Variance measures the variability from an average or mean value. Phenotypic variance is partitioned into components attributable to different causes such as genetic variance and environmental variance. Genetic variance has additive and non-additive components. Genotype-environment interactions exist when genotypes perform differently in different environments. Studying genotype-environment interactions helps identify genotypes with general or specific adaptability. The best genotype in one environment may not be the best in another if genotype-environment interactions are present.

1. TOPIC: Variance
GE Interactions
Dr S. Shanaz
Assoc. Prof
Division Of AGB

2. VARIANCE
 Variation: Differences in phenotypic values of quantitative traits
among individuals of a population
 Amount of variation is measured and expressed as variance
Variance measures the variability from an average or mean
 The basic idea in the study of variance is its partitioning into
components attributable to different causes
 For genetic improvement variation is important
 Components into which the phenotypic variance is partitioned are
the same as the components of phenotypic value (P= G+E)
 The relative magnitude of variance components is determined by
the degree of resemblance between relatives.

3. COMPONENTS OF VARIANCE

4. Components of values and
corresponding variance

5. Important difference between components of value and
variance
 In case of phenotypic value, each component can have
positive or negative values on the other hand
phenotypic variance are always positive
INTANGIBLE VARIATION
Amount of non genetic variation whose cause is unknown
and which cannot be eliminated by experimental design

6. Types of Variation
• Phenotypic variation (VP) is the total variation in a
trait (VE + VG)
• Environmental variation. (VE) is the variation
among individuals that is due to their environment
• Genetic variation (VG) is the variation among
individuals that is due to their genes

7. GENOTYPE VARIANCE
• Variances are obtained by squaring the values multiplying
by the frequency of the genotypes concerned and summing
over all the genotypes
• Genotypic variance is due to additive effects of genes and
non-additive effects of genes
• Additive effects are connected with breeding values of the
individual because parents pass their genes to their
offspring not their genotype

8. Total genetic variation (VG) actually
has two components
• Additive Genetic Variation (VA) = Variation
among individuals due to additive effects of
genes
• Dominance Genetic Variation (VD) = Variation
among individuals due to gene interactions such
as dominance
VG = VA + VD

9. Genotype A1 A1 A1 A2 A2 A2
Frequencies p2 2pq q2
Assigned values a d -a
Breeding values 2q a (q-p) a -2p a
Dominance deviation - 2q2 d 2pqd -2p2 d
Variance is obtained by squaring the values then multiplying by the
frequency of the genotype concerned, and summing the three
genotypes
Additive and Dominace variance

10. • The additive variance which is the variance of breeding value is
obtained as follows
VA = (2q a )2p2 + [(q-p) a ] 22pq + (-2p a )q2
VA = 4p2q2 a 2 + (q2-2pq+p2) a 2 2pq + 4p2q2 a 2
VA = 2pq a 2 (2pq + q2 - 2pq +p2 + 2pq)
VA = 2pq a 2 (1)
VA = 2pq [a + d (q-p)] 2
• The variance of dominance deviation is
VD = (-2q2d)2 + (2pqd)2 + (-2p2d)2
VD = (2pqd)2
• Total genetic variance
VG = VA + VD
VG = 2pq [a + d (q-p)]2 + (2pqd)2
VG = 2pq a 2 + (2pqd)2

11. Interaction variance
• When more than one locus is under consideration the
interaction deviations give rise to the interaction
variance.
• Variation of the interaction deviations brought about by
the epistatic interactions at different loci
• Two factor interactions arise from interaction of two loci,
three factor from three loci etc.
• In two factor interaction
VI = VAA + VAD + VDD + etc

12. ENVIRONMENTAL VARIANCE
It includes all variations of non genetic origin ; environmental variance
is a source of error that reduces precision in genetic studies
Environmental variance may be partitioned into
• Special environmental variance (VEs) - within individual variance
General environmental variance (VEg)

13. GENOTYPE – ENVIRONMENT CORRELATION
• The correlation between genotype and environment arises when
better genotypes are given better environment or vice versa.
– Example: Milk yield in dairy cattle.
• Normal practice of dairy husbandry is to feed cows according to their milk yield,
the better genotypes being given more feed. This introduces correlation between
phenotypic value and environmental deviation.
• Since genotypic and phenotypic values are correlated there is a correlation
between genotypic value and environmental deviation.
• When G x E correlation is present, the phenotypic variance is increased by twice
the covariance of genotypic values and environmental deviations
• Thus, VP = VG + VE + 2 covGE
• If VG and VE are estimated, the G x E correlation component 2
covGE can be estimated as 2 covGE = VP - (VG + VE)
• Correlation G and E is normally neglected in experimental
populations, where randomization is important part of an experimental
design.

14. Genotype x Environment
Interactions

15. What are Genotype x
Environment Interactions?
Differential response of genotypes to varying
environmental conditions
 Delight for statisticians who love to investigate
them
 The biggest nightmare for plant breeders (and
some other agricultural researchers) who try to
avoid them like the plague

16. Definition GE interaction
• The G × E interaction is defined as the relative change in
the performance of two or more genotypes in two or more
environments.
 The phenomenon is reflected by the differential expression
of different genotypes over environments;
• Genotype can be breeds, strains or lines & environments
can be nutrition, climate, housing and management etc
• For example the genotype A may be superior to
genotype B in the environment - I, but inferior in
environment – II, when G × E interaction is present.

17. Why to study GE ?
• To investigate relationships between genotypes and
different environmental (and other) changes
• To identify genotypes which perform well over a
wide range of environments  General
adaptability
• To identify genotypes which perform well in
particular environments  Specific adaptability

18. What reflects Genotype x
Environment interactions?

19. • Under certain combination of genotype and environment, the
phenotype may not be equal to the sum of these two variables but
rather be smaller or larger.
P < or > (G + E)
• When interaction is absent the phenotype equals the sum of
genotype and environment.
P = (G + E)
• If the ranking order of two (or more) genotypes varies from
environment to environment in which they are conducted then there
is G × E interaction
• The best genotype in one environment is not the best in another
environment.

20. Why do researchers conduct multiple
experiments?
Effects of factors under study vary from location to
location or from year to year. To obtain an unbias
estimate
Interest in determining the effect of factors over
time
To investigate genotype (or treatment) x
environment interactions.

21. • Each genotype has its specific adaptability for which
the G × E interaction is responsible
• When there is no interaction the best genotype in one
environment will be the best in all
• When the interaction between genotype and environment
is present, the phenotypic value becomes P = G + E + IGE.
The interaction component also makes changes in the sources
of variation for the phenotypic variance and result in
Vp = VG + VE + VGE.
Since the variance occurring in genetically uniform groups is
entirely due to environmental differences among the
individual, the variance due to interaction is included with
environment variance.

22. • Genotype – Environmental (G × E) Interaction are very important
for individuals in population , reared under different conditions,
where environment cannot be controlled
• Experimental evidences shows that the best dairy breed sires in
the temperate countries were not the best in the tropical
countries.
The importance of IGE was also found between countries with a high
level of concentrate feeding versus pasture feeding base.
 The best sires in low environment level were not the best in the
high environment level
The G × E interaction requires additional efforts in selection of
breeding stock with a general adaptability to more than one
environment condition or specifically suitable for desired
environmental condition.
Importance of G×E interaction

23. In practical breeding, an important concept w.r.t G × E interaction is adaptability.
In temperate climate, Zebu cattle (Bos indicus) are inferior to the various European
breeds of cattle (Bos taurus). In tropical climate, Zebus are superior. The ranking of
European breeds and Zebus depend upon the climate in which they are tested
Ranking of bull varies according to the country in which performance of their
daughters is measured.