Transcript Hardy Weinberg Equiibrium with more than 2 alleles

Chapter 8 Quantitative Genetics
 Traits
such as cystic fibrosis or flower color
in peas produce distinct phenotypes that
are readily distinguished.
 Such discrete traits, which are determined
by a single gene, are the minority in
nature.
 Most traits are determined by the effects of
multiple genes.
Continuous Variation
 Traits
determined by many genes show
continuous variation.
 Examples in humans include height,
intelligence, athletic ability, skin color.
 Beak depth in Darwin’s finches and beak
length in soapberry bugs also show
continuous variation.
Quantitative Traits
 For
continuous traits we cannot assign
individuals to discrete categories. Instead
we must measure them.
 Therefore,
characters with continuously
distributed phenotypes are called
quantitative traits.
Quantitative Traits
 Quantitative
traits determined by influence
of (1) genes and (2) environment.
East’s 1916 work on quantitative
traits
 In
early 20th century debate over whether
Mendelian genetics could explain
continuous traits.
 Edward East (1916) showed it could.
 Studied longflower tobacco (Nicotiana
longiflora)
East’s 1916 work on quantitative
traits
 East
studied corolla length (petal part of
flower) in tobacco.
 Crossed
pure breeding short and long
corolla individuals to produce F1
generation. Crossed F1’s to create F2
generation.
East’s 1916 work on quantitative
traits
 Using
Mendelian genetics we can predict
expected character distributions if
character determined by one gene, two
genes, or more etc.
 (You
need to understand how to do
Punnett Squares)
East’s 1916 work on quantitative
traits
 Depending
on number of genes, models
predict different numbers of phenotypes.
 One gene: 3 phenotypes
 Two genes: 5 phenotypes
 Six genes: 13 phenotypes. Continuous
distribution.
East’s 1916 work on quantitative
traits
 How
do we decide if a quantitative trait is
under the control of many genes?
 In one- and two-locus models many F2
plants have phenotypes like the parental
strains.
 Not so with 6-locus model. Just 1 in 4,096
individuals will have the genotype
aabbccddeeff.
East’s 1916 work on quantitative
traits
 But,
if Mendelian model works you should
be able to recover the parental
phenotypes through selective breeding.
 East
selectively bred for both short and
long corollas. By generation 5 most plants
had corolla lengths within the range of the
original parents.
East’s 1916 work on quantitative
traits
 Plants
in F5 generation of course were not
exactly the same size as their ancestors
even though they were genetically
identical.
 Why?
East’s 1916 work on quantitative
traits
 Environmental
 Because
effects.
of environmental differences
genetically identical organisms may differ
greatly in phenotype.
Genetically identical plants
grown at different elevations
differ enormously
(Clausen et al. 1948)
 Skip
section 8.2 QTL mapping
Measuring Heritable Variation
 A person’s
height is determined by their
genes operating within their environment.
 Heritability
measures what fraction of
variation in height is due to variation in
genes and what fraction is due to variation
in environment.
Measuring Heritable Variation
 Heritability
measured based on population
data.
 Total variation in trait is phenotypic
variation Vp.
 Variation among individuals due to their
genes is genetic variation Vg
 Variation among individuals due to their
environment is environmental variation Ve.
Measuring Heritable Variation
 Heritability
= Vg/Vp
 Heritability
= Vg/Vg+Ve
 This
is broad-sense heritability. Heritability
always a number between 0 and 1.
Estimating heritability from
parents and offspring
 If
variation among individuals is due to
variation in genes then offspring will
resemble their parents.
 Can
assess relationship using scatter
plots.
Estimating heritability from parents
and offspring
 Plot
midparent value (average of the two
parents) against offspring value.
Estimating heritability from parents
and offspring
 If
offspring don’t resemble parents then
best fit line has a slope of approximately
zero.
 Slope
of zero indicates most variation in
individuals due to variation in
environments.
Estimating heritability from parents
and offspring
 If
offspring strongly resemble parents then
best fit line will be close to 1.
Estimating heritability from parents
and offspring
 Most
traits in most populations fall
somewhere in the middle with offspring
showing moderate resemblance to
parents.
Estimating heritability from parents
and offspring
 Slope
of best fit line is between 0 and 1.
 Slope
represents narrow-sense heritability
(h2).
Narrow-sense heritability
 Narrow-sense
heritability distinguishes
between two components of genetic
variation:
 Va additive genetic variation: variation due
to additive effects of genes.
 Vd dominance genetic variation: variation
due to gene interactions such as
dominance.
Narrow-sense heritability

h2 = Va/(Va + Vd + Ve)
Narrow-sense heritability
 When
estimating heritability important to
remember parents and offspring share
environment.
 Need
to make sure there is no correlation
between environments experienced by
parents and offspring. Requires crossfostering experiments.
Smith and Dhondt (1980)
 Smith
and Dhondt (1980) studied
heritability of beak size in Song Sparrows.
 Moved
eggs and young to nests of foster
parents. Compared chicks’ beak
dimensions to parents and foster parents.
Smith and Dhondt (1980)
 Smith
and Dhondt estimated heritability of
bill depth about 0.98.
Estimating heritability from twins
 Monozygotic
twins are genetically identical
dizygotic are not.
 Studies
of twins can be used to assess
relative contributions of genes and
environment to traits.
McClearn et al.’s (1997) twin study
 McClearn
et al. (1997) used twin study to
assess heritability of general cognitive
ability.
 Studied
110 pairs monozygotic and 130
pairs dizygotic twins in Sweden.
McClearn et al.’s (1997) twin study
 All
twins at least 80 years old, so plenty of
time for environment to exert its influence.
 However,
monozygotic twins resembled
each other much more than dizygotic.
 Estimated
heritability of trait at about 0.62.
Measuring differences in
survival and reproduction
 Heritable
variation in quantitative traits is
essential to Darwinian natural selection.
 Also
essential is that there are differences
in survival and reproductive success
among individuals. Need to be able to
measure this.
Measuring differences in
survival and reproduction
 Need
to be able to quantify difference
between winners and losers in trait of
interest. This is strength of selection.
Measuring differences in
survival and reproduction
 If
some animals in a population breed and
others don’t and you compare mean
values of some trait (say mass) for the
breeders and the whole population, the
difference between them (and one
measure of the strength of selection) is the
selection differential (S).
Measuring differences in
survival and reproduction
 Another
measure of the strength of
selection is the selection gradient.
 Assign absolute fitnesses to members of
population.
 Convert absolute fitnesses to relative
fitnesses (absolute fitness/mean fitness).
 Make scatterplot of relative fitness against
trait if interest. Slope of best-fit line is
selection gradient.
Selection gradient
 Selection
gradient = (selection
differential/variance of trait of interest.)
Evolutionary response to
selection
 Knowing
heritability and selection
differential can predict evolutionary
response to selection (R).
by formula: R=h2S
 R is predicted response to selection, h2 is
heritability, S is selection differential.
 Given
Alpine skypilots and bumble bees

Alpine skypilot perennial wildflower found in the
Rocky Mountains.

Populations at timberline and tundra differed in
size. Tundra flowers about 12% larger in
diameter.

Timberline flowers pollinated by many insects,
but tundra only by bees. Bees known to be
more attracted to larger flowers.
Alpine skypilots and bumble bees
 Candace
Galen (1996) wanted to know if
selection by bumblebees was responsible
for larger size flowers in tundra and, if so,
how long it would take flowers to increase
in size by 12%.
Alpine skypilots and bumble bees
 First,
Galen estimated heritability of flower
size. Measured plants flowers, planted
their seeds and (seven years later!)
measured flowers of offspring.
 Concluded
20-100% of variation in flower
size was heritable (h2).
Alpine skypilots and bumble bees

Next, she estimated strength of selection by
bumblebees by allowing bumblebees to pollinate
a caged population of plants, collected seeds
and grew plants from seed.
 Correlated number of surviving young with
flower size of parent. Estimated selection
gradient at 0.13 and the selection differential (S)
at 5% (successfully pollinated plants 5% larger
than population average).
Alpine skypilots and bumble bees
 Using
her data Galen predicted response
to selection R.
 R=h2S
 R=0.2*0.05
= 0.01 (low end estimate)
 R=1.0*0.05 = 0.05 (high end estimate)
Alpine skypilots and bumble bees
 Thus,
expect 1-5% increase in flower size
per generation.
 Difference
between populations in flower
size plausibly due to bumblebee selection
pressure.
Modes of selection
 Three
majors modes of selection
recognized.
 Directional
 Stabilizing
 Disruptive
Directional selection
 In
directional selection fitness increases or
decreases with the value of a trait.
Directional selection
 E.g
bumblebees and Alpine skypilots.
Flower size increases under bumble bee
selection.
 Darwin’s
finches beak size increased
during drought
Stabilizing Selection
 In
stabilizing selection individuals with
intermediate values of a trait are favored.
Stabilizing Selection
 Weis
and Abrahamson (1986) studied fly
Eurosta solidaginis.
 Female lays eggs on goldenrod and larva
forms a gall for protection.
 Two dangers for larva. 1. Galls
parasitized by wasps and 2. birds open
galls and eat larva.
Stabilizing selection
 Parasitoid
wasps impose strong directional
selection on wasps favoring larger gall
size.
Stabilizing selection
 Birds
impose strong directional selection
favoring smaller gall size
Stabilizing selection
 Net
result of selection by birds and wasps
operating in opposite directions is
stabilizing selection.
Disruptive selection
 In
disruptive selection individuals with
extreme values of a trait are favored.
Disruptive selection
 Bates
Smith (1993) studied black-bellied
seedcrackers.
 Birds
in population have one of two distinct
bill sizes.
Disruptive selection
 Bates
Smith found that among juveniles,
individuals with beaks of intermediate size
did not survive.