Agriculture Reference
In-Depth Information
On the other hand, if we go for the method
given by Finney, then we shall have
components is of utmost importance. Relative
magnitude or proportions of these variations actu-
ally govern the genetic properties of the population.
Again, covariability of different characters is
measured in terms of covariance. Covariability
measured between two characters is the phenotypic
value. Similar to that of phenotypic variability,
phenotypic covariability can also be partitioned
into genotypic and environmental (nonheritable)
components. The partitioning of variances and
covariances will facilitate the estimation of various
genetic/breeding parameters like heritability, co-
heritability, and genotypic correlations which can
help breeders tremendously.
2
y:x
4
2
s
þ
T
xx
=ðt
1
Þ
E
xx
V y
0
i
y
0
j
¼
1
¼
7
:
4965
:
H
0
: α
1
¼ α
2
2
ð
127
:
49745
151
:
7449
Þ
F ¼
7
:
4965
¼
78
:
43 with
ð
1,11
Þ
d
:
f
:
H
0
: α
2
¼ α
4
2
ð
151
:
7449
130
:
5051
Þ
F ¼
7
:
4965
11.2.1 Components of Variance
¼
60
:
18 with
ð
1,11
Þ
d
:
f
:
p
7
During the analysis of variance, the mean sum of
squares obtained due to the treatments consists of
two components: (1) genotypic differences
among the treatments and (2) environmental
variations. Thus,
CD
0
:
05
¼
:
4965
t
0
:
025
;
11
¼
2
:
7379
2
:
201
¼
6
:
0263
:
If we arrange the adjusted treatment means,
we have the following:
2
e
2
g
E
ð
MS
G
Þ¼σ
þ rσ
;
where
e
E
and MS
G
and MSE are the mean
sum of square
ð
MSE
Þ¼σ
;
y
0
i
Treatment means:
Value
due to genotype and
error
;
y
0
2
151.74
respectively
;
in ANOVA table. It can be seen
y
0
4
130.51
¼
E
MS
G
ð
Þ E
MSE
ð
Þ
g
that
σ
.
y
0
1
127.5
r
g
g
Thus,
σ
is
estimated
by
σ
¼
y
0
3
115.25
MS
G
MSE
r
e
is estimated by
σ
e
¼
MSE
:
;
and
σ
Feed two is significantly producing higher
gain in body weight compared to the other
feeds, and feed three provides the lowest gain in
body weight among all feeds. On the other hand,
feed four and feed one are the same; they are
statistically at par.
e
are the phenotypic, genotypic, and environmen-
tal variances, respectively. From the given data,
one can estimate
σ
; σ
p
¼ σ
g
þ σ
e
where
σ
p
; σ
g
;
σ
Hence
and
p
¼ σ
g
þ σ
e
:
g
¼
0 means the genotypes do
not differ significantly among themselves. The
test
To test
H
0
: σ
MSg
MSE
with
statistic
under
H
0
is
F ¼
11.2
Partitioning of Variance
and Covariance
ðt
1
Þ; ðr
1
Þðt
1
Þ
d
:
f
:
If
F
is significant, we
can say that
the genotypes differ among
themselves.
Phenotypic characters which we measure on
individuals are the manifestation of the interaction
between the genetic architecture and the environ-
ment around them. The environmental factors
mainly include all the nonheritable components.
The variation in phenotypic values is therefore
governed by the variances attributed to genotypic
values and environmental deviations. Thus, the
partitioning of phenotypic variations into different
11.2.2 Components of Covariance
The covariances can also be partitioned due to
environmental and genotypic factors in a similar
way as that of the partitioning of treatment
variances from the analysis of variance table.
Thus, the phenotypic covariance between any
