Chapter 9 Quantitative Genetics

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Chapter 9 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.

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Continuous Variation

• Traits determined by many genes show continuous
  variation.
• Examples in humans include height, intelligence,
  athletic ability, skin color.
• Beak depth in Darwins finches and beak length in
  soapberry bugs also show continuous variation.

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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.

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Quantitative Traits

• Quantitative traits determined by influence of
  (1) genes and (2) environment.

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Easts 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)

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Easts 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
  F1s to create F2 generation.

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Easts 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)

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Easts 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.

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Easts 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.

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Easts 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.

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Easts 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?

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Easts 1916 work on quantitative traits

• Environmental effects.
• Because of environmental differences genetically
  identical organisms may differ greatly in
  phenotype.

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Genetically identical plants grown at different
elevations differ enormously (Clausen et al.
1948)
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• Skip section 9.2 QTL mapping

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Measuring Heritable Variation

• People differ in many traits e.g. height.
• Is height heritable?

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Measuring Heritable Variation

• A persons height is determined by their genes
  operating within their environment.
• A woman who is 5 feet tall did not get four feet
  of her height from her genes and a foot of height
  from her environment.
• It is important to realize that her height
  resulted from her genes operating within her
  environment.

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Measuring Heritable Variation

• How can we disentangle the effects of genes and
  environment?
• We cant do it by looking at one individual. But
  we can ask for example is the smallest woman in
  our distribution shorter than the tallest woman
  because they have
• (i) different genes
• (ii) grew up in different environments or
• (iii) both

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Measuring Heritable Variation

• In practice what population geneticists try to do
  is to figure out what fraction of variation in a
  trait is due to variation in genes and what
  fraction is due to variation in environmental
  conditions.
• The fraction of total variation in a trait that
  is due to variation in genes is called the
  heritability of a trait.

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Measuring Heritable Variation

• Heritability is often misinterpreted as the
  extent to which the phenotype is determined by
  the genotype or by the genes inherited from the
  parent.
• This is not correct because many loci are fixed
  and so do not contribute to variation. A locus
  can affect a trait even if it is not variable.
• The fact that humans have two eyes is genetically
  determined, but heritability of eye number is
  zero.

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Measuring Heritable Variation

• Definition Heritability measures what fraction
  of variation in a trait (e.g. height) is due to
  variation in genes and what fraction is due to
  variation in environment.
• Heritability estimates are based on population
  data.

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Measuring Heritable Variation

• 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.

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Measuring Heritable Variation

• Heritability symbolized by H2 Vg/Vp
• H2 Vg/Vp
• Because VpVgVe
• H2 Vg/VgVe
• H2 is broad-sense heritability. Heritability
  always a number between 0 and 1.

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Estimating heritability from parents and offspring

• If variation among individuals is due at least in
  part to variation in genes then offspring will
  resemble their parents.
• Can assess this relationship using scatter plots.

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Estimating heritability from parents and offspring

• The midparent value (average of the two parents)
  is regressed against offspring value and a best
  fit line is determined.
• The slope of the relationship is the change in
  the y variable per unit change in the x variable.

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Estimating heritability from parents and offspring

• If offspring dont 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.

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Estimating heritability from parents and offspring

• If offspring strongly resemble parents then best
  fit line slope will be close to 1.

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Estimating heritability from parents and offspring

• Most traits in most populations fall somewhere in
  the middle with offspring showing moderate
  resemblance to parents.

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Estimating heritability from parents and offspring

• Slope of best fit line is between 0 and 1.
• Slope of a regression line represents
  narrow-sense heritability (h2).

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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 and
  epistasis.

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Narrow-sense heritability

• h2 Va/(Va Vd Ve)

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Narrow-sense heritability

• When estimating heritability important to
  remember parents and offspring share environment.
• To make sure there is no correlation between
  environments experienced by parents and offspring
  requires cross-fostering experiments.

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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.

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Smith and Dhondt (1980)

• Smith and Dhondt estimated heritability of bill
  depth about 0.98.

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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.

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McClearn et al.s (1997) twin study

• McClearn et al. (1997) used twin study to assess
  heritability of general cognitive ability.
• Studied 110 pairs of monozygotic identical
  twins i.e. derived from splitting of one egg and
  130 pairs of dizygotic twins in Sweden.

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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.

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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.

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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.

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Measuring differences in survival and reproduction

• If some animals in a population breed and others
  dont 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).
• This term is derived from selective breeding
  trials.

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Measuring differences in survival and reproduction

• Another way to assess selection differential is
  to use linear regression.
• To do this we can regress fitness against the
  value of a phenotypic trait.
• Slope of best-fit line is the selection
  differential.

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Evolutionary response to selection

• Knowing heritability and selection differential
  we can predict evolutionary response to selection
  (R).
• This is how much of a change in a trait value we
  expect to see from one generation to the next.
• Given by formula Rh2S
• R is predicted response to selection, h2 is
  heritability, S is selection differential.

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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.

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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.

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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).

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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).

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Alpine skypilots and bumble bees

• Using her data Galen predicted response to
  selection R.
• Rh2S
• R0.20.05 0.01 (low end estimate)
• R1.00.05 0.05 (high end estimate)

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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.

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Modes of selection

• Three majors modes of selection recognized.
• Directional
• Stabilizing
• Disruptive

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Directional selection

• In directional selection fitness increases or
  decreases with the value of a trait.

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Directional selection

• E.g bumblebees and Alpine skypilots. Flower size
  increases under bumble bee selection.
• Darwins finches beak size increased during
  drought

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Stabilizing Selection

• In stabilizing selection individuals with
  intermediate values of a trait are favored.

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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.

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Stabilizing selection

• Parasitoid wasps impose strong directional
  selection on wasps favoring larger gall size.

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Stabilizing selection

• Birds impose strong directional selection
  favoring smaller gall size

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Stabilizing selection

• Net result of selection by birds and wasps
  operating in opposite directions is stabilizing
  selection.

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Disruptive selection

• In disruptive selection individuals with extreme
  values of a trait are favored.

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Disruptive selection

• Bates Smith (1993) studied black-bellied
  seedcrackers.
• Birds in population have one of two distinct bill
  sizes.

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Disruptive selection

• Bates Smith found that among juveniles,
  individuals with beaks of intermediate size did
  not survive.

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