Download Lecture 2 The genetic Model for Quantitative Traits

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Components of Phenotypic variation
• The phenotype of an individual for a repeated
quantitative trait can be modeled as:
P =GA + GD +GI + Ep + Et
• GA = Additive genetic effect (breeding value)
• GD = Dominance effects
• GI = Epistasis effects
• Ep = Permanent environmental effects
• Et = Temporary environmental effects
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• Based on this model, the phenotypic variance can be
decomposed (ignoring covariances) into:
VP = VA + VD + VI + VEp + VEt
VP = phenotypic variance
VA = additive genetic variance
VD = variance due to dominance effects
VI = variance due to effects of epistasis
VEp = variance due to permanent environmental effects
VEt = variance due to temporary environmental effects
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Heritability
• Heritability in the broad sense (H2): is the
proportion of the phenotypic variance that is due to
genetic effects including additive, dominance and
epistasis:
VG VA  VD  VI
H  
VP
VP
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•It measures the strength of the relationship between the
phenotypic values for a trait and the genotypic values. It can be
viewed as the squared correlation between the phenotypic values
and the genotypic values:
H 2  rP2,G
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Heritability in the narrow sense (h2): is the
proportion of the phenotypic variance that is due to
additive genetic effects only.
h
2
VA

VP
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What does the heritability in the narrow sense
measure?
• The strength of the relationship between the phenotypic values
and the breeding values for a trait in the population. Therefore,
it can be viewed as the coefficient of regression of the
breeding value on the phenotypic value.
• It measures the degree to which the offspring resemble their
parents in performance for a trait. If a trait has a large
heritability, individual with high performance for the trait will
produce offspring with high performance. If a trait has a small
heritability, performance records of parents reveal little
information about the performance of their offspring.
Breeding value is defined as the value of an individual as a
parent. Parents transfer a random sample of their genes to their
offspring. Estimated breeding value gives an estimate of the
transmitting ability of the parent.
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• The h2 can be estimated from the regression of the
phenotype of the offspring (one offspring or the mean
of all offspring) on the phenotype of one parent or on
the midparent value (mean phenotype of both
parents).
• If we use midparent value, then
h2= regression coefficient
• if we use the phenotype of one parent then
h2= 2 (regression coefficient).
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Var=0.98
Var=0.68
The slope of the regression line is an estimate of the narrow-sense heritability for traits with a heritability
of 0.2 (a) and 0.8 (b) and phenotypic variance of 1. The variances of the observations about the
regression line are 0.98 (a) and 0.68 (b), demonstrating that the average phenotypic value of the
parents (midparent phenotypic value) is a better predictor of the offspring phenotypic value if heritability
is high.
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• Notes on heritability:
• Heritability is a population measure not a value
associated with a single individual.
• Heritability of a trait varies from one population to
another and from environment to another.
• Heritability is always positive ranging from 0 to 1.0.
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Importance of heritability
1. Heritability is important in selection: The accuracy
of selection is higher for a highly heritable trait than
a low heritable trait. The larger the accuracy of
selection, the larger is the expected response due to
selection. With selection based on phenotypic
values:
• Large h2 high accuracy of selection (phenotypic
value is a good indicator of breeding value)
• Small h2  low accuracy of selection (phenotypic
value is not a good indicator of breeding value)
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2. Heritability is important in prediction of breeding
values, predicted differences, and producing
abilities.
• Prediction of BV of individual i based on
phenotypic value, Pi is obtained as:

BVi  h 2 ( Pi  P )
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3. Heritability is important in management:
- Large h2  genetic factors have important role as in
growth traits (performance can be improved by
selection).
- Small h2  environmental factors are important as in
reproductive traits (selection is less effective and
performance is improved mainly by improving the
environmental effects such as improving nutrition
and management practices).
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Repeatability
1.
In the breeding of perennial species the coefficient of repeatability
is an important parameter because it allows effective early
selection of superior plants and/or progenies (Dias and Kageyama
1998).
2.
The analysis of repeatability describes the correlation between
successive measurements of a trait and can serve as a basis for
the estimation of the likelihood that the initial superiority or
inferiority of a genotype will remain over time and/or space.
3.
Several studies on repeatability are found in the literature for a
variety of perennials such as coffee, peach, custard apple and
grape.
4.
The repeatability can vary depending on the nature of the trait, on
the genetic properties of the population, and on the environmental
conditions under which individuals are maintained.
Repeatability (r) is the proportion of the phenotypic variance that is
due to permanent effects (genetic effects and permanent
environmental effects):
r
V A  VD  VI  VEP
VP
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What does the repeatability measure?
1.
2.
3.
Repeatability tells about the strength of relationship between
repeated records. Therefore, repeatability can be estimated as the
correlation between repeated records on the same individuals.
The strength of the relationship between single performance
records and producing ability (permanent effects). Therefore,
repeatability can be viewed as the regression of PA on the
phenotype.
The repeatability analysis measures the amount of variation that
does not over the time.
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Importance of repeatability
1. It is useful in prediction of producing ability and
therefore the individual’s next record from the
current and previous records:
- If r is high, we can predict the individual’s next
record more accurately
- If r is low then the prediction of the next record
has low accuracy.
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Pi
To predict the producing ability (most probable
producing ability) from n previous records:
PAˆ 
Pi
P
nr
( Pi  P )
1  (n  1)r
is the average of the n records of the
individual i
is the mean for all individuals.
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• Example: suppose a cow has three milk records:
4000kg in the first record, 5000 kg in the second, and
6000 kg in the third. Suppose also that the mean of all
cows is 4600 kg and the repeatability of milk yield is
0.60, then the predicted producing ability of this cow
is:
PAˆ i 
(3)(0.60)
(5000  4600)  327kg
1  (3  1)(0.60)
ˆ  4600  327  4927kg
Pˆi  P  PA
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2. Repeatability is important in prediction of breeding
values from multiple records on the same
individuals:
2
nh
BVˆi 
( Pi  P )
1  (n  1)r
For the previous example if heritability of milk yield
in this population is 0.25 then
BVˆi 
(3)(0.25)
(5000  4600)  204.6kg
1  (3  1)(0.60)
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3. Repeatability is important in making culling
decisions:
When r is high we can cull animals of poor
performance on the basis of the first record
When r is low one should wait for more records
before making a culling decision on the animal.
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