.07

320.3

3266.87

3345.96

H

22

226.4

2359.82

254.2

2983.44

2619.10

T otal

54

558.1

5858.89

574.5

6250.31

5965.06

Sum
Sum of
Squares of X of Y

35

TABLE 10b. ANALYSIS OF COVARIANCE OF BIRTH WEIGHT OF DAMS
AND THEIR OFFSPRING OF RAMBOUILLET
Source of
V ariation

Sums of Squares and P roducts

D egrees
of F reedom

T otal

Sxy

53

90.82

27.50

138.27

1

0.08

-1.50

31.12

52

90.74

29.00

107.15

Between S ires
W ithin S ires

Sy2

Sx2

TABLE 10c. CORRELATION AND REGRESSION DATA FOR THE TWO
RAMBOUILLET SIRES (B.Wt.)

S ire

D egrees
of
F reed o m

Sums of
Squares and Products
Sx2

Sxy

Sy2

C orrelation
Coefficient

R egression
Coefficient

I

31

60.79

25.85

60.87

0.4250

0.4252

II

21

29.96

3.15

46.28

0.0846

0.1051

T otal

52

90.75

29.00

107.15

0.2941

0.3196

36

TABLE 11a. PRELIMINARY DATA FOR THE STATISTICS OF BIRTH
WEIGHT OF SHROPSHIRE

S ire

N um ber
of P a irs
of Dam
O ffspring

Sum
of X

Sum of
Sum
Squares of X of Y

Sum of
P roducts
Sum of
of
Squares of Y
X and Y

I

30

271.6

2559.48

274.1

2590.59

2493.98

Xt

46

408.3

3682.63

423.2

4029.58

3779.85

in

48

428.8

4004.90

429.2

4047.24

3924.16

IV

U

95.0

841.08

106.0

1031.08

914.15

V

11

107.9

1081.51

100.0

956.58

1003.92

VI

5

41.9

360.35

42.8

374.02

365.73

VII

20

189.6

1829.24

188.9

1834.65

1782.35

T otal

171

1543.1

14359.19

1564.2

14863.74

14264.14

TABLE l i b . ANALYSIS OF COVARIANCE OF BIRTH WEIGHT OF DAMS
AND THEIR OFFSPRING OF SHROPSHIRE
Source of
V ariatio n
T otal
Between S ire s
W ithin S ires

D egrees
of F reedom

Sums of Squares and P roducts
Sx2

Sxy

Sy2

170

434.29

148.84

555.43

6

16,07

2.56

8.32

164

418,22

146.28

547.11
------------------------------------------------ -------4

37

TABLE l i e . CORRELATION AND REGRESSION DATA FOR THE SEVEN
SHROPSHIRE SIRES (B.Wt.)
Sums of
S quares and P roducts

D eg rees
of
F reed o m

Sx2

Sxy

Sy2

I

29

100.60

12.46

86.23

0.1337

0.1238

II

45

58.53

23,49

136,14

0.2631

0.4013

III

47

174.29

89.97

209,48

0.4708

0.5162

IV

10

20.63

*1.30

9.63

-0.0923

-0.0630

V

10

23.11

23.01

47.49

0.6947

0.9956

VI

4

9.23

7,07

7.65

0.8414

0.7659

VII

19

31.83

-8.42

50.49

-0.2100

-0.2645

T otal

164

418.22

146,28

547.11

0.3058

0.3497

S ire s

C o rrelatio n
C oefficient

R egression
Coefficient

TABLE 12a. PRELIMINARY DATA FOR THE STATISTICS OF BIRTH
WEIGHT OF SOUTHDOWN

S ire

Num ber
of P a irs
of Dam
O ffspring

Sum
Sum
Sum of
of X S quares of X of Y

Sum of
Sum of
Products
Squares of Y
of
X and Y

I

16

142.8

1313.28

137,7

1222.93

1249.44

n

11

105.4

1019.90

97.9

876.59

941.91

m

9

75.4

679.84

73,7

618.45

640.12

IV

7

58.1

496.45

55.8

454.48

462.90

V

6

46.9

383.81

53.5

481.47

410.98

VI

2

12.2

74.42

18.6

172.98

113.46

51

440.8

3967.70

437.2

3826.90

3818.81

T otal

38

TABLE 12b. ANALYSIS O F COVARIANCE OF BIRTH WEIGHT O F DAMS
AND THEIR OFFSPRING O F SOUTHDOWN
S ource of
V ariatio n

Sums of S quares and P roducts

D egrees
of F reed o m

T o tal

Sx2

Sxy

Sy2

30

157.81

40.03

78.98

5

29.45

0.48

6.81

45

128.36

39.55

72.17

Between S ire s
W ithin S ire s

TABLE 12c* CORRELATION AND REGRESSION DATA FOR THE SIX
SOUTHDOWN SIRES (B.Wt.)

S ire s

D eg rees
of
F reed o m

Sums of
S quares and Products
Sx^

Sxy

Sy^

C orrelation
Coefficient

R eg ressio n
Coefficient

I

15

38,79

20.47

37.85

0.5343

0.5277

H

10

9.98

3.85

5,28

0.5304

0.3857

III

8

48,18

22.68

14.93

0.8458

0.4709

IV

6

14.22

-0.24

9.88

*0,0205

*0,0169

y

5

17,21

*7,21

4.43

*0,8297

*0,4189

VI

1

0

0

0

0

0

128,38

39.55

72.17

0.4108

0.3081

T o tal

43

To su m m arise the re s u lts of the various breed s it was thought
p ertin en t to give the data of the various sta tistic s in a sep a rate table*
T able 13 gives the distrib u tion of re c o rd s by b re e d s, which enables the
r e a d e r to find a t a glance, the num ber of s ire groups and the num ber of
p a irs of dam -offspring used in the calculation of h eritab ility of b irth
weight and weaning weight. T ables 14 and 15 give the required e stim a te s
of h e rita b ility by b reeds and m ethods sep arately .

30

TABLE 18, DISTRIBUTION OF RECORDS BY BREEDS (1048-1048).
B re e d

Ho. of p a irs of
D am -offspring
fo r B irth Weight

Ho. of
S ires

No. of p a irs of
D am -offspring
fo r Weaning Weight

H am p sh ire

137

7

85

Oxford

@1

4

51

R am bouiliet

54

2

36

S h ro p sh ire

171

7

137

Southdown

51

6

39

504

36

348

T otal

TABLE 14, CORRELATIONS, REGRESSION AND STANDARD ERRORS
OF THE CORRECTED BIRTH WEIGHT OF LAMBS
B reed

P atern a l h a lf-sib
c o rre la tio n
*1

In tra -s ire
re g re ssio n
b

Sb

In tra -s ire
co rrelatio n
r

Sr

-0.0314

0.0880

0.4431

0.1105

0,3281

0.0769

Oxford

.0523

.1057

.3080

.1387

,2870

.0972

E am houillet

.3509

.1218

.3196

.1439

.2941

.1286

S h ro p sh ire

-.0264

.0768

.3407

.0837

,3058

.0697

Southdown

-.0185

.1428

.3081

.0878

.4109

,1187

H am pshire

40

TABLE 15. ESTIMATES OF HERITABILITY AND STANDARD ERRORS
FOR THE CORRECTED BIRTH WEIGHT
P a te rn a l
half -sib
method

B reed

H e rit­
ability
H am pshire

I n tr a - s ir e
co rrelatio n
method

I n tra -s ire
re g re ssio n
method

Standard H e rit­ Standard H e rit­ Standard
e rro r
ability
e rro r
ability e r r o r

-.1256

.3436

.8862

.2210

.6522

.1538

.2092

.4228

.7900

,2794

,5740

,1944

R am bouillet

1,4036

,4864

.6392

.2878

.5882

.2532

S hropshire

-.1056

,3072

.6994

,1674

.6116

.1394

Southdown

-.0740

.5712

.6162

,1952

.8218

.2374

Oxford

la view of the larg e sam pling e r r o r s , the estim ates of heritability
calculated fo r each breed and by each of the th ree m ethods m ay not be
a s ac c u ra te an estim ate a s if they w ere all averaged. T h erefo re, the
values w ere averaged to get the best estim ate fo r this set of data. These
av erag es w ere calculated by weighting each of the individual estim ates
in tab le 15 by the re c ip ro c a l of its squared standard e r r o r , as outlined
by H azel (1945). Although this method of weighting has some e r r o r s it
gives g re a te r weight to those estim ates which a r e based on the la rg e st
num ber of data.
The weighted average of heritab ility was obtained by the use of the
fo rm u la as follows:
Weighted A verage = P H /8!!* +
+ ~~~ * (hn/ Shn>
H eritab ility ( l / s 2^) + (1/ S| 2) + — + (l/sg ^ )
w here h i

hn 51 h eritab ility e stim a te s, and S h j

e r r o r s of h eritab ility .

S^n « standard

41

T he weighted av erag e of the standard e r r o r s of h e rita b ility was
calcu lated by the following fo rm u la:
W eighted A verage E r r o r
of H eritab ility * i m
w here

i

—

j T s ^ g iv ;- .:- + a /s ^ )

a r e the individual standard e r r o r s of heritability*

TABLE 16. SQUARED STANDARD ERRORS AND THEIR RECIPROCALS
OF THE HERITABILITY OF BIRTH WEIGHT
B reed

H alf-sib
method

In tra -s ire
method
■gjt

sit

i/s |t

H am p sh ire

*1161

8,5

*0488

Oxford

4768

5*6

Raznbeuitlet

.6886

S h ro p sh ire
Southdown
R eciprocal
sum of 6
b re e d s

In tra -s ire
c o rrelatio n
m ethod

R ecip ro cal
sum of 3
m ethods

s hg

i/si3

B ( l/s |)

20.S

*0237

42*2

71*2

*0781

12.8

.0378

26*5

44*9

4.2

,0826

12.1

,0641

15*6

31*8

*0944

10*6

*0260

3S.7

*0184

51*5

87*8

,3263

34

*0361

28.1

.0564

17*7

46*8

153.5

202*7

S3*0

i/s l2

107.2

In o rd e r to facilitate the calculations, the squared standard e r r o r s
and th e ir re c ip ro c a ls fo r the individual estim ates of h e ritab ility found
in tab le IS w ere f ir s t calculated and entered ha table 16. Then, substituting
in the fo rm u la, th e corresponding values fro m tab les IS and 16, the
weighted av erag e of th re e m ethods, the weighted average of five b re e d s ,
and, in tu rn , the weighted av erag e of 3 m ethods and S b reeds w ere obtained.
T h ese re s u lts a r e sum m arised in tab les 17a, b and c. A s a re su lt of this

m ethod of weighting, the b est estim ate of h eritab ility of birth weight of
lam bs in this flock was found to be 0,61 ± .06.
TABLE 17a. WEIGHTED AVERAGE OF THREE METHODS (B irth Weight)
B reed

H eritability

Standard e r r o r

H am pshire

0,6267

0.1185

Oxford

.5901

.1492

R am bouillet

.7149

.1771

S h ro p sh ire

.5659

.1011

Southdown

.6482

.1460

TABLE 17b, WEIGHTED AVERAGE OF FIVE BREEDS
Method

H eritability

Standard e r r o r

P a te rn a l h alf-sib co rrelatio n

0.1453

0.1768

I n tr a - s ir e re g re ssio n

.7189

.0966

I n tr a - s ir e co rrelatio n

.6381

.0807

TABLE 17c, WEIGHTED AVERAGE OF 3 METHODS AND 5 BREEDS
T ra it

H eritability

Standard e r r o r

B irth Weight

0.6138

0.0584

43

WEANING WEIGHT AND INFLUENCE OF ENVIRONMENTAL FACTORS
Weaning Weight is im portant in Iam bs because it is soon a fte r
weaning that ewe lam bs a r e selected to add to the breeding flock, and
the re m a in d e r sent to m ark et. Weaning weight is one of the m e a su re s of
th e producing ab ility of ew es. The weaning weights re p o rted in this
study a r e 120-day weights.
A ll lam bs w ere weighed when they w ere 120 t 4 days of age. A
sm all c o rre c tio n was m ade fo r those lam bs which w ere weighed a few
days before o r a fte r the exact 120th day. Thus, the weights w ere all
brought to a standard fo r com parison. The average weaning weights
and th e ir standard deviations fo r the five b reeds w ere calculated as a
p re lim in a ry routine study and entered in table 18. The average standard
deviation fo r the five b reed s combined was found to be 14.5 lbs. This
w ill be used, la te r, fo r estim ating the expected gain per generation in
weaning weight with c e rta in intensities of selection.
TABLE 18, MEAN AND STANDARD DEVIATION OF THE UNCORRECTED
WEANING WEIGHT OF LAMBS OF FIVE BREEDS (1945-1948)
B reed

Number
of Lambs

Mean + Standard
Weight ~ e r r o r

Standard + Standard
Deviation “ e r r o r

H am pshire

95

70.08 + 1.82

14.79 ± 1.07

Oxford

59

67.24 t 2.31

17.76 ± 1.63

R am bouillet

50

62.10 t 1.59

11.22 ± 1.12

S h ropshire

175

59.14 t 0.86

11.39 ± 0.61

Southdown

39

50.18 t 1.78

11.11 ± 1.26

44

F ro m the values In table 18, the standard deviation fo r a ll the b reed s
com bined was calculated as follows;
Sx3 * Sni(S2 + S * )/N

- (S niX i/N )2

• l/4 l8 (9 5 (1 4 .7 9 2+70.082) + 59(17.782+87.242) + 50(11.222+82,102)
+ 178(11.3 92+89»142 ) + 3 9 (1 1 .i l 2+50.182^ - (28036.28/418)2

» 210.21S8
Sx

• V 210.2155 * 14,50

Influence of V arious F a c to rs on Weaning Weight

An adjustm ent fo r environm ental fa cto rs which influenced the weaning
weight was found n e c e ssa ry because of the differences in weight due to
sex , age of dam , type of b irth and type of re a rin g . The e a rly works of
H azel and T e r r ill (1945a, 1948b); and T e r rill e t ml, (1847) indicated that
g en erally ra m lam bs, single lam bs and lam bs from m ature dam s w ere
su p e rio r in growth ra te to ewe iam bs, twin lam bs and lam bs from tw oy e a r-o ld dam s, resp ectiv ely . H azel and T e r r ill (1945a) found that about
50 p e r cent of the to tal v ariatio n in weaning weight was due to the environ­
m en tal fa c to rs. They re p o rted that ra m lamb® w ere 8,3 lbs, heavier
than ewe lam bs; single lam bs w ere 9,2 lb s, heavier than twin lam bs; and
the lam bs fro m m ature ew es weighed 6*1 lbs* m ore than the lam bs fro m
tw o -y ear-o ld ewes* A difference of 2*5 lbs* between singles and twins
ra is e d singly was observed in favor of singles*
In this study, the weaning weights w ere grouped according to the sex,
age of dam , type of b irth and type of rearing* The type of re a rin g was
of th re e kinds; (1) sin g les, (2) twins ra ise d together, and (3) twins ra ise d

45

singly* The twins ra ise d singly w ere expected to gain m ore than the
tw ins ra is e d tog eth er. If the two individuals of a twin lived m ore than
30 days on the m o th e r's m ilk they w ere considered as a twin ra ise d
together* If one of them was dead o r separated then, the other Iamb was
con sid ered a s a twin ra is e d singly.
T h ere was no significant difference in the average weaning weight of
lam bs fro m one y ea r to another. Hence, the data fo r all the y e a rs w ere
analyzed together. In each b reed , the ra m lam bs outweighed the ewe
lam bs. Twins w ere L ighter than the singles; and the lam bs from
m a tu re dam s averaged m ore than those of the tw o-year-old dam s. The
av erag e of a ll the five b reed s combined showed that ra m lam bs weighed
3.8 lb s. m o re than ewe lam bs; single Iambs weighed'*6 .7/lbs. m ore than
twin lam bs; and lam bs from m ature dam s w ere heavier by 2 .8 lbs.
than lam bs fro m tw o-year-old dam s. T here was no significant difference
in the av erag e weaning weight of single lam bs and twins ra ise d singly
in this flock. T h erefo re, the singles and twins ra ise d singly w ere
com bined fo r the study.
The conversion fa cto rs w ere found by the straig h t average method
fo r the five b reed s combined; and the m ultiplicative method was adopted
to convert the weaning weight to the equivalent b a sis of ra m lam b, m atu re
dam and single lam b.
The average weaning weight of all the singles and a ll the twins ra ise d
singly divided by that of a ll the twins ra ise d together is 66.72/57.13 =
1.168. The conversion facto r fo r the type of re a rin g is 16.8 p er cent.
The average weaning weight a ll the m ales divided by that of all the fem ales

46

is 64.17/60.35 * 1.063* The conversion fa cto r fo r sex is 6.3 per cent.
The av erag e weaning weight of lam bs fro m a ll m ature dam s divided
by th at of lam bs fro m tw o -y ear-old dam s is 62.89/60.13 3 1,046, The
co n v ersio n fa cto r fo r the age of dam is 4.6 per cent. T hese conversion
fa c to rs w ere used to adjust fo r the environm ental variations in weaning
weight due to these th ree fa c to rs. F o r exam ple, the weaning weight
say, 70 pounds of a twin ewe lam b born to a tw o-year-old dam and
ra is e d together will be adjusted to 70 x 1.277 ® 89.39 lbs. to bring it
to the equivalent b asis of single, m ale lamb and m ature dam.

47

CALCULATION OF HERITABXLITY OF WEANING WEIGHT
The method of calculation was identically the sam e as fo r the
calculation of h e r liability of b irth weight. Hence, the repetition of the
sam e statem en ts has been avoided as fa r as possible. The adjusted
weaning weights w ere grouped on an in tr a - s ir e b asis. The weaning
weight of dam was trea te d a s one variable - X, and that of offspring as
the other v ariab le - Y. Some of the X -variables w ere repeated and the
an a ly sis of covariance was m ade between X and Y. As an exam ple,
R am bouillet was chosen at random to d escrib e the procedures in detail.
TABLE 10a. PRELIMINARY DATA FOR THE STATISTICS OF WEANING
WEIGHT OF RAMBOUILLET
Num ber
of P a irs
of Dam
O ffspring

Sum
of X

1

22

1566.5

113045.09

1669.6

IX

14

1044.3

78740,35

958,3

36

2610.8

191785.44

2627,9

S ire

T otal

Sum of
Sum
Squares of X of Y

Sum of
Sum of
P roducts
of
Squares of Y
X and Y
129175.02 119240,07
66281.37

71545.07

195456.39 190785.14

C alculation P ro ced u res fro m Table 10a
C o rrectio n fo r X = (2610.8)2/36 = 189341,01
C o rre ctio n fo r Y = (2627.9)2/S6 = 191820.40
C o rrectio n fo r XY « (261Q.8)(2627.9) / 36 = 100981.14
T otal
Sum of Squares fo r X * 191785.44 - co rrectio n * 2444.43
Sum of Squares fo r Y * 195456.39 - co rrectio n « 3626.99
Sum of P roducts fo r XY a 190785.14 - co rrectio n = 204.00

48

Betw een S ire s
Sum of S quares fo r X = (1568.5)2/22 + (1044.3)2/14 - co rre c tio n = 98.23
Sum of S quares fo r Y * (1669.6)2/22 + (958.3)2/ l 4 - c o rrectio n = 473.69
Sum of P roducts fo r XY ■ (1566.5)(1669.6) / 22 + (1044.3)(958.3) / 14
- co rrectio n * -215.71
TABLE 19b. ANALYSIS OF COVARIANCE OF WEANING WEIGHT OF
DAMS AND THEIR OFFSPRING OF RAMBOUILLET
Source of
V ariatio n
T otal
Between S ire s
W ithin S ire s
(or e r r o r )

D egrees
of F reed om
35
1

34

Sums of Squares and P roducts
Sxy
2444*43
98.23 ^
2346.20

Sy 2

204.00

3626.99

-2 1 5 ,7 1 ^

473.69

419.71

3153.30

TABLE 19c. ANALYSIS OF VARIANCE OF WEANING WEIGHT OF
DAMS (X) IN RAMBOUILLET
Source of
V ariatio n
T otal
Betw een S ire s
W ithin S ires
(or E rr o r)

Mean
Square

F -value

58.23

98.23

1,42

2346.20

69.00

D egrees of
F reedom

Sum of
Squares

33

2444,43

1

34

49
T A B L E 10d, A N A LY SIS O F VARIANCE O F W EANING W EIGHT O F
O F F S P R IN G (Y) IN R A M B O U IL L E T

S ource of
V ariation
T otal

Sum of
Squares

35

3026,99

1

473,69

473,69

34

3153,30

92,74

Between S ire s
W ithin S ire s
(or E r r o r )

Mean
Square

D egrees
of F reed o m

F -value

5,1*

* Signifies probability of chance occurrence a t le ss than 5% level.
TABLE 19e. CORRELATION AND REGRESSION DATA FOR THE TWO
RAMBOUILLET SIRES (W.Wt.)

S ire

D eg rees
of
F reedom

Sums of
Squares and Products
Sx 2

Sxy

Sy 2

C o rrelatio n
Coefficient

R egression
Coefficient

I

21

1503,17

396,97

2467.58

0.1853

0.2374

n

13

843,03

62.74

685.74

0,0825

0,0744

T otal

34

2346.20 419.71

3153.30

0,1543

0.1788

@0

C o rre la tio n coefficient * r * Sxy/JsxZ*8y£ * 4 1 9 * 7 l//p 5 $ C 3 ) p l5 O 0 )
*

0*1543

S tandard e r r o r of the c o rre la tio n coefficient was calculated by using
the form ulas Sr * ( l - r 2 ) / / 5 ^ f * (l~04S432>/|/5¥^¥ * 0 .9 7 6 2 //S ? * 0.1674
T he h e rita b ility e stim a te is obtained by m ultiplying th is co rrelatio n
coefficient by 2 « which is equal to 2 a 0.1543 * 0.3086. The standard e r r o r
of h e rita b ility is , likew ise, obtained lay m ultiplying the standard e r r o r
o r c o rre la tio n coefficient by 2, which is equal to 2 x 0.1674 » 6.3346. Thus,
the h e rita b ility of weaning weight of R am bouillet lam bs by the in tr a - s ir e
c o rre la tio n method is 0,3686 t 6,334®,
R eg ressio n of offspring on dam is the req u ired re g re ssio n coefficient.
R eg re ssio n coefficient • b * Sxy/Sx^ * 418,71/2348.20 » 0,1788
Standard e r r o r of the re g re ssio n coefficient was calculated a s follow s:
S-S- g^Standard e r r o r of estim ate of the e r r o r te r m /n -2
s b “ — s S r W » « S r a r a w « r B » «?n s n s s p s ------Sy^ - ffxy)2/S x 2
tirVOI" J'

3153,38 - (419,711^/2346.20

—

—

—

....

—

m

s :m

—

—

-

--------------- -

« 80*53/2348.20 * 0.03858
Sb * /o T o ia ss * 84084
The h e rita b ility estim ate is obtained by m ultiplying th is re g re ssio n
coefficient by 2* which is equal to 2 x 0*1788 * 0,3576, S im ilarly, the
stan d ard e r r o r of h eritab ility Is calculated by m ultiplying the standard
e r r o r of re g re s s io n by 2* which is equal to 2 x 04964 » 0.3828, T husr

51

the h e rita b ility of weaning weight of R am bouillet lam bs fey the in tr a - s ir e
re g re s s io n method is 0*3578 t 0*3028*
H alf-sib Method
The in tra -c la s s c o rre la tio n was calculated fro m the data in table
3d. *. A nalysts of V ariance of B irth Weight of O ffspring (Y),
In tra c la s s co rrelatio n * r$ «* S ^ /(S 2 4& ^) w here S 2 * the m ean square
of th e e r r o r te rm .
g 2 ^ M ean sq u are between s ir e s - Mean square of e r r o r te rm
F i r s t , calcu late the av erag e num ber as follows;
&0 * t/( a ~ l) * (Bk - Sk^/Sk) w here n

mnum ber of s ir e groups* and k * num ber

in each s ir e group*
* l / ( 3 ~ t ) - (38 - 233+ 14*/**) * 17*1

How* substituting in the in tra c la ss co rrelatio n formula* we get the
h a lf-sib co rrelatio n :
S* * 02*74
S 2 - (473.60<*02,74)/17,l * 22.28
m
r t * 22.28/(92.74+22.28) * 0.1037
Standard e r r o r ot th is c o rre la tio n was calculated by the form ula a s
show s below:
S . - ( l~ r 2 ) / / n 3 f • (1 - 0.19372)//3 6 ^ 2 * 0 .9 6 3 //3 4 - 0,1682

T his h alf-sib c o rre la tio n and its e r r o r a r e sep arately m ultiplied by
4 to get the estim ate of h eritab ility and the standard e r r o r of h eritab ility .

Thus* the h eritab ility of weaning weight of Ram bouillet lam bs by the
h a lf-sib m ethod is 4 x 0*1537 * 0,7748 and the corresponding standard
e r r o r of h e rita b ility is 4 x 0.1652 * 0.60O8,

T he calculations w ore m ade in the sam e m anner fo r the other fo u r
b re e d s and hence, only th e data of sum s, sum s of sq u ares and products,
the an aly sis of covariance and the c o rre la tio n and re g re ssio n data fo r
each s ir e group a r e given in the following tab les. T ables 20a, b and e
p e rta in to the b reed H am pshire; tables 21a, b and c to Oxford; tables
22a, b and c to S hropshire; tab les 23a, b and c to Southdown,
TABUS 20a, PRELIMINARY DATA FOR THE STATISTICS OF WEANING
WEIGHT OF HAMPSHIRE

S ire

I

N um ber
of P a irs
of D am
O ffspring

Sum
of X

37

s o t i .a
f*

ti

Sum
Sum at
S quares at X of Y
238716.49

2830.6
9

31868.40

311.3

Sum of
P roducts
Sum of
of
S quares of Y
X and Y
223^89.14 235033.45

>

24896.67

11

4

III

aa

23^0 t

184773.81

2274.5

IV

a

tia u

10118.63

130,0

10501.00

10013.30

v

7

552.2

44604.10

524.6

41189.12

41549.19

VI

4

383*7

33361.43

324.0

26483.58

29708.86

VII

3

205.6

14263.10

275.7

25602.60

16607,40

T otal

83

7001,0

588885.10

8670,7

no

27870.84

169020.55 138346.40

542367.73 551209.33

S3
T A B L E 2 0 b . A N A L Y SIS O F CO V A R IA N C E O F W EANING W EIGHT O F
DA M S A N D TH EIR O F F SP R IN G O F H AM PSHIRE

S ource of
V ariatio n
T otal
Betw een S ire s
W ithin S ire s

Sums of S quares and P roducts

D egrees
of F reed om

Sjc2

Sxy

Sy2

84

12249.80

1037*81

17465.48

6

1410*54

-238.84

1172.07

78

10830*26

1276.45

18293.41

V

TABLE 20c. CORRELATION AND REGRESSION DATA FOR THE SEVEN
HAMPSHIRE SIRES (W.Wi.)

S ire

D eg rees
of
F reed o m

Sums of
Squares and P roducts
Sxy

I

36

47 33*40

11

3

41*84

in

27

4347,80

IV

1

22,45

V

8

1043,41

VI

3

482,03

VH

2

T otal

78

C o rrelatio n
Coefficient

R egression
C oefficient

Sy^

53,40 7240,59

0*0095

0.0117

069,75

0.8134

2,4541

773,20 5158.03

0,1833

0.1778

840,80

1.0000

8,1180

183,75 1874,10

0.1185

0.1588

249,18

244,36

0,7237

0,5168

182,85 -207,18

203,80

*0.9959

-1,2735

10838,26 1278.48 16293.41

0.0900

0.1177

102,68

137,33

54
PRELIMINARY D A T A FO R T H E ST A T IST IC S O F W EANING

TABLE 21a.

W EIGHT O F O X FO R D

N um ber
of P a irs
of Dam
O ffspring

Sum
Of X

I

20

72
1556.4

123545.86

II

12

1 0 ^ .0

HI

IT

IV

Sir©

T o tal

Sum of
Sum
S quares of X of Y

Sum of
P roducts
Sum of
of
Squares of Y
X and Y
128717.25 123837.10

88768,10

1551.5
73
871.6

1416.0

123295.28

ta io .o

91539.34 101708.88

3

125.4

8046.20

146.4

51

4114.8

341644.14

3788.5

13

66768.38

11070,26

73622,20

9434.64

288085.23 306402.91

TABLE 21b. ANALYSIS O F COVARIANCE OF WEANING WEIGHT OF
DAMS AND THEIR OFFSPRING OF OXFORD
Source of
V ariation

D egrees
of F reedom

T o tal

Sxz

Say

Sy2

SO

8852*40

1880,31

16032.48

3

1125,40

-818,73

312.86

47

8527.00

2186.04

15710.82

B etw een S ire s
W ithin S ire s

Sum s of Squares and P roducts

TABLE 21c. CORRELATION AND REGRESSION DATA FOR THE FOUR
OXFORD SIRES (W.Wt.)

S ire

D eg rees
of
F reedom

Sums of
Squares and Products
Sx*

Sity

Sy2

C orrelation
Coefficient

R egression
C oefficient

9359.64

0,6083

1,1947

11

568.35 -245,35 3481,17

-0,1768

-0.4346

III

16

5350.81 -742.88 2545.23

-0.2013

—
0,1388

IV

I

353,78

1.0000

1.3864

8327.30 2166,14 15719.82

0,1871

0.2540

I

18

11

T otal

47

2426.82 2889,37

184,32

255.36

ss
TA BLE 22a.

S ire

PR E L IM IN A R Y DATA FO R TH E ST A T IST IC S O F W EANING
W EIGHT O F SH RO PSH IRE

H um ber
of Pair®
of Dam
O ffspring

X

Sum
of X

Sum of
Sum
S quares of X of Y

Sum of
P roducts
Sum of
of
Squares of Y
X and Y

28

1603.4

100516,26

1787,0

126835,38 109840.96

II

33

2250,5

157363,09

2182.1

149543.67 147721.00

III

42

2600.0

164685.63

2719,3

182002,29 169527.88

IV

9

571.8

37152.44

883.8

38641.38

37208,25

V

3

503.3

32204.33

440.8

24568.52

27610,46

VI

5

303.3

18309.15

260.1

14060.35

15788,25

VH

14

934,1

83289.51

831.0

50247.56

85421,17

T otal

137

$776,3

573500,41

8803,9

585890.15 563178.03

TABLE 22b. ANALYSIS OF COVARIANCE OF WEANING WEIGHT OF
DAMS AND THEIR OFFSPRING OF SHROPSHIRE
Source of
V ariation
T o tal
Between S ires
W ithin S ires

Sums of Squares and P roducts

D egrees
of F reedom

S*2

136

11375,51

-804,04

20142.85

6

1151,51

50.70

2408.08

130

10224.G0

-881.64

17734,47

Sxy

Sy^

56
T A B L E 2 2 c . C O R R E L A T IO N AN D REG RESSIO N D A T A F O R TH E S E V E N
SH R O PSH IR E SIRES (W .W t.)

S ire

Sums of
Squares and Products

D eg rees
of
F reed o m

Sx2

Sxy

C o rrelatio n
Coefficient

R egression
Coefficient

Sy2

I

25

1635.82 -361.95

4013,50

-0,1412

-0.2212

II

32

2655.81 -1880.63

5253,97

-0,4515

-0,6350

HI

41

3021,01 1131.07

8040.57

0,2440

0.3125

IV

S

824.08

207,40

772,22

0,2601

0.2517

Y

?

540.47 -108.78

302.48

-0,2600

-0.2012

VI

4

0.98

-18,41

529.05

-0,8813

-19.800

VII

13

045.03

-24,33

921.78

-0,0261

-0,0257

T o tal

130

10224.00 -881.84 17734.47

-0,0639

*0,0842

TABLE 23a.

DATA FOR THE STATISTICS OF WEANING
WEIGHT OF SOUTHDOWN

P R E L IM IN A R Y

Number
of F a irs
S ire of Dam
O ffspring

Sum of
Sum of
Products
of
Squares of V
X and Y

Sum
of X

Sum of
S quares of X

Sum
of it

10

861.4

32238.88

596.8

36512.20

34032,48

II

8

474.8

28415.32

406,8

20835,30

24183,22

III

8

458.6

26664,34

485.0

30694,80

28337,80

IV

5

232,7

10855.71

212.8

0389,30

9979,49

y

6

295,8

14684.42

406.1

27748.87

19925.72

VI

2

93,6

4380.4S

122*6

7567.40

5737.68

39

2116.9

117239*17

2230.1

132625.87

122196.39

I

,.y

T otal

87
T A B L E 2 8 b . AH A LYSIS O F COVARIANCE O F W EANING W EIGHT O F
D A M S AN D T H EIR O F F SP R IN G O F SOUTHDOW N

S ource of
V ariation

Sam s of Squares and P roducts

D egrees
of F reed o m

Sx^

Sxy

Sy2

33

2334.93

1147,7%

8104.18

5

874.64

83.99

2242.87

88

1460.29

1083*72

2861.61

T o tal
Between S ire s
W ithin S ire s

TABLE 28c. CORRELATION AND REGRESSION DATA FOR THE SIX
SOUTHDOWN SIRES (W.Wt.)
D eg rees
of
F reed o m

S ire

Sums of
Squares and Products
Sx^

Sxy

Sy2

C o rrelatio n
Coefficient

R egression
Coefficient

I

9

721,89

828.18

895.1 G

0*8808

0.7316

II

7

239*94.

39.64

149,52

0,2110

0*1680

hi

7

878*12

535.10 1181*88

0.8O04

1*4266

IV

4

28,86

78.78

312*84

0.8429

2.9292

v

$

191*48

-95,01

260.87

-0.5843

-0,9362

VI

1

0

0

52.02

T otal

83

1460.29 1083*72 2861.61

0

0

0,8301

0*7421

T he m ain s ta tis tic s re q u ired fo r the estim ates at h eritab ility a r e
su m m arized in table 24, whence the d esired re s u lts a r e tabulated in table
28 fo r a ll the five b re e d s. The b est estim ate of h eritab ility was found by
th e a v e rag e of the th ree m ethods, by the av erag e of the five b re ed s and
th en , by the av erag e of 3 m ethods and 8 b reed s. T hese av erag es w ere

fatran by weighting each of the individual estim ates by the re c ip ro c a l of its

58
s q u a re d s ta n d a rd e r r o r , L ik e w ise , th e w eig h ted a v e ra g e of th e s ta n d a rd
e r r o r s o f h e r ita b ility w as c a lc u la te d by ta k in g th e s q u a re ro o t o f th e
r e c ip r o c a l o f th e su m o f th e r e c ip r o c a ls o f th e s q u a re d s ta n d a rd e r r o r s .

TABLE 24, CORRELATIONS, REGRESSION AND STANDARD ERRORS
OF THE CORRECTED WEANING WEIGHT OF LAMBS

B reed

P a te rn a l h alf-sib
c o rre la tio n

I n tra -s ire
re g re ssio n

I n tr a - s ir e
co rrelatio n

rl

® rl

b

%

r

®r

•0,0666

0.109?

0.1177

0 4 330

0.0000

04087

-,o«a§

.1423

.2540

4 006

4871

4370

R am bouillet

.1931

.1052

.m s

4064

4543

4674

S h ro p sh ire

.0089

.0853

-.0848

4131

-.0640

.0857

Southdown

,3984

.1383

,7421

4 051

.5302

4182

H am pshire
O xford

TABLE 25. ESTIMATES OF HERITABILITY AND STANDARD ERRORS
FOR THE CORRECTED WEANING WEIGHT

B reed

Pate trust
half -sib
method
H e rit­
ability

Intra - s i r e
regr« jssion
m e fchod

In tra -s ire
co rrelatio n
method

Standard H e rit­ Standard H e rit­ Standard
ability e r r o r
ability e r r o r
e rro r

H am pshire

-.0204

.4388

.2354

.2878

4320

.2174

Oxford

*'$540

.5602

.5080

.3810

*3742

*2766

R am bouillet

.7748

.6608

.3576

.3328

*8086

.3348

S h ro p sh ire

.3878

.3412

-4 6 8 8

.2262

-4 2 8 0

.1714

Southdown

1.5038

.5532

1.4042

.3802

1.0604

.2364

90
T h e w eig h ted a v e ra g e h e r ita b ility « (S • b n /S ? )

«n
The weighted av erage standard e r r o r of h e rita b ility *
/ l / ( 8 » 1 /s J ^ )

w here t o * h eritab ility ; and

/

(S . i/s '? )
bn

« standard e r r o r of

h e rita b ility , hi o rd e r to fa cilitate this calculation, the n e c e ssa ry data a r e
given in tab le 26, The fig u res in tab les 2$ and 26 w ere used to get the
fin al av erag e values of h eritab ility a s shown in tab les 27a, b and c. T hus,
the b e st e s tim a te of h eritab ility of weaning weight of lam bs was found to
be 0*30 t 0.08 by the weighted average of 3 m ethods and 5 breeds*
TABLJS 26. SQUARED STANDARD ERRORS AND THEIR RECIPROCALS
OP TOE HERITABI14TT OP WEANING WEIGHT

—
f&®
hi

Ultra--sire
r e g r e ssion
m et bod

R eciprocal
sum of 3
m ethods

In tra
c o rrs
me

1 1 1

H alf-sib
method

*h2

1/s
'f cfL
2

g2
h3

•/&

,0717

13.8

,0473

2 14

40.2

S { l/s £ )

H am pshire

4*3*

8*2

Oxford

.3240

34

6.9

,0760

13.2

23.2

R am bouillet

.4367

2.3

6.5

4121

8.9

17.?

S h ropshire

4184

8.6

,0812

18.5

.0284

34.0

62.1

Southdown

.3080

3.3

4823

8.8

.8559

17.9

27.8

88*1

171.0

R eciprocal
sum of 5
b re e d s

22.8

83.4

60
TABUS 27a. WEIGHTED AVERAGE O F THREE METHODS (Weaning
Weight)
B reed

H eritab ility

Standard e r r o r

H am pshire

04788

04577

Oxford

.3301

,2076

R am bouillet

,3872

,2377

S h ro p sh ire

-.0693

4260

Southdown

1.2243

4807

TABLE 2?b. WEIGHTED AVERAGE OF FIVE BREEDS
Method

H eritability

Standard e r r o r

P a te rn a l h a lf-sib co rrelatio n

0,4200

0,2108

I n tr a - s ir e re g re ssio n

,2923

4368

I n tr a - s ir e c o rre la tio n

.2772

4028

TABLE 27c. WEIGHTED AVERAGE OF 3 METHODS AND S BREEDS
T ra it
W eaning Weight

H eritability

Standard e r r o r

0,8007

0,0788

61
DISCUSSION OF RESULTS
The Individual e stim a te s of h eritab ility of adjusted b irth weight range
fro m negative values to o v er 100 p e r cent by the h alf-sib method* T hese
a r e obviously due to sam pling e r r o r s since the negative re su lts cannot
be in te rp re te d except th at th ese amount to ssero value o r a© heritability*
Anything o v er 100 p e r cen t Is m eaningless since the lim it is 10© p e r cent*
However* the weighted av e rag e of 8 b re ed s by the h alf-sib method is
approxim ately ©.IS t *18 fo r b irth weight. Evidently, the advantage of
taking a weighted av erag e of se v e ra l breeds is to a t le a st p artly rem ove
the sam pling e r r o r s . The standard e r r o r of h eritab ility by ibis method
is g re a te r than the h eritab ility itse lf, which indicates the la rg e sam pling
e rro r* On account of the negative values fo r th re e out of five b reed s
the a v e ra g e re s u lt is v e ry low when com pared with Hie estim ates by Hie
o th e r two methods*
The individual e stim a te s by the in tra -s ire re g re ssio n and c o rre la tio n
m ethods a r e con sisten tly uniform although the ran g e is 87 to 88 p er cent*
The av erag e of 3 m ethods and 8 b re ed s, which is 0.61 t .08# seem s to be
the b e st estim ate of h e rita b ility of adjusted b irth weight of lam bs in this
flock* In o rd e r to show how m uch p ractical confidence one can put in
th ese values* the fiducial lim its a t 08 p e r cent a r e calculated a s follows:
L im it • h i t #o i « % * 0*6138 Z 2*808 * 0*0584 « 0*0138 i 0*15* The "t**
value a t 1 per cent level should be taken fo r (n-2) d eg rees of freedom ,
w here a * to tal num ber of p a irs . Here* a * 804. T h erefo re, the 88 p er
cent fiducial lim its a r e 0*4638 and 0*7638* T his m eans that the chances

62
a r e v e ry good (99 out of 100) th at the r e a l h eritab ility of adjusted b irth
w eight tie s within these lim its*
The h e rita b ility of adjusted weaning weight fo r Southdown is
co n sisten tly over 100 p e r cent by the th re e m ethods, which is# again#
probably due to the sm a lle st sam ple num ber in the group. However,
the av erag e h eritab ility by 3 m ethods and 5 b reed s seem s to be the b e st
e stim a te and is 0,30 £ .08 fo r adjusted weaning weight. The 99 p er cent
fid u cial lim its# in this case# a r e 0.300? t 2,802 a 0.0768 which a r e 0*1024
ami 0.4990. (The upvalue# here# is 348), The r e a l h eritab ility of adjusted
weaning weight of lam bs probably lies between 10 p e r emit and S0 p e r cent.
S ources of E r r o r s
1. n eg ativ e r e s u lts of h eritab ility and estim ates o ver 100 p er cent
a r e obviously an e r r o r which could be attributed m ainly to the s ise and
n atu re of the sam ple, in this study a sm all sam ple num ber is a chief
so u rce of e r r o r . T hese sam pling e r r o r s may also include c e rta in unknown
environm ental circ u m stan c es.
2. hat the h a lf-sib method# the n ec essary adjustm ent fo r the p resen ce
of tw ins Is not m ade. The twins a re genetically fu il-sib s and not h alfsib s. However# the e r r o r due to this source m ay be insignificantly sm all
sin ce the num ber of fu ll-sib com parisons is too sm all a proportion of the
to tal co m p ariso n s.
3. System of m ating (inbreeding) re q u ire s an additional c o rre c tio n
depending upon the amount of inbreeding practiced in the flock. The e r r o r
due to th is source is v ery sm all since th e re has been no inbreeding in this

63

flock except a sm all amount in the R am bouillets. F o r all p ra ctic al
p u rp o ses, the flock is considered non-inbred.
Inbreeding in c re a se s the homozygosity and reduces the genetic
v a ria n c e fo r a p a rtic u la r trait* This would show a low er estim ate of
h e rita b ility fo r the inbred stock than in a non-inbred population. If th ere
is co n siderable amount of inbreeding practiced in the flock from which
the data a r e obtained fo r the study of h eritab ility , then, a c o rrectio n m ust
be m ade a s outlined by Hazel and T e r rill (1945).
4.

The e r r o r due to the source of the environm ental differences has

been p ra ctic ally elim inated in this study by following the method on the
in tr a - s ir e b a sis. M oreover, the usual practice in the flock has been to
u se one o r two s ir e s in a breed each y ea r. The m anagement in the college
h erd would v ary le ss fro m tim e to tim e than would be the case in the
average sheepm an’s flock where much depends on his crop yields, the
m ark et p ric e he receiv es fo r, and so on* Although it is practically
im possible to control the environm ent absolutely and perfectly, the e r r o r
due to this source is negligibly sm all.
P ra c tic a l A pplications
In the light of the differences in weaning weight of lam bs due to
environm ental fa c to rs, it seem s highly recom m endable as a good m anage­
m ent p ra c tic e to sep arate the lam bs into groups according to sex, type of
b irth and age of dam . T his would enable the b reed er to make selection of
lam bs on a m ore com parable b asis on the re a l genetic m erit of the
individuals.

64

The tw in sex ra tio of SOSd'd? 682d^ 3 2 6 ^ ia th is n o ck gives no positive
proof of the existence of any identical twins in sheep. Hence, th e re is no
point in seeking lik e-sex ed tw ins fo r controlling genetic variance in e x p e ri­
m ents on n u tritio n and m anagem ent of sheep*
The expected gain in b irth weight o r weaning weight p e r generation
would fee proportional to half the product erf the percentage of h eritab ility ,
th e stan d ard deviation and the to tal ©election d ifferen tials. Assum ing that
the rep lacem en t ra te s in a static population a re about 50 p e r cent fo r
ewe lam bs and about 3 p er cent fo r ra m lam bs, the corresponding
selectio n d ifferen tials a r e 0,80 and 2,27, resp ectiv ely , in a norm ally
d istrib u ted population (Lush, 1945). Since the average standard deviation
of b irth weight is 2,09 pounds and the average h eritab ility of b irth weight
is 61 p er cen t, the expected gain p e r generation would be equal to
(O,6i)(2*09)(0,8O't2*27)/2 * 1,96 pounds if all the selection w ere directed
tow ard the im provem ent of b irth weight alone* Likewise, since the
av e rag e standard deviation of weaning weight is 14,50 lb s, and the average
h e rita b ility of weaning weight is 30 p er cent, the expected gain p e r
generation would be equal to (O*3O)(14,50)(O,8O^2,27)/2 * 6,88 lb s ,, granting
that the selection was mad© fo r the im provem ent of weaning weight alone.
T hese gains a re the estim ates per generation. In sheep, since the
av erag e in te rv a l between generations, that is , the average age of ew es
when th e ir offspring a re born is between 4 and 4 -1 /2 y e a rs according to
L ush, the m axim um gain o r im provem ent p er y e a r would be le s s than 0,5
pound in b irth weight and le s s than 1,8 pound in weaning weight. H azel
and L ush (1942) have shown that with n equally im portant but u n co rreiated

65

tr a i t s , the gain possible in any tra it is only l / / n tim es as g re a t as if a ll
selection w ere d irected toward im proving one tra it alone. So, when
allow ance is made fo r em phasis on other tr a its , as is n ec essary in a
p ro p erly balanced breeding pro g ram , it seem s probable that the gains
actu ally m ade w ill be considerably le ss than the figures deduced above.

66
SUMMARY
1, A study of

lam bing re c o rd s of H am pshire, Oxford, R am bouillet,

S h ro p sh ire, Southdown, Cotswold, c ro ssb re d s and grades kept a t the
M ichigan S tate College flock fro m 1330 to 1346 showed that 51,3 p e r cent
of a to ta l of 2305 pregnancies w ere sin g les, 46,4 p e r cent w ere tw ins
and 3,4 p e r cent trip le ts ,
2, About 60 p e r cent of the b irth s in the tw o-year-old ewes w ere
a ll sin g les a s against only 46 p e r cent singles in the m ature ew es, showing
th at m ultiple b irth s in creased ms the age of the ewe advanced,
3, A to tal of 4470 lam bs gave a m ale percentage of 40,6 t 6,70,
4, Id en tical tw ins in sheep ap p ear to be very r a r e , as evidenced by
the tw in sex ra tio of 308 dc^: 0 8 2 : 326
6, Only the re c o rd s of H am pshire, Oxford, Ram bouillet, S hropshire
and Southdown fro m 1040 through 1048 w ere used to study the estim ates
of h e rita b ility . Tim h eritab ility estim ate by the weighted average of 3
m ethods and 5 b re ed s w as 0,61 i 0*08 fo r b irth weight and 0,30 t 0*08 fo r
w eaning weight*

67

LITERATURE CITED
Chapm an, A . B* and J , L . Lush, 1632. Twinning, Sex R atios and Genetic
V ariab ility to B irth Weight in Sheep* Jo u r. H eredity, 23(ll):4?3~478.
C la rk , Richard* 1031* The Mode of Production of Twins to Sheep, A m er.
So©, An. P ro d ,, Free*, pp. 207*200.
H azel, L, H, 1043, The Genetic B asis fo r C onstructing Selection Indexes,
G enetics 28*476*400,
H azel, L. N. and J , L. Lush* 1042, The Efficiency of T hree Methods of
Selection. Jo u r, H eredity 33:393-300,
H azel, L. M, and C* M« T e r r ill. 1045a. Effects of Some Environm ental
F a c to rs on W eanling T ra its of Range Ram bouillet Lam bs, Jo u r,
A nim al S et,, 4(4):331 -341,
H azel, L, N, and C, B. T e r r ill, 1945b. H eritability of Weaning Weight and
Staple Length to Range Ram bouillet Lam bs, Jo u r. Animal S ci.,
4 (4) *347-358,
H azel, L, N, and C, E . T e r rill. 1946a, H eritability of Weanling T ra its
to Range Colum bia, C o rried ale and T ar ghee Lam bs. Jour, A nim al
S c i., 5(4):371~S77,
H azel, L . M, and C, E. T erriU , 1048b, Effects of Some Environm ental
F a c to rs on F leece and Body C h a ra c te ristic s of Range R am bouillet
Y earling Ew es, Jo u r. Animal Sci., 5(4);382~388.
Henning, W, L, 1037, A Double Sheep Pregnancy with a Stogie C orpus
Luteum . Jo u r, H eredity, 28(1):81-62,
Henning, W, L, 1938, P ren a ta l and P ostnatal Sex R atio to Sheep. Jour.
A gr, R e s., 58(8)2565-580,
Johansson, Iv ar. 1932, M ultiple B irth s to Sheep, A m er. Soc, An, P ro d ,,
P ro e ., pp. 285-291,
S arah V. H. and J , B. R ouse, 1920, The R elation o f Age of Dam
to O bserved Fecundity to D om esticated A nim als, F a rt I. Multiple
B irth s to C attle and Sheep. Jo u r. D airy S ci., 3(4):260-29O,

Jones,

K ronacher, C. and B. S anders, 1936. Heue E rgebnisse d e r Zwillingsforschung
beim Rind, Z eitechrift F u r Zuchtung. Reihe B, Band XXXIV. (Recent
R esu lts of the Investigation of Twins to C attle. 34:1-172.)

63
Irtish* J . L* 1 9 3 5 , T h e In h e r ita n c e o f P r o d u c tiv ity in F a r m L iv e s t o c k .
F a r t V* D is c u s s io n o f P r e c e d in g C o n tr ib u tio n s. E m p . J o u r . E x p .
A g r ic . 3 :2 5 -3 0 .

Lush* J . L. 1937. Identical Twins in Cattle* T h eir P ossible Value in
Genetic Be se a rc h . A Review, Jo u r. H eredity, 28:415-418*
Lush* J . L* 1940* I n tra -s ire C o rrelatio n s o r R eg ressio n s of O ffspring
on D am a s a Method of E stim ating H eritability of C h a ra c te ris tic s .
Amer* Soc. An. Prod.* F ro c ., pp. 293-301.
Lush* J* L. 1945. Anim al B reeding P lans. 3rd Edition* The C ollegiate
P r e s s . A m es, Iowa* 443 pp.
Lush* J , L*, H, W, Horton* 111 and F , Arnold, 1941. E ffects Which Selection
of D am s May Hhve on S ire Indexes* Jo u r, D airy S ci., 14(8):695-721,
N elson, R , H. 1941* The Influence of H eredity on the M arket Score of
D uroc J e rs e y Hogs. M.S. T h esis. Oklahoma A gricultural College
L ib ra ry . S tillw ater, pp. 35-38.
N elson, K. H* 1943* The E ffects of Inbreeding on a Herd of H olsteinF rie s ia n C attle, Ph.D. T h esis. Iowa State College Library* A m es,
Iowa. pp. 31-37.
Phillips* R. W, 1943-1947* B reeding B etter L ivestock - Science in
F arm in g . Y earbook of A griculture, tJ.S.D.A. pp. 33-60.
S nedecor, G. W* 1946* S ta tistic a l M ethods. 4th Edition. The Iowa State
C ollege P re s s . Ames* Iowa, 485 pp.
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E nvironm ental F a c to rs on Y earling T ra its of Columbia and Targhee Ewes.
Jo u r. A nim al Set,* 6<2) i l l 5 ~122.
Wright* Bewail, 1821, System s of Mating* Genetics* 6(2)1111-178,
Wright* Sewall. 1034, The Method of Path C oefficients. Annals of Math,
Stat, 5:181-215.
Wright* Sewall, 1939. Genetic P rin cip les Governing the R ate of P ro g re ss
of L ivestock B reeding, A m er, Soc, An. Prod.* P ro c ., pp. 18-26,