Agriculture Reference
In-Depth Information
Y
ij
¼ μ
i
þ β
i
E
j
þ δ
ij
; i ¼
1,2,
......t
genotypes and
j ¼
1,2,
...l
situations or locations,
where
Y
ij
¼
mean of
i
th genotype in
j
th situations,
μ
i
¼
mean of the
i
th genotype over all the situation
;
β
i
¼
i
regression coefficient
th genotype on the environmental indices,
E
j
¼
j
Environmental index for
th situation,
δ
ij
¼
Deviation of the regression of
i
th genotype on the environmental indices
:
from the
The environmental index is defined as
S
2
d
i
2. The mean square deviation
regression is given as
P
t
P
l
j¼
1
Y
ij
t
l
P
t
1
Y
ij
t
for
X
l
j¼
1
E
j
¼
i¼
1
i¼
P
l
j¼
1
δ
E
j
¼
:
0
2
ij
2
e
r
Þ
S
S
2
d
i
¼
;
ð
l
2
The environmental index is an index to mea-
sure the capabilities of different environments
under the given condition. In Eberhart and
Russell model, there are two stability parameters,
namely, (1)
where
2
P
l
j¼
1
Y
ij
E
j
the regression coefficient
and (2)
the
"
#
X
X
l
j¼
1
δ
l
j¼
1
Y
mean squared deviation from the regression
.
1. The regression coefficient
2
i:
t
ij
Y
2
2
ij
¼
is the regres-
sion of the performance of each genotype
under different environments on environmen-
tal average over all the genotypes. This model
considers
βðÞ
P
l
j¼
1
E
2
j
2
and
e
is the estimate of a pooled error.
A stable genotype is one which has
S
b
i
as a measure of responsiveness,
and accordingly a genotype having the regres-
sion coefficient unity (i.e.,
S
2
d
i
¼
0.
2
Thus, when the null hypothesis
0is
accepted, then the genotype is stable, and when
the null hypothesis is rejected, then it is less
stable. Actually, while testing the above null
hypothesis,
H
0
: S
d
i
¼
b
i
¼
1) is aver-
agely responsive. A regression coefficient
less than unity means that the genotype is
less responsive to environmental factors like
nutrient status, soil status, and plant situation.
On the other hand, the regression coefficient
greater than unity for a genotype indicates
high responsiveness of the genotype towards
environmental factors. This type of genotypes
generally performs well under rich environ-
mental conditions. On the other hand,
2
ij
δ
S
e
through
is compared against
F
-test.
Thus, using both stability parameters, it can
be concluded that for a genotype to be stable, the
regression coefficient should be in unity with the
mean square deviation
not significantly
S
2
d
i
the
different from zero
. Genotype means are also
considered while selecting the best stable suit-
able genotype (Table
11.3
).
b <
other groups of genotype for which
1
are
suitable
for
poor
environmental
conditions.
