Stability parameters for comparing varieties (eberhart and russell 1966)

STABILITY PARAMETERS FOR
COMPARING VARIETIES (EBERHART
AND RUSSELL 1966)
-DHANUJA N
2019508005

STABILITY ANALYSIS
• The phenotype of an individual is determined by the effects of
its genotype and environment surrounding it.
• The interplay in the effect of genetic and non-genetic on
development is termed as 'genotype-environment interaction'.
• P=G+E+GE

GE INTRACTION
• GENOTYPE- environment interactions are of major importance
to the plant breeder in developing improved varieties.
• When varieties are compared over a series of environments, the
relative rankings usually differ. This causes difficulty in
demonstrating the significant superiority of any variety.
• Large genotype-environment interactions reduce the progress
from selection (Comstock and Moll )

STRATIFICATION
• Stratification of environments has been used effectively to
reduce the genotype-environment interaction.
• This stratification usually is based on macro-environment
• Even with this, the interaction of genotypes in a subregion, and
with environments at the same location in different years,
remains too large.
• Allard and Bradshaw classify as unpredictable the
environmental variation, for which stratification is not effective.

STRATIFICATION
• Select stable genotypes that interact less with the environments
in which they are to be grown. If stability of performance,
(minimum of interaction with the environment), is a genetic
characteristic, then preliminary evaluation could be planned to
identify the stable genotypes.
• With only the more stable genotypes remaining for the final
stages of testing, the breeder would be greatly aided in his
selection of superior genotypes.
• However, selection for stability is not possible until a model
with suitable parameters is available to provide the criteria
necessary to rank varieties for stability.

SUGGESTIONS TO REDUCE GEI
• The use of genetic mixtures rather than homogeneous or pure-lines
• Multiline variety (Jensen)
• Heterozygous and Heterogeneous populations (Allard and Bradshaw)
• They used the term "individual buffering" (each member of the
population is well adapted to a range of environments), and
"population buffering" (variety consists of a number of genotypes
each adapted to a different range of environments).
• Heterozygous or homozygous genotype may possess individual
buffering
• Heterogeneous population will possess population buffering.

• Double crosses interact with environments less than single
crosses. Double crosses are superior to single crosses for
stability (Sprague and Federer)
• Hybrid x Year interactions were significantly greater for single
crosses than for three-way crosses (Eberhart, Russell, and
Penny)
• Some single crosses may show more, phenotypic stability than
the most stable three-way or double cross. Because the variance
of a mean is less than the variance of an individual, the average
genotype-environment interaction of a mixture may be
expected to be less than the interaction for a single genotype.

STEPS IN STABILITY ANALYSIS
Done from replicated data over several environments
1. Environment wise analysis of variance
• Following usual method of analysis of variance, the data are
analyzed for a quantitative trait in all the environments
separately. The data of environments, where significant
difference for genotypes are observed, are used for pooled
analysis.

• Before proceeding to pooled analysis, the test of homogenity of
variances (Bartlets‘ chi square test) is to be done for the
environments.
• If the X2 value is non-significant, there is homogeneity of
variance among the environments. Hence, pooled analysis can
be carried out.
• In case, the X2 value is significant, it can be concluded that
there is heterogenity of variances among the environments
• If the error variances are heterogeneous, divide each value by
square root of corresponding mean square of error variance and
use for the combined analysis.

2. POLLED ANALYSIS OF VARIANCE
• A two way table is formed
for tabulating the data of
genotypes in different
environments.
• If GE interaction is non-
significant, no need to
proceed further
• If significant, estimate
phenotypic stability.
Geno
types
E1 E2 …….. En
1
2
:
:
n

MODELS FOR STABILITY ANALYSIS
A. Conventional models
Stability factor model
(Lewis 1954)
Ecovalence model
(Wricke 1964)
Stability variance model
(Shukla 1972)
Lin and Binns model
(198)
B. Regression coefficient model
Finlay and Wilkinson model
(1963)
Eberhart and Russell model
(1966)
Perkins and Jinks model
(1968)
Freeman and Perkins model
(1971)
Genotypic stability model
(Tai 1971)

• C. Principle component
analysis
• Perkins (1972); Freeman
and Dowkar (1975); Seif
et al (1979)
• Additive main effect and
multiplicative interaction
effect
• Shifted multiplication
model
• Redundancy analysis
• Factor regression analysis
• GGE biplot
• D. Cluster analysis
Grouping by cluster
analysis (Westcot 1987)
Webber and Wricke (1990)
• E. Pattern analysis
Mungomery et al 1974
Delacy et al (1990)
• F. Factor analysis
Johnson and Wichern
(1982)
Calinski et al (1987)

REGRESSION COEFFICIENT MODEL
• For phenotypic stability analysis, regression analysis has proved
to be valuable for assessing response under changing
environments.
• The regression of each variety in an experiment on an
environmental index and a function of the squared deviations
from this regression would provide estimates of the desired
stability parameters

EBERHART AND RUSSELL (1966)
In 1966, Eberhart and Russell (1966) made further improvement
in stability analysis.
Three parameter model
1. Mean yield over locations or seasons
2. Regression coefficient (b)
3. Deviation from regression (s2
d)

PARTITION
Total variance
1. Genotypes
2. Environment + interaction (E + G × E)
1. Environment (linear)
2. G × E (Linear)
3. Pooled deviations
Sum of square due to pooled deviations is partitioned in to sum
of square due to individual genotype

The model considered by Eberhart and Russell may be written as
yij = μi + bi Ij + δij
• yij - Mean of ith variety in jth environment
• μi - Mean of all varieties over all environments
• bi - Regression co-efficient of ith variety on environmental index
which measures the response of this variety to varying environments
• Ij - Environmental index i.e. the deviation of the mean of all the
varieties at a given environment from the over all mean
• δij - The deviation from regression of ith variety at jth environment

MAIN FEATURES
• Analysis of stability is simple as compared to other models
• Degree of freedom for environment is 1
• Less expensive than Freeman and Perkins model
•It does not provide independent estimation for mean
performance and environmental index
• Stable genotype is one with bi = 1, s2
d = 0 and high mean yield

STABILITY PARAMETERS
• With this approach, the first stability parameter is a
regression coefficient, bi which can be estimated by
• The deviation can be squared and summed to provide
an estimate of another stability parameter, mean
square deviation

THE MODEL PROVIDES A MEANS OF
PARTITIONING THE GE INTERACTION OF EACH
GENOTYPE INTO TWO PARTS
The variation due to the response of genotype to
varying environmental indices (sums of square
due to regression)
The unexplainable deviation from regression on
the environmental indices.

STABLE GENOTYPE
1. A genotype with high/ desirable mean value
2. A genotype with deviation not significantly deviating
from 0 is stable
3. A genotype with unit regression coefficient
• average responsive suitable for all
environmentb=1
• highly responsive suitable for favourable
environmentb>1
• low responsive suitable for unfavourable
environmentb<1

• Further, they define that the stable variety will be one with bi =
1.0 and s2
d = 0; and the null hypothesis
H0 : μ1 = μ2 = … = μm (To test the significance among the genotype means)
can be tested by the F-test (approximately)
F = MG / Md (F=MS1/MS3)
with homogeneous deviation mean squares, being Md the
pooled deviations.
• The hypothesis that there are no genetic differences among
phenotypes for their regression on the environmental index
H0 : β1 = β2 = … = βm (To test if the varieties differ for their regression on EI)
can be tested by the F-test F = MEI / Md (F=MS2/MS3)

• The deviations from regression for each genotype can be
further tested by
• Thus, in this approach one can see that two measures of
sensitivity of the genotype to changes on environment are
worked out:
(i) the linear sensitivity measure in terms of the linear
regression coefficient, bi of the ith genotype to the
environmental change
(ii) the non linear sensitivity measure in terms of the
deviation from regression mean square

APPLICATION OF THE MODEL TO MAIZE
YIELD TRIALS
• Single crosses were grown in the Iowa State University
experimental yield trials for 1945-51.
• Data for a diallel set of single crosses from 11 lines
grown in 8 environments in 1945-47 and for a diallel
set frown 8 lines in 12 environments in 1948-51 were
extracted and analyzed.

PARTITION
• The differences among regression coefficients [SC x Env
(linear)] can be partitioned into General x Env (linear) and
Specific X Env (linear).
• Since the Specific X Env (linear) squares are not significantly
greater than the respective deviation mean squares, there is no
evidence that regression coefficients differ because of non
additive gene action.
• However, the General x Env (linear) mean squares were
significant (P ~ .05) for both diallels.

Differences in stability of 2 single crosses and their
performance in relation to average of the test
1.WF9 X M14 is a very
desirable hybrid because
its performance is
uniformly superior
b=1.06, s2
d = 0
2.M14 X B7 is expected to
equal or exceed average
performance only under
very unfavorable
conditions b=.76, s2
d=5

The vertical
lines are one
SD above and
below the GM,
whereas the
horizontal
lines are one
SD above and
below the
average slope
(b=1.0).
The relation of yield stability of 28 single crosses. Estimates
of s2
d were significant only for those hybrids indicated by +

• The single cross with above-average performance and
satisfactory stability in the 1945-47 diallel is WF9 x Oh28
• WF9 x M14 had above-average performance over environments,
but the estimate of s2
d was 30.
• In the 1948-51 diallel, two single crosses gave high yields with
stability WF9 x M14 and WF9 x W22
• The line Hy performed consistently better in favorable
environments (b = l.15 and 1.15), whereas O8420 performance
was relatively better in less favorable environments (b = .95 and
.55)

AVERAGE LINE PERFORMANCE IN DIALLEL
CROSSES

• Three-way crosses involving three single-cross testers and six inbreds
• The difference in the response of three-way crosses to varying
environments was due to the different responses of the lines as
indicated by the large Lines X Env (linear) mean square.
• Three-way crosses involving W22 performed much below average in
unfavorable environments, whereas N22A and B37 did extremely well
under less favorable conditions.
• The performance of B37 in three-way crosses was much more
predictable than hybrids involving B54 or B46, as indicated by the
estimates, s2
d

Analysis of 18 three way cross and three single
cross testers grown at 2 locations

AVERAGE PERFORMANCE OF SIX INBRED
LINES WITH THREE TESTERS

PERFORMANCE OF THE TESTERS (SINGLE CROSSES)
COMPARED WITH THEIR AVERAGE TESTCROSS
PERFORMANCE (THREE-WAY CROSSES)

• None of the three-way crosses falling in the center section to the right
had a non significant deviation mean square. However, the hybrid
(WF9 x M14) N22A (x = 119.8, b = 1.05, s2
d = 41) is the most nearly
acceptable even though s2
d is larger than desirable.
• (WF9 X B14) B37 (x = 119.5, b — .74, s2
d — 0) would be especially good
under less favorable environments but not good under favorable
conditions. The hybrid with the highest mean yield (WF9 X M14) B37
is unacceptable for both stability parameters

• Although the inbred lines of maize in this experiment differed in
their average responses to varying environments, the Variety X
Env (linear) sum of squares was not a very large proportion of
the Variety X Environmental interaction.
• Hence, the second stability parameter (s2
d) appears very
important.
• Because the variance of s2
d is a function of the number of
environments, several environments with minimum replication
per environment are necessary to obtain reliable estimates of s2
d.
• However, a good estimate of the regression coefficients can be
obtained from a few environments if they cover the range of
expected responses.

MERITS AND DEMERITS
• This model measures three parameters of stability, viz. (1) mean
yield over environments (2) regression coefficient and (3)
deviation from the regression line.
• This model provides more reliable information about varietal
stability than Finlay and Wilkinson model.
• The analysis is also simple. In this model, the estimation of
mean performance and environmental index is not
independent.
• There is combined estimation of S.S. for environments and
interactions, which is not proper.

REFERENCES
• Eberhart, S., and Russell, W.A., 1966, Stability parameters for
comparing varieties, Crop Sci., 6: 36–40
• Nadarajan N, Manivannan M, Gunasekharan M, Quantitative
genetics and biometrical techniques in plant breeding, kalyani
publishers, 253-260.

Stability parameters for comparing varieties (eberhart and russell 1966)

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Stability parameters for comparing varieties (eberhart and russell 1966)