Dr Gulzar Singh

2. Effects of factors under study vary from location to
location or from year to year. To obtain an unbiased
estimate.
Interest in determining the effect of factors over time.
To investigate genotype (or treatment) x environment
interactions.
(Wider adaptation of Technology)

3. • Yield / performance stability has always been considered as an important
topic in plant breeding but will be more concern by the continued variation in
climatic condition
• The phenotype of an individual is a mixture of both genotype (G) and
environment (E)
• P = G + E + G × E
• As a consequence of G × E interaction, crop varieties/ technologies may not
show uniform performance across different environments
• So, one of the most significant goals of the phenotype stability analysis is
to distinguish the genotypes whose phenotypic performance remains
constant while the environmental conditions change.
 Differential response of genotypes / technologies to varying environmental
conditions.

4. The biggest nightmare for plant breeders (and other
agricultural researchers) who try to avoid them like the
plague.
Delight for statisticians/ biometricians who love to
investigate them.

5. • G × E interaction is the differential yield response of a genotype to
environments.
• As a direct consequence of G × E interaction, the approximate performances
of two genotypes vary with the environment stimuli ]
B
A
Yield
Locations
Yield
Locations
B
A
Yield
Locations
No interaction
Scalar interaction
Cross-over
interaction

6. , where the
researcher manipulates the environment. For
example, variable nitrogen.
, where there is
an opportunity to predict conditions from year to
year. For example, soil type.
, where there is little
chance of predicting environment. For example,
rainfall, temperature, high winds.

7. Plant breeder grows advanced breeding
selections at multiple locations to determine those
with general or specific adaptability ability.
A pathologist is interested in tracking the
development of disease in a crop and records
disease at different time intervals.
Forage agronomist is interested in forage harvest
at different stages of development over time.

8. • To investigate relationships between genotypes
and different environmental (and other) changes.
• To identify genotypes which perform well over a
wide range of environments.
• To identify genotypes which perform well in
particular environments. .

9. Where should they be?
Availability of planting material.
Diversity of environmental conditions.
Magnitude of error variances and genetic variances in
any one year or location.
Availability of suitable cooperators
Cost of each trial ($’s and time).

10. Points to Consider before Analyses
Normality.
Homoscalestisity (homogeneity) of error
variance.
Additive.
Randomness.

11. Statistical test that is used to determine whether or
not the variances between several groups are equal
This test uses the following null and
alternative hypotheses:
H0: The variance among each group is equal.
HA: At least one group has a variance that is not
equal to the rest.

12. B = (n-k)lns2 – Σ(nj-1)lnsj
2 / c
where:
n: The total number of observations across all groups
k: The total number of groups
ln: This stands for “natural log”
s2: The pooled variance
nj: The number of observations in group j
sj
2: The variance of group j
c = 1 + (1/3(k-1))*(Σ(1/(nj-1)) – (1/(n-k))
This test statistic follows a Chi-Square distribution
with k-1 degrees of freedom. That is, B ~ X2(k-1).

13. What can We do where there is significant
heterogeneity of error variances?”
Transform the raw data:
Often  ~ ; cw Binomial Distribution
where  = np and  = npq Transform to square roots
or
Homogeneity of error variance can always be achieved
by transforming each site’s data to the
Standardized Normal Distribution
[xi-]/

14. Analyses of Variance

15. Yijk =  + gi + ej + geij + Eijk
i gi = j ej = ij geij
Environments and Replicate blocks are usually
considered to be Random effects. Genotypes are usually
considered to be Fixed effects.

16. Source d.f. EMSq
Sites (s) s-1 2
e + g2
rws + rg2
s
Rep w Sites (r) s(1-r) 2
e + g2
rws
Genotypes (g) g-1 2
e + r2
gs+ rs2
g
Geno x Site (g-1)(s-1) 2
e + r2
gs
Replicate error s(r-1)(g-1) 2
e

17. Yijkl = +gi+sj+yk+gsij+gyik+syjk+gsyijk+Eijkl
igi=jsj=kyk= 0
ijgsij=ikgyik=jksyij = 0
ijkgsyijk = 0

18. Source d.f. EMSq
Years (y) y-1 2
e+gy2
rwswy+rg2
swy+rgs2
y
Sites w Years (s) y(s-1) 2
e + g2
rwswy + rg2
swy
Rep w Sites w year (r) ys(1-r) 2
e + g2
rwswy
Genotypes (g) g-1 2
e + r2
gswy + rs2
gy + rl2
g
Geno x year (y-1)(g-1) 2
e + r2
gswy + rs2
gy
Geno x Site w Year y(g-1)(s-1) 2
e + r2
gswy
Replicate error ys(r-1)(g-1) 2
e

19. STABILITY ANALYSIS
• The term stability refers to the ability
of the genotypes to be consistent,
both with high or low yield levels in
various environments over time
• Static mean of stability- Performance
of a genotype does not change under
different environmental conditions
• Dynamic mean of stability- Response
to environment is parallel to mean
response of all genotypes in the trial
• A genotype is consider to be stable if it
has a low contribution to the G × E
interaction

20. • It consists of following steps:
• Location/environment wise analysis of variance
•Pooled analysis of variance for all the
locations/environments
• If G × E interaction is found significant, stability
analysis can be carried out using one of the four
methods:
1. Finlay and Wilkinson model (1963)
2. Eberhat and Rusell model (1966)
3. Perkins and Jinks model (1968)
4. Freeman and Perkins model (1971)

21. 1. FINLAY AND WILKINSON MODEL (1963)
• First systematic approach to the analysis of phenotypic stability of cultivars or
genotypes
• Used two parameters
– Mean performance over environments
– Regression performance in different environments
Genotype regression coefficients plotted
against genotype performance
In deciding about the worth of a genotype, its
mean performance must be considered alongwith
its phenotypic stability.
Mean- high Most widely adapted
Regression-1
Mean- high Better in high yielding env.
Regression>1
Mean- average Better in low yielding env.
Regression<1
Mean- low Poorly adapted
Regression>1

22. Merits and Demerits of model
• Merits
– Analysis of model is simple
– 2 parameters - mean yield over locations and
regression coefficient are used to asses the phenotypic
stability
• Demerits
– The deviations from the regression line are not
estimated which are important for the stability analysis
– Greater emphasis is given on mean performance over
environments than regression coefficients

23. 2. EBERHAT AND RUSELL MODEL (1966)
• Most popular and useful model
• Model consists of three parameters
– Mean yield over locations or seasons
– Regression coefficient
– Deviation from regression
• G × E interaction of each variety is further partitioned
into 2 parts
– Slope of regression line
– Deviation from regression line
• Total variance is first divided into 2 components
– Genotypes (G)
– Environment (E) plus interaction (E + G × E)
• Second component is further divided in to 3 components
– Environment linear
– G × E linear
– Pooled deviation
• Sum of squares due to pooled deviations are further
divided into sum of squares due to individual genotypes
Source of variation d.f.
Genotypes (G) g-1
Environment (E) + G×E g(e-1)
Environment (linear) 1
G×E (linear) g-1
Pooled deviations
Genotype 1
Genotype 2
:
Genotype g
g(e-2)
e-2
e-2
:
e-2
Pooled error ge(r-1)

24. Merits and Demerits of model
• Demerits
– Combined estimation of sum of squares of environment and interactions
is not proper
– Estimation of mean performance and environmental index is not
independent
• Merits
– 3 parameters - mean yield over
environments and regression coefficient
and deviation from regression line
– Provides more reliable information about
varietal stability than Finlay and
Wilkinson model
– Analysis of model is also simple
– Model is less expensive as it requires less
area for experimentation

25. 3. PERKINS AND JINKS MODEL (1968)
• Total variance is divided into 3
components
– Genotypes
– Environments
– Genotypes × environment
• G × E variance is sub divided into
• Heterogeneity due to regression
• Sum of square due to remainder
• Less expensive than Freeman and
Perkins
• Requires less area for experimentation
• Analysis is more difficult than Eberhart
and Rusell model
• Does not provide independent
estimation of mean performance and
environmental index
Source of variation d.f.
Genotype (G) g-1
Environment (joint
regression)
e-1
Genotype*Environment (g-1)(e-1)
Heterogeneity among
regressions
g-1
Remainder (g-1)(e-2)
Error ge(r-1)

26. 4. FREEMAN AND PERKINS MODEL (1971)
• Better method for partitioning of sum of squares in
stability analysis
• Independent estimation of mean performance and
environmental index
• Total variance is divided into three components
– Genotypes
– Environments
– Interactions (G*E)
• The environmental sum of squares is subdivided into
2 components
– Combined regression
– Residual 1
• The interaction variance is also subdivided into 2
parts
– Heterogeneity of regression
– Residual 2
• Analysis of this model is more difficult as compared
to other models
• Model is more expensive as it requires more area for
experimentation
Source of variation d.f.
Genotype (G) g-1
Environment (E) e-1
Combined regression 1
Residual (1) e-2
Interaction (G*E) (g-1)(e-1)
Heterogeneity among
regressions
g-1
Residual (2) (g-1)(e-2)
Error (between
replications)
ge(r-1)

27. ADVANTAGES OF STABILITY ANALYSIS
• Helps in understanding the adaptability of crop varieties over a wide range
of environmental conditions and in the identification of adaptable
genotypes
• The use of adaptable genotypes for general cultivation over wide range of
environmental conditions helps in achieving stabilization in crop
production over locations and years
• Use of stable genotypes in the hybridization programme will lead to
development of phenotypically stable high potential cultivars of crops
species
• Stability analysis is the an important tool for plant breeders in predicting
response of various genotypes over changing environments

28. Thank You