DOCTORAL DISSERTATION SERIES
PUBLICATION: 5931
AUTHOR: Ram Baran Prasad, Ph. D ., 1951
Michigan State College
TITLE:

ESTIMATES OF THE HERITABIUTY
OF GREASE FLEECE WEIGHT AND
GRADE AND THE REPEATABILITY OF
GREASE FLEECE WEIGHT IN SHEEP

University Microfilms, Am Arbor, Michigan

ESTIMATES OF THE EERITABILITY OF GREASE
FLEECE WEIGHT AND GRADE AND THE
REPEATABILITY OF GREASE FLEECE
WEIGHT IN SHEEP

By
RAM BARAN PRASAD

A THESIS
Submitted to the School of Graduate Studies of Michigan
S t a t e .College of Agriculture and Applied Science
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Animal Husbandry
1951

ESTIMATES OF THB HERITAB ILITY OF GREASE
FIEECE WEIGHT AHD GRADE AND THB
REPEATABILITY OF OREASE FLEECE
WEIGHT IN SHBBP

Bjr

RAM BARAN PRASAD

AS ABSTRACT
Submitted to the School of Graduate Studies of Michigan
State College of Agriculture and Applied Science
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Animal Husbandry
Year
Approved

19S1

Mam B# Prasad
Abstract
Herltability estimates for grease fleece weight and grad#
and repeatability #itlmat# for g m « « flacc# weight war# de­
termined from sheep records from the Michigan State College
sheep flock*

Hie data included 1,699 records from 412

ewes of the Oxford, Shropshire, Hampshire and Southdown
breeds, covering the period from 1939 to 1949#

A study

of the contribution of oertain environmental factors to
grease fleece weight was made and appropriate adjustments
were indicated*
The study of environmental factors included the effects
of age, number of lambs raised, breed and year on grease
fleece weight*

The least squares proceedure of analysis

was used to study these environmental effects and the fol­
lowing is the estimate of the effects of different environ­
mental factors!

General Means
(Constant Environment)

7+99

Deviation from General
lieans for age
2 years*•»••»•••« 0*36 .
a
3
4

»

9

«

•••«••*»•* 0*04.

6

a

****»•••**.—0*48

7

a

•*

•***—0*44

Ran B* PraseA

Deviation from General
limmrtm fnw tesweefl
CksfAMi -*

0*94
0*18

Shropshire **.* ••• — 0*06
— 1*08
Deviation from General
Means for Ho* of iambs Raised
0*18

Single**4

0*09
Triplet*<

— 0*17

Deviation ^rox* General Mean
for year oir
Records made*1984*•****0*151
1988* *•••*0* 104
1986.... *0*727
1987***** *0*ISO
1938**•bm *0*6831999* *••• *0*636
1940* *****0*999
1941* ***•*0«169

1949**••
1949...* **0*980
•w——18mmnr
1944*••• **1*479
1946*••• *•1*304
1946..*. **0*948
194?*#** **0*071
1948** ****0*911
1949**•« •*0*711

The analysis or variance was dona by the method of fitting
constants and only tha environmental factors which accounted
far at laast 6 percent of tha total variations were eon-*
aldarad to ba important enough to justify adjustment in a
salaetlon program*

Th* environmental factors that needed

adjustment vara braad and yaars in grease fleece weight*

On

Ram B* PrtMd
- 3 comparison of the genotypic parameters of gntit fleece
weight to grade it woo found that tha heaviest flaaoa
weight was associated with tha poorest grade*

Tha

phenotypic correlation coafficiant between grease flaaoa
i

waight and grade was estimated by correlating tha two ;
j

characters in tha same animal and waa found to ba *0*3Sf
0*j04#,
Repeatability for grease fJs aea waight waa estimated
by tha method of intra class correlation from records of
156 awes of the Shropshire bread and this estimate was
<>♦44 t

0*02*
i
,1;

Estimates of heritablllty, after adjusting for 1st*
1

portent environmental effects, ware first made for each of
tha four breads by the method of lntra~slre regression of
f

offspring on dam and lntra-sire daughter-dam correlation*
Than the weighted average of the four breads and two/
methods ware taken to give the bast estimate of hep^tablllty<
For grease fleece waight 160 daughter-darn pairs were used
In analysis and the bast estimate of heritability was found
to be 0*38 ± 0*11*

For grease fleeoa grade 167 daughter-

dam pairs ware used and the estimate of
found to ba 0*20 1

l^ty was

*10*.

I * ,y

The. genetic correlation waa estimated by t h ^ W m a l a t
'5 S'-

Vi

0J = M

n rn J b B B n M

.

J f® Mr it ii) (oov ja Ji)

|
ft

Ran B# Ps^kead
- 4 •

\

.

\
s

.
\

When the aubaorlpta (l) and (8) represent tha parental and
I

t

fllllal generation respectively and I, J are two characters#
Tha estimate waa found to ba -0*57#
\ !
\

< i
!

Under tha aaauaptlon that 85 percent pf tha' awaa ere
■
;

replaced aaeh year with awa lambs front tha beet 00 paroant of
V.';

I /

tha awaa and that tha average loss due to daath ^hd aoeldente
la 15 paroant} tha antloipated gain for a flock ?f 100 awaa
•

s

:

r

1

In ona yaar waa aatlaatad to ba 0*17 pound for gjpeaae flaaoa
waight and a llttla laa8 than 0#10 tinit for greaae flaaoa
-f

'

grade. The gain in grade whan interpreted In t|0ma of tha par*
'■

•

/

eantaga of anlaala which may be expected to toove up one grade
In ana year la a llttla laaa than 10 kkdreent*

A CK N OVJ DEDGi.CENT

The author is grateful to the Government of Bihar
(India) for financial aid involved in stay and study in
U# S. A. and to Dr. Ronald H. Nelson, Head of the Depart­
ment of Animal Husbandry for his major help and suggest­
ions in preparation of this thesis.
A word of appreciation is extended to the men of
letters of the guidance committee and to Dr. Y/illlam D.
Baten, Research Professor of Statistics, for his help
in statistical procedures.

TAB HE OF CONTENTS
Page
INTRODUCTION
(a) General, . ..........................

1

(b) Heritability................................

5

(c) Repeatability...............................

8

(d) leans of Increasing Expected C ai n ......

10

FETECDS AND KATERIAL
(a) Source of Da t a ................

13

(b) Characters Observed.........................

15

ESTIMATES OF PHENOTYPIC PARAMETERS
(A) Phenotypic Leans, Variance and Correlation. 16
(B) Study of Environmental Effects on Fleece Wt.22
(a) Method of Analysis......................

23

(b ) Results.................

30

ESTIMATE OF REPEATABILITY
(a) Methods of Estimating Repeatability........ 37
(b) Calculation of Repeatability...............

38

(c) Comparison with Published Results.......... 40
ESTIMATES OF HERITABILITY
(a) Methods of Estimating Heritabi li t y......... 43
(b) Calculation of Heritability of Fleece Wt... 46
(c) Calculation of Heritability of Fleece Grade 55
(d) Comparison with Published Results.......... 59
ESTIMATE OF GENETIC CORRELATION
(a) Definition................................... 61
(b ) Calculation........

61

TABLE OF CONTENTS CONTD
Page
DISCUSSION...... :....................................

66

APPLICATION...........................................

72

SUMMARY.................................

78

LI TERATU RE CI TED......................................

80

INTRODUCTION
(a ) - General.
Biological investigations on sheep production have
tended to concentrate on- the Important problems o.f pathology,
parasitology, and nutrition.

The impressive losses from

disease and drought have directed research to problems whose
solution was an immediate necessity.

fore recently the need

for basic information on genetic factors has been recognised.
The theoretical basis for genetic studies that might be
applied to most economic characters has been developed
largely by his her (191b, 1930) and ’7ri_,ht (1931, 1931).
The logical consequences of hendellan inheritance, have
been interpreted in statistical terms, so that the results
of various systems of selection can be predicted with some
degree of accuracy.

Lush (1935, 1945, and 1948) has de ­

veloped applications of genetic theory to animal breeding
practice.
Since improvement in the genetic composition of one gener­
ation of a population is transmitted to succeeding generations,
each rung in the ladder of genetic improvement is permanent and
may be considered a capital gain.

Hence, a small genetic ad­

vance is worth considerable effort because the expense Incurred
in advancing one rung will yield dividends for many generations
In order to better understand the genetic advance that can
be made in wool production, the purpose of this study was to
estimate heritability of grease fleece weight and grease fleece
grade, and repeatability of grease fleece weight.

- 2 Since genetic gain may be increased by the elimination
of identifiable sources of environmental variation the
following environmental effects on grease fleece weight
were also studied:1-Age of shearing.
2-Ereed.
3-Itumber of lambs raised.
4-Year in which the record was made.
Little need be said concerning the importance of fleece
yield.

Fleece contributes an important source of income in

sheep production.

Winter, etal.

(1946) found that fleece

yield was responsible for fifteen to twenty five percent of
the income in sheep production.
The following discussion will explain concepts funda­
mental to this study.

The phenotype of any individual

organism is determined by its genotype and the environment
in which it lives.

Its phenotype will also be affected by

interaction of genotj’-pe and environment; that is, the value
of a given genotype will depend on the environment in which
its possessor -1
- develops.

In case of traits such as fleece

weight, which are expressed more than once in an animals
life^environment can be divided into two portions; one
portion the effect of which is constant for all expressions
of tne trait, and another portion, the effect of which is
variable for different expressions of the trait.

- 3 Let P symbolize the phenotypic measurment of a p ar ­
ticular trait.

For example, in the case of wool production,

P would be the pounds of wool obtained in one shearing.

If

p is used to symbolize the phenotypic deviation from the
population mean,

(p*P - P) the deviation may be expressed

as a function of the contributing effects such that:
+

"*j.

■*"

-h ZljKet

C K.

whereis the phenotypic deviation from the population
mean for the oC th expression of the k th in­
dividual with I th genotype developed In the
j th environment.
J/v

is the effect of the i th genotype
is the effect of the j th environment

Ck

is

any environmental effect constant for all the

expressions of the k th individual.
Is the sum of the Interactions among the par­
ticular combination of

and cifc.

Is the error In measurement associated with the
Ijk*C th expression.
Under the assumption that the genotypes occur among the
various environments at random,

the phenotypic variance

may be partitioned in the following manner;
**

+ <r£

+

<r?i

+

<r£

,

- 4 For convenience let Co^ and < * £ be included in

<ri includes

Thus

Cl such

that

all the observed variance other than

the portion attributable to constant differences between in­
dividuals.
I'ow consider •the quentit^- y, which is the genotypic
effect contributing to the phenotypic expression of the
trait.

Let g be the least squares approximation to y for

this population on assigning additive effects to each gene
replacement for all pairs of genes contributing to the ex­
pression of the trait.
to dominance,

Let d be the deviation from g due

that is, d is the sum of the deviations from
-n

'

the additive scheme for each pair of genes because of domi­
nant effects.

Let r be the deviations from g because of

interactions of non-allelic gene pairs such that
•

j

9 +

j

.

and the variance of y,
=
where

6 $

+

, is partitioned;
<rJt

+- ga.

is the total genotypic variance and

, d u and (TJt

are the variances due respectively to additive gene effects,
dominance deviations and non-allelic gene interactions or
epistatic effects.(Wright 1935).

- 5 »

(t> ^Heritability
In a broad sense, heritability (Hb) of a characteristic
is then
Hb 5.

i .
CPp

This simply answers the question; what fraction of the
observed phenotypic variance is due to hereditary differences
between those Individuals; heredity being considered as the
whole combination of genes in each individual? Theoretical­
ly heritability can range from zero to 1.0, although actually
these extremes are rarely encountered, A heritability estimate
pertains
at

to a particular characteristic in a certain population

somedefinite moment. It can be raised or lowered by any

breeding system or practice or any alteration of environment
which will increase or decrease either

y,

(T*c

or

(T\ .

Lush (1948) discussed the following features of
heritability in the broad sense which seem to deserve mention
heres(a) Presence or absence of a characteristic at birth
is not a criterion of its heritability,
(b) Rarity or abundance is no criterion of heritability.
Rarity or abundance comes into the picture only in
that a rare contrast contributes little to the total
varience in a population while if the same contrast
were more abundant It would supply much variance.

- 6 (c) Dominance or recessiveness has nothing to do
with heritability in the broad sense, although it
does lower the resemblance between relatives,

A

completely recessive trait is as truly hereditary
as a completely dominant one.
(d) Perfect heritability does not mean perfect likeness
of parents and offspring.

The sampling at segre­

gation, and the fact that the individual has two
parents not necessarily alike in the characteristic
being considered, are enough to keep the resemblance
between parent and individual offspring from being
perfect, even when heritability is perfect.
As far as the animal itself is concerned its genotype
functions as a whole.

This actual functioning of the

genotype as a whole is what is meant in the broad defini­
tion of heritability.

But the gene, not the whole genotype

is the unit in transmission from parent to offspring.

If

it is assumed that each gene substitution has, in every
genotype, exactly the same effect as the average effect
which it actually does have in that population, then by
adding all these average effects of the constituent genes
we can get an "expected" functioning or value for each
genotype.

Variance among these "expected" values con­

stitutes the additively genetic variance in that population.
Therefore, the narrowest definition of heritability, H n , for
a particular trait is defined as the fraction of the total
phenotypic variance which is additively genetic, ff-j,

__2•

- 7 Permanent improvement from phenotypic selection is pro­
portional to this heritable fraction of the observed variance
and varies from trait to trait (Lush 1935).

Thus, herit­

ability is important to the breeder because it represents
the portion of superiority in selected parents which can be
expected to be passed on to their offspring.

This expected

genetic gain, g s , from a single cycle of selection for a
single trait measured in terms of the difference between the
expected mean performance of the offspring of selected
parents and of the offspring of all possible parents may be
estimated,

(5)?in the following manner;

Ss (=)

sH

where the selection differential, s, is the mean difference
in performance of selected parents and all possible parents#
When the economic value of an organism is a function
of more than one characteristic, selection for a single trait
may result in selection for or against or have no effect on
other traits depending on the genetic correlations existing
between the trait selected for and these other traits.

Hazel

and Lush (1942) showed that it is more efficient to base
selection in every generation on an index involving all
traits which affect the net merit of the organism provided
each trait is given its proper weight relative to the others
than to follow the plan of Improving the individual traits
one at a time or the plan of improving the traits simultane-

ously by the use of minimum culling levels.

Heritability

estimates are included in the information needed to arrive
at optimum weights to be given to several traits in an index.
Even in the other two methods of selection, heritability
estimates would aid in properly weighting the various traits.
In addition, heritability estimates are essential
in determining the efficiency and choice of different breed­
ing systems (Wright,

1939).

If heritability Is high for the

desired characteristics, the best method will be mass
selection with little use for pedigree, relatives or progeny
test selection.

If heritability is low, a better plan would

be to make considerable use of pedigree and some use of
progeny tests,

(Dickerson and Hazel, 1944) and of selection

on the basis of family.
(c ) - Repeatability
For traits which are expressed more than once by
the same individual, repeatability may be defined as the
regression of future performance or phenotype on past per­
formance as measured by one expression of the trait.

Using

previous notations, repeatability, R, Is defined such that;
p

< % +

which amounts to the fraction of the phenotypic variance
that is attibutable to constant differences between individuals
This repeatable fraction of the total variance Is the portion
of the superiority in selected individuals that may be ex­
pected in future performance.

Thus the expected gain, p s>

- 9 future performance from a single cycle of selection,
measured in terms of the mean difference between the ex­
pected future performance of selected Individuals and
the performance of all individuals, may be estimated in
the following manner;
/ j (-)*£
s is again the selection differential which is defined as
the mean difference in performance of selected individuals
and all individuals of that population.
It may be worthwhile to mention the relationship
of heritability to repeatability.

Since neither the genes,

nor the dominance, nor epistatic deviations change duhing
the individual’s lifetime, repeatability should be at least
as large as heritability in the broad sense.

Repeatability

may be still larger because it also includes the permanent
effects of environment.

For exaraiple, the kinds of feeding

to which calves and young heifers are subjected, do affect
their production all through the rest of their lives.
These effects would be included in the repeatability but
they would not be heritable.

Consequently repeatability

is useful in setting,; an upper limit to heritability.
Repeatability may not be much larger than heritability in
the broad sense but it can hardly be less.

Using previous

notations the relationship can be represented as;

R

<rg +

<rj[ -f

+ o-c

(d) - Means of Increasing expected gain from selection.
When selection is based on an average of n records
per individual the expected gain per cycle of selection is
increased by the fraction
T

+

n
(n - I)it'

(Lush,

1947)

such that
_
/_\ „ nR
ps
s 1 + "('ri~T'')'H
Similarly

the expected genetic gain, g s ,

from

selection based on n records per individual is increased
such that
Ss (=) s
However,

the picture of increasing the gain by

averaging records is not complete because the selection
differentials are different for different values of n.por the
purpose of illustration and in theoretical problems the
selection differential may be defined such that

s.
when q is the selection differential in units of the
phenotypic standard d e v i a t i o n , ^ , (Hazel and Lush, 1942).
The magnitude of q depends on the portion of individuals
selected and the size of the population.
Rewriting previous notations;

- 11 And substituting

^pi

ds

‘p 5*

which, is equivalent to

v
G f r ________

^

%

^ a f ’.+ irt 4-<r«

The effect of averaging n records per individual
i.
in essence is to reduce < T l
to
j and the expected
_

genetic gain for this condition, gs (n), expressed as a
fraction of the expected genetic gain for one record,
So (1), is

u>
which reduces to

n z r '-i
+
"/

*— t. ■, a t
"

0 R
q was assumed to be constant for this illustration.

Thus

it is seen that the effect of using n records is to increase
genetic gain directly proportional to

per cycle of selection,

1

4-

—

&

Ps is increased by the use of n

records in the same manner.
Other means of increasing genetic gain are worthy
of consideration.

Since g s (= ) q _ t
V
(T
by increasing q or
or by reducing

>gs raay p e Increased

q may be increased by reducing the portion of in­
dividuals selected and/or by increasing the size of the

- 12 population.

The latter condition is practically of no

importance except that by increasing the size of the popu­
lation the portion selected can possibl?/ be reduced.

How­

ever, t ese conditions depend on the reproduction rate and
longevity of the species under consideration and the state
of development of the population with respect to numbers,
about which breeders generally have little control.
It has already been shown that <fp may be reduced by
the use of an average of n records per individual for the
basis of selection.

Carrying this concept one step further

(Jp may be reduced by basing selection on averages of groups
of individuals such that (Tp is reduced to <Tp, the phenotypic
standard deviation of means of groups of individuals.

How­

ever, it should be pointed out if the use of averages of n
records of an Individual effectively reduces the number of
cycles of selection over a period of time, then the total
gain for the entire period could actually be reduced al­
though the gain per cycle of selection was Increased.
The method most readily available to the breeder for
reducing c'p has yet to be mentioned.
(^e»

Consider the quantity

which is the sum of all variances among phenotypic

expressions other than those attributable to constant dif­
ferences between Individuals.

Among these summed variances

- 13 there may be certain identifiable sources of environmental
variation which can be adjusted for.

As an example, con­

sider that the year,the record was made,exerts considerable
influence on the grease fleece weight.

If selection occurred

among individuals whose fleece weight occurred in the same
year, the effects of years would be automatically eliminated,
or if the weights occurred among different years they could
be adjusted for yearly differences.
portion eliminated be
■

Let the environmental

and let

-

Then
Gf
ft*
‘ T j y i a - * )
ncrease in g s is directly
dii
Thus the increase
proportional to

{

jjZZ)

f where a is the fraction of the total variance ad­

justed for.

The effect on H is

(Tl
h

=

and the increase in H is directly proportional to
Similar concepts hold for p s and R.

*

O-V

•

However, as would seem

logical, only adjustments that are practical for use in
routine selection programs should be applied to the data
In estimations of appropriate H and R.
METHODS AND MATERIAL
(a) Source of Data: - Data used in this study were obtained
from the flock of sheep at Michigan State College.
contained the following breeds:

The flock

- 14 Shropshire, Hampshire, Oxford, Rambouillet,

South-

down, Cotswold and Black top Delaine.
There were also some grades and cross breads.

The

feeding and management of the flock have been as good as
practicable in keeping with its objects of teaching, re­
search and extension demonstration.

A general survey on

the productivit:,r of the flock made by Venkatachalam (1949)
showed that of the two-year-old ewes, 65.3 percent gave
birth to singles; 33.7 percent to twins and one percent
to triplets and of the mature ewes, 51.9 percent gave
birth to singles; 46.4 percent to twins and 2.4 percent
to triplets.

There has not been a major disease problem

among ewes since the early 3 0 ’s; but there was high lamb
mortality during recent years.

All sheep were usually

shorn about the middle of February.

The lambing season

was from the middle of February to April.
The data included the shearing records made by the
college flock from the year 1933 to 1949.

The records

from only medium-wooled breeds, Southdown, Oxford, Hamp­
shire, and Shropshire were used in this study.

A grand

total of 1599 records from 412 ewes were used in the analysis.
Out of the 412 ewes, there were 240 Shropshire, 77 Hampshire,
38 Southdown and 57 Oxford ewes.

The ewes that lambed as

yearlings were not included in this study.

In order to

facilitate statistical analysis of grease fleece grade the

- 15 following numerical figures were assigned to the different
grades:
Grade

Numerical Figure Assigned

blood

5

3/8 blood

4

l/4 blood

3

low l/4 blood

2

common

1

braid

0

1/2

(b) - Characters observed:
A series of characters, bifcth. weight, weaning weight,
grease fleece weight and grade have been routinely recorded
in this flock.
Grease fleece weight: Grease fleece weight is the weight of
fleece immediately after shearing, expressed in pounds.

The

weight includes not only wool substance, but also wool wax,
suint, dirt, vegetable matter, moisture and other materials.
Prenny and Turner,
weight.

(1958) discussed factors which affect this

In particular,

the moisture content varies in dif­

ferent fleeces even at constant relative humidity.
fleece was weighed at the first shearing (about
old).

The lamb’s

11-12

months

A year later when the sheep was about 23-24 months old

the second fleece was weighed and so on.

Grease fleece weight

at the ages of one, two, three, four, five, six and seven
years have been Ineluded in this study.
used.

Machine shearing was

V

- 16 Important errors in evaluating the fleece producing ability
of a sheep are likely to arise from less subtle causes such
as variations in shearing techniques,

loss of portions of

fleece when weighing and errors in weighing and recording.
Grease fleece g r a d e : - The fleece was graded in a warehouse
by a competent wool buyer.

The grading was done by in­

spection and no laboratory methods were employed.

The

American system of grading was used and the grade recorded
in the same terminology.
ESTIMATES OP PHENOTYPIC PARAMETERS
A - Phenotypic means, variances and correlation.
Data on grease fleece weight were available from 1599
shearing records made by 412 ewes.

Data on grease fleece

grade were available from 1155 records made by 310 ewes.
The means and variances are shown in Table I, II and
III.

In Jmble IV are given the average fleece weights of

ewes of different ages as published by different workers.
On studying Table I and Table XV it appears that the age of
heaviest fleece weight varied from two to four years of age
with the present data showing the heaviest fleece weight at
three years of age.
There was a gradual but steady decline in fleece weight
with increasing age after the ewes had reached the age of

- 17 Table I
Phenotypic Means, Variances, Standard Deviations
and Coefficients of Variations For Grease Pleeea

Weight and Gi*ade at Various Ages
Trait

Group
Estimate

D.P.

Means

Grease Age 1 y r .

325

fleece

2

yr.

weight

3 yr.

c.v.

■Variance

S.D.

%

6.68

3.09

1.76

26.35

459

7.32

2.92

1.71

23.36

369

7.43

2.32

1.52

20.46

4 yr. 273

7.23

2.46

1.57

21.71

5 yr.

161

7.91

2.49

1.55

22.11

yr.

97

6.65

1,71

1.31

19.70

7 yr.

48

6.50

1.93

1.93

21.38

6

Grease

1

yr.

193

3 •64*

.28

.53

14.56

fleece

2

yr. 293

3*61*

.38

•62

17.17

grade

3 yr.

265

3.6 8 #

.35

.59

16.03

4 yr. 194

3.64*

.27

.52

14.28

5 yr. 123

3.72*

.26

.51

13.71

yr.

77

3.70*

•2 Ty

•52

14 .05

7 yr.

33

3.76*

.33

.57

15.16

6

* Low 3/8 blood.

-

13

-

Table II
Phenotypic Means. Variances. Standard Deviations and
Coefficients of Variation of Weiafet ani

for

Number of Lambs Raised.

Trait

Group
Estimate

D.F.

Means -Vsrisnce

S»D»

% C.¥.

No. of
Lambs
Raised
Grease

Single

306

7.27

2.00

1.41

19.39

Fleece

Twin

563

7.14

2.97

1.72

Weight

Triplets

30

7.34

2.13

1.43

24.09
20.16

Grease

Single

543

3.64*

.29

.54

14.33

Fleece

Twin

431

3.64*

.51

19.51

Grade

Triplets

20

3.67*

.39

.71
•62

* Low 3/S Blood.

16.39

-

19

-

Table III
Phenotypic Means. Variances♦ Standard Deviations and
Coefficients of Variation of Weight and Grade
for Breeds.

Trait

Group
Estimate

D.F.

Means

Variance
2.74
2 .OS

1.65

19 .SI

1.44

19.75

2.40

1.55

21.39

1.76

1.33

21.76

S *D. % C.T

Breed
Grease

Oxford

207

S.33

Fleece

Hampshire

279
912

7.29
7 .OS

Southdown

14S

6.11

Grease

Oxford

151

3.14***

.12

.35

11.15

Fleece

Hampshire

279

3.56***

.29

.54

15.16

Grade

Shropshire

623
12S

3.71*
4.22**

.29

.54

14.55

.14

.37

S.77

Weight v Shropshire

Southdown
***
**

Over % Blood
Over 3/S Blood

* Low 3/S Blood

- 20 -

Table IV
Published Average Fleece Weight of Different Aged Ewes
Investigators________Breed________ D.F. Age In Yrs. Av. Fleece wb
Jones etal.

(1944)

Rambouillet

753

1

7,85

B and G type 624

2

9.16

508

3

9.40

429

4

9.41

351

5

9.16

273

6

8.90

292

7

8.63

______
Cockerham (1949)
5rccd

Mixed
Breed

2

6.44

3

6.38

4

6.32

5

6.01

6

6.16

7

5.33

u

AO B
»

Avmj*

fl**c*

f

»

w«l jht

T —
AOR

of

difforont

r

1«

fra. s
•

__ 5.

3 .

:

fl*®®* j gr*d® ofj , d lffo ro n t «god ®w« i .

ttrtgt fleece weight
.verege fleece grese

I
!
■
-jnwm»yi»gfr ©f th*
jpmfte of the four brwwda.

■■■'■'■•"I
BREEDS
;ri». s
.fleece- weight- end everege fleece

- 21 three years (Fig. 1).
and Jones

Similar declines were reported by Lush

(1923) and Spencer (1925).

No significant difference

was found in the fleece weight of ewes raising single, twins,
or triplets.

Among the four breeds under consideration,

Oxfords had the heaviest fleece weight and Southdowns had
the lowest while Hampshires and Shropshires were inter­
mediate.

With regard to grease fleece grade, it is apparent

from Tables I, II and III that there was no significant dif­
ference In grease fleece grade among the ewes of different
ages (Fig. 2) and also among ewes raising different numbers
of lambs.

But It was interesting to note the significant

differences among the breeds.

In the four breeds studied it

was found that Oxfords, having the heaviest fleece weight,
had poorest fleece grade, while Southdowns, having lowest
fleece weight, had highest grade as shown In Table V and
Fig. 3.
Table V
Comparison of Average Grease Fleece Weight
and Grade of The Four Breeds
Breed-

Grease Fleece
Weight (lbs)

Grease Fleece Grade

Oxford

8.33

3.14 (over 1/4 blood)

Hampshire

7.29

3.56 (lower 3/8 blood)

Shropshi re

7.08

3.71 (lower 3/8 blood)

Southdown

6.11

4.22 (over 3/8 blood)

- 22 The correlation coefficient between grease fleece
weight and grease fleece grade was estimated by correlat­
ing the two characteristics on the same animal and was
found to be -.35:!: 0.04.

Therefore, the individual with

heaviest fleece weight might be expected to have poor
fleece grade in this study.
8

- Study of Environmental Effects on Fleece Weight
The data used for this study were collected from 1273

shearirg records of 412 ewes belonging to Oxford, Hampshire,
Shropshire and Southdown breeds.

The effects of age, number

of lambs raised, breed, and year on grease fleece weight
were studied.

For this study ewes were classified accord­

ing to age, number of lambs raised, breed and year.
age groups were considered,

two through seven.

Six

Since the

proportion of six year old and older ewes in a flock is
small relative to the young aged ewes, there was some ques­
tion as to whether they warranted inclusion.

However, in

fhe older records used for this study a good proportion of
the older ewes had been retained in the flock and it was
decided that the inclusion of six and seven year old ewes
might present a clearer picture of the effect of age of ewe
qn the fleece weight and cpuld strengthen trends observed in
the younger ewes.

Three groups, according to the number of

lambs raised, were made as follows:- ewes raising single, twins,
or triplets.

It should be noted that generally ewes were shorn

-

23

-

k

a few days before lambing and, therefore, only the effects
of intra-uterine nourishing of foetus were studied.

Four

breed groups were included, Oxford, Hampshire, Shropshire
and Southdown.

For studying the effect of year, sixteen

year groups of ewes were made, 1934 through 1949.
Method of Analysis:- The least squares procedure of analysis
was used to study these environmental effects.

Consider the

sample set of data of fleece weight in Table VI classified
according to breed and number of lambs raised.
A regression model can be written expressing each
figure in the data in terms of the effects to be considered
as follows:
Xc
Xc

• u + b j + ck + eqC
(1)
t*V*
isthe observed fleece weight of the «c
animal,

u

isthe effect common to all groups,

bj

isthe effect common to all individuals,
of the j

breed group (j runs from 1 through 4 )
,
bl
b2
b3
b^

ck

-

Oxford
Hampshire
Shropshire
Southdown

is the effect common to all individuals of k

type of
"number of lambs raised".

K runs from 1 through 3 .
(ci - single
02 - twin
03 - triplet)

and e«c is the error in measurement of the grease fleece

- 24 Table VI

Sample set of data - Fleece Weight
No, of
lambs raised
K
Single
Kl

TOE®'
Oxford Hampshire Shropshire Southdown tfotai
jl ..... 3.8
14
... 13......
6.2

9.0

7.3

9.0
-----

8.6

8. 1

6&9.0
n=74

— 7.3
933.6
n«125

9.4
6.5

6.3
7.9

6.2

8.5

5.5
4.9

------—
------

— ------

-----------

— .
. . .

6.8

7.0
198'S7S
n=279

5.9
36”S775
n=60

7.2
7.3
5,5

6.3
6.5
7.2

11.0

Twins
K2

Triplets
k3

9.0
61U77
n=75

69T7S
n-93

10.0

6.0

7.5

9.1
6.5
8*3
6.3

6.0

6.5
Tsrs
nslO

Total

7.8

6.3
4.9
5.8
...

n*159
Yield«
1326.3

n*5

n*223
yield=
1667.6

6.0

352T7S
n»489

6.0

13TS73
n*50

---

7.3
77375
nslO

n*778
yield.
5586.2

n=738
yield*
5411.0

n=507
yields
3664.3

ns28
yield*
203.1

2TT7&0
ns3

n=113
yield*
698.3

nsl273
yield*
9278.4

-

25

-

weight for the •© th animal.
By reference to Fisher (1946) and Snedcor (1946) it
is found that the appropriate 'fc’s and 4 ’s (estimate of b’s
and cfs) can be obtained.

Hence u, bj and c^ are unknown

constants and e«c is expected to be zero.

The method of

least squares is to find the estimates of u, bj and c^; the
particular values which minimize the sum of squares of
deviations; i.e*
the sum of (y<

- u - bj - c^)2.

or as we write it

^

- u - bj - ck)2.

The values of u, bj and c^, which minimizes this sum of
squares are given by the so called normal equations which
may be obtained by differentiation of the sum of squares
with respect to u, the bj.’s and the cjj's respectively.
In most Cased, these equations can bd written down by
simple rules.

To write out these equations, the number of

observations in the jk

cell is denoted by n ^ and let

* NJ.
f f n j k * N **

Similarly
£ yjk*

» Jjk.
s

Y j..

f $ yjk*

* Y*k.
=

Then the equations for
u:N. .u + N^#bi+ ^2,b2 + ^3.^3 + N4.*)44'

N.2c2 +-1^.303*1 ,

-

26

-

bl: % . u + % . bl* N2.b2^ N3.b3 4 N4.b4 + nllcl +n 12c2 + n13c3 = *1 ..
b2 :

b3 :

V
ci s
c2 s
! N»^u

^ ® 2 3 ^ 2 ^ ®33b3 ^ ®^3bi^"^ N*^c^+ ^*2®2

Thus, £ simultaneous equations have been set up with
eight unknowns which can be solved by several methods.
Now consider the set of data of grease fleece weight
(in appendix 1 ) classified according to age, breed, number
of lambs raised and year.

The above regression model (1)

can be extended to include all the variables expressing each
in terms of the effects to be considered.
9

u + ai * bj 4-0* + d! +*e*

(2 )

Yac is the observed grease fleece weight of «c

animal,

u

is the effect common to all groups

a^

is the effect common to all individuals, of the i th
age group
(i runs from 1 to 6 )
ai m

2

years

a^ * 5 years

a2 •

3 years

a^ « 6 years

a^ ■

4 years

a$ « 7 years

bj is the effect common to all individuals of the j^ breed
group;

(j runs from 1 to 4 )

^*3.

- 27 bi - Oxford
bg - Hampshire
b 3 - Shropshire
b 4 - Southdown
die is

©ffect common to all individuals of the kth type

of "number of lambs raised";

(k runs from

1

to

3

)

•pi - single
d'g - twin
<?3

- triplet

di is the effect common to all individuals of the dth year
group.
runs from

(1

1

to 16)

dx is 1934
dg is 1935

dig is 1949
eoc is again the error in measurment of the grease fleece
weight for the<£#animal.
Then following the above teohaique and by reference to
Pisher (1946) and Snedcor)

(1946) it is found that the

appropriate 'si*a , ^ ' s and £ ’s and cl’s are obtained from
simultaneous solutions of the following thirty equations.
Equations for
^

*

N. • •.It 4-Ni* • •fii+Ng.. .agf N 3 .• .a^fN^. • *a^ 4.
N5 .. .a5+N6 .. •aJg^N.l..b1 + N.j^.bg+N.g. .b3 *
N.4 . .b4 + N . .l.ci 4-H. .2.Cg 4>N^.3. C3 +-N. •.Id 2.

28 -

N...12d1 2 4 N...I3d1 3 + N...14d1A +N...15d,K -f- ± ±
N.^lSd^sY
-L°
14
15^
^ 1 *•
a
nn »
^12 • .bg 4- 1^2 3 * «bg 4
ni 4 ..b4 + n 1 1 l.®l + n 112.°2 4 n 113*c3 + n l l l A
”lll2d 2 * n 1113 3 ^ n 1114d4 + j tt1115d 5 + n 1116d 6 + n 1117<i7
n 1118a8....... -»-n 11165 16 = Y l*«*

d l 6 *”
A convenient and compact manner of writing the above
set of normal equations for the whole data Is given in
appendix 1 in the form of -t-c, a, b, c, d, matrix and fY ’
column.
The figures under the matrix (■«.,a, b, c, d) represent
the coefficient of these constants respectively and the fig­
ures in the Y column represent the sum of the weights for
that particular equation.

Although the constants are not

written in each equation, since they are constants for each
column, their mental inclusion is necessary to complete the
equations.

In appendix 1, “*■***• z 1273, is the total number

of weights ,* fcibi=-H8 is the number of weights for the Southdown breed and so on.

Similarly, Ytc= 9278.4 lbs. is the

sum of all weights jY&i -« 3061.2 lbs. is the sum of the
weights for the two year age group and so, on.

- 29 All the constants (u,a,b,c,d) may be solved Tor
directly.

In this case a less laborious computational pro­

cedure than solving for all the constants directly is to
reduce the set or normal equations in such a manner that
the year effects along with
and

(for this example d^ to

) are eliminated and thus leaving thirteen equations

only.

This elimination process may appear at first to be

quite a task but with a little practice one can soon de­
velop some systematic technique to facilitate reduction.
It may be remembered that tre matrix is only a compact
manner of writing the normal equations and in the reduction
process the sum of weights, i.e.
reduced.

fY ’ column must also be

Then the coefficients of a 6 elements were sub­

tracted from a^, a2 , ag, £4 , a 5 j b 4 from bj, bg and bg*,
and c 3 from cj and c2 .

Thus the thirteen equations were

reduced to ten equations.

These ten unknowns with ten

simultaneous equations were solved by iterative method
(Hovelling, 1943).

As these values are measured as devia­

tions about the mean, the stun of each class is zero,
a2 +

a 3 + a4 + a 5 + a 6

dl+ d 2 + ... d 16 =
b 4 and eg.

0 .)

0

; b X 4 bg + .. b4 -

0

; ci + c2

4

(a^
c3 ■

0;

thereby enabling an estimate of ag,

Now it is-a simple matter to substitute the

estimates of a i ; bj; and

in the equations(n.4-

___

(lA. + dig)which were eliminated first and written in terms
of ai, bj and c^.

Thus the sum of all the sixteen equations

(tt+di) • • • ("<l-4'd 16 ) were obtained.

But using the relation

30
(dl+cL2 »«»» d-j^g s

0

), the sum of all the sixteen equations

was equal to 16H, and thereby the estimate of *H. was obtained.
Then substituting the estimate o f x in (il+ d^ )...(**«- d^g )
equations, the estimates of d ^ . ^ . d j g were obtained.
It Is clear from the way the model has been set up
that there are not unique solutions for all the constants.
If all the a ^ ’s are increased by a constant amount, say K
and reduce

by K, then the same prediction of the class mean

will hold true.

It may be noted that thirty unknowns In

the thirty linear equations are not independent.

The first

equation is the same as the sum of a^ equations, and as the
sum of the di equations.

There is obviously no estimate of

any a^, bj, or c^ by itself.

The estimates of any quantities

that can be estimated are given by the solutions of the least
squares equations.
Then the analysis of variance was carried out by this
method of fitting constants as suggested by Yates (1934),
and Hazel (1946).

It may be noted that In setting up the

above regression model it was assumed that the effects
combine additively or without Interaction, i.e. differences
in fleece weight due to age and number of lambs raised com­
bine additively.
Results - The results of the .analysis are given in Table Vll.
The same trend for age and breed effects was found as was

- 31
given in Table I, II and III.

As expected, the f i e ece

weight was found to decline with increase in the number
of lambs raised.
It is questionable if the time and labor involved
in estimating the environmental effects by the method
of fitting constants is worthwhile in face of the esti­
mates found in Table I#

But the value of this method Is

unquestionable for analysis of variance of data having
multiple classification table with unequal subclass num­
bers.
The percentage of variation attributed to each of
the environmental factors under study has been given in
Table VIII.

Yearly differences were the most Important

environmental source of variation accounting for

10.2

per-,

cent of the total variation. WdrkS by Terrill, Sidwell and,
Hazel (1948, a and 1948, b) and Cockerhfipn (1949) indicate
that years do appreciably affect the grease fleece weight.
Included in yearly effects are any differences in man&gement, nutrition, and others as well as climate.
Breed differences were another important factor,
accounting for

8.8

percent of total variation.

Age at shearing accounted for only 3.2 percent of total
variation, which is in line with the findings of Terril^.,
Sidwell and Hazel (1948) who found It accounted for two

percent of total variation*
Number of lambs raised has very little effect on fleece
weight,accounting for 0*2 percent of total variation* Sum­
ming up all the effects,it may be stated that the effects of
these four factors account for

2 2 *I
4. percent

of the total var­

iation for grease fleece weight. Many other factors of less
tangible or measurable nature,such as sex,age of dam, type
of birth,age at weaning,parasitism,(external or internal) etc*
may also be expected to affect this trait*
Although the effects may be real,they must account for a
substantial portion of the total variation in order that ad­
justment for them will effectively increase genetic gains
from selection. From previous concepts, the expected gain for
I
one cycle of selection is directly proportional to
where

,a* is the fraction of the total variance adjusted for*

The following table gives a rough idea of the increase ex­
pected from adjusting for different percentages of the total
variation*

A
Percent of total variation
adjusted for )a)

B
Percent increase expected
in genetic gain
1.0

- 33 From the above table It is readily seen that the rate
of increase in genetic gain increases with the percentage
of variation adjusted for*

It does not seem that an adjust­

ment of less than six percent of the total variation would
be a very effective means of increasing genetic advance*
Under a restriction of six percent, fleece weights
were only affected enough by breed of ewes to justify ad­
justment*

Yearly differences had also significant effects

which were probably worthy of adjustment.

- 34 Table VII
Statistics for Grease fleece Weight of Ewes
Statistics
General mean { ^ )

Grease Fleece Weight (lb)
7.28

Deviation from general mean for age
year (ai)
3 year (a2 >
4 year (a3 j
5 year (a4 )
6 year (a5 )
7 year (afi)
2

0.36
0.46
0.20
0.04
0.42
0.64

Deviation from general mean for breed
Oxford (b^)
Hampshire (bo)
Shropshire (h^)
Southdown (134)

0.94
0.13
-0.02
-1.05

Deviation from general mean for no.
of Iamb3 raised.
Single (Gt )
Twin (Cg)
Triplet (C3 )

0.15
0.02
-0.17

Deviation from general mean for
year of records made
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949

dl
d
d4
5
d6
8
d9
)
d lcN
d 11
d
d 12
13)
d 14 )

)

d
d 1^
16)

-0.151
-0.104
-0.727
-0.160
-0,583
-0.636
-0.253
-0.165
0.420
0.230
1.473
1.304
0.345
-0.071
- 0.211
-0.711

- 35 -

Table VIII
Summary of Analysis of Variance Showing the Percentage of
Variation
Source of Variation
Total
Total reduction

p.p.

s.S.

1272

2957.6

29

659.6

Direct Effects;-

Age
Percent of

5
total

Breed
Percent of

Percent of

total
2

6.5
0.2

15
total

259.4
8.8

total

Year
Percent of

3.2
3

No. of lambs raised

93.9

300.2
10.2

t--

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W .- -

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V'■'■

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: ■:-.

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Bag* 36 lacking In zmnbering only.

’1

*r>~ .j
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UNIVERSITY mOBOFZIMS

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,

- 37 ESTIMATE OF REPEATABILITY
(a)

- Methods of Estimating Repeatability; Since

repeatability (R) is defined as the regression of future
performance on phenotype as measured In one expression of
the trait, it may logically be estimated by the regression
of the second record on the first as was demonstrated by
Stewart (1945).

Let (1) and (2) denote the first and second

records respectively by the same Individual; then the re­
gression •coefficient is

Cov. 2.2 estimates <J^y +^j‘2c and

estimates (fp such that

and b gl (z) R.
The correlation coefficient of the first and second
record isj
Provided there has been no selection the expectation of
S§ and sf
are Identical, and thus

which is equivalent to the regression procedure*
Another means of estimating R which permits the use
of all the records by each Individual Is the method of
Intra-class correlation (Snedcor 1946) demonstrated by

- 38 Lush and Mollin (194?).

To illustrate this method consider

the following analysis of variance (Table IX) where the mean
squares are broken up into their expected component of
variances (Winsor and Clarke, 1940).
Table IX
Analysis of Variance Showing Mean Square Expectation
Source of variation
Between individuals
Between records by
the same individual

Mean Square
ml
--------- 2 2 -

Mean sq. expectation
<re

+

Kcr?

____

ft is the number of records per individual providing the
number is equal for all Individuals otherwise K is something
less than the mean number of records per individual and
varies with the type of analysis (Snedcor, 1946).

is

the variance from record to record by the same Individual
and estimates

| . (fj[ is the variance attributable to con­

stant differences between individuals and thus estimates
( J § t<T© *

^n '
tra“c;i-ass correlation coefficient, r^, is

found such that
<Ti*
and substituting
I-J.

r±

( = ) < rf * g f „

<rp

(=) R

(b) - Calculation of Repeatability{-Repeatability was estimat
ed for grease fleece weight, by the method of intra class

correlation from 460 records of 155 Shropshire ewes.
Jones, etal,

Since

(1944) showed that rearing a lamb may lower

fleece weight, ewes were divided into groups according to
year of first record and fecundity so that all ewes in
each group were of the same age and had or had not reared
lambs in the same year.

Analysis of variance was then

carried out in each of the eight groups resulting from this
classification.

This procedure resulted in a separation of

the variance due to age, year and fecundity from the variance
due to permanent differences among ewes and to random devi­
ations fid m them.

An example is provided in Table X by the

analysis of the second group in which e a c h h . a d s a o r < 6 c6 rd in
1946, 1947, 1948 and 1949,

Each of the ewes in

this group

reared a lamb during the year which the fleece was grown.
Table X
Analysis of Variance

Source of variation

D.F.

S.S.

M.S.

Between years

3

.98

Between ewes

8

15.59

1.95

Error

24

8.58

.35

Total

35

25.05

Now (.M.S. Ewes) r ^ i + %■?
(M.S. Error) •g'f
The S.S. among ewes and the S.S. error, were then pooled
to give the following combined analysis of variance in Table

Table XI
Combined Analysis of Variance

D. F.

S.S.

Ewes

147

392.30

2.67

Error

313

244.28

.78

Source of variation

M.S.

M.S. Expectation
tf2 + Kg?
<T2

Then cr2 and g-? were estimated to get an estimate of R.
Then Ewes (M.S. - 2.67) a (S’2 -f-Ktff ®
= .61;
and
and

cf

<r2 = .78

r ' T 7B 6i ' .61* -45S
r (a) R (a) .438

An approximation of the sampling variance of R, V (R),
when R is found in the above manner, is given,by the follow­
ing formula as used by Cockerham (1949):
V
When a and Z are the respective degrees of freedom for
ewes and error.
The estimate of repeatability and its approximate
standard error is .44 + .02.
c-Comparison with Published Estimates
In comparing these findings with some of thOse in pub­
lished material it was necessary to transform correlations
between first record and total subsequent records to an

41
estimate of repeatability, using the formula
^ 7

Where

r

xy

•

'’ r

Z correlation between first record and the
total or average subsequent records.

R ; repeatability
n a the number of subsequent records.
The value obtained is subject to considerable error,
especially if the correlations between first and subsequent
records is lower than other correlations.
Several estimates of repeatability are available for
grease fleece weight.

Lush and Jones (1923) obtained an

average correlation of 0.61 between the weights of fleece
of Rambouillet ewes in Texas.

These authors did not correct

for fecundity; but this would have caused little error, since
most of the ewes lambed each year after their first shearing.
Joseph (1928) obtained correlations of 0.29 to 0.84 between
fleece at various ages.

Joseph’s figures could not be com­

pared directly with the ones in this study.

Rasmussen (1942)

obtained estimates of 0.56 for RambouilJb t and Corriedale
ewes, and 0.43 for Romney crossbred ewes.

Terrill(1939) ob­

tained estimates which when transformed gave a repeatability
of 0.45.

Cockerham (1949) obtained a combined estimate of 0.60

for several breeds at the North Carolina Experiment Station.
In considering these estimates of repeatability one Is
impressed by the fact that the estimate obtained from this

- 42
data (.44 + .02) Is not greatly different from these
published estimates.

43
ESTIMATES OF HERITABILITY
a - Methods of Estimating Heritability
Estimates of heritability most commonly availalSe for
animals are those based on intra-sire regression of off­
spring on dam, intra-sire correlations between dam and off­
spring; and the sire component of variances among progeny
of different sires ^parental half-sib correlations^

Lush

(1940) discussed the methods of intra-sire regression and
correlation*
ing manner.

The regression is interpreted in the follow­
let U and v represent records of offspring and

dam respectively.

Then the regression coefficient, buv is

found as follows:

When Cov and S® are estimated coveriance and variance
respectively.
CovU v estimates l k & g

and

estimates C p

80

that

and
H (=)

2 buv

Provided that there has been no selection among parents
the method of intra-sire correlation is for all practical
purposes identical with the regression method*

The correla-

- 44 tion coefficient,
is found such, that
T»
uv

Coy

The expectations of the variance among dams is

e (sf ) = cr§ -tCoL +(T? -f(Jc -fdi : (r|
where E (S?) denotes expectation.

The expectation of the

variance among daughters by the same sire is

e (s§ ) * s/4 <r§+

+ <r§

m g ~ 1/4 <r§

:/?" §.

i/sifi

< = i

cf

____

(<rf - 1/4 <rg.

Since the additive genetic portion of the total variance
is generally small for traits of quantitative inheritance the
correlation procedure is for all practical purposes identical
with the regression procedure.

Whether or not selection has

been practiced on the dams,the regress ion method gives an
unbiased estimate of heritability provided there are no en­
vironmental correlations between offspring and dam.

This con­

dition is generally achieved when the regression is conducted
on a within sire basis.

However, if individual sires occur

with different breeding groups, that is with different breeds
or at different locations, it is best to restrict the analysis
accordingly to a W i d environmental correlation.
For the case where V, the average .of n records for each
dam, is used in the computation of the intra-sire regression
of offspring on dam, H is dedu<c**d-i from this regression in

45 the following manners
H (*) gbufr ^ 1 « Hn-l)R
(Lush and. Straus, 1942)*

Averaging records for the off­

spring has no effect on the deviation of H.
Where data with progenies of different sires within
a breeding group are available the sire component of
variance is a handy tool to get intra-class correlation
for estimating heritability as demonstrated b y Baker,
Hazel and Reinmuller (1943).
This method of paternal half-sib resemblance^ is
usually not as accurate as the previens method of pafentoffspring relationship.

However, when the data are

analysed by the analysis of variance, the intra-class
correlation as outlined by Snedcor (1946) gives the re­
quired statistic which, on multiplying by four gives an
estimate of heritability.

Here the Statistic is imiiti-

plied by four because the relationship between half-sibs
is twenty five per cent.

Even a small error when multi­

plied by four apneai*s to be large, and hence the method
is often inaccurate.
Nelson (1941) demonstrated the mid-parent offspring
correlation or regression method to estimate heritability.
This method is the same as the parent-off spring,relatdonship
method.

•

46

except that in the place of one parent the average of both
the parants is used*

There is not much literature on this

method j||nce nest of the studies of heritability were con­
cerned with characters which could be directly measured in
one parent only.

However, this mid-parent offspring method

may be used if the trait can be measured in both parents;
for example, fleece-weight. To get the estimate of herit­
ability by this method, the regression or norrsla:
tion co­
efficient is multiplied by 1.41 for the following reasonjThe correlation between the offspring and one of its
parents is 0.5 for characters which are completely heredi­
tary.

According to the thObry of path coefficients squaring

this correlation gives 0.25 as the degree of determination
of the offspring by one of its parents,

fhus^ the inheritance

of the Individual is twenty five percent, determined by each
parent; and the degree of determination of the offspring by
both parents is fifty percent.

The square root of .5 gives

.707 As the correlation between the parental average (midparent) and the offspring
«

hereditary.

for

traits which are completely

Consequently, the correlation (or the regression)

between the offspring and the mid-pshiot would be multiplied
bv J.O

or 1.41 in olaee of

or 2 as ushd for the cor­

relation between the offspring and only one of its parents.

aatli.liife,*
Of the four methods, the following three methods Were
ehoseh b©';heused for this study:

1 - Intra-sir© regression of daughters on dams*
2 - Intra-sire daughter-dam correlations.
3 - Faterh&l half-sib correlations.
As previously pointed out the data needed adjustment
for years and breeds In order to estimate heritability.
Tlie difference in the records made In different years
was tested for significance in each year separately.

It

was found that the records made in 1944 and 1945 were
significantly different from the rest of the years.

Then

there were three alternatives.} one was to develop a con­
version factor to correct the data to one standard year;
or to adjust the estimate of heritability on the basis of
percentage of variation accounted for by years according
to formula on page 13 ; or to eliminate from the data the
records made in the significantly different years.

There

were very few records made in these three years (13 in all)
which would have been used in the analysis.

Therefore, the

data after eliminating these records were used for analysis.
With regard to the adjustment for breed, the estimate of
heritability was made separately for each of the four breeds
under study and then tlieir weighted average was taken.

It

may be worthwhile to mention that only single records (two
years old records) were used for both dams/ and daughters
so that the age and fecundity status was the same for all.
Table XII gives the number of sire groups and the number of

daughter-dam pairs in each breed used in the calculation of
heritability*
Table XII
Distribution of Records by Breeds

Breed
Shropshire

No* of Daughter-Darn Pairs

No. of Sires

.. 65

12

Hampshire

60

'9

Oxford

26

5

Southdown
Total

For this analysis,

618

jt

169

30

\

the fleece weight of dams was treated

as one variable, X, and that of their daughters as the other
variable Y.

The fleece weight of the dam which had more than

one daughter was repeated for each offspring for the analysis.
The weights were grouped on an intra-sire basis*

Then,

the

usual analysis of covariance was run between the two vari­
ables as outlined by Snedcor (1946).

The results of the

analysis of covariance of the four breeds are given separate-

-

49

-

Table XIII
Analysis of Covariance of Fleece-Weight of Dams
and Their Daughter for Hampshires
Source of Variation Degrees of Sum of Squares and Products
Freedom
Sx2(Dam) Sxy Sy^(Offspring)
Total

59

Between sires
Within sire (error)

114.09

1.17

137.63

3

39.31 -13.73

33.95

51

74.23 14.90

103.63

Table XIV
Analysis of Covariance of Fleece Weight of Dams
and Their Offspring for Shropshires
Source of Variation Degrees of Sum of Sauares and Products
Freedom
Sxz(Dara) Sxy Sy2(Offspring)
Total

64

132.65

55.69

263.20

Between sires

11

33.69

42.09

120.21

Within sires

53

93.96

13.60

142.99

Table XV
Analysis of Covariance of Fleece Weight of Dams
and Their Offspring for Oxford
Source of Variation Degrees of Sum of Sauares and Products
Freedom
9x2(Dam) Sxy Sy2(Offspring)
Total
Between sires
Within sire (error)

25

33.53 -5.53

70.44

4

J27.53 -15.25

33.23

56.00

32.16

21

9.67

-

50

Table XVI
Analysis of Covariance of Fleeoe Weight of Dams
and Their Offspring for Southdown
Source of Variation

Degrees of
Freedom

Between Sires
Within Sire (error)

17

7.96

4.74

17.36

3
14

v\
to•

Total

Sum of Sauares and Products
Sx2(Dam) Sxy Sy2(Offspring)

.29

3.66

7.11

4.45

13.70

The following formulas were used to estimate regressions,
correlations and their standard errors#
Dam-Daughter correlation coefficient * r ■

■
JSx2. Sy*

Standard Error of the correlation coefficient - Sr - 3*"^
fn-T
Regression coefficient of Daughter on Dam - b 3x*

sy2- t t o

X'

Standard Error of the regression coefficient - Sb x ■
Half-sib correlation coefficient a r^ « .

g - =
'g^‘
2

...

where S2 is the mean square of the error terra
s2m ... M.S. between sires - M.S. of Error term
Average number in each sire group
Standard error of the Half-sib correlation coefficient
1

As already pointed out heritability was estimated by
doubling the regression coefficient and daughter-darn
correlation coefficient and multiplying by four the half-sib

- g

)2

51

-

correlation coefficient*

-

The respective standard error of

heritability was calculated by doubling the standard error
of regression and daughter-dam correlation coefficients and
multiplying by four the standard error of half-sib correla­
tion coefficient.
Table XVXX summarizes the results and gives the estimate
of heritability by breeds and methods separately*
Table XVII
Estimates of Heritability and Standard Errors
for the Fleece Weight
Intra-sire
, P&fggglofl
Breed Herit-Standard

Intra-sire
Paternal halfCorrelation method sib method
Herit-standard
Herit- Standard

.300

•223

.243

1.434

.436

Hampshire

.274
.402

.304

.256

1.252

.613

.604
.220

.512

Southdown

.340
.903

.996

.345

.302

.456

2.060.

.596

Shropshire

Oxford

.393
.330

The large sampling error in the estimate of heritability
is evident in the Paternal half-sib method and in Southdown
breed*

In view of this, the estimate of heritability calcu­

lated for each breed and by each of the three methods is not
as accurate an estimate as an average of them all.

Therefore,

the values were averaged to get the best estimate for this set
of data.

These averages were calculated by weighting each of

the individual estimates in Table XVII (above) by the re­
ciprocal of its squared standard error, as outlined by Hazel

- 52 (1945).

Although this method of

weighting has some error'it

gives greater weight to those estimates which are based on
the largest number of data.
The weighted average of heritability was obtained by the
use of the formula as follows:
Weighted average heritability. =—

---- »2----------— OH-----^

where h-^

hn z heritability estimates, and

Shi....Shn= Standard error of heritability.
The weighted average of the standard error of herit­
ability was calculated by the following formula:
Weighted Average error ____________________________
of heritability sj -...r........
•N (‘3 ^ )

,.....
" * * * (^-)

where Sh^. .. .Sft^ are the individual standard errors of heritability.
In order to facilitate the calculations, the squared
standard errors and their reciprocals for the individual
estimates of heritability found in Table XVII were first
calculated and entered in Table X V I H . Then substituting
the corresponding values from Table XVII and XVIII the
weighted average of four breeds and the weighted average
of three methods and four breeds was obtained.

In view of

a large sampling error in the estimate of heritability by
the paternal half-sib method, it was decided to take the
weighted average of four breeds and two methods only

*■ 53 (Intra-sire regression and Daughter-Darn Correlation) as
the best estimate of heritability of fleece weight in
this flock and It was found to be 0.38 +■ .11.

It should

be pointed out that the intra-sire regression of daughter
on dam and intra-sire daughter-darn correlation are not
actually two different methods of estimating heritability.
Therefore, it does not seem fundamentally sound to weight
the estimates derived from the two for one estimate since
both are based on the same data.
Table XVIII
Squared Standard Errors and Their Reciprocals of
the Heritability of Fleece Weight
{Half-sib jIntra-sire :Dam-daughter; Reciprocal
•method
{regression {correlation : sum of three
:__________ {method_____ {method______ t methods_____
Breed

t

•

•

fS2 h 1 Jl/Shf
•

0
0

•

:
:
fS 2 h g : l/s2hgS

I

*
i
1

:
S 2 h 3 : l/S 2 h 3
8
»

S

<t...... . ......
S. 09 {10.96

5
s.14

8
; 6 • 93

i

20.71

Oxford

•35 {2.82

Shropshire

.19 {5.26

.09 {11.11

•
S . 06

{16.26

32.63

Hampshire

.26 S3.65

.09

s.05 {17.95

32.67

•

.99 sl.Gl
:
s
Reciprocal
:
Southdown

sum of four
breeds

s1 2 . 94
1

•
e
*

{ 10.87

1.58s 0.63

•
• • 16

*

•
« 6 • 31
:

*
•

t

s

•

♦

*
m

833.57

8

{47.45

3

:

s

8

••
•

«
•

7.95

93.96

54 Table XIX
Weighted Average Heritability Estimate
of Four Breeds (Fleece Weight) ■

Method

Heritability

Standard Error

Intr^.-sire regression

.36

.17

Intra-sire dam-daughter
correlation

.39

.14

1.25

.28

Paternal Half-sib
correlation

Table XX
Weighted Average Heritability Estimate
of Three Methods and Pour Breeds

Trait

Heritability

Standard Error

0.50

Grease-fleece Weight

0.10

Table XXI
Weighted Average Heritability Estimate
of Two Methods (Intra-Sire
Regression and Intra-Sire Correlation) and Four Breeds

Trait
Grease-fleece Weight

Heritability
0.38

Standard Error
0.11

55 Calculation of Heritability of Grease-fleece Grade,
or the four methods, the following two methods were
chosen to be used for the set of data available for this
estimated—
Intra-sire regression of Daughter on Dam and IntraSire Baiighter-Dam correlation method#
Paternal Half-sib correlation method was not used due
to the large sampling errors associated with it in such
small number of data,(particularly a small error when mul­
tiplied by 4 becomes serious).

The data suitable for this

estimate were available in three breedsonly.

The herit­

ability was estimated seperately for each of the three
breeds and then their weighted average was taken.

Only

single records (two year old records) were used for both
dams and daughters.
Table XXII gives the distribution of records by breeds
which shows the number of sire groups and the number of
daughter-dam pfcirs.used In the calculation.

- 56 Table XXXI
Distribution of Records by Breeds

Breed

No. of Pairs of
Dam-Daughter

No. of Sires

Shropshire

75

11

Hampshire

66

9

Oxford

26

4

167

24

Total

-

For the purpose of analysis, the fleece grade of dams
was treated as one variable, X, and that of their daughter
as the other variable Y.

The fleece grade of the dam which

had more than one daughter was repeated for each daughter.
The weights were grouped on an intra-sire basis.
usual analysis of covariance was imjn

Then the

between the two

variables and the results of the three breeds are given
seperately in Tables XXIII, XXIV and XXV.
Table XXIII
Analysis of Covariance of Fleece Grade of Dams
and Their Daughters flor Shropshires
'
Source of Variation
Total

D.F.
74

Sum of1 Squares arid Products
■
Sx2 (Dam
Sxy
Sy2 (Offspring)
27.1

Between Sires

10

8.6

Within sire (error)

64

18.5

2.0

16.7

- .2

3.4

2.2

13.3

Table XXIV
Analysis of Covariance of Fleece Grade of Dams
and their Daughters for Hampshlres

Source of Variation

D.F.

Sum of Squares and Products
Sxy (Dam)
S^j
Sy2(Offspring)

Total

65

15.3

-2.2

8

6.5

-2.9
.7

H
H

CO

57

.
00

Within Sire (error)

00 H
• .

Between Sires

15.9

Table XXV
Analysis of Covariance of Fleece Grade of Pama
and Their Daughters For Oxfords

Source of Variation
Total
Between sires
v;ithin sire (error)

D.F.

Sum of1 Squares and Produces
Sx^lDam)
Sxy
Sy^(6ffspring)

25

2.7

.3

4.6

3

.2

.2

2.0

22

2.5

.1

2.6

According to the formulas as given in the section of
wCalculation of Heritability of Fleece Weight" the estimates
of heritability and standard error were calculated.
Table XXVI summarises the results and gives the estimate
of heritability by breeds and methods seperately.

- 58
Table XXVI
Estimates of Heritability and Standard
Error for the Fleece Grade

Shropshire

Inter-sire regression
method

Intra-sire
Daughter-dam
Correlation Method

Herit­
ability

Herit­ Standard
ability Error

•
CO

Breed

Standard
Error
.18

.28

.22

Hampshire

.Id

.28

'.14

.24

Oxford

.08

.41

00
o
•

.40

Following the method of weighted average as outlined
above in the section of Calculation of heritability of fleece
weight; the weighted average of three breeds and the weighted
average of three breeds and two methods was obtained as the
best estimate of heritability of grease fleece grade in the
flock and it was found to be .20

*10.

59 Table XXVII
Weighted average of three breeds (Fleece grade heritability)

Method

Heritability

Intra-sire regression
Intra-sire Daughter-Dam
correlation

Standard error

.20

.14

.20

•15

Table XXVIII
Weighted Average of Three Breede and Two Methods
•(Fleece-grade Heritability)

Heritability

Trait
Grease fleece grade

.20

Standard error
.10

Comparison with Published Results#
Comparison of observed values of heritability of
f’leece weight with those of other workers Indicates rather
good agreement, considering that breeds and environment'
differ so widely*
in Table XXIX*

The estimates are set

out for comparison

Heritability as estimated in these studies

Is not a fixed parameter, but rather a description of the
relative importance of heredity and environment in determin-

- 60 ing differences among individuals in a particular en­
vironment belonging to a particular breed and at a
particular time.

The relative importance of sources of

variation may differ depending upon the control of en­
vironmental variation and the gene frequency character­
istic of the population studied.
The discrepancy in heritability of fleece weight
in the Romney as compared with the Rambouillet and the
estimate found in this study seem to be a fairly clear
example of a true breed difference.

Environmental differ­

ences and previous selection for fleece weight are some
of the probable reasons for breed differences.

This dis­

crepancy draws attention to the possibility of error in
applying to one breed values of heritability which were
obtained in another.

There may even be station to station

differences in this respect.
Table XXIX
Some Estimates of Heritablllty for the Qrease-fleece
weight from the literature.
(After Morley, 1950)
Estimate
.40
.28
.24
.40
.14
.39
,10-.15

Reference

Breed

Rasmussen (1943)
Rambouillet
Hazel & Terril (1943)
n
Ra s e a s o n (1943)
Oorriedale
Cockerhan (1949)
Mixed breeds
Rasmussen (1943)
Romney crose
Morley (1950)
Aust. Merino
McMohen (1943)
N.2U Romneys

Remarks
70prs i parentedff
1622 prst parent-off.
173 prst parent-off.
233 prs: parent-off,
213 prst parent-off.
529 prss farent-off^
Ext. data, but year,/
diff. confounded Y

61 ESTIMATE OF GENETIC CORRELATION

a ~ Definition*

The linear relationships between a set

of variables may be described by the variance and covari­
ances; similarly the relationships between the genic
(additively genetic) causes of variation and covariation
in different characters may be described by genetic
variances and covariances*

A genetic correlation is

thus a description of the relationship between the addi­
tive deviations caused by genes in the two characters*
In rather more precise terms a genetic correlation is
the ratio

of the genetic covariance between two charact­

ers to the product of their genetic standard deviations;
i.e.

.
rGi GJ -

Gov. Gi G.1
-flm X T G '3

when Gl and Gj are the genic values of Individuals for
traits i and j.

The most important cause of genetic

correlations would be that some of the genes which af­
fect one trait also affect the other.
meant by pleiotropy.

This is what is

Other usually minor causes Include

linkage andthat previous selection may have been practised
with varying emphasis in different partially Isolated por­
tions of the population.
b- Calculation of genetic correlation:

Hazel (1943) de­

scribed the basis of methods of calculating genetic cor­

62 relation and. gave the following formula*
rGi Gj

s

(Cov l g ^ )

(Cov jgli)

(Cov lgii) (Cov jgj^)
When the subscripts (1) and (2) represent the parental
and filial generation respectively and i, j, are two
characters*

Lush (1948) stated thatsampling errors of r

when computed thus are large and likely to be complex*
He suggested taking the arithmetic mean of the numerator
rather than the geometric mean as Indicated here, especially when sampling errors are a major concern or when
the volume of data is small*

That would avoid such dif­

ficulties as arise when one of the observed covariances
In the numerator is negative and the other is positive*
Therefore the following formula was used with the same
meaning of ti e subscripts s

r

Cov 1 2 3 i
Gi G j

Jr
2

Cov jgii

(Cov Igl'x) (Cov j2 Jl)
-Y
The statistics to be used for the estimate of
genetic correlation are given in Table XXX, XXXI, XXXII
and XXXIII*

- 63 Table XXX
Statistics for the Estimation of Covariance of Fleece Grade

Breed

Number

Sum of D a m fs
Grade

Sum of bffsprlng’s Grade

Sum of
CrossProduct

Shropshire

65

237.0

238.0

894.0

Hampshire

60

225.0

205.0

742.0

Oxford

24

73.0

77.0

241.0

149

535.0

520.0

1877.0

Total

Intrabreed Covariance

s

*04

Table XXXI
Statistics for the Estimation of Covariance of Fleece Weight

Sum of barn’s

Sum
spring’s

Sfum or
Cross
Product

Number

Grade

Hampshire

60

447.2

452.7

3410.6

Shropshire

65

514.2

480.1

3896*6

Oxford

24

214.5

216.5

1944*7

149

1175.9

1149.3

9253.9

Breed

Total

Intrabreed Covariance

g

1.01

Grade

64
Table XXXII
Statistics for the Estimation of Covariance of Fleece
Weight of :Dam and Fleece Grade of Offspring.

Sum of

Sum of

Sum of

Number

Dam* s Fleece
Weight

Offspring1s
Fleece Grade

Cross
Product

Hampshire

60

451,6

207.0

1558.6

Shropshire

65

538.8

233.0

1930.6

Oxford

24

216.5

74.0

663.1

149

1206.9

514.0

4152.3

Breed

Total

Intrabreed Covariance

s

-*04

Table XXXIII
Statistics forthe Estimation of Covariance of Fleece Grade
of Dam and Fleece Weight <
of Offspring.

Breed

Number

Sum of Dam's
Fleece Grade

Sum of Off­
spring Fleece
Weight

Sum. of
CrossProducts

Hampshire

60

220.0

458.7

1674.1

Shropshire

65

241.0

509.4

1878.4

Oxford

24

76.0

219.0

694.7

149

537.0

1187.1

4247.2

Total

Intrabreed Covariance

s

-*11

- 65 substituting these values of covariances in the formula*

Gi Gj

(Oov igix ) (00 V

)

-•075

-.37

(1.01) (.04)
Therefore the genetic correlation between grease
fleece weight and grease fleece grade is -.37.

-

66

-

DISCUSSIOH
The effects of environmental factors and pheno­
typic parameters have already been discussed in the ap­
propriate section.

A discussion of estimates of repeat­

ability and heritability may become somewhat abstract
unless a clear concept of their meaning and application
is kept in mind.

Although defined and developed some­

what differently to withstand a rigorous proof, repeat­
ability is simply the average rate of change in future
performance per unit change in present performance; and
heritability is the average rate of change in performance
of offspring per unit change in performance of parents.
When estimates of repeatability and heritability are not
accompanied by standard errors which warrant a great deal
of confidence in them, as is true for the estimate of
heritability, a comparison of the estimates with those of
other workers may aid considerably in conditioning one's
evidence.
The estimate of 0.44 for repeatability of grehaefleece weight is well within the limits of the findings
of other workers given on page 41 • This estimate for
these data indicates that the methods of shearing, weighing,
recording etc. of fleece weight (temporary environmental
factors) are not accurate and improved techniques to con­
trol these factors may raise the repeatability of this

-

67

-

character• But this finding is unimportant for when
repeatability is high, repeated observations are un­
likely to be important aids to selection.

In general

the use of repeated observations will delay decisions.
Variation due to years and age were removed from these
data by analysis of variance.

The breeder makes his

selection of young stock on a within-year basis, before
the young ewes are mated.

Therefore he does not have to

consider years, age or fecundity in his selections, except
in so far as he may base part of his selection on the dams
of these ewes.

Further this estimate gives a fair indica­

tion of improvement that might be expected from selection
under practical conditions.
The heritability estimate of .3# compares favorably
with the estimates found by different workers given in
Table XXVI.

Although it is within the limits of the above

estimates, it may be high.
In any case, heritability of fleece weight seems
to be high enough for considerable improvement to be made
by selection and without doubt would warrant a position
in a selection programme for sheep, particularly since
fleece weight is also of direct economic importance.
The value obtained for genetic correlation is un­
satisfactory because of the limited number of degrees of
freedom available; hence general conclusions are probably

68 not justifiable.

Nevertheless it does give some indica­

tions of the pattern of relationship among the characters
considered.
Accepting the computed estimates of genetic cor—
relation •( f( -.37) at

dBr face value, it seems that

selection for increased fleece weight will be accompanied
by decrease in fineness.

lush (1948, chap. 26) suggested

that past selection for two or more traits is likely to
have caused genetic correlations to become prevailingly
negative rather than positive, ■where the direction of
past selection has been positive.

The hypothesis requires

that pleotropic effects of genes be reasonably common,
and that selection has increased the frequencies of genes
favorable to all traits to near untiy.

Most of the genetic

variance will then come from genes with frequencies near
0.5.

For gene frequencies to remain near 0.6 in spite

of continued selection requires that genes affect one
character favorably, the other unfavorably.

The situa­

tion then would appear as a paradox wherein genetic vari­
ance would still exist for each character, but possible
improvement in both characters simultaneously would be
limited or even zero*
Dobzhansky (1927) found that ten out of twelve
mutants studied in Drosophila were associated with changes
in the shape of spermatheca.

The mutants studied were

not previously suspected of having any effects upon internal

- 69 organa and certainly not on spermatheca shape.

Results

such as these could have been caused by closely linked
genes but critical experiments to test whether any gene
has manifold effects were not possible.
Dobshansky (1941) discussed the evidence for mani­
fold effects of genes and expressed the opinions
"There is • • • no evidence that every gene
has a circumscribed province of action, in­
cluding only a single character of physio­
logical function. This problem belongs to
the field of developmental genetics, and
concerns us here only in connection with
the so called neutral characters. Differ­
ences between races, species, and genera
frequently involve characters whose value
in the struggle for existence is uncertain.
Yet the prevalence of manifold effects of
genes makes caution necessary in reaching
the conclusion that a given property of an
organism Is devoid of any adaptive significance."
It would be indeed surprising If some of the
characters studied were not determined in part by the
same genes.

For example, the weight of fleece is partly

determined by diameter of fibres composing the fleece,
so that genes affecting fibre diameter would probably also
affect fleece weight.
Mather (1943) suggested an alternative reason for
unfavorable correlated responses.

Polygenic combinations,

In which a balance was achieved by linkage of plus and
minus genes along the chromosome, were postulated,

Se­

lection Imposed on a population in equilibrium will tend
to destroy the balance of polygenes, so that ’unfavorable

70 combinations for apparently unrelated characters may
limit progress until new favorable combinations are
formed by selection of suitable cross over types#
But there appears to be an important distinction
between the results expected from selection in Droso­
phila and in domestic animals#

Because of the small

number of chromosomes and because there is no crossing
over in the male, Drosophila has relatively few segregat­
ing units#

Extremely intense selection can be practiced

and there is a distinct possibility that the effect of
linkage may be important#

Selection in sheep, wl-lch have

several times the number of segregating units, is un­
likely to be affected b; linkage to the same extent#

In

sheep selection for any one segregating unit Is unlike­
ly to be sufficiently Intense to seriously distort the
random order of gene combinations#

In Drosophila, It

possibly could be so Intense that Individuals with the
preferred linkage combinations would have more descendants
than those with "unbalanced" combinations#

Matherfs

theory seems unlikely to apply to domestic animals be­
cause In them selection for desirable linked combinations
must necessarily be weak, particularly where large numbers
of genes Influence the character In question#

Yet another

possible reason for negative genetic correlations Is
provided by physiological limitations*

If two traits

71 both require a substrate which is available only in
limited quantities, then selection for genes favoring the
expression of one trait must also cause a decrease in
the other.
Heritability of fleece weight seems high, but
the nature of genetic correlation may limit progress*
Consequently breeders may have to be satisfied with an
intermediate expression in any particular characteristic
in order to achieve greatest overall performance for
their livestock.

APPLICATION
Tii© breeder, confronted with the problem of im­
proving his flock by selection requires answers to the
following questions:
1-

What characters should be considered in a selection

program?

Probably no two breeders are wholly agreed on

this question, which is perhaps a fortunate situation,
for no single authority is likely to be completely cor­
rect.

Some diversity of ideals will assure diversity

of selected types,

thereby creating reservoirs of de­

sirable germ plasm which would be valuable should price
structures change radically In directions not predicted
by the majority of breeders.

In this study only two

traits, grease fleece weight and grade, have been con­
sidered which account for fifteen to twenty five percent
of the productive rating in sheep.

There are other Im­

portant economic characters as mentioned by Winter et
al (1946) which must be considered in selection programs
2-

What progress may be expected with the information

available in this study?

The actual advance that one may

make by mass selection for a trait can be estimated by
computing the anticipated progress from a single cycle of
selection.

As was previously pointed out the estimates

used in the computation of expected advance sh#hhtilste
justed for the environmental effects and only the environ*

-

73

-

mental effects that are to be eliminated in the routine
breeding program.

These effects may be eliminated in

two ways, first if selection occurs among animals which
do not differ with respect to the environmental effects
considered,

then the effects are automatically eliminated.

This is the most accurate method of, adjustment.

Examples

are, fleece weights which occured in the same year need
no adjustment for yearly differences and lamb weights
taken at a constant age need no adjustment for age.

The

latter case is an excellent example of how a little fore­
thought in record keeping may materially aid in a selec­
tion program.

The second method is to actually adjust

tiie records to a common basis for the differences in en­
vironment.

Using this method, if the fleece weights oc­

cured in different years, they would be adjusted to a
common year by competing the average fleece weight for
each year and the overall average fleece weight and adjusting the records for the average yearly differences
to this overall average.
To illustrate the method of computing anticipated
progress by selection, the expected gain per year will be
estimated for grease-fleece weight and grade in a flock
of 100 ewes.

Assuming that the lamb crops average one

hundred percent and that half the ewe lambs are retained,
then about 25 percent of the ewes are replaced each year.

-

74

-

This replacement is made with ewe lambs from the best
50 percent of the ewes having ewe lambs.

It may be as­

sumed further that the sires of ewe lambs are of same
genetic ability as dams.

Death and other accidents would

eliminate about fifteen percent leaving about 85 percent
of the entire flock to select from.

If 75 percent of the

flock must be retained and only 85 percent of the flock
is available to select from, then the proportion that may
be selected is actually (jlHL) or .88 or 88 percent.
.*5

When 88 percent

of the

individualsareselectedthe

average performance

of the

selectedindividualswould be

expected to deviate about 0.2 standard deviation,
from the average performance of the entire flock.
1947, pp. 14#). The

(Lush,

is the standard deviation of fleece

weight corrected for years.

The

adjusted for years may

be estimated from O';1'+ <TX for fleece weight in Table H
such that:
Gp - (.61

and

- .78)

m

1.39

Op * 1.18

Therefore, the average fleece weight of the selected
ewes

(i.e.

88% of the ewes)

pounds above the flock average.

is (.2 x 1.1$) or .24
Since these ewes consti­

tute only 75 percent of the entire flock, the expected
Increase in fleece weight that this group will bring about
would be (75 x .24)

or 0.1$ pounds above flock average.

- 75 -

1

But the expected production the next year would he
(0*18 x *44) or *08 pounds above the flock average of
the previous year.

(0*44 being the estimate of repeat­

ability )

remainl'ngn a 25 percent of the flock is, con­

The

stituted by the ewe lambs from the best
ewes*

The average fleece weight of this

ewes is. expected to deviate about

0. 8

50 percent of
50 percent pf

standard deviation,

# from the average performance of the flock*

There­

fore, the average fleece weight of these ewes would be
expected to be
age.

(.8

x 1.18) or

.94 lb* above flock ayer-

The expected production of the offspring of these

ewes is the product of the selection differential of
the dams selected and the heritability estimate# -Actual­
ly, the selection differential, which is the

main diff

ference in performance of selected individuals and:all
individuals among which selection was practiced, has
already been estimated -to be
average*

0*94 pounds above flock
h e ritebiliby for g re a se

The best esttmate

.fleece^weight. In this flock

is

0 *5 8 *

T h e r e f o r # i.the ex­

pected average fleece weight of ewe lambs next,year is
(*9£ x *58)

or *56 pounds above f lock average this year.
25 peneert-©f the entire

Since the

ewe lambs constitute;

■flock-:the

expected-*-increase in fleece?-height 'that this

group W i l l :bring;,about would be* .(•2 6 x *56) or?.;m - 0 S h pounds

- 76 -

above the flock average previous year.
Thus the total expected progress per year may be
obtained by summing up the gains made in the ewes-group
constituting 75 percent of the flock and in ewe-lambgroup constituting the rest of the 25 percent of the
flock.

In other words, the expected flock average fleece

weight next year would be (.09+ .OS) or .17 pounds above
flock average of this year.
Similarly, the anticipated progress in grease fleece
grade can also be worked out.

Its phenotypic standard

deviation is 0.56 and estimate of heritability is .20.
The expected increase in grade of ewes constituting 75
percent of the entire flock would be (.2 x .56)

.75 or

.06 units above the flock average and expected increase
in grade of ewe lambs constituting 25 percent of the en­
tire flock would be (.6 x .56 x .20) x .25 or .02 units
above flock average the previous year.

By summing them

the expected flock average fleece grade next year is
estimated to be (.06 + .02)
average this year.

or .10 units above flock

But the estimate of repeatability

for grease fleece grade was not found in this study and,
hence, could not be used in computing the anticipated
gain.

Therefore, the expected gain in one year in fleece

grade would be a little leas than .10 units as estimated
above.

The gain in grade may be interpreted in terms of

- 77
the percentage of animals which may be expected to move
up one grade In one year and it is estimated to be a
little leas than

10

percent*

- 78 SUMMARY
Heritability estimates for grease-fleece weight and
gr$ase-fleece grade, and repeatability estimate for
grease fleece weight were determined from sheep records
from the Michigan State College sheep flock#

The data

included 1599 records from 412 ewes of Oxford, Shropshire,
Hampshire and. Southdown breeds covering the period from
1933 to 1949#

A study of the contributions of certain

environmental factors to grease fleece weight was made
and appropriate adjustments were indicated#
The study of environmental factors included the
effects of age, number of lambs xborad, breed, and year
on grease-fleece weight#

Only the environmental efffcti

which accounted for at least six percent of the total
variation were considered to be i m p o r t a n t e n o u g h to justi­
fy adjustment in a selection program#

The factors found,

to be important enough on grease fleece weight to justify
adjustment were breeds and years#

The phenotypic corre­

lation between grease fleece weight and grease fleece
grade was found to be -0#35

O.#04#

Repeatability estimates after adjusting for the
important environmental effects, were determined by the
method of intraclass correlation and the estimate for
grease-fleece weight was 0,44

0,02#

79
Estimates of heritability after adjusting for
important environmental effects, were deduced from the
weighted average of the heritability calculated by intrasire regression of offspring on dam and intra-sire daughterdam correlations, on 169 daughter-dam pairs for grease
fleece weight and 167 daughter-dam pairs for grease
fleece grade.

The best estimate of heritability for

grease fleece weight was 0.38
fleece grade was

0.20

.11 and for grease

^ .1 0 .

Estimate of genetic correlation between fleece
weight and grade was found to be -0.37.

The causes of

negative genetic correlation were discussed.Under the as­
sumption that 25 percent of the ewes are replaced each
year with ewe lambs from the best 50 percent of the ewes
and that the average loss due to death and accidents is
15 per cent; the anticipated gain for a flock of 100 ewes
in one year was estimated to be .17 lb. for grease fleece
weight and a little less than

.10

unit for grease fleece

grade ^when selection was based entirely on one or the other
of these traits.

-

80

LITERATURE CITED
Baker, Marvel L., L. N. Hazel, and C. F. Reinmiller*
1943
The Relative Importance of Heredity and
Environment in the Growth Rate of Pigs
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Jour, Animal Sci,,
2: 3-13,
Cockerham,
1949

Darwin, C,
1920

C, C,
Estimates of Repeatability and Heritability
in Sheep, Unpub -i shed M,S, Thesis,
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The Origin of Species,
Sixth Edition,
W e w y o r k j D . Appleton and Co, 35 pp.

Dickerson, G. E, and L. N. Hazel,
1944
Effectiveness of Selection in Progeny Per­
formance as a Supplement to Earlier Culling
in Livestock,
Jour, Ag. Res* 6 9 : 457-476,
Dobzhansky,
1927

Th,
Studies on the Manifold Effects of Certain
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Ind, abst, u, Ver 43s 330-338,

Dobzhansky,
1941

Th,
Genetics and the Origin of Species,
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Fisher, R. A,
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The Correlations between Relatives on the
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Edinburgh. 52s 399-433.
Fisher, R. A,
1930
The Genetical Theory of Natural Selection.
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Fisher, R, A,
1946
Statistical Methods for Research Workers,
10th edition.
Oliver and Boyd.
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Freney, M. R. and H. W. Turner.
1938
The Yield of Fleece Wool.
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Jour. Text. Inst,

- Si Gruneberg, A,
Congenital Hydrocephalus in the Mouse.
1943
A Case of Spurious Pleiotropism.
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Hazel, L. N e
1943
Hazel, L. N
1946

The Genetic Basis for Constructing Selection
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Table with Unequal Subclass Numbers.
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Hazel, L. N . and C. E. Terrill.
1945
Heritability of Weaning Weight and Staple
Length in Range Rambouillet Lambs. Jour.
Ani. Sci..
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‘
Hazel, L. N . and J. L. Lush.
1942
The Efficiency of Three Methods of Selection.
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Hotelling,
Some New Methods in Matrix Calenlation.
1943
Annals of Math. Statist. 14: 1-34.
Joseph, W.
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Lush, J. L•
1935

Lush, J. L.
1940

Lush, J. L•
1947

Factors Related to Production by Range
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Intra-sire Correlations of* Regressions
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Animal Breeding Plans. 3rd Edition, second
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- 82
Lush, J • L
1948

The Genetics of Populations.
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Mimeographed
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Lush, J* L
1923

and J . M* Jones.
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Lush, J. L
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and P. S. Straus.
The Heritability of Butterfat Production in
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Lush, J . L
1942

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Mather, K,
1943

Polygenic Inheritance and Natural Selection.
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Morley, P. H. W.
1950
Selection for Economic Characters in MeariLno
Sheep. Unpublished Ph.D. Thesis.
Iowa
State College, Ames, Iowa.
Nelson, R. H.
1941
The Influence of Heredity on the Market.
Score of Duroc Jersey Hogs.
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Oklahoma Agricultural College Library.
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Rasmussen, K.
1942
The Inheritance of Fleece Weights in Range
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Snedecor,
1946

. W.
Statistical Methods.
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The
Iowas State College Press, Ames, Iowa.

Spencer, D
1925

A .
Factors which Influence Fleece Weights of
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:
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!

Stewart, H
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A.
The Inheritance of Prolificacy in Swine.
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- 33 -

Terrill, C. £•
1939
Selection of Range Rambouillet Ewes.
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Terrill, C. E. and L. N. Hazel,
1943
Heritability of Yearling Fleece and Body
Traits of Range Rambouillet Ewes. (Abst.)
Jour. Ani. Sci. 2: 353-359
Terrill, C. E., G. H. Sidwell and L. N. Hazel,
1943
Effects of Some Environmental Factors on
Yearling Traits of Columbia and Targhee
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Terrill, C. E., G. M. Sidwell and L. N. Hazel.
1943
Effects of Some Environmental Factors on
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Venkatachalam, G.
1949
Estimates of Heritability of Birth Weight
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»

r

Winsor, C. F, and G, L. Clarke.
1940
A Statistical Study of Variation in the
Catch of Plankton Nets, Sears Foundation:
Jour. Marine Res. 2.: 1-34,
Winters, L. M., D. L. Dailey, 0. M. Kiser, P. S. Jordan,
R. E. Hodgson, and W. W. Green,
1946
Factors Affecting Productivity in Breeding
Sheep. Univ. Minn. Ag. E x p . Sta. Tech. Bull.
176: 23 pp.
Wright, S•
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Wright, S.
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Wright, S•
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Systems of Mating.

Genetics.

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The Analysis of Variance and the Correlations
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- 84 Wright, S.
1939

Yates, F.
1934

Genetic Principles Governing the Rate of*
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APPEHDIX 1

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APPEHDIX 1
■■Htdclaaglfled according to e.ge)breed,Ho, of laiabs
raised and year of record;