4 gpb 621 components of variance

COMPONENTS OF VARIANCE,
NATURE OF GENE ACTION & ITS SIGNIFICANCE
Class - 4
Dr. K. SARAVANAN
Professor
Department of Genetics and Plant Breeding
Faculty of Agriculture
Annamalai University
GPB 621 – PRINCIPLES OF QUANTITATIVE GENETICS

.
are three main sources of maintaining genetic
Spontaneous mutations,
Natural out-crossing, and
Recombinations.
There
1.
2.
3.
variability in nature, viz.,
• Besides these natural forces, there are three important measures for
conserving the genetic variability, ie.,
1.
2.
3.
Thus
Maintenance of global gene pool,
Deliberate use of heterogeneous populations. and
Use of multiline varieties.
• insight into the magnitude of genetic variability is of paramount
importance to a plant breeder for starting a judicious breeding programme.
Dr. K. Saravanan, GPB, AU

.
• Primarily, biological variation present in the plant population is of
three types.
• Phenotypic (P) – Phenotypic Variance (VPh)
• Genotypic (G) – Genotypic Variance (VG)
• Environmental (E) – Environmental Variance (VE)
• P = G + E
• VPh = VG + VE

.
PHENOTYPIC VARIATION (VPh)
• It is the total variability which is observable. It includes both
genotypic and environmental variation and hence changes under
different environmental conditions. Such variation is measured in
terms of phenotypic variance.
GENOTYPIC VARIATION (VG)
•
•
The heritable part of the phenotypic variance.
It is the inherent or genetic variability which
environmental conditions.
remains unaltered by
• This type of variability is more useful to a plant breeder for
exploitation in selection or hybridization. Such
in terms of genotypic variance.
variation is measured
• The genotypic variance consists of additive, dominance and epistatic
components.

ENVIRONMEN
. TAL VARIATION
• It refers to non-heritable variation which is entirely due to environmental
effects and varies under different environmental conditions. This
uncontrolled variation is measured in terms of error mean variance. The
variation in true breeding parental line and their F1 is non-heritable.
• Any
and
two
variance observed in a non-segregating population (like inbred parents
F1s) has been shown statistically as due to environment only, hence the
simple methods of estimating environmental variance are as follows
F1 is also included
VP1  VP2

VE or VP1 X VP 2
V V V
2 P1 P2 F1
V 
E
3
where, VE = Environmental variance
VP1
VF1
= Variance of parent 1 , VP2 = Variance of parent 2
= Variance of F1 generation

.
ESTIMATION OF GENOTYPIC VARIANCE (VG) :
•
•
It is the most important part of the variation in a breeding material.
This is the total variation caused by the segregating genotypes in the
population.
• The
due
The
genotypic variance is again sub divided into genetic variance, variance
to dominance deviation and variance due to non-allelic interactions.
• genetic variance (VD) is ascribable entirely to additive gene action, while
the variance due to dominance deviation (VH) is due to interactions between
genes of the same locus (intra allelic interaction).
The variance caused by the interactions between genes at different loci is
•
called as ‘epistasis’ and is due to non allelic interaction (inter allelic
interaction). The epistatic variance is of three types viz., Additive x Additive,
Additive x Dominance and Dominance x Dominance.

.
VG = VD + VH + VI
Where VG = Genotypic Variance
VD = Additive Variance
VH = Dominance Variance (or) non additive variance
VI = Epistatic Variance/ Interaction genetic variance
The epistatic variance is of three types viz.,
Additive x Additive (i) ,
Additive x Dominance (j) and
Dominance x Dominance (l).
Hence, VG = VD + VH + VI (or) VG = VD + VH + Vi +Vj + Vl
VPh
VPh
VPh
=
=
=
VG
VD
VD
+
+
+
VE
VH
VH
+ VI + VE (or)
+ Vi +Vj + Vl + VE

.
Phenotypic Variance
Non Heritable variance
/Environmental Variance
Heritable variance /
Genotypic Variance
Variance due to
epistasis
Variance
dominance
due to
deviation
Genetic variance
Interation between genes of
different loci (Inter allelic /
between loci)
Additive gene effects Interation between genes of
the same locus (Intra allelic /
with in locus)
Fixable
Fully Non Fixable Partly Non Fixable
E

d 
H (or) h
D (or)  
i , j

l
and Dr. K. Saravanan,
GPB, AU
Non Herit

.
Five types of gene action governing a polygenic trait.
1. Additive – D or (d)
2. Dominance – H or (h)
3. Additive x Additive interaction – (i)
4. Additive x Dominance interaction – (j)
5. Dominance x Dominance interaction – (l)

.
ADDITIVE VARIANCE – D
• It refers to that portion of genetic variance which is produced by the
deviations
segregating
due to average effects of the alleles or genes at all
loci. Thus it is the component which arises from
and aa.
intermediate
differences between two homozygotes of a gene, Le., AA
• The additive genes show lack of dominance, ie.,
expression.
The additive genetic variance is associated with homozygosity and,
therefore, it is expected to be maximum in self-pollinating crops and
minimum in cross-pollinating crops.
•
• Additive variance is fixable and, therefore, selection for traits
governed by such variance is very effective.

.
genetic
Additive variance is important for following major reasons
(Arunachalam, 1989).
(a) It is required for estimation of heritability in narrow sense and response
to selection is directly proportionate to narrow sense heritability.
It is a pre-requisite for selection because this is the only variance which
responds to selection.
(b)
(c) Breeding value of an individual is measured directly by the additive gene
effects. The general combining ability (gca) effect of a parent is a
measure of additive gene effects.
(d) In natural plant breeding populations, additive variance is the pre-
dominant one closely followed by dominance variance.

DOMINAN.
CE VARIANCE
• It arises due to the deviation from the additive scheme of gene action
resulting from intra-allelic interaction, ie., interaction between alleles of
the same gene or same locus.
It is due to the deviation of heterozygote (Aa) from the average of two
homozygotes (AA and aa). Such genes show incomplete or over-
dominance.
•
• The dominance variance is associated with heterozygosity and,
therefore, it is expected to
minimum in self-pollinating
be maximum in cross pollinating crops and
species.
• Dominance variance is not fixable and, therefore, selection for traits
controlled by such variance is not effective.
• Heterosis breeding may be rewarding in such situation. Dominance
variance differs from additive variance in several ways.

.
S.No Additive variance Dominance variance
1 It refers to difference between It refers to deviation of Aa from
homozygotes (AA/aa) the mean of AA and aa
2 Genes show lack of dominance. Genes show incomplete, complete
or overdominance
3 Associated with homozygosity Associated with heterozygosity &
& is more in inbreeders is more in outbreeders
4 It is fixable It is non-fixable
5 Selection is very effective as it is Selection is ineffective as it is non-
fixable fixable
6 It is the chief cause of It is the chief cause of heterosis or
transgressive segregation hybrid vigour

.
EPISTATIC VARIANCE
• It arises due to the deviations as a consequence of inter-allelic
interaction, i.e., interaction between alleles of two or
genes or loci. The epistatic variance is of three types,
more different
viz., additive x
additive, additive x dominance and dominance x dominance

.
A. ADDITIVE x ADDITIVE:
• In this case both the interacting loci have homozygous condition. Thus this type of variance results
due to interaction of alleles AA/aa with BB/bb.
ADDITIVE x DOMINANCE:
In this case one locus is homozygous and the other is heterozygous for the interacting genes. Thus this
type of variance results due to interaction of alleles AA/aa with Bb or BB/bb with Aa.
DOMINANCE x DOMINANCE:
In this type of epistasis both the interacting loci have heterozygous condition. This type of variance
results due to interaction between Aa and Bb.
The first type of epistasis is fixable and, therefore, selection is effective for traits governed by such
variance. The last two types of epistatic variances are unfixable and, therefore, heterosis breeding
may be rewarding for traits exhibiting such variance. In the natural plant breeding populations,
epistatic variance has the lowest magnitude.
B.
•
C.
•
•

Epistat.ic variance differs in many aspects from
dominance variance
S.No Dominance variance Epistatic variance
1 It is due to interaction between It is due to interaction between genes of
genes of the same locus two or more different loci
2 It is of three types, viz incomplete, It is also of three types, viz., additive x
complete and overdominance additive, additive x dominance and
dominance x dominance
3 It is unfixable A x A type is fixable
4 Magnitude is higher than epistatic Magnitude is lower than dominance
variance variance.

.
The implications of all the types
programmes
of gene action in two major breeding
1. Recombination breeding
2. Heterosis breeding

.
action
• Gene in different breeding programme
Types of Gene Action Breeding procedure to be followed
Self Pollinated Crops
1. Additive Pureline selection, Mass selection, Progeny selection and
Hybridization and selection with pedigree breeding
2. Non-additive Heterosis breeding and recombination breeding with
postponement of selection at later generations.
Cross Pollinated Crops
1. Additive Synthetic breeding, composite breeding and population
improvement by recurrent selection for gca
2. Non-additive Heterosis breeding and population improvement by recurrent
selection for sca
3. Both Additive and Non- Population improvement by Reciprocal recurrent selection
additive

.
ESTIMATION OF D, H AND E :
• Mather (1949) developed
phenotypic
formulae
variance
of genetic components, for
separating the found in various segregating
populations.
� 𝟒
𝟒 𝟒
the parents)
Where D = Variance
H = Variance
due to additive gene effect
due to dominance deviation
E = Environmental variance
Generation Component of variation
F2
� D + � H + E
Backcrosses (to any one of
� D + � H + E

.
• In an experiment where as F2 was tested with its respective parents,
F1 ad both back cross generations, the D, H and
A) Phenotypic variance of F2 :
E can be derived
� � �
(i) VF2 = D + H + E (ii) 2VF2 = D + H + 2E
� 𝟒 �
� �
B) (i) Variance of Back cross to Parent 1 (B1)
(ii) Variance of Back cross to Parent 2 (B2)
:
:
VB1
VB2
=
=
D + H + E
𝟒
�
𝟒
�
D + H + E
𝟒 𝟒
� �
(iii) Total of (i) and (ii) VB1 VB2
+ = 2 x ( D +
𝟒
H + E)
𝟒
� �
= D + H + 2E
� �

.
C) Additive variance – D
2VF2
�
= D + H + 2E
�
� �
VB1 + VB2 = D + H + 2E
� �
�
2VF2 – (VB1 + VB2) = D
�
VP1  VP2  VF1

V
D) Environmental Variance – E E
3

.
E). As D and E are derived H can be calculated from the formula
� �
VF2 = D + H + E (or)
� 𝟒
� �
VB1(or) VB2 = D + H + E
𝟒 𝟒

.
Components of Variance (work sheet)
• Results on cotton Single Plant yield in gram in a cross between Reba
Bo50 x Laxmi.
Generation Mean Variance
P1 7.20 24.38
B1 20.42 294.68
F1 24.07 160.24
F2 21.66 380.30
B2 19.25 220.52
P2 9.20 44.13

A). Estimation.of “D”
� �
Step 1. VF2 = D + H + E = 380.30
� 𝟒
---------------------------------------------------
� �
Step 2. VB1
VB2
VB2
=
=
D + H + E = 294.68
= 220.52
𝟒
�
𝟒
�
D + H + E
𝟒 𝟒
1
� �
VB1 + = D + H + 2E = 515.20
� � 2
----------------------------------------------------
�
Step 3. 2VF2 = D + H + 2E = 760.60
= 515.20
� 2
� �
deduct VB1 + VB2 = D + H + 2E
� �
-----------------------------------------------------
�
D
D
--
--
--
--
= 245.40
= 490.80 ------(A)
�
P1 7.20 24.38
B1 20.42 294.68
F 24.07 160.24
F 21.66 380.30
B2 19.25 220.52
P 9.20 44.13

.
B). Estimation of “E”
VP1  VP2  VF1
V 
Step 4. E
3
24.38160.2444.13 228.75
3
 
V E
3
E = 76.25 --------(B)
P1 7.20 24.38
B1 20.42 294.68
F1 24.07 160.24
F2 21.66 380.30
B2 19.25 220.52
P2 9.20 44.13

.
C). Estimation of “H”
� �
VF2 = D + H +
+
E
�
= 380.30
H + 76.25 = 380.30
H = 380.30 – 245.40
H = 58.65
�
�
𝟒 1
490.80
� 𝟒
�
– 76.25
𝟒
�
𝟒 2
H = 234.60 -------- (C)
P1 7.20 24.38
B 20.42 294
.68
F1 24.07 160.24
F2 21.66 380.30
B2 19.25 220.52
P 9.20 44.13

.
Results :
VF2 = 380.30 (Phenotypic variance)
D = 490.80 (Variance due to additive effects)
H = 234.60 (Variance due to dominance deviation)
E = 76.25 (Environmental variance)

.
• Problem 2 : Estimation of components of variance
gram.
for the given
population. The results on single plant yield in
Generation Variance
P1 36.48
B1 294.18
F1 120.54
F2 270.45
B2 240.63
P2 42.63

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4 gpb 621 components of variance

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4 gpb 621 components of variance