1. The document discusses various concepts related to genotype by environment interaction (GxE) in plant breeding including stability analysis models. It introduces key terms like genotype, environment, phenotype, and patterns of GxE interaction. 2. Several stability analysis models are described including conventional models like ANOVA, regression models like Eberhart and Russell, and multiplicative models like AMMI and GGE biplot. Case studies demonstrate applications of models like AMMI biplots and GGE biplots. 3. The value of stability analysis is emphasized for identifying stable high-yielding genotypes, subdividing geographic regions, understanding actual genotypic performance, and deciding breeding strategies. Software tools can assist with stability analysis.

1. 1
WELCOME

2. 2
Ashwini Gopal Lamani
PALM6001
Sr. M.Sc.(Agri.)
Department of Genetics and
Plant Breeding
SEMINAR - I
UNIVERSITY OF AGRICULTURAL SCIENCES, BANGALORE
COLLEGE OF AGRICULTURE, V C FARM, MANDYA
‘Development of Concept of Stability
Analysis in Plant Breeding’

3. Flow of seminar
3
Introduction
G×E
Stability models
Case studies
Softwares in stability analysis
Conclusion

4. Genotype
Environment
GXE interaction
Phenotype
4

5. What is GXE interaction??
‘The differential response of genotypes from one
environment to another is known as Genotype by
Environment interaction’
5
Kang and Gorman, (1989)

6. Patterns of the genotype behavior in different environments outlining
the two fundamental types of interaction, considering only a simple
case of two genotypes and two environments.
Ferreira et al., (2006) 6

7. Environmental
variation
Predictable
Eg. Features of
climate, soil features,
day length, planting
date etc..
Unpredictable
Eg. Fluctuation in
weather, such as
amount and
distribution of RF
Allard and Bradshaw (1964) 7

8. Significance of Genotype and
Environment Interaction
Identify differences in environmental variation.
Subdivision of geographic region into relatively
homogeneous sub-regions
Actual genotypic performance
Deciding breeding strategies
8

9. Phenotypic stability
 Well buffered variety.
Two concepts: a. Biological concept
b. Agronomic concept
Population buffering: heterogeneous
population.
Individual buffering: pure line varieties or
single crosses.
Allard and Bradshaw (1964)

10. Detection of G×E interaction
10
MLT- with replicated trials, several
locations, several years
Test for homogeneity of experimental
error by Bartlett’s test
Pooled analysis
Find genotype and G×E significance
from pooled ANOVA
Stability analysis using statistical
models

11. Stability Models
Conventional Models
Regression Models
Multiplicative Models
Use of external variables in models
Mixed models
Non-parametric approach
11
Elias et al., (2016)

12. 1. Conventional Model
12
A in E1 A in E2
Yield
1. Stability Factor Model-Lewis (1954)
S.F= XHE
XLE
SF=1, Stable
genotype

13. Conti.. 1. Conventional Model
2. Basic ANOVA model
13Elias et al., (2016)
Where,
𝛾𝑖𝑗𝑘 =yield response variable
µ=overall mean
αi= genotypic effect
βj= jth environmental effect
(αβ)ij= interaction effect
εijk= residual error

14. ANOVA for g genotypes evaluated at e
environments in trials having r replications
14
Source of
variance
df SS MSS F value
Genotypes
(G)
g -1 GSS GMS
Environment
s(E)
e - 1 EnSS EnMS
Replication
within
environments
e(r -1) RSS RMS
G x E (g-1) (e -1) GESS GEMS
Error e (g -1)(r-1) ESS EMS

15. Basic ANOVA model
Advantages
i. Quantifies magnitude of
classifiable main effects and
interactions
ii. Presence of G×E
iii. Identifying environments as
TPE when
 no significant G×E is
present and
 similarity in the
magnitude of G×E
Disadvantages
i. Does not describe the
pattern of G and E
response
ii. Requires replications
within environments.
iii. Quantifies G×E in single
dimension
iv. Assumes homogeneity of
experimental errors.
Elias et al., (2016)

16. 2. Regression Models
16

17. 2. Regression Models
1. Finley and Wilkinson model (1963)
2. Eberhart and Russel model (1966)
3. Perkins and Jinks model (1968)
4. Freeman and Perkins model (1971)
17

18. 1. Finley and Wilkinson model (1963)
Genotypic mean (gi).
Regression coefficient (bi) as phenotypic
stability.
18

19. 19
A generalized interpretation of genotypic pattern obtained when, genotypic
regression co-efficients are plotted against genotypic mean

20. 2. Eberhart and Russel model (1966)
Three parameters of stability:
(i) Genotype mean (gi).
(ii) Regression value bi (predictable linear response)
(iii) Deviation from linearity (unpredictable non
linear response)
20
sdi
2

21. 2. Eberhart and Russel model (1966)
General features
MSS due to G and
GXE interaction is
partitioned into
three components
E(linear)
GXE(linear)
Pooled deviation
Stable with:
High mean yield(X)
bi=1
 approaching
zero
21

22. Format of ANOVA (Eberhart and Russel Model,1966)
SV df SS MSS
Genotypes (v-1)
Env.+GE v(n-1)
Env.(linear) 1
GE(linear) v-1
Pooled deviations v(n-1)
G1 n-2
G2 n-2
.
Gv n-2
Pooled error n(r-1)(v-1)
Total nv-1 22

23. Perkins and Jinks model (1968)
• Three stability parameters viz.,
– mean (Yi ),
– regression coefficient (bi) and
– deviation from regression ( sdi )
• Regression of G x E interaction on
environmental index was obtained rather than
regression on mean performance.
23
2

24. Freeman and Perkins model (1971)
• Joint regression analysis
• Three stability parameters viz.,
– mean (Yi),
– regression coefficient (bi)
– mean square deviation from regression [S2di]
• Environment is completely independent.
24

25. Advantages of Regression Models.
• Response pattern over environment and stability of
genotype.
• Environment quality in single dimension.
.
• GEI signal retained as much as possible.
25Malosetti et al., (2013)

26. Disadvantages of Regression Models.
Fails to explain large portion of G×E
Assumes linear relationship between G×E and
environment means
Model does not fit if extreme environments are
involved.
Less informative where G×E is too complex
Assumes homogeneity of environment errors
Environment characters is based on single
dimension
26
Malosetti et al., (2013)

27. Multiplicative Models
27

28. Multiplicative Models
 Explains complex G×E
Assumes fixed effect
Eliminates much of noise in data.
Explains pattern of GxE interactions.
28Elias et al., (2016)

29. Multiplicative Models
29
1. AMMI model 2. GGE biplot
Elias et al., (2016)

30. Multiplicative Models
30
3. Shifted Multiplicative Model
4. Genotype Regression Model
5. Completely Multiplicative Model
Elias et al., (2016)

31. Principal component analysis
31

32. AMMI Model
Additive Main Effect and Multiplicative
Interaction.
Partitions variations into:
 Additive effect (G,E)by ANOVA
 Multiplicative effect(GXE) by PCA
Use biplots
32Gauch, H. G., (2013)

33. AMMI model
33
Yge= yield of the genotype (g) in the environment (e);
μ= grand mean
αg= genotype mean deviation
βe= environment mean deviation;
N = No. of IPCAs (Interaction Principal Component Axis)
retained in the model
λn= singular value for IPCA axis n
ϒgn= genotype eigenvector values for IPCA axis n
δen= environment eigenvector values for IPCA axis n
ρge= the residual.
Zobel et al., (1998)

34. Analysis of variance of the AMMI model
34
Ferreira et al., (2006)

35. 35
Illustration of a biplot graph with PC1 vs mean yield, presenting the
main types of genotypes and patterns of stability and adaptation.
Ferreira et al., (2006)

36. 36
Zobel et al., (1998)
Biplot of the AMMI model for a New York soybean yield trial with 7 genotypes
grown in 35 environments. Genotype and environment codes are given in materials
and methods. The grand mean is represented by a ‘’ plus ‘’

37. 37
Biplot from the AMMI model used to describe GEI in the maize example data. Gray
circles represent genotypes, and filled triangles environments , with triangles pointing
in the direction of increasing GEI (at origin GEI = 0). The projection of two genotypes
(G041andG091)on the NS92a axis is shown by a dashed line.
Malosetti et al., (2013)

38. Evaluation of Genotype × Environment
Interaction in Rice
Based on AMMI Model in Iran
38
Sharifi et al., 2017

39. 39
AMMI 1 biplot for nine rice genotypes and nine rice environment

40. 40

41. GGE Biplot
41

42. GGE Biplot
ANOVA – main effects(E)
PCA- interaction effects(G+GE)
Addresses crossover GEI more effectively
Addresses three important issues:
Mega-environment evaluation
Genotype evaluation
Test environment evaluation
42Malosetti et al., (2013)

43. Mega-environment evaluation
43
The “which-won-where” view of the GGE biplot based on the G × E
Yan et al., (2007)

44. Genotype evaluation
44
Yan et al.,(2007)

45. TEST ENVIRONMENT EVALUATION
45
Discriminating power and representativeness of the test environment
Yan et al.,(2007)

46. Comparing Two Statistical Models for Studying
Genotype x Environment Interaction and Stability
Analysis in Flax
46Mohsen, A. A. and Amein, M. M. (2016)

47. Table1. The environments used in this study
Code Growing
season
N
rate(k
g/fed)
Description
E1 2011-12 20 E1 is 1st Fertilizer rate(20kgN per fed) in the first
season
E2 2011-12 35 E2 is 2nd fertilizer rate(35kg/fed) in the first season
E3 2011-12 50 E3 is the 3rd fertilizer rate (50kg/fed) in the first
season
E4 2012-13 20 E4 is the 4th fertilizer rate(20kg/fed) in the second
season
E5 2012-13 35 E5 is the 5th fertilizer rate( 35 kg/fed) in the second
season
E6 2012-13 50 E6 is the 1st fertilizer rate (50kg/fed) in the second
season
47
Mohsen and Amein (2016)

48. 48
Estimates of stability and adaptability parameters of straw yield
(ton/fed) for 7 flax cultivars across 6 environments.
Mohsen and Amein (2016)

49. 49

50. 50
Table 6. The estimates of stability and adaptability parameters of seed
yield(ton/fed) for 7 flax cultivars across 6 environments.
Mohsen and Amein (2016)

51. 51
Fig 2. The relationship between the regression coefficients and seed
yield(ton/fed) for 7 flax cultivars. The horizontal solid line represents the mean
coefficient of regression and the vertical solid line denotes the mean seed yield.

52. 52

53. 53
Fig. 5. Ranking of cultivars based on mean and stability GGE biplot of for 7
cultivars under six environments.

54. Shifted Multiplicative Model
• Developed by Seyedsadr and Cornelius(1992)
• Main effects not fitted into ANOVA.
• PCA is performed on the combined effects
rather than just interaction.
54
Elias et al., (2016)

55. Shifted Multiplicative Model
• Shift parameter ϴ, to minimize the residual
error
• Used to identify environment in which
genotypic effects are separable from
environmental effects
55
Elias et al., (2016)

56. Genotype Regression Model(GREG)
• Each genotype as multiple regression on the
interaction.
• Main effects from the G effect, multiplicative
term for E+GE.
56
Elias et al., (2016)

57. Completely Multiplicative
Model(COMM))
• Only multiplicative term: i.e G+E+GE
• Effective when the grand mean of the real
data is close to zero
57
Elias et al., (2016)

58. Use of external variables in Models
1. Factorial Regression Model:
 Estimate genotypic sensitivity to environmental
covariates.
 Not effective for multi-colinearity of large external
variable.
2. Partial Least Square Model:
 no limit to number of external variables used
58
Elias et al., (2016)

59. Use of Mixed Effects in Models
Random effects
Effective for unbalanced data
No restriction for replications within
environment
Considers heterogeneous variance
Eg: BLUPs, FAMM, BLUEs
59
Elias et al., (2016)

60. To know QTL×E
1. Single environment analysis.
2. Genomic best linear unbiased
prediction(GBLUP) model.
3. GBLUP model with deviation
coefficient for each environment
assumed.
4. M×E GBLUP
60
Elias et al., (2016)

61. Non-parametric methods
Based on ranks of genotypes across
environment.
No assumptions
Easy for interpretation
Stable genotype: having same rank across
environments.
Eg: Shukla(1972), Nassar and Huhn(1987),
Kang(1988), Fox et al.,1990, Thennarasu(1995)
61Elias et al., (2016)

62. Softwares used in stability analysis
 Windostat
 Genstat
 Genes software
 MATLAB
 SAS program
 R program
62

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64. 64
CONCLUSION

65. 65