Quantitative Genetics - Chapter 22
Traits whose phenotypes vary continuously
from one extreme to the other such that no
distinct phenotypic classes can be
distinguished are said to be under
quantitative genetic control.
The individual contribution or affect of an
allele or gene in a quantitative trait is small
compared to qualitative genes.
polygenic trait - a trait that is controlled by
many genes each contributing a small affect
on the phenotype.
examples With a quantitative trait the gene action can
be either additive, non-additive, or a
combination of the two.
Additive gene action - The number of genes
or alleles control the degree of expression.
This is sometimes considered a dose effect.
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Example: seed color in wheat
There are 3 genes in wheat that control seed
color. Each dominant allele gives one dose of
color.
white seed
aabbcc
X
dark red seed
AABBCC

F1 medium red seed
AaBbCc
X

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An interesting result of additive genetic
control is transgressive segregation. Here the
extremes in an F2 population can exceed the
expression in the parents.
example: body size in chickens.
Hamburgh
(large)
X
Sebright Bantam
(small)

F1 medium size X F1 medium size

Larger
Smaller
than  --------------------------------  than
Hamburgh
Bantam
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Non-additive gene action - Where the
expression of an allele can express like a
homozygous individual (dominance) or a gene
can mask the expression of another gene
(epistasis).
example: hybrid vigor in crops
homozygous
inbred line
(small-weak)
X homozygous
inbred line
(small-weak)

F1 heterozygous at
many alleles
(large-vigorous)
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By crossing two homozygous individuals that
differ in genetic makeup you can maximize
the non-additive gene action in the F1. This
results in a very vigorous individual because
for most of the genes there will be at least one
dominant or functional allele at every gene
loci.
The term for this is heterosis. This could also
explain what is actually being observed with
over-dominance.
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If you can identify the completely
homozygous genotype in a population, you
can estimate the number of genes and
genotypes involved in the quantitative trait.
Number of genes
Look at the fraction of the population
showing the extreme expression of the trait.
If 2 genes involved = 1/16
If 3 genes involved = 1/64
So you can develop a formula to determine
the number of genes
(1/2)2N where N = number of genes
So if you solve for N you can determine the
number of genes involved.
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Number of genotypes
If 1 gene = 3 genotypes
2 genes = 9 genotypes
3 genes = 27 genotypes
then a formula of (3)N where N = number of
genes can be used to determine the
approximate number of genotypes.
When the quantitative trait is controlled by
many genes then it may be difficult to identify
the extreme genotype
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In traits under quantitative genetic control
the F2 segregating population shows a wide
range of phenotypes that can not be divided
into distinct classes.
What causes the phenotypic variability?
 genetic variability
 additive
 non-additive
 environmental variability
causes modifications in genetic expression
So phenotypic = genetic + environmental
variability variab. variability
8
When working with quantitative traits it is
difficult to work with gene expression in
individuals and expect to see much change.
To observe changes in quantitative traits it is
better to work with populations. You can
estimate the phenotypic variation in a
population for a trait by the amount of
variation for the trait from the mean
(average) of the population.
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What you need to know with a quantitative
trait is how much of the variation you observe
for a trait is genetic in nature.
The more the variation is under genetic
control the easier it is to modify expression of
the trait in the population.
You can estimate the genetic variation by
manipulating the equation: Vp = VG + VE to
VP - VE = VG
To estimate the environmental variance you
can use uniform genetic controls (individuals
that do not vary genetically in your
population.
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If all the variation observed was genetic then
a graph of individuals with the same genotype
would look like this:
Any deviation or variation from the expected
appearance would be caused by the
environment.
11
Example: height in corn
Tall parent
x
short parent
VP1 = VE
VP2 = VE
F1
VF1 = VE
self
F2 VF2 = VG + VE
12
What good is knowing the genetic variation
(VG)?
You can use the estimate of genetic variation
to determine how heritable a trait is and how
fast improvement or change can be made in a
trait.
Heritability
heritability (h2) is an indication of how much
of the variation observed for a trait is under
genetic control.
formula: h2 = VG/VP
This is called broad-sense heritability
A better estimate of the genetic variation that
can be manipulated is to work with just the
additive genetic variation. The overall
genetic variation (VG) can be partitioned into
an additive (VA) component and a nonadditive (VD) component. So VG = VA + VD.
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So for the narrow-sense heritability where
only the additive genetic variation is taken
into account the formula changes to:
h2 = VA/VP
example of estimating broad-sense
heritability: if the VP is 150 and VG is 75 then
h2 = 75/150 = .50
so 50 % of the variation observed is under
genetic control.
Estimating heritability: height in corn
Generation
mean + s
F1
F2
76 + 4
72 + 10
s2 = variance
VF1 = 16 = VE
VF2 = 100 = VG + VE
VG = VF2 - VF1 = 100 - 16 = 84
h2 = VG/VP = (VF2 - VF1)/VF2 = 84/100 = .84
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The closer h2 is to 1 the more the trait is under
genetic control and the more heritable the trait.
example:
Cattle
h2
birth weight
.49
milk yield
.43
white spotting
.95
Mice
h2
tail length (6 wks)
.40
body weight (6 wks)
.35
litter size
.20
Which traits are under more genetic control?
15
Genetic Gain
You can also use h2 to estimate the genetic
gain in breeding to improve a trait.
So the question that can be asked is how
much will the population mean change if only
the selected individuals are allowed to mate.
example: height in humans
if the population mean is 5’ 7’’ or 67’’
and the selected population mean is 6’ 2’’ or
74’’
and h2 = .3
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The genetic gain can be calculated by the
following equation:
genetic = (sel. pop. mean - pop. mean) x h2
gain
= (74’’ - 67’’) x .3
= 7’’ x .3
= 2.1’’
so population mean height should change
approximately 2 inches in the next
generation, 5’7’’ to 5’9’’.
To continue realizing a 2’’ gain in height
every generation you would need to continue
increasing the selected population mean each
generation (6’2’’ to 6’4’’ etc.)
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