1. 4 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
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

2. Quantitative Traits Quantitative characters:
inheritance controlled by several to many genes (Poly genes) at different loci, that express major phenotypic effects,
Inheritance unlike simple Mendelian traits
Segregating population result in continuous classes
expression under strong influence of 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 i.e. high and low rather it would be in curve ranging from low to high,
Yield will be affected by
Genetic component
Environmental component
Genotype X environment interaction
G X E E1 E2 E3 A 10 15 14 B 8 12 C 6 9

3. 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.

4. Minimum Population required
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
256 5
1024 10 20

5. 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

6. 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.

7. 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 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’) * 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

8. Deviation ofX from Mean
Frequency distribution of sample data set with calculations of descriptive values
Observed values
Frequency
Product
Deviation ofX from Mean
Deviation Squared x f fx
(x-x)
(x-x)2
f (x-x)2 8 1 -3 9 7 63 -2 4 28 10 25
250 -1 11 35
385 12 23
276 13
104 2 32 14 3
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

9. 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

10. 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

11. Deviation ofX from Mean
Frequency distribution of sample data set with calculations of descriptive values
Observed values
Frequency
Product
Deviation ofX from Mean
Deviation Squared x f fx
(x-x)
(x-x)2
f (x-x)2 8 1 -3 9 7 63 -2 4 28 10 25
250 -1 11 35
385 12 23
276 13
104 2 32 14 3
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

12. 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

13. 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. AA Aa A aa X Aa AA B aa X
Scenario B
Overdominance
Over-expression of certain genes in the heterozygous offspring. (The size of the circle depicts the expression level of gene A)

14. Effect of gene action alleles of 2 genes at different loci
GENOTYPE AA Aa aa
Additive Gene
Effects BB +4 +3 +2 Bb +1 bb
Dominance Gene
Epistatic Gene
Over-dominance
GeneEffects

15. 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

16. 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

17. 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

18. Heritability from F2 Population
P1, P2, F1, F2
H(bs) = Vg/ Vp
H(bs) = Vp-Ve/ Vp
Ve = (Vp1+Vp2+VF1)/3

19. Heritability from variance Components
H = 2g/ ( 2gy+ 2gl+ 2gyl+ 2ge+ 2g)
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

20. 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)

21. 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

22. 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 = or 67%
i (5%) = 2.063, Vp = 0.171
THEN Gs = * SQRT * 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

23. 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

24. 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 = * = 0.36
A1A2 = 2A1A2 = 2(0.6*0.4) = 0.48
A2A2 = A22 = * = 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.

25. 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