2. Quantitative Genetics
Quantitative genetics: The quantitative genetics deals with
the inheritance of those differences between individuals that
are of degree rather than of kind, quantitative rather than
qualitative.
Character/Trait: Any measurable or observable property of
living individual that exhibit inherited differences among the
individuals of a population is called the character or trait.
Inherited VS heritable character:
A genetically determined character is called the inherited
character.
All the inherited characters are not heritable.
The term heritable character is used to designate those
inherited characters which show differences among individuals
of a population 2
3. Genetic Classification of characters
(i) Qualitative Characters
(ii) Quantitative Characters:
(iii) Threshold Characters
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4. (I) Qualitative Characters:
•These characters are governed by one or few pairs of genes
with major effect and hence express Mendelian ratios.
•These characters are not or rarely affected by the variations
in environment.
• This makes it possible to classify the genotypes accurately
based on phenotypes.
•Thus, these traits show discontinuous variation, which is
expressed in genetic ratios.
•Further, these characters can not be measured in quantitative
measurement.
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5. Examples in farm animals:
• Colour of body or parts of the body viz. coat color in different
cattle breeds (Black, Red, Roan, White etc.),
• Plumage colour in chicken viz. back, splashed white and
slate blue) etc.
• Presence or absence of horns in cattle and sheep
• Biochemical polymorphic traits like hemoglobin types, blood
potassium types ( high & low concentration), transferrin types,
and other blood and milk polymorphs,
•Hair texture in dogs (wire vs. smooth haired),
• short wings and legs in chicken called creepers
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6. Genetic control of qualitative characters-
• These characters are controlled by one, two, or few pairs of
genes, with major gene effect and express Mendelian ratio.
• These genes are called the major genes.
• The inheritance pattern of these characters is called as
qualitative inheritance.
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7. Environmental effects on qualitative characters:
• The qualitative characters are usually not affected by
the environment, but only in a very few / rare cases.
• Thus the genotypic value is not modified/ affected by the
variation in environment and hence the individuals may
be grouped in to a few defined and distinct classes.
• The classical examples of environmental modification of
genotype of qualitative characters are:
(a) Flower color of Chinese primrose,
(b) Color pattern in rabbit,
(c) Sex limited and sex influenced characters,
(d) Occurrence of diabetes etc.
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8. Characteristics of qualitative characters:
(I) Measurement of character: Can only be counted and
there is no quantitative measurement.
(II) (ii) Distribution- binomial: All the individuals in a
population for a qualitative trait are grouped in to discrete
classes. For example- coat color of 100 sheep may be
recorded distinctly as black and white.
(iii) Type of variation- discontinuous: All the individuals can
be classified in to distinct classes with no connections with
intermediates e.g. horned vs. polled, back vs. white, red
vs. white , dwarfs vs. normal etc.
(iv) Causes of variation: mainly genetic. Usually not affected
by environmental factors.
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9. (ii) Quantitative Characters:
• These characters are governed by many gene pairs with
minor effect of each gene pair for which these genes are
called as minor genes or polygene, whose effect is modified
by the environment.
• These traits are governed by polygene, hence are called
polygenic traits.
• The phenotypic expression of these characters is affected
by gene pairs ( Genotype) as well as by environment,
Examples in farm animals:
• Physical or morphological traits,
• Growth traits,
• Reproduction traits,
• Productive traits etc. in all species of farm animals. 9
10. Characteristics of quantitative characters:
1. Measurement of character:
• These characters are measured in metric units (gm, kg,
cm, days) rather than assigning a rank or a value to each
individual.
• Therefore, the phenotype of each individual expresses
the quantity of the phenotype rather than it’s quality and
called as the phenotypic value.
2. Distribution-Normal:
• Quantitative characters follow the normal distribution and
the phenotypic values are clustered at mid point (population
mean) and thinning out continuously (symmetrically) towards
both extremes giving a bell shaped curve and is called
normal distribution.
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11. 3. Type of variation- continuous variation :
• These characters show continuous variation among the
phenotypic values of different individuals of a population.
• The reason for continuous variation is that they are
governed by many gene pairs segregating at many loci with
small effect and by the environmental factors.
4. Causes of variation: are two-
• Genetic: The genes at many loci (polygene).
• Environment: Feeding, management, diseases, and other
climatic factors
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12. Genetic factors affecting quantitative characters:
• The phenotypic expression is controlled by genes at
many loci.
• Each gene/ locus contribute very small effect.
• Thus such genes are called as minor genes because of
their minor or small contribution in affecting the
characters and causing the variation in the phenotypic
expression.
• This variation is called as the polygenic variation and
their inheritance is called as polygenic or multifactor
inheritance.
Continue--
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13. • Mendelian ratios are not obtained for these traits because
of the segregation at many loci affecting the character as
well as affected by the variation in environment.
• The genetics concerning with the inheritance of
quantitative character is known as quantitative genetics and
the inheritance pattern is called the quantitative inheritance.
• All the quantitative characters are affected by the
environmental conditions, also called as non genetic causes
(Nutrition, management diseases and several climatic factors).
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14. Differences and similarities among qualitative and quantitative characters:
(1). Differences:
__________________________________________________________________
S.No. Quantitative characters Qualitative characters
__________________________________________________________________
1. Controlled by many gene pairs and each 1. These traits are controlled by
gene has minor effect, hence called polygenic one two or few gene pairs.
traits.
2. These characters are affected by environment.2.Usually not affected by
environment
3. Variation is continuous type and all short of 3. Variation is discontinuous
gradations can be observed. type and distinct classes/
groups can be observed
4. Distribution is normal-bell shaped curve. 4. Distributions is binomials &
discrete .
5. Measured quantitatively in metric units. 5. Can not be measured but
can be counted
__________________________________________________________________
(2). Similarities: The only similarity among the quantitative and qualitative traits
is that both type characters are controlled by genes.
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15. (iii) Polygenic characters in discontinuous variation:
• There are some traits which are polygenic in nature but show
the discontinuous variation between phenotypes. Such traits
can be further divided in two categories viz.
1. Meristic traits and
2. Threshold traits.
1. Meristic traits: The phenotypes of these traits are
expressed in discrete, integer numbers.
Examples: Number of offspring carried by a dam (litter size),
number of bristles in Drosophila, number of ears on a stalk of
corn plant, number of flowers on a petal
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16. 2. Threshold characters:
• These traits are polygenic but shows discontinuous variations.
These are either expressed (present) or not expressed (absent)
in any individual, in contrast to the meristic traits which are
expressed in all individuals of a population.
Examples:
- Resistance to diseases ( healthy – sick),
- Survivability (Survive- dead),
- Fertility (pregnant –non pregnant),
- Hatchability of eggs ( hatched- not hatched ),
- Presence or absence of any organ or structure (present-
absent).
•These traits are called as “quisi - continuous “because the
phenotypic values are discontinuous like qualitative traits but
the mode of inheritance is polygenic like that of a quantitative
trait.
•The causes of variation: are both genetic and environmental in
these traits like in quantitative traits. 16
17. Genetic Models for Quantitative Traits
• The genetic models used in quantitative genetic analysis of
quantitative traits are almost universally linear.
• A linear model is defined as an equation which is a linear
function of certain parameters and variables.
• A simple example is:
P= µ +G + E
Where,
P = the phenotypic value or performance of an individual
animal for a trait.
µ = the population mean or average phenotypic value of the
trait for all animals in the population.
G = the genotypic value of the animal for the trait and
E = the environmental effect on the individual performance
for the trait.
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18. • The phenotypic value: is an individual’s performance record
for a specific trait, while
• The genotypic value: refers to the effect of the individual’s
genes (Singly or in combination) on its performance for the
trait. Unlike phenotypic value, it is not directly measurable.
• The environmental effect: is comprised of all non-genetic
factors influencing an animal / individual’s performance for
a trait.
Example: Considering body weights of 3 calves a, b, and c as,
If µ = 500 lb,
If (a). G = 30 lb, and E = 70 lb (If G & E were measured as
deviations from the mean)
Then, P = 500 + 30 + 70 = 600 lbs
If (b). G = -10 lb, and E = - 40 lb
Then P = 500 – 10 – 40 = 450 lb
If (c). G = 30 lb, and E = - 80 lb
Then P = 500 + 30 – 80 = 450 lb 18
19. • A positive deviation means above average
• A negative deviation means below average
• The basic genetic model for quantitative traits is
nothing more than a mathematical representation
of how the performance (P) is affected by
nature/genotype (G) and nurture/ environment (E).
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20. Breeding Value:
• In Selecting for polygenic traits breeder try to choose as
parents those individuals with the best breeding values.
• But breeding value does not appear in the basic genetic
model for quantitative traits (P = µ +G + E)
• In fact the genetic component (G) in the model is
genotypic value.
• What is the difference between BV and genotypic value?
•The genotypic value represents the overall effect of an
individual’s genes, (Genotypic Value = Additive effect of
the genes + Dominance + epistasis + any other gene
interaction). While
•The breeding value represents only that part of genotypic
value that can be transmitted from parents to offspring
(Additive effect of the genes).
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21. Example:
• Assume that there is B locus with two possible alleles, B
and b that affect mature body weight of calves.
•The average effect of each B gene is to increase mature
body weight by 10 grams, and
• The average effect of each b gene is to decrease mature
weight by 10 grams.
•These 10 gram gene effects are known as independent
gene effects.
•The B.V. for mature body weight is the sum of the
independent effects of genes at the B locus and all other
loci affecting mature weight.
• Because dominance and epistasis are broken down at the
time of gametogenesis
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22. • In our hypothetical example of mature body weight, let
us assume that genotypes at all loci affecting mature body
weight except the B locus are identical for all animals.
•Then BV for each of the three B- locus genotypes (BB,
Bb, and bb) is:
Genotypes Breeding Values
BB = 10 + 10 = 20g
Bb = 10 + (–10) = 0 g and
bb = -10 + (–10) = - 20g
•The animals with the BB genotype have the highest B. V.
•The animals with bb genotype have the lowest breeding
value for mature body weight.
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23. • Now let us assume complete dominance at the B locus,
means BB = Bb in expression and both individuals have the
same genotypic value.
•The genotypic values of the genotypes will be as
Genotypes Genotypic value
BB = 10 + 10 = 20g
Bb = 10 + (-10) = 20g (Since BB=Bb due to dominance)
bb = -10 + (-10) = -20g
•So genotypic value represents the overall effect of an
individual’s genes (Singly and in combination) on that
individuals own performance for a trait.
• Not all of genotypic value is inheritable. 23
24. • However, BV is the part of an individual’s genotypic value
that is due to independent gene effects that can be
transmitted from parents to offspring.
• The remaining portion of genotypic value is called gene
combination value (GCV) – which is due to dominance and
epistasis gene interactions.
• An animal’s BV and GCV together constitute its genotypic
value (GV) for a trait.
• In model form,
G = BV + GCV
GCV = G - BV
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25. Considering the BV and GV from the above
example, the GCV will be as follows:
Genotypes B. V. G.V. G. C. V.
BB 20g 20g 0g
Bb 0 g 20g 20g
bb -20g -20g 0g
• In this case the GCV is due to the complete dominance of
B to b genes.
• Because of their lack in the additivity, the gene
combination value is called as non-additive genetic value.
• It is possible for some genes to be entirely additive in
their influence on a trait, but no gene can be entirely
non-additive in its influence.
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26. • The basic genetic model for quantitative traits can now be
expanded to include breeding value (BV) and gene
combination value (GCV). Mathematically
P = µ + BV + GCV+ E
• The new model for quantitative trait has many
characteristics same of the basic genetic model.
• Like genotypic value, BV and GCV are expressed as positive
and negative deviations from the population mean.
•The average BV and GCV across the entire population are
zero.
•Furthermore, BV and GCV are considered independent of
environment and of each other. 26
27. Expended Genetic model:
The genotypic value (G) is determined due to
• Additive gene effects (A)
• Intra- allelic and inter allelic gene combination effects or
gene interactions ( Dominance and epistasis)
Thus
G = A + (D + I)
• The additive effects of genes produce a value to the genotypic value
known as the breeding value, denoted by.
B.V. = the breeding value is the parental value (A value of
an individual as a contributor of genes to the next
generation) and represent the part of the genotypic value
which is transmitted from parent to progeny. 27
28. Difference between genotypic value and breeding value:
• The genotypic value of an individual’s genes is to its own
phenotypic value
• Whereas, the B.V. (A) is the value of an individual’s gene
to its progeny phenotypic value.
• Thus A is the part of the G that can be transmitted from
parent to progeny.
• The remaining part of the G is the interaction effect of
genes (Dominance, (D) and epistasis, (I)).
• The interaction effects of genes are not transmitted
because of segregation and independent assortment of
genes during meiosis ( halving process of inheritance) and
recombination of genes to form zygote ( New individual –
progeny).
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29. • Now the basic genetic model by dividing the G in to its
component parts can be written as
P = µ + A + (D + I) + E
• The average B.V. (A) and the average interaction effect of
genes ( D+ I ) across an entire population are zero, because
these are expressed as deviations from population mean.
Thus
(A) + ( D + I) = G+ E = 0
• The breeding values and gene combination values (gene
interaction values) are independent of each other as well as
to the environment.
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30. Genetic model for repeated traits:
• When an individual has more than one performance
records for some traits at different times known as repeated
traits, for which a value known as the producing ability (PA)
is important that refers to the performance potential of an
individual for a repeated trait.
• The performance potential of an individual for a repeated
trait (Producing Ability) is a function of the genotypic value
(G) and of the permanent environmental effect (Ep).
• Permanent environmental effects (Ep) may be the nutrition
during calf hood age, blind teat, training of young horses
etc.
Thus
P.A. = G + Ep = A + (D + I) + Ep
• The P.A. is a combination of genetic value and of
permanent environmental effects .
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31. Now the genetic model for a single record of an individual
which have multiple records can be written as:
P = µ + G + Ep + Et
= µ + A + (D + I) + Ep + Et
Where,
µ = Population mean
G = Genotypic Value
Ep = Permanent environment effect.
Et = temporary environmental effect.
• All the components of the genetic model for repeated
traits are expressed as deviation (positive and negative)
from the population mean.
•Therefore, the average of each component across entire
population is zero.
•Thus, ( A)= (D +I) = G = Ep= Et = 0. All these components
are independent of each other 31
32. Genetic and non- genetic variation and its partitioning:
• Simple genetic model which we have considered so far:
Phenotype = Genotype + Environment
The same genotype can lead to different phenotypes and vice
versa.
General mathematical form: P = f (G, E)
With P = phenotype, G = genotype, E = environment
Exact function of G and E is unknown because G and E may
not be observed directly
Verbal definition of the phenotype
"The phenotype is the visible reaction of the genotype on
the environment" 32
33. Statistical definition of the phenotype
Pij = + gi + ej + (ge)ij
Pij = Phenotype (observed trait value) of individual i in environment j
= population mean (PM)
gi = deviation of Pij from , caused by genotype i
in an average environment
ej = deviation of Pij from , caused by environment j given an average
genotype
(ge)ij = deviation of Pij from , that might not be explained by gi or ej alone
and is caused by specific interaction of gi and ej
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34. Composition of the phenotype variance
δ2
P = δ2
G + δ2
E + δ2
GE
• Genotype-environment interaction = Interaction of G and E:
This interaction exists when different genotypes react
differently on a particular change in environment.
Frequent situation in practice: high yielding genotypes are
more affected by environmental deterioration than low
yielding genotypes.
• Genotype-environment correlation:
= measure of joint variation of genotypes and environments
Frequent situation in practice: High yielding genotypes live
often in more favourable environments than low yielding
genotypes;
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35. • Effects of random halving of genome during
gametogenesis On :
Parent: Decay of all genetical interaction components due
to specific combinations of parental chromosomes in this
individual.
Offspring: Formation of new genetical interaction
components due to formation of new pairs of chromosomes
inherited from the two parents.
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36. 2 Categories of genetic effects:
• Due to the effect of random halving of the genome, we
have 2 fundamentally different categories of genetic
effects:
• Effects that come into play by mating an individual to a
random sample of the population and are effective as the
average of the offspring (= additive effects).
• Effects determined by specific combination of gametes in
a particular individual, but not the offspring (= dominance
and epistatic effects
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37. Splitting the genetic effect:
g = ga + do + ep
• ga = "additive" gene effect (relevant for breeding value)
ga is the part of g, which comes into effect when the
individual is mated to a representative sample of the
population in the average of its offspring.
do = "dominance effect"
do is the part of g, not explained by ga and due to
interactions of alleles of the same locus within a
particular individual.
ep = "epistatic effect"
ep is the part of g, not explained by ga or do and due to
interactions of alleles of different loci within a particular
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38. Partitioning of Variances
2
(G) = 2
(A) + 2
(D) + 2
(E)
2
(E) = 2
(Ep) + 2
(Et)
Note: Covariance between ga, do and ep as well as. Ep and
Et is zero by definition.
For breeding purposes the following partitioning of
variances is of practical relevance:
2
(P) = 2
(A) + 2
(E')
where E' stands for all non-additive plus the environmental
effects. 38
