Agriculture Reference
In-Depth Information
Table 11.2
Table of variance, covariance, and correlation
Level
Variance
Covariance
Correlation coefficients
Phenotypic
2
p
i
2
p
i
0
σ
p
ii
0
r
p
ii
0
σ
and
σ
Genotypic
σ
g
i
and
σ
2
g
i
0
σ
g
ii
0
r
g
ii
0
Environmental
2
e
i
2
e
i
0
σ
e
ii
0
r
e
ii
0
σ
and
σ
two characters can be written as a combination of
genotypic and environmental covariances, that
is,
are the genotypic and phenotypic covariances
between characters 1 and 2 as obtained
from the partitioning of the mean sum of
products in the analysis of covariance.
σ
p
12
¼ σ
g
12
þ σ
e
12
. One can have the correla-
tion coefficients at the genotypic, phenotypic,
and environmental levels by using the variance
and covariance of appropriate level in the for-
mula for the correlation coefficient. The signifi-
cance of the correlation coefficients can usually
be tested using
(e)
Genetic
: The difference
between the mean of the selected individuals
XðÞ
advance/gain
and the mean of the population from
which the selection has been made
X
p
is
known as genetic gain or advance. But for all
practical purposes, the genetic gain or
advance is worked out as GA
t
-test described already in Chap.
9
with (
n
2) degrees of freedom where
n
is the
number of genotypes under consideration.
We can write for any two characters
2
¼ k:h
:σ
p
,
i
0
i
and
where
is the standardized selection differ-
ential having constant values at different
selection intensities (e.g., the values of
standardized selection differentials at 1, 5,
10, and 20 % selection intensities are, respec-
tively, 2.64, 2.06, 1.40, and 1.16) and
k
(Table
11.2
):
From the above variances and covariances at
the genotypic, phenotypic, and environmental
levels, one can work out different genetic
parameters like (a)
phenotypic coefficient of var-
2
and
h
iation (PCV),
(b)
genotypic coefficient of varia-
σ
p
have their usual meanings.
(f)
Genotypic and environmental correlation
:
The correlation coefficient between two
characters at the genotypic and environmen-
tal levels is worked out using the variances
and covariances due to the genotype and
nonheritable factors.
The association between two characters is
measured in terms of the correlation coefficient
which is based on the phenotypic values of the
variances and the covariances between the
characters. Since the phenotypic values are deter-
mined by the genotype and the environmental
interactions, the phenotypic correlation is also
governed by these factors.
tion (GCV),
(d)
co-heritability
, which are of paramount impor-
tance in the selection process of breeding
experiments:
(a)
(c)
broad sense heritability, and
Phenotypic coefficient of variation (PCV%)
:
¼
σ
p
X
100.
Genotypic coefficient of variation (GCV)
(b)
:
¼
σ
g
100.
(c)
Heritability (broad sense)
: Another parame-
ter, heritability (broad sense), for any charac-
ter, is expressed as the ratio of the genotypic
variance to the phenotypic variance
X
2
g
σ
2
.
This gives an abstract idea about the amount
of variability for a particular character due to
its genotypic feature.
h
¼
σ
p
Example 11.2.
The following table gives the
information on four yield components and the
yield of ten genotypes of mulberry. Analyze the
data with respect
(d)
Co-heritability
: Co-heritability between two
characters is defined as the ratio of the
genotypic and the phenotypic covariances
between the two characters under consider-
ation and is given as
σ
g
ii
0
σ
p
to the variability and
covariabilities
to work out
the correlation
, where
σ
g
12
and
σ
p
12
coefficients
and
the
path
of
correlation
ii
0
