Agriculture Reference
In-Depth Information
Fresh wt
of leaf (
Covariance component
Yield/plant (
Y
)
Shoot length (
X
1
)
X
2
)
Leaf area (
X
3
)
Shoot length (
X
1
)
2108.02
Genotypic
σ
g
ij
2115.78
Phenotypic
σ
p
ij
σ
e
ij
7.75
Environmental
Fresh weight
of leaf (
X
2
)
1346.68
1681.85
Genotypic
σ
g
ij
1344.68
1667.36
Phenotypic
σ
p
ij
σ
e
ij
2.00
14.49
Environmental
Leaf area (
X
3
)
609.77
1069.49
1451.58
Genotypic
σ
g
ij
608.64
1070.89
1452.16
Phenotypic
σ
p
ij
σ
e
ij
1.12
1.41
0.59
Environmental
Leaf
weight/m
2
(
984.42
1405.20
2757.10
927.09
Genotypic
σ
g
ij
X
4
)
982.31
1392.70
2757.84
928.16
Phenotypic
σ
p
ij
σ
e
ij
2.10
12.50
0.74
1.07
Environmental
After partitioning the variances and the
covariances into genotypic, phenotypic, and
environmental components, the next task is to
calculate the correlation coefficients among the
variables at
environmental levels, which will be used in
path analysis. The usual formula for the correla-
tion coefficients as described in Chap.
9
, Sect.
9.1.1
of Sahu (2007) is also used for obtaining
the correlation coefficients at different levels:
the genotypic, phenotypic, and
Cov
Y; Xð Þ
gen
VðYÞ
gen
VXð
gen
r
yx
1
¼
q
;
where Cov
ð
Y; X
1
Þ
gen
¼
covariance between
Y
and
X
1
at genotypic level,
VðYÞ
gen
¼
variance of the character
Y
at genotypic level,
VXð
gen
¼
variance of the character
X
1
at genotypic level
:
Similarly, the correlation coefficients at the
phenotypic and environmental levels can be
worked out by using the covariance and
variances at the phenotypic and environmental
levels, respectively. Thus, the correlation coef-
ficient at the genotypic, phenotypic, and envi-
ronmental levels for the characters leaf yield
and total shoot length can be worked out as
follows:
Correlation coefficients between leaf yield
and total shoot length
Y; Xð Þ
gen
VðYÞ
gen
VXð
gen
Cov
Genotypic level
: r
yx
1
¼
q
02
903
2108
:
¼
p
:
95
18452
:
68
¼
0
:
516
;
