Transcript quantitative genetics

Quantitative Genetics
Quantitative Traits
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Mendel worked with traits that were all discrete, either/or traits: yellow or
green, round or wrinkled, etc. Different alleles gave clearly distinguishable
phenotypes.
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However, many traits don’t fall into discrete categories: height, for example,
or yield of corn per acre. These are “quantitative traits”.
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The manipulation of quantitative traits has allowed major increases in crop
yield during the past 80 years. This is an important part of why today
famine is rare, a product of political instability rather than a real shortage of
food. Until very recently, crop improvement through quantitative genetics
was the most profitable aspect of genetics.
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Early in the history of genetics is was argued that quantitative traits worked
through a genetic system quite different from Mendelian genetics. This idea
has been disproved, and the theory of quantitative genetics is based on
Mendelian principles.
Types of Quantitative Trait
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In general, the distribution of
quantitative traits values in a
population follows the normal
distribution (also known as Gaussian
distribution or bell curve). These
curves are characterized by the mean
(mid-point) and by the variance
(width). Often standard deviation, the
square root of variance, is used as a
measure of the curve’s width.
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1. continuous trait: can take on any
value: height, for example.
2. countable (meristic) can take on
integer values only: number of bristles,
for example.
3. threshold trait: has an underlying
quantitative distribution, but the trait
only appears only if a threshold is
crossed.
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Punchline and Basic Questions
• The basic tenet of quantitative genetics: the variation
seen in quantitative traits is due to a combination of
many genes each contributing a small amount, plus
environmental factors.
• Or: phenotype = genetics plus environment.
• Basic questions (plus answers):
– 1. What is the genetic basis of quantitative traits? (they are
caused by normal genes following Mendel’s rules).
– 2. How can we separate the effects of genetics from the effects
of the environment? (by inbreeding to eliminate genetic
variation).
– 3. How can we predict and control the outcome of a cross? (by
artificial selection).
Quantitative Traits are Caused by
Mendelian Genes
• In 1909 Herman Nilsson-Ehle from Sweden did a series
of experiments with kernel color in wheat.
• Wheat is a hexaploid, the result of 3 different species
producing a stable hybrid, an allopolyploid. There are
thus 3 similar but slightly different genomes contained in
the wheat genome, called A, B, and D.
• Each genome has a single gene that affects kernel color,
and each of these loci has a red allele and a white allele.
We will call the red alleles A, B, and D, and the white
alleles a, b, and d.
• Inheritance of these alleles is partially dominant, or
“additive”. The amount of red pigment in the kernel is
proportional to the number of red alleles present, from 0
to 6.
Wheat Kernel Color
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The cross: AA BB DD x aa bb dd. Red x white.
F1: Aa Bb Dd phenotype: pink, intermediate between the parents. Now self
these.
F2: alleles follow a binomial distribution:
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1/64 have all 6 red alleles = red
6/64 have 5 red + 1 white = light red
10/64 have 4 red + 2 white = dark pink
15/64 have 3 red + 3 white = pink
10/64 have 2 red + 4 white = light pink
6/64 have 1 red + 5 white = very pale pink
1/64 have all 6 white = white
Add a bit of environmental variation and human inability to distinguish
similar shades: you get a quantitative distribution.
This demonstrates that a simple Mendelian system: 3 genes, 2 alleles each,
partial dominance--can lead to a quantitative trait.
More Wheat Kernel Color
Separating Genetics from
Environment
• Three experiments by Wilhelm Johannsen,
from Denmark, using the common bean
(Phaseolus vulgaris). Johannsen coined
the words “genotype” and “phenotype”.
• First Johannsen experiment: he weighed a
group of beans, then grew them up and
weighed their progeny (after selfing them).
Johannsen’s First Experiment
The relation between the seed weight of the parental generation and the filial
generation in a variety of brown beans.
The figures in the table represent the filial numbers of beans of the different weight
categories
weight of the filial beans
weight of the
parental beans
weight categories
10
20
30
40
50
60
70
80
90
average
20
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1
15
90
63
11
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43,8
30
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15
85
322
310
91
2
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44,5
40
5
17
175
776
956
283
24
3
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44,2
50
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4
57
305
521
196
51
4
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48,9
60
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1
23
130
230
168
46
15
2
51,9
70
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5
53
175
180
64
15
2
56,0
total
5
38
170
1676
2255
928
187
33
2
47,92
according to W. JOHANNSEN; 1903, 1926
Interpretation
• In general, heavy parents gave heavy offspring and light
parents gave light offspring. That is, there is a significant
correlation between parent and offspring weights.
• However, there is also a considerable variation among
the offspring weights. This is due to variations in both
genetics and environment.
• Most offspring of extreme parents (very heavy or very
light) are more average than their parents. This is a
phenomenon called “regression to the mean”. Extreme
members of a population benefit from very lucky
environmental conditions, which can’t be inherited.
Johannsen’s Second Experiment
• Johannsen then worked on separating environmental
effects from genetic effects. He did this by inbreeding
the beans for 10 generations.
• Inbreeding means doing the closest possible cross, in
this case, selfing them.
• Half if the remaining heterozygosity (percentage of
heterozygotes) disappears for each generation of selfing.
This is because when a Aa heterozygote is selfed, 1/4 of
the offspring are AA, 1/4 are aa, and 1/2 are Aa. Selfing
the AA and aa offspring gives only homozygous offspring
forever. Thus is each generation, 1/2 the offspring
become homozygotes and all their offspring stay
homozygotes.
• After 10 generations of selfing, the percentage of
heterozygotes is less than 1/1000 of the original level.
Results
• Johannsen created 19 inbred lines. The inbred
lines had some variation, but less than the
original random-bred population. The remaining
variation was due to environmental variations.
• The mean weight of each line was different, but
it was stable across generations. The reason is
that the lines are genetically different from each
other, but they are genetically (more or less)
identical. The variance was also stable between
generations.
Johannsen’s Third Experiment
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Johannsen then started to work
out the basis of artificial selection:
how to improve a species as
efficiently as possible.
Start with a random-bred
population. Take the best ones to
be parents of the next generation.
The next generation has a mean
that is shifted in the desired
direction .
This procedure doesn’t work for
inbred populations, because there
is no genetic variation to inherit.
The next generation’s mean is the
same as the previous generation’s
mean despite having selected the
best parents.
Selection
• Edward M. East from the United States worked out the formal basis
for modern artificial selection, following the work of George Shull on
maize. East worked on both maize and tobacco.
• East measured the length of the tobacco corolla (the straight part of
the flower). He crossed 2 inbred lines with different lengths, then
selfed the F1 to get and F2, then selfed the F2’s to get a series of F3
lines.
• The variation in the plants can be observed in the width of the
distribution curves. Environmental variation is constant among all
plants.
• Genetic variation is minimal in both the inbred parental lines and in
the F1’s. The F1’s are heterozygous, but they are genetically
uniform, because all of their parents were homozygous. The F2
displays the maximum variation: for every gene, all possible
genotypes (AA, Aa, and aa) are present in the population. The F3’s
show less variation than the F2’s, as inbreeding starts to eliminate
heterozygosity.
Heterosis
• Both the parental lines and the F1’s are genetically
uniform. However, the parental lines are relatively small
and weak, a phenomenon called “inbreeding
depression”: Too much homozygosity leads to small,
sickly and weak organisms, at least among organisms
that usually breed with others instead of self-pollinating.
• In contrast, the F1 hybrids are large, healthy and strong.
This phenomenon is called “heterosis” or “hybrid vigor”.
• The corn planted in the US and other developed
countries in nearly all F1 hybrid seed, because it
produces high yielding, healthy plants (due to heterosis)
and it is genetically uniform (and thus matures at the
same time with ears in the same position on every plant).
Mathematical Basis of Quantitative
Genetics
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Recall the basic premise of quantitative genetics: phenotype = genetics plus
environment.
In fact we are looking at variation in the traits, which is measured by the
width of the Gaussian distribution curve. This width is the variance (or its
square root, the standard deviation).
Variance is a useful property, because variances from different sources can
be added together to get total variance.
However, the units of variance are the squares of the units used to measure
the trait. Thus, if length in centimeters was measured, the variances of the
length are in cm2. This is why standard deviation is usually reported: length
± s.d. --because standard deviation is in the same units as the original
measurement. Standard deviations from different sources are not additive.
Quantitative traits can thus be expressed as:
VT = VG + VE
where VT = total variance, VG - variance due to genetics, and VE =
variance due to environmental (non-inherited) causes.
This equation is often written with an additional covariance term: the
degree to which genetic and environmental variance depend on each other.
We are just going to assume this term equals zero in our discussions.
Heritability
• One property of interest is “heritability”, the proportion of
a trait’s variation that is due to genetics (with the rest of it
due to “environmental” factors). This seems like a
simple concept, but it is loaded with problems.
• The broad-sense heritability, symbolized as H
(sometimes H2 to indicate that the units of variance are
squared). H is a simple translation of the statement from
above into mathematics:
H = VG / VT
• This measure, the broad-sense heritability, is fairly easy
to measure, especially in human populations where
identical twins are available. However, different studies
show wide variations in H values for the same traits, and
plant breeders have found that it doesn’t accurately
reflect the results of selection experiments. Thus, H is
generally only used in social science work.
Additive vs. Dominance Genetic
Variance
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The biggest problem with broad sense heritability comes from lumping all
genetic phenomena into a single Vg factor. Paradoxically, not all variation
due to genetic differences can be directly inherited by an offspring from the
parents.
Genetic variance can be split into 2 main components, additive genetic
variance (VA) and dominance genetic variance (VD).
VG = VA + VD
Additive variance is the variance in a trait that is due to the effects of each
individual allele being added together, without any interactions with other
alleles or genes.
Dominance variance is the variance that is due to interactions between
alleles: synergy, effects due to two alleles interacting to make the trait
greater (or lesser) than the sum of the two alleles acting alone. We are
using dominance variance to include both interactions between alleles of
the same gene and interactions between difference genes, which is
sometimes a separate component called epistasis variance.
The important point: dominance variance is not directly inherited from
parent to offspring. It is due to the interaction of genes from both parents
within the individual, and of course only one allele is passed from each
parent to the offspring.
Narrow Sense Heritability
• For a practical breeder,
dominance variance can’t be
predicted, and it doesn’t affect
the mean or variance of the
offspring of a selection cross in
a systematic fashion. Thus,
only additive genetic variance
is useful. Breeders and other
scientists use “narrow sense
heritability”, h, as a measure of
heritability.
h = VA / VT
• Narrow sense heritability can
also be calculated directly from
breeding experiments. For this
reason it is also called
“realized heritability”.
Heritability in a Selection
Experiment
• There are 3 easily measured parameters in a selection experiment:
the mean of the original random-bred population, the mean of the
individuals selected to be the parents, and the mean of the next
generation. These factors are related by the narrow sense
heritability:
• The denominator is sometimes called the “selection differential”, the
difference between the total population and the individuals selected
to be parents of the next generation. The numerator is sometimes
called the “selection response”, the difference between the offspring
and the original population, the amount the population shifted due to
the selection.
h
next _ generation_ meanoriginal_ mean
 parent _ meanoriginal_ mean
Example
• In Drosophila, the mean number of bristles on
the thorax (top surface only) is 6.4.
• From this population, a group was chosen which
had an average bristle number of 7.2.
• The offspring of the chosen group had an
average of 6.6 bristles.
• h = (next gen - original) / (selected - original)
• h = (6.6 - 6.4) / (7.2 - 6.4)
• h = 0.2 / 0.8
• h = 0.25
Realized Heritability
• The value of h as measured by selection experiments is
remarkably constant over many generations, and
selection can be continued for a very long time without
apparently running out of genetic variation.
• In one experiment using Tribolium (flour beetles), the
original population had a mean weight of 2.4 mg, with a
range of 1.8 to 3.0 mg. After 125 generations of
selection, the mean weight was 5.1 mg, more than twice
the original weight and far outside the original range.
• Similar experiments at the University of Illinois on maize
for high protein and high oil content have shown
consistent improvement for more than 100 generations
(i.e. 100 years, since 1896).
Summary of Equations
• You will need to know these equations, and then
demonstrate them in solving problems.
• VT = VG + VE
• for an INBRED population, VT = VE, because VG
=0
• H = VG / VT
• VG = VA + VD
• h = VA / VT
• h = (next gen - original) / (selected - original)
• Note that h can be calculated from either of the 2
equations.
Example Problem
• In a quest to make bigger frogs, scientists started with a
random bred population of frogs with an average weight
of 500 g. They chose a group with average weight 600 g
to be the parents of the next generation. A few other
facts: VE = 1340, VA = 870, VD = 410.
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What is the genetic variance? VG = VA + VD = 1280
What is the total variance? VT = VG + VE = 2620
What is the broad sense heritability? H = VG / VT = 0.49
What is the narrow sense heritability? h = VA / VT = 0.33
What is the mean weight of the next generation?
h = (next gen - original) / (selected - original)
0.33 = (next_gen - 500) / (600 - 500) = 533 g