Quantitative genetics

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Quantitative genetics
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Measuring Heritable Variation

• The value of quantitative traits such a persons
  height or fruit size or running speed is
  determined by their genes operating within their
  environment.
• The size someone grows is affected not only by
  the genes inherited from their parents, but the
  conditions under which they grow up.

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Measuring Heritable Variation

• For a given individual the value of its phenotype
  (P) (e.g. the weight of a tomato in grams) can be
  considered to consist of two parts -- the part
  due to genotype (G) and the part due to
  environment (E)
• P G E.
• G is the expected value of P for individuals with
  that genotype. Any difference between P and G is
  attributed to environmental effects.

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Measuring Heritable Variation

• The quantitative genetics approach depends on
  taking a population view and tracking variation
  in phenotype and whether this variation has a
  genetic basis.
• We measure variation in a sample using a
  statistical measure called the variance. The
  variance measures how different individuals are
  from the mean and the spread of the data.
• FYI Variance is the average squared deviation
  from the mean. Standard deviation is the square
  root of the variance.

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• We want to distinguish between heritable and
  nonheritable factors affecting the variation in
  phenotype.
• It turns out that the variance of a sum of
  independent variables is equal to the sum of
  their individual variances.
• Because P G E
• Then Vp Vg Ve
• where Vg is variance due to genotypic effects, Ve
  is variance due to environmental effects and Vp
  is phenotypic variation.

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Measuring Heritable Variation

• Heritability measures what fraction of variation
  is due to variation in genes and what fraction is
  due to variation in environment.

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Measuring Heritable Variation

• Heritability Vg/Vp
• Heritability Vg/VgVe
• This is broad-sense heritability (H2). It
  defines the fraction of the total variance that
  is due to genetic causes.
• Heritability is always a number between 0 and 1.

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Measuring Heritable Variation

• The genetic component of inheritance (Vg)
  includes the effect of all genes in the genotype.
• If all gene effects combined additively then an
  individuals genotypic value G could be
  represented as a simple sum of individual gene
  effects.
• However, there are interactions among alleles
  (dominance effects) and interactions among
  different genes (epistatic effects).

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Measuring Heritable Variation

• To account for dominance and epistasis we break
  down the equation for P
• P G E
• G (genetic effects) is the sum of three
  components A additive component, D dominance
  component and I epistatic or interaction
  component.
• G A D I
• So therefore P A D I E

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Measuring Heritable Variation

• Similarly, if we assume all the components of the
  equation P A D I E are independent of
  each other then the variance of this sum is equal
  to sum of the individual variances.
• Vp Va Vd Vi Ve

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Measuring Heritable Variation

• Breaking down the variances allows us to produce
  a simple expression for how a phenotypic trait
  changes over time in response to selection.
• Only one component Va is directly operated on by
  natural selection.
• The reason for this is that the effects of Vd and
  Vi are strongly context dependent i.e., their
  effects depend on what other alleles and genes
  are present (the genetic background).

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Measuring Heritable Variation

• Va however exerts the same effect regardless of
  the genetic background. Therefore, its effects
  are always visible to selection.

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Measuring Heritable Variation

• Remember we defined broad sense heritability (H2)
  as the proportion of total variance due to any
  form of genetic variation
• H2 Vg/VgVe
• We similarly define narrow sense heritability h2
  as the proportion of variance due to additive
  genetic variation
• h2 Va/(Va Vd Vi Ve)

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Measuring Heritable Variation

• Because narrow sense heritability is a measure of
  what fraction of the variation is visible to
  selection, it plays an important role in
  predicting how phenotypes will change over time
  as a result of natural selection.
• Narrow sense heritability reflects the degree to
  which offspring resemble their parent in a
  population.

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Estimating heritability from parents and offspring

• Narrow sense heritability is the slope of a
  linear regression between the average phenotype
  of the two parents and the phenotype of the
  offspring.
• Can assess the relationship using scatterplots.

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• Plot midparent value (average of the two parents)
  against offspring value.

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

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

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• 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 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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Berthold and Pullido study

• Berthold and Pullido studied the heritability of
  migratory restlessness in European Blackcaps.

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• Berthold and Pullido estimated heritability of
  migratory restlessness as about 0.453.

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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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Selection differential and response to selection
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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 whatever trait we are
  interested in. 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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Evolutionary response to selection

• We want to be able to measure the effect of
  selection on a population.
• This is called the Response to Selection and is
  defined as the difference between the mean trait
  value for the offspring generation and the mean
  trait value for the parental generation i.e. the
  change in trait value from one generation to the
  next.

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Evolutionary response to selection

• Knowing heritability and selection differential
  we can predict evolutionary response to selection
  (R).
• 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.