Download Quantitative Genetics: Traits controlled my many loci Quantitative

Quantitative Genetics:
Traits controlled my many loci
Quantitative Genetics I:
Traits controlled my many loci
So far in our discussions, we have focused on
understanding how selection works on a small number of
loci (1 or 2).
Learning Objectives:
1. To describe how segregation at multiple loci can produce a
pattern of quantitative variation in a trait.
However in many cases, evolutionary biologists ask
questions about traits or phenotypes (for example…)
2. To define the breeding value (A) and relate it to the average
effects of alleles.
Many factors may affect a trait, including the action of
alleles at one or more loci, and the environment in which
an individual exists.
3. To define and differentiate broad and narrow sense heritability.
4. To describe the components of trait (phenotypic) variation and
describe how and why additive genetic variation is the key
component of variation relevant to narrow sense heritability and
the response to selection.
Quantitative genetics provides the framework for
understanding how evolutionary forces act on complex
traits.
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Readings: Chapter 9 in Freeman
1
Quantitative genetics vs.
population genetics
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Sir Ronald Fisher (1890-1962):
Linking quantitative traits
variation and Mendelian genetics
• In 1918, Fisher showed that a large number of Mendelian
factors (genes) influencing a trait would cause a nearly
continuous distribution of trait values. Therefore, mendelian
genetics can lead to an approximately normal distribution
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Wheat kernel
colour variation
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Wheat kernel
colour variation
This figure shows
measured phenotypes in a
population of F2 plants
from parents that differ
in kernel colour.
We can see that more
than two or three
phenotypes are seen in
the F2. This pattern is
explained by the action of
three loci.
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Population genetics
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With three loci, each
with two alleles, six
phenotypic classes are
obtained, and the
distribution of
phenotypes begins to
look like a normal
curve.
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6
Quantitative genetics
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What are the conditions that will lead to a shift
in
the mean value of a trait under selection?
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8
Breeder’s equation
Human Height: An example of a quantitative trait
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The first big question in
quantitative genetics:
Breeder’s equation: R = h2S
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Building a Quantitative Genetics
Model: lessons from agriculture
• How much phenotypic variation among
individuals is due to the presence and
interaction of different alleles, and how
much is due to differences in the
environment?
• Answers to this question will determine
the degree to which traits can respond
to selection.
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In quantitative genetics, the phenotypic value (P) of an
individual (e.g. height) is attributed to the genotype of
the individual and to its environment:
P = G + E
The genotypic value (G) reflects the influence of every
gene carried by the individual on the phenotypic value.
The environmental deviation (E) is a measure of the
influence of the environment of the phenotypic value of
an individual.
We can see how these components are estimated in an
example from crop yield in wheat.
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Average Yield of three wheat strains over
a ten year period (bushels/acre)
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Average Yield of three wheat strains over
a ten year period (bushels/acre)
Year
Roughrider
Seward
Agassiz
Year
Roughrider
Seward
Agassiz
1986
47.9
55.9
47.5
1986
47.9
55.9
47.5
1987
63.8
72.5
59.5
1987
63.8
72.5
59.5
1988
23.1
25.7
28.4
1988
23.1
25.7
28.4
1989
61.6
66.5
60.5
1989
61.6
66.5
60.5
1990
0.0
0.0
0.0
1990
0.0
0.0
0.0
1991
60.3
71.0
55.4
1991
60.3
71.0
55.4
1992
46.6
49.0
41.5
1992
46.6
49.0
41.5
1993
58.2
62.9
48.8
1993
58.2
62.9
48.8
1994
41.7
53.2
39.8
1994
41.7
53.2
39.8
1995
53.1
65.1
53.5
1995
53.1
65.1
53.5
Mean
45.63
52.18
43.49
Mean
45.63
52.18
43.49
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Using Genetic values in breeding:
The Breeding Value
Mean yield of population
Genetic value of a parent
(60 bushels/acre)
(80 bushels/acre)
Expected genetic value of
offspring (70 bushels/acre)
The genetic value of a genotype reflects the sum total
effect of all alleles at the loci that affect the trait of
interest.
Given that a parent in a sexual species passes half of
its alleles to the offspring, what is the expected
genetic value of the offspring? (assume a randomly
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chosen mate)
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Environmental values (E)
63.8 - 45.63 = 18.17
49.0 - 52.18 = -3.18
Genetic values (G)
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Using Genetic values in breeding:
The Breeding Value
Mean yield of population
(60 bushels/acre)
Actual genetic value of
offspring (67 bushels/acre)
Genetic value of a parent
(80 bushels/acre)
In reality, the yield of the offspring may differ from
that predicted on the basis of the genetic value of the
parent.
Why?
- Dominance (interactions among alleles at a locus)
- Epistasis (interactions among alleles at different loci)
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Using Genetic values in breeding:
The Breeding Value
d
d
Mean yield of population
(60 bushels/acre)
Actual genetic value of
offspring (67 bushels/acre)
Breeding Value (A)
of the parent genotype
(74 bushels/acre)
The breeding value of a genotype (A) is obtained by
adding twice the deviation of the mean (d) of the
offspring from the population mean.
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Breeding Value Example 1
To increase milk yield, dairy farmers estimate the
breeding value of bulls from the average dairy
production of each bull’s daughters.
When a particular bull is mated to several cows,
his daughters produce an average of 100 liters of
milk per day, in a herd with an average
production of 75 liters.
In terms of dairy production,
...what is the breeding value (A) of the bull?(125)
...what is the phenotypic value of the bull? (!!)
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Effects of Dominance
Breeding Value Example 2
Now say that a particular cow produces 100 liters of milk
per day, compared to a herd average of 75 liters per
day.
When mated to different bulls, this cow’s daughters
produce an average of 80 liters of milk per day.
In terms of dairy production,
...what is the breeding value (A) of the cow? (85)
...what is the phenotypic value of the cow? (100)
What contributes to this difference (assuming no
environmental effects)?
If alleles at some loci affect traits differently
depending on the rest of the genotype (Interactions)
Dominance (D) (interactions at the same locus)
Epistasis (I) (interactions at different loci)
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Dominance relationships among alleles at a locus affect
the way in which a trait is transmitted to the
offspring.
A parent that is homozygous (e.g. BB) at a locus that
affects a trait cannot transmit this condition to its
offspring.
If B is recessive to b, a high fitness BB parent mated to
a low fitness bb parent produces only Bb (low fitness)
offspring.
Such dominance effects have an impact on trait
expression of the offspring from any cross.
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Effects of Gene Interactions
/Epistasis
Average Allele Effect
Similarly, good interaction among the alleles at different
loci are not faithfully transmitted, as illustrated in these
card hands. Even though Mom and Dad have good
combinations, they may not combine well in the offspring.
Because of dominance and epistasis, a given allele may not
always have the same effect of the phenotype.
5
6
7
8
9
6
4
"
"
"
"
"
!
"
Mom
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A
A
# $
A
"
Dad
6
4
7
A
9
!
"
"
$
"
Offspring
The average effect of an allele accounts for the
difference in the effect of an allele paired with any
other alleles /genes currently found within the population
(e.g., accounting for the chance that it is found in a
heterozygote or homozygote, in any particular genetic
background).
The breeding value of an individual (A) represents the
average effects of all of his/her alleles.
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Expanding the basic quantitative
genetics equation
We earlier described the relationship,
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From individuals to populations:
patterns of phenotypic variation
With an understanding of factors
that determine the phenotype of an
individual, we can move back up to
the level of the population to
develop our understanding of how to
estimate the genetic component of
quantitative trait variation.
P = G + E,
Which describe the factors that determine an individual’s
phenotype, but we now understand that the component G can be
further broken down into:
G= A + D + I,
to describe the components of Genetic effects on the phenotype
attributed to Additive genetic effects (as measured by he
Breeding value), Dominance effects and Interaction effects
(Epistasis).
Our description of the Breeding value (A) showed that the
phenotype
of an individual’s offspring is mainly determined by the
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breeding value of its parents.
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Q: How much of the phenotypic
variation that we observe is due to
genetic variation?
How much of this genetic variation
contributes to the response to
selection?
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From individuals to populations:
patterns of phenotypic variation
From individuals to populations:
patterns of phenotypic variation
VP = VG + VE
The phenotypic variance (VP)
measures the extent to which
individuals vary in phenotype for a
particular trait.
The genetic variance (VG) can be
further broken down into additive,
dominance and interaction
components, analogous to those
used to describe an individual
phenotype:
The phenotypic variance within a
population may be due to genetic
and/or environmental differences
among individuals:
VP = VG + VE
VG = VA + VD + VI
The additive genetic variance (VA)
equals the variance in breeding
values within a population and
measures the degree to which
offspring resemble their parents.26
(Ignoring interactions between
genes & environment)
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Calculating phenotypic and
additive genetic variances
Calculating phenotypic and
additive genetic variances
Example: Milk yield in cows
Example: Milk yield in cows
Variance:
_
Vx= !i (Xi – X)2
--------------(n – 1)
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Cow
yield
1
75
2
88
3
52
4
83
5
82
6
43
7
100
8
48
9
79
10
100
mean
75
Variance:
VP = (75-75)2 + (88-75)2 +…
n-1
= 425.6
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_
Vx= !i (Xi – X)2
--------------(n – 1)
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Cow
yield
Offspring
Yield
1
75
2
88
81.5
3
52
65.5
4
83
79
5
82
78.5
6
43
66
7
100
84
8
48
64.5
9
79
79.5
10
100
78
mean
75
A = (offspringmean) X 2 + mean
74.5
A = 83
A = 93
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Calculating Phenotypic and
Additive Genetic Variance
Calculating Phenotypic and
Additive Genetic Variance
Example: Milk yield in cows
Variance:
_
Vx= !i (Xi – X)2
--------------(n – 1)
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Cow
yield
Offspring
Yield
A
1
75
74.5
74
2
3
88
81.5
88
52
65.5
56
4
5
83
79
83
82
78.5
82
6
43
66
57
7
100
84
93
8
48
64.5
54
9
79
79.5
84
10
100
78
mean
75
VP = 425.6
VA = 205.5
81
75.2
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Knowledge of the phenotypic
variance and additive genetic
variance allows us to predict
how similar we expect the
phenotypes of parents and
offspring to be.
It will also allow us to
predict the magnitude of the
response to selection when
individuals with different
phenotypic means have
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different probabilities of
survival or reproduction.
Narrow-Sense Heritability
h2 = VA / VP
In the previous example,
nearly half of the
phenotypic variance was
the result of additive
genetic variance.
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Broad sense heritability describes the
proportion of phenotypic variance due to total
genetic variance among individuals.
H2 = VG / VP
Broad-sense heritability will be 1 if all of the phenotypic
variation within a population is due to genotypic
differences among individuals (VG = VP).
Broad-sense heritability will be 0 if all of the phenotypic
variation is caused by environmental differences.
h2 = VA / (VA + VD + VI + VE)
Heritability can be low due to:
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VA = 205.5
Broad-Sense Heritability
H2 = VG / VP
Narrow sense heritability describes the
proportion of phenotypic variance due to
additive genetic variance among individuals, or
the extent to which variation in phenotype is
caused by genes transmitted from parents.
Conversely, h2 will be 1 only if there is no
variation due to dominance, epistasis, or
environmental effects. When h2 = 1, P = G = A.
VP = 425.6
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Important points about
heritability
1. When we use the term ‘heritability’, we are almost
always referring to narrow sense heritability.
2. Estimates of heritability are not transferable. They
are specific to the population and the environment
in which they are estimated.
3. Heritability estimates are for populations, not
individuals
4. Heritability does not indicate the degree to which a
trait is genetically based. Rather, it measures the
proportion of the phenotypic variance that is the
result of genetic factors.
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