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Quantitative Inheritance in Plant Breeding
Mendelian Inheritance: Peas, black or white hulls, smooth or rough awns in barley,
Progeny test: To learn breeding behavior of an individual plant.
From the progeny test breeder learns that a superior looking plant is superior
due to its genetic make up or environmental influence: By growing progeny of
selected superior plant, approves or disapprove its genetic superiority
Test cross: To identify the genotype of a plant
Crossing of F1 plant to a homozygous recessive plant
Back cross: The back cross is a cross of a hybrid to one of its parent.
•
Succession of back crosses helps to add a gene
–
Accumulation of desirable genes
1.
Qualitative Characters
–
controlled by few genes that that express major phenotypic effects
–
simple Mendelian inheritance,
–
mixed population results in discrete classes,
–
Least influenced by environment
–
Inheritance= Transmission of variation from parents to off-springs
–
Qualitative Inheritance
Quantitative Traits
• Quantitative characters:
– inheritance controlled by several to many 30
genes (Poly genes) at different loci, that 25
express major phenotypic effects,
20
– Inheritance unlike simple Mendelian traits 15
– Segregating population result in
10
continuous classes
5
– expression under strong influence of
0
environment
– Quantitative Inheritance, is concerned with
inheritance of multigenic traits.
• Example, Yield of a plant,
– sample from a genetically mixed
population will not be in discrete classes
A
i.e. high and low rather it would be in curve
ranging from low to high,
B
– Yield will be affected by
– Genetic component
C
– Environmental component
– Genotype X environment interaction
Yield
GXE
E1 E2
E3
10 15
17 14
8
12
15 12
6
9
13
8
12
15
9
Transgressive Segregation
• Plants with traits that arise by segregation of genes for a
quantitative character that fall outside the range of of the
parents are known as Transgressive Segregates.
•
Very Dark red (R1R1R2R2) and white (r1r1r2r2) grain
color in wheat results in Very dark red, Dark red(1
recessive gene), Medium red (2 recessive genes), light
red (3 recessive genes) and white (4 recessive genes) in
1:4:6:4:1, when medium red is crossed with medium red,
F1 is Medium red whereas F2 segregates to produce Very
dark red and white segregates, both beyond the range of
parents.
• Similar observations are made in quantitative traits i.e.
yield.
Gene Interaction
•
•
•
•
•
•
•
Complementary: Two non-allelic genes are
required to produce a single effect. In oats AB=
resistant to crown rust, Ab,aB,ab = susceptible
Modifying: One gene produces an effect only in
the presence of a second gene at another locus.
In corn
Inhibiting: One gene may act as an inhibitor of the
expression of other
Masking: One gene may hide the effect of a
second gene when both are present.
Duplicate: Either of two genes may produce a
similar effect or same effect is produced by both of
them together.
Additive: Two genes may produce the same effect,
but the effects are additive if both genes are
present
Pleiotropic: A single gene may have more than
one effect. In barleyUz=normal in appearance, uz
= semi-dwarf, short awns, small seeds, short erect
flag leaf, dense spike
Gene
Pair
Minimum
Population
required
1
4
2
16
3
64
4
256
5
1024
10
1048576
20
1099511627776
Characteristics of Multiple Gene Inheritance
• Multiple genes or Poly genes are genes at different loci that affect the
expression of same phenotypic character.
• Quantitative Trait Loci (QTL): The location of these genes on the
chromosome controlling quantitative traits is termed as QTL.
• Genes follow the same principles of inheritance in quantitative and
qualitative, differences are due to number and expression
– Each multiple gene has a small effect on the phenotype relative to the total
variation, normally, it is not possible to identify individual gene effect
– Many genes at various loci (QTLs) contribute to the expression of a
quantitative character. Distinct segregation ratios are not observed.
– Individual effects of the gene are cumulative, the net effect enabling
measurement of phenotypic values. In a random mating population, phenotypic
values will exhibit continuous variation.
– Phenotypic values of a quantitative trait include both genetic and
environmental component and G X E interaction.
– Effects of multiple genes are expressed through different types of gene action:
additive, dominant, over-dominant and epistasis.
– Transgressive segregates may arise due to multiple genes resulting in superior
genotypes than parents
Quantitative Inheritance and its measurement
• Quantitative character can not be classified into distinct classes
• Classification is dependent on measurement of character taken from a large
number of random plants (the sample should be large enough to represent
the range of variability present in the population)
• These numerical values form a continuous series and are studies through
various statistical parameters
• These parameters include range, mean, variance, standard deviation and
coefficient of variation
• Of these mean and variance are most important
• RANGE: is the distance on the scale of measurement from the lowest to
highest observed value
• MEAN: is an arithmetic average of of the sample measurement for the
character being studied
• VARIANCE: The dispersion of the observations in the population is
designated by the variance.
• The variance is used to calculate standard deviation (SQRT Var) in making
heretability estimates or break down into its components in an analysis of
variance.
Measurement of Continuous Variation
• In case of normal distribution when variance and standard deviation are
normal, it is supposed that + 1 sd from the mean will include 68.26 of the
observations, whereas + 2 sd from mean will include 95.45% of the
observations.
• A small variance and small sd will result in clustering of observations around
mean
• Whereas large variance and large sd will show widely spread observations
around mean.
• For making comparison of variability of data groups with quite different
means, the CV may be used
• CV = (s/X’) *100 where s=standard deviation, x’ = mean
– CV of 10% or less ids generally desired
– The difference in case of heterogeneous population (open pollinated
corn) may be due to genotype, environment and GXE
– The differences in case of homogeneous or uniform population (Wheat)
may be due to G X E
Frequency distribution of sample data set with
calculations of descriptive values
Observed
values
Product
Deviation ofX
from Mean
Deviation
Squared
Frequency
Product
x
f
fx
(x-x)
(x-x)2
f (x-x)2
8
1
8
-3
9
9
9
7
63
-2
4
28
10
25
250
-1
1
25
11
35
385
0
0
0
12
23
276
1
1
23
13
8
104
2
4
32
14
1
14
3
9
9
100
1100
126
Number of Observations (n)
= 100
Mean (x)
=SUM fx / n = 1100/100
= 11
Variance (V)
=sum [f (x-x)2 ]/ n-1
=126/99 = 1.27
Standard deviation (s)
=SQRT Var.
=SQRT 1.27 = 1.13
Coefficient of Variation (CV)
= (s/ x) x 100
=10.3
Number of Genes Contributing to a Quantitative Character
n = (Xp1-Xp2)2/{8[sdF2)2 – (sdF1)2]}
Where
n = number of genes
Xp1= mean of one parent
Xp2= mean of 2nd parent
sdF1= standard deviation of F1 generation
sdF2= standard deviation of F2 generation
Assumptions
• Genes have equal effect
• No epistasis, no dominance, no linkage
– Due to absence of these assumptions, estimated number may be quite
lower than actual
– Method is not reliable when more than 4 or 5 genes are involved
Multiple Alleles
Allele:
• Alternate forms of a gene present at one locus (location) on a
chromosome are termed as allele. E.g. Gene for height in peas, It
may be tall (TT) or dwarf (tt).
• An individual may be homozygous (TT, tt) or heterozygous (Tt).
Multiple Alleles:
• As quantitative characters are controlled by several genes so a
locus may have more than two alleles. So more than one pair of
alleles that occupy the same locus is termed as Multiple allele.
• With 2 alleles at a locus (A1,A2), three combinations are possible
(A1A1, A1A2, A2A2), with three alleles(A1,A2,A3), six combinations
are possible (A1A1, A1A2,A1A3, A2A2, A2A3, A3A3) and with 4
alleles, 10 combinations are possible.
• Number of combinations = n(n+1)/2 where n= no. of alleles
• In quantitative characters, multiple alleles may be present at more
than one loci, depicting the huge no. of possible combinations
Frequency distribution of sample data set with
calculations of descriptive values
Observed
values
Product
Deviation ofX
from Mean
Deviation
Squared
Frequency
Product
x
f
fx
(x-x)
(x-x)2
f (x-x)2
8
1
8
-3
9
9
9
7
63
-2
4
28
10
25
250
-1
1
25
11
35
385
0
0
0
12
23
276
1
1
23
13
8
104
2
4
32
14
1
14
3
9
9
100
1100
126
Number of Observations (n)
= 100
Mean (x)
=SUM fx / n = 1100/100
= 11
Variance (V)
=sum [f (x-x)2 ]/ n-1
=126/99 = 1.27
Standard deviation (s)
=SQRT Var.
=SQRT 1.27 = 1.13
Coefficient of Variation (CV)
= (s/ x) x 100
=10.3
Types of Gene Action
Four Types of gene action are recognized
• ADDITIVE Effects: Action of each gene enhances expression of the trait. e.g.
if the affect of one gene adds one unit, the two genes will increment 2 units etc.
if aabb=0, Aabb=1, AaBb=2, AABb=3 and AABB=4
• DOMINANCE Effects: Heterozygote is more like dominant parent. With
complete dominance,the heterozygote and one homozygote have equal effect.
e.g. aa=0, Aa=2, AA=2.
• EPISTATIC Effects: are the results of non-allelic interactions i.e. genes
present at different loci. Two genes may have no effect individually, yet have an
effect when combined. AAbb=0, aaBB=0, A_B_ =4
• OVERDOMINANCE Effects: occur when each allele contribute an effect
greater than that of either allele separately i.e. non-additivity exists. If the effect
of each allele is one, aa=1, AA=1, Aa=3
• Additive = Selection of superior individual is efficient
• Dominance & Epistasis = Selection of superior individual is less efficient
• Over dominace can be fixed in F1 hybrid through Apomixes or wide
crossing following chromosome doubling
Scenario A.
Dominance
Fewer genes are under-expressed in the homozygous individual.
Gene expression in the offspring is equal to the expression of the fittest parent.
A
B
AA
AA
X
X
aa
aa
Aa
Aa
Scenario B
Overdominance
Over-expression of certain genes in the heterozygous offspring. (The size of the circle
depicts the expression level of gene A)
Effect of gene action alleles of 2 genes at different loci
GENOTYPE
AA
Aa
aa
Additive Gene Effects
BB
+4
+3
+2
Bb
+3
+2
+1
bb
+2
+1
0
Dominance Gene Effects
BB
+4
+4
+2
Bb
+4
+4
+2
bb
+2
+2
0
Epistatic Gene Effects
BB
+4
+4
0
Bb
+4
+4
0
bb
0
0
0
Over-dominance GeneEffects
BB
+2
+3
+1
Bb
+3
+4
+2
bb
+1
+2
0
Heritability
• Plants from a mixed population may differ due to
– Genetic differences
– Environment
– G X E interaction
• Selection from such population will depend upon
– Extent of variability due to genetic component and its expected transmission
to progeny
– Extent of variability due to environment
• Heritability
– The proportion of the observed variation in the progeny that is inherited
– If the genetic component is high than the environmental component, then
heritability will be high AND
– If the genetic component is lower than the environmental component, then
heritability will be low.
WHY ESTIMATES OF HERITABILTY?
– For plant improvement, Selection of better individual is required
– For efficient selection, the performance should remain stable in progeny
– AND Selection will be more effective when genetic component is higher than
environmental component i.e. high heritability
Heritability Estimates
Variance (V) calculated from observed variation in the quantitative
character is phenotypic variance (Pv).
Vp = Vg + Ve + Vge
Vg = Va+ Vd + Vi
Va = Additive genetic variance
Vd = Dominance variance
Vi = non-allelic or epistasis variance
Types of Heritability Estimates
• Heritability is the proportion of the phenotypic variance that is due to
genetic cause
– H = Vg/Vp
– H = Vg/ (Vg + Ve + Vge)
– H = (Vg/Vp) x 100
• Heritability estimates made on the basis of all genetic effects is
termed as broad sense heritability
• h2 = (Va/Vp) x 100
– Heritability estimates made as percentage of additive variance
are termed as narrow sense heritability
– Heritability narrow sense can never exceed broad sense
heritability
Heritability from F2 Population
• P1, P2, F1, F2
– H(bs) = Vg/ Vp
– H(bs) = Vp-Ve/ Vp
– Ve = (Vp1+Vp2+VF1)/3
Heritability from variance Components
• H=
•
•
•
•
•
2g
2g/
( 2gy+
2gl+
2gyl+
2ge+
2g)
= Total genetic variance
2gy = genotype X year variance
2gl = genotype x location variance
2gyl = genotype x year x location variance
2ge = genotype x environment variance
Heritability and Selection
• Characters under environment influence have low heritability
estimates as compared to characters under low environment
influence.
• Selection in F2 will be less effective for the traits with low heritability
and Selection will be more effective for the traits with high heritability
• The principal uses of heritability estimates are:
– To determine the relative importance of genetic effects which
could be transferred from parents to off-spring
– To determine which selection method would be most useful to
improve the trait and
– To predict gain from selection (genetic advance)
Heritability from Parent – offspring regression
Basic assumptions for use of Parent- progeny regression
• Traits has diploid Mendelian inheritance
• No linkage
• Parents are non-inbred
• The population from which parents were extracted is in random mating
equilibrium
• No environmental relationship between the performance of parents and
offspring
b = Σ (x – x) * ( y – y) / Σ (x – x)2
Where x = parent values, y = progeny values, b = regression of y on x
• Regression of progeny performance on parent performance is based on
resemblance between relative and measured additive variance
• This narrow sense heritability is calculated as
h2 = b x 100
In case of open pollinated crop
h2 = 2b x 100
Selection intensity and Genetic Advance
• Superior plants in the population may be superior due to genetic
potential, favorable environment or both (G X E)
• e.g. If high yield is the breeding objective, can it be achieved by 5%
selection pressure or by keeping 10% of the population
• Expected gentic gain with one cycle of selection can be predicted
Gs = (i) (SQRT Vp) * h2
Where
Gs = genetic advance, SQRT Vp = square root of phenotypic variance (sd)
h2 = narrow sense heritability of the trait under study, i = selection Intensity
• Heritability (ns) estimates are used in sexually reproducing plants
• Heritability (bs) estimates are used in Asexually reproducing plants
SELECTION INTENSITY
IF h2 = 0.67 or 67%
i (5%) = 2.063,
Vp = 0.171
THEN Gs = 2.063 * SQRT 0.171 * 0.67 = 0.57
if the mean of trait in the unselected population is 4.5
THEN Gain expressed after one cycle of selection will be = (0.57/4.5)*100
= 12.6%
SHIFT IN MEAN DUE TO SELECTION
Gene Frequency and Genetic Equilibrium
GENE FREQUENCY : refers to the proportions of the different alleles
in a gene pool of a breeding population.
GENOTYPE FREQUENCY : refers to the proportions of various alleles
in a population.
IF we consider a population of 100 diploid individuals with 2 alleles (A1
A2) at one locus
There are three genotypic classes with
X (A1A1) 36 individuals, Y (A1A2) 48 individuals and Z (A2A2) 16
individuals
The genotype frequencies will be
X (A1A1) = 36/100 = 0.36
Y (A1A2) = 48/100 = 0.48
Z (A2A2) = 16/100 = 0.16
Allele frequencies will be
A1 = (2*36) + 48 = 120/ 200 = 0.60
A2 = (2*16) + 48 = 80/ 200 = 0.40
Gene Frequency and Genetic Equilibrium
HARDY-WEINBERG LAW: The probability of two alleles mating is the
product of the frequency of the alleles in the population.
If the gene frequencies of two alleles among the parents are p & q and
p+q=1
THEN genotype frequency = p2 +2pq + q2
IF we put the values of A1 & A2
THEN Genotypic frequency of A1A1 = A12 =
0.6*0.6 = 0.36
A1A2 = 2A1A2 = 2(0.6*0.4) = 0.48
A2A2 = A22 =
0.4*0.4 = 0.16
This population is not in genetic equilibrium
But may reach genetic equilibrium after one generation of random
mating, which is a general rule for any single, independently
segregating locus.
IMPLICATIONS OF HARDY-WEINBERG LAW FOR
PLANT BREEDERS
Following propositions should be kept in mind while using Hardy-Weinberg
law in plant breeding
• Random mating does not occur in natural populations of self pollinated
crops. Gene frequency will remain same but genotype frequency will
change
• Random mating will occur in only cross pollinated species
• Selection for a particular allele may change the frequency of that allele
in population and consequently its genotypic frequency
• Selection for a dominant allele will not eliminate recessive genes from
the population but selection for recessive gene may eliminate the
dominant gene from population