The document discusses various statistical models for analyzing genotype by environment interactions (GEI) in plant breeding. It provides an overview of early approaches like analysis of variance (ANOVA) and linear regression models. It then focuses on additive main effects and multiplicative interaction (AMMI) models and GGE biplots, which help partition GEI into meaningful components to better identify stable, high-yielding genotypes adapted to different environments or "mega-environments". The document aims to compare trends in biometrical models for GEI analysis and help breeders select appropriate statistical tools to exploit interactions.

1. Trends and Comparison of
Biometrical Model for The
Analysis Genotypes by
Environment Interaction
By
Fikru Mekonnen
Wollo University
E-mail: tiewoast@gmail.com

2. Introduction
• to control environmental
noise and
• to reduce error variance and
• to increase response to
selection
• G x E I is major problems for
the breeders. in developing
countries, because of
complex problem
Most
breeders
commonly
do their
selection
in
research
stations

3. Assumption and effect of G X E I
breeder recommendation of G across Es.
reduces the association between phenotypic and
genotypic values
Some Gs are more sensitive than others to
environmental differences.
the environmental variance are the source of error
that reduces precision

4. Impact, Assumption and Gap of GXE
 the aim of the experimenters or the
breeder is, to reduce this variation
 But GEI
limits yield estimates because of changes
in ranks of genotypes,
and obscures, the identification of superior
and stable genotypes.

5. Why we need it?
 Measuring GXE is important
to determine an optimum breeding strategy
releasing Gs with adequate adaptation to target Es
developing mega-environments.
to determine the basis for explaining different
patterns of response of different Gs to the varying
Es
understanding of the causes of GEI can be used to
establish breeding objective,

6. Why we need it?
 the environmental factor that can be
manipulated to facilitate selection
 To allocate target G identification and
analysis of mega – environment is important.
 identify traits that contribute to better G
performances and Es that facilitate G
evaluation

7. How
Success is selecting appropriate
statistical tools to exploit interaction
This review paper will answer and
largely focused on the trend and
comparison of the biometrical model
development in the analysis of GEI
Emphasis will be on the latest
models

8. analysis

9. G by E I have been studied by several
statistical models.
such as
ANOVA,
Linear
regression
on the
environmen
tal model
Multivariate
analysis
such as
principal
component
analysis
AMMI
models
GGE
biplot

10. Review Objective
The Review will give a clue
that, there are too many
options to consider for the
analysis of G by E I to
identify mega-environment
and target genotype.

11. 2. Adaptation and Stability
–Adaptation
 According to Allard (1988), adaptedness is the
degree to which an organism is able to live
and reproduce in a given set of environments.
 A G of cultivated plants will be consider
adapted to a given type of conditions, when it
is able to give an economic production, and
not necessarily only survive in that set of
conditions.

12.  This recognizes that there could be
– adaptation economic productivity,
– economic productivity adaptation
 An E may include sites, year, management
practices
 The controversial issues improvement for
specific agro-ecological V wide E.

13. Concept of Stability
 a much higher priority should be given to improve
yield stability
 there is less agreement on the definition of ‘stability’
and the methods to measure and to improve yield
stability.
 Thus, a number of methods to assess stability have
been developed, each with its own strengths and
weakness.

14. According to (Leon 1985):
the static concept of
stability: unchanged
performance= variance
among E is zero
the dynamic concept of
stability: a predictable
response to the E, i.e
has no deviation from
this response to E.

15. Backer (1981) two types of genetic stability.
 1. Biological Stability:
 2. Agronomic stability:
 The stable variety performs relatively better
under adverse condition and not so well in
favorable E,
 stable variety in most case they have a value
of regression coefficient of βi one and S 2
d
equal to zero

16. 3. Genotype and Environment
3.1. Heredity and Environment
 Heredity the transmission of traits from parents to offspring
through genes.
 Genotype an individual’s genetic makeup
 Phenotype refers to physical appearance an individual,
 Environment the sum total of circumstances surrounding or
affecting an organism or a group of organisms.
 Qualitative traits, a highly reliable indicator/predictor of
genotype.
 Because of the considerable influence of E, quantitative traits
generally have relatively low heritability.
 As environmental influence increases, the reliability of
phenotype as a predictor of genotype decreases.

17. Genotype by Environment interaction
 The observed phenotype is a function of G,
E, and GEI.
 GEI is said to occur when different cultivars
or genotypes respond differently to diverse Es.
 GEI is important when different Gs are
superior in different E

18. Causes of Genotype by Environment
Interaction
 To make accurate predictions of Gs the
Es causes has to be known.
 aids in interpreting and exploiting GEI.

19. The Biological Complexity of G x E I
 Differential response of G from one E to
another is called G x E interaction.
 The presence of high GEI complicates
breeding works,
 These GE I commonly influence yield
variation that cannot be explained by the G
main effect and E main effect.

20. emphasizes the interaction of genes and
environment.

21. Figure 1-3 A model of phenotypic determination that shows how genes,
environment, and developmental noise interact to produce a phenotype.

22. The different kinds of GEI
no interaction
Non-crossover
type of interaction
crossover interaction Gic
modification by E in
opposite direction but interGic
difference remains the same

23. Statistical Concept of G x E I
 two conceptual approaches for studying GEI.
 The one is empirical and statistical that
involves relating observed genotypic
responses usually in terms of yield, to sample
of E conditions.
 The second is analytical approaches that
define E and phenotypes in terms of biotic
and abiotic factors.

24. G x E I and Implication for Breeding Strategies
 Developed countries versus under developed
country paradox
 breeding for wide versus specific E s is a very
controversial topic
 Three obvious ways of dealing with GEI in a
breeding program are:
– ignore it, (2) avoid it, or (3) exploit it.
 Most breeders agree that GEI should not be ignored
when it is significant and of crossover rank change

25. In developed nation
in research station with high input
in order to control
environmental noise
to make the error variance
small,
response to selection high.
very efficient in Selection
Therefore, GEI is unlikely to
pose a major problem.

26. But in case of developing countries,
complex
problems.
Resource-poor
farmers have
adopted
strategy based
on both
interspecific
and
intraspecific
diversity to
overcome the
risk
if a breeder
wants to
improve
performance in
environment A,
he should
select in
environment A.
Plant breeding
strategies
different in stress
and non-stress
environment
because of the
intensity of cross-
over interaction

27.  However, breeding for more specific Es is a very
controversial topic, especially in reference to stress
environments.
– heterozygous and heterogeneous population
offers the best opportunity to produce varieties which
show small GEI
 because Eal effects are much larger than
genetic effects and heritability and response
to selection are expected to be lower than in
favorable E
 the consequence of GE I on breeding
philosophies depends on the environmental
range considered.

28. 4.Biometrical Models for Analysis of G E I
 Various methods of statistical analysis of (GEI)
 All are attempted "data = pattern + noise"
 Two main approaches
– one is purely statistical origin,
– The other approach is based on the fitting model
A + D + E gene action to genetic and interaction
components
 Conclusion emerge from the analysis of the
data is the same for both kind of analysis,
 the magnitudes of GEI are a linear function of
the environmental effects.

29. 4.1 Early Approaches to Study of G X EI,
Including the Variance Components.
 the analysis of variance, pioneers, being
Fisher and Mackenzie
 variance components could be used to
separate out the effects of G, E and their I
 The mathematical model is:
– Yijk = μ +di + εj + gij +eijk (1)

30. Limitation
Simple partition of statistical
analysis captures irrelevant
features of variation of the data
which greatly hinders effective
mega-environment identification
ANOVA give overall picture of the
relative magnitude of the G, E and
G by E variance terms.
E is always the most important
source of yield variation, which is
irrelevant to G evaluation and mega-
environment investigation

31. Limitation
test of the
significance of the
GEI may declare it
non-significant
when in reality, the
interaction is
agronomically
important.
This problem
arises because
the interaction
contains a
large number of
df

32. 4.2. Linear Regression and Related Stability Parameter
 4.2.1. Linear Regression
 the most widely used and abused statistical
technique in plant breeding
 widely used for selecting high-yielding and
stable G targeted to several Es.
 Model is, gij = βi εj + δij, (2)
 The biometrical genetic model developed
 Yijk = μ + di + (1+ βi ) εj + δij, + eijk (3)

33. Linear Regression
 G with a low value of βi are to be regarded as stable
while those with a high value are unstable.
 The G x E term from analysis of variance is
partitioned between heterogeneity of regression and
deviation from regression
 G with slop near one and a high mean yield were
regarded as being well adapted to all E
 As mean yield decreased, Gs with high or low slopes
were regarded as being specifically adapted to
favorable or unfavorable Es, respectively.

34. 4.2.2. Stability Parameter for Comparing
Varieties
 method has to be developed to select stable
Gs that interact less with the Es in which they
have to be grown.
 The model is: Yij = μ +βi I j + δij (4)
 These model have two parameters,
– the first is the stability parameter of the regression
coefficient
 βi = YijIj / Ii
2 (5)
– The second stability parameter
 Sdi
2 = [δij /(n-2)]- Se
2/r (6)

35. 4.2.3 Multiple Regression Method for
Studying Genotype–Environment Interaction
 multi factorial experiment and growth
analysis, to analyze GEI, by regression on E
variables rather than to use regression on the
environmental mean.
 The model is then,
 Yij = μ + pi + ai1xj1 + ai2xj2 + - - - + aipxjp + eij (7)

36. Factorial Regression and Partial Least
Square Regression
 incorporate external environmental and/or
cultivar variables for studying and
interpreting GEI.
 As in factorial regression, partial least square
regression describes GEI in terms of
differential sensitivity of cultivar to
environmental variables

37. 4.3. Non Parametric Statistics
 This model largely concentrates on the
analysis of ranking based on the method like
stratified ranking
 any genotypes ranks in the top, middle or
bottom third of entries.
 A genotype usually found in the top third of
entries across sites can be considered
relatively well adapted.
 The advantage of non-parametric technique
includes:
– freedom from assumption

38. 4.4. Multivariate Analysis
Multivariate technique may be applied to
describe the relationship among sites and
among genotypes
pattern analysis, was coined
Classificatory technique such as
‘clustering’, is another multivariate
analysis, assumes discontinuities
within data, while PCA and other
higher methods of ordination
assume a continuous distribution.

39.  Genotypic grouping doesn’t indicate
stability as such
 When we consider patterns of
relationships among sites for breeding
purposes
site main effect are removed so that grouping is
determined more by G x E effects than by
production level

40. 5. Additive Main Effect and Multiplicative
Interaction /AMMI/
The ANOVA model
an additive model
that identifies the
interaction as
residual source of
variation, but
doesn’t sub-
partition the
interaction
statistical
analysis
targeting G E I
has been
largely ignored
in genotype
evaluation
therefore
interactions are
unable to be
exploited fully
in crop
breeding
programs

41.  GE interaction are problematic because
there is lack of effective statistical tools
available to adequately summarize complex
data structure in multi-environmental yield
trial
 The remaining task, therefore, is that of
finding an effective partitioning of the
interaction.

42. Among the different method
of partitioning interaction,
PCA of the interaction is a
method of choice is AMMI.
applying PCA to the residual from the additive
ANOVA model, that is, to the interaction. This is
the AMMI model
The model was developed called biplot
analysis, used before the introduction of the
term AMMI analysis.

43. The effectiveness of AMMI analysis lies
because it captures a large portion of the G by E
sum of square
it cleanly separates main and interaction
effects
it p Provides agricultural researcher with
different kind of opportunities
provides agronomically meaningful interpretation of
the data
performing mega-environment analysis
simplifying cultivar recommendation

44. AMMI Analysis and its Component
 The AMMI model first applies (ANOVA)
 then applies the multiplicative principle
component analysis(PCA) model to the
residual i.e the interaction
 The AMMI model
 Yik = μ+ α g + β e + ∑N
n=1 λnζ gn ήen + εij

45. AMMI HOW THEY MAKE IT ?
The first is the main
effect in the additive
model grand
mean (μ),
genotype
means,
environment
means are
analyzed by
the ordinary
ANOVA.
The second,
component the
non-additive
interaction in
the
multiplicative
part of the
model, is
analyzed by
PCA.

46. GGE BIPLOT

47. Theory of Biplot
• Ranking of the rows in each column
• Ranking of the columns in each row
• Comparison of two rows for all
columns
• Comparison of two columns for all
rows
• Identification of the largest value (row)
within each column
• Identification of the largest value
(column) within each row
• Visualization of the interrelationships
among rows
• Visualization of the interrelationships
among columns
a biplot
allows
visualization
of the
product
matrix

49. METHODS OF SINGULAR VALUE
PARTITIONING
1. GENOTYPE-FOCUSED SCALING
 PC1 and PC2 same unit
 G and E different PC unit
2. ENVIRONMENT-FOCUSED SCALING
3. SYMMETRIC SCALING
 Same G and E PC unit
4. EQUAL-SPACE SCALING
5. Regression Equal-space Scaling

50. Visual comparison of two rows or genotypes (a) and of two
columns or environments (b) based
on the biplot.

51. Visual identification of columns with the largest values for the rows. The
column with the largest value for row G2 is E2, the column with the largest
value for row G1 is E1, and the column with the largest values for rows G3
and G4 is E3.

52. Visual identification of rows with the largest values for the columns. The
row with the largest value for column E2 is G2, the row with the largest value
for column E1 is G1, and row with the largest value for column E3 is G4. Row
G3 does not have the largest values for any of the columns.

53. PERFORMANCE OF DIFFERENT CULTIVARS IN A GIVEN
ENVIRONMENT

54. Comparison of the performance of cultivar fun in
different environments

55. Comparison of two cultivars, zav and fun, based on the GGE biplot. The two cultivars
to be compared are connected with a straight line, and a perpendicular line passing
through the biplot origin separates environments in which zav performed better from
those in which fun performed better.

56. Environment-centered yield of cultivars fun (x-axis) and zav (y-axis) in various
environments. The guidelines indicate zero or average yield in each environment. The
equality line represents environments where the two cultivars yielded the same.

57. “WHICH-WON-WHERE” PATTERN OF on MET
DATASET

58. Polygon view of the GGE biplot, showing which cultivar
yielded best in which environments

59. Polygon view of the GGE biplot after the signs of the E are reversed,
showing which cultivar yielded lowest in which E.

60. showing the mean yield and stability of G

61. Comparison of all genotypes with the ideal cultivar. having the highest yield
in all environments. That is, it has the highest mean yield and is absolutely
stable.

62. Comparison of all environments with the ideal E

63. Visual comparison of two cultivars: 2375 and Alsen, for all traits.

64. Vector view of the genotype-by-trait biplot, showing the interrelationships among traits.
The cosine of the angle between the vectors of two traits approximates the correlation
coefficients between the traits.

65. FIGURE 7.7 Vector view of the genotype by trait biplot, showing the
interrelationships among grain yield, flour extraction rate, and loaf volume for 21
HRSW cultivars. The three traits are negatively Correlated with one another,
revealing a major challenge for HRSW breeding.

66. FIGURE 7.8 Cultivar ranking based on grain yield.

67. GGE biplot (con…)
 the GGE biplot graphically display G plus
GEI of a MET data
– visual cultivar evaluation and
– mega-environment identification.
– yearly winning genotypes and
– their winning niches.
 In addition selecting superior cultivar provided that
the genetic PC1 score, have a near-perfect correlation
with the genotype main effects,
ideal cultivars should have a large PC1 scores high
yielding ability a small PC2 scores that is high
stability.

68. Flow chart indicating strategies for studying the causes of
GE interaction

69. COMPARISON WITH THE AMMI BIPLOT
 both the mean yield and interaction scores of
the G and of the Es in a single plot.
 The unit of the main effects is the original
unit of the trait, whereas the unit of the IPC1
scores is square root of the original unit.
Consequently, the shape of such a biplot is
highly subjective
 misleading regarding the “which-won-where”
issue
 Most researchers agree that the GGE biplot is
the better choice.

70. Other application
 Cultivar Evaluation Based on Multiple
Traits
 Inter character correlation
 QTL Identification Using GGE biplot
grouping of linked markers
gene mapping using biplot
interconnectedness among traits and
pleiotropic effects of a given locus

71. Advantage
of GGE
biplot over
the other
model can
be
generalized
by
“one picture is
worth a
thousand
words”.

72. Summary
 the efficiency of adaptation through plant
breeding, two strategies has to be considered.
 The first to improve crop production with a
specific agro-ecological environment;
 the second to improve crop production across
macro-environments.
 Adaptations affected by
– the environment: adaptedness have been difficult
to quantify.
– due to GEI.

73. Summary (con...)
 yield stability is largely affected by GEI depend on
the particular environmental condition
 A number of methods and concepts have been developed
to assess and overcome the problem of stability, each with
its own strength and weakness.
 GEI exists whenever the differences between a
Performance of G change with changes in the E.
 GE I commonly influence yield variation that cannot
be explained by the G main effect and E main effect.

74. Summary (con...)
 To optimize growers yield despite GEI winning
genotype has to be identify
 To do this job different biometrical model are
developed.
 All statistical models are attempted to get
– pattern from the MET data
– while eliminating the maximum noise.

75.  The conventional analysis of variance gives an
overall picture of the relative magnitude of
the G , L, GL and GxLxY variance terms.
 E is always the most important source of yield
variation, which is irrelevant to G evaluation and
mega-environment investigation.
 This model is less powerful in partitioning
the interaction components.

76. Cont…
 AMMI statistics presented in biplot can be
used to provide insightful interpretation of
data from large, complex experiments.
 AMMI analysis has been shown to be more
effective than the conventional two-way fixed
effect model with interaction

77. Cont…
 Finally more advanced model GGE biplot has
many applications.
 It has wide application
1. the ranking the environments
2. the ranking of genotype
3. comparing performance of any pair cultivar in
different environment.
4. to identify the best genotype in each
environment
5. grouping the environments based on the best
genotype.

78. 6. to analyze a desire genotype by trait biplot;
7. to study of the genotype by trait data and useful to
visualize genotype trait relationship
Generally maximum genetic gains will result from
optimum allocation resource between the two
approaches.
Advances in computerization of analysis model
influenced plant breeding results.

79. Finally
 I believe that statistical analysis of
genotypic by environment interaction is
needed, not to replace breeder
impressions, but to complement them.