Transcript Chapter 9 Population genetics Heritability

Quantitative genetics
Measuring Heritable Variation
 The value of quantitative traits such a person’s 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.
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.
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.
 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.
Measuring Heritable Variation
 Heritability measures what fraction of variation is due
to variation in genes and what fraction is due to
variation in environment.
Measuring Heritable Variation
 Heritability = Vg/Vp
 Heritability = Vg/Vg+Ve
 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.
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
individual’s 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).
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
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
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).
Measuring Heritable Variation
 Va however exerts the same effect regardless of the
genetic background. Therefore, it’s effects are always
visible to selection.
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/Vg+Ve
 We similarly define narrow sense heritability h2 as
the proportion of variance due to additive genetic
variation
 h2 = Va/(Va + Vd + Vi + Ve)
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.
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.
 Plot midparent value (average of the two parents)
against offspring value.
 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.
 If offspring strongly resemble parents then best fit line
will be close to 1.
 Most traits in most populations fall somewhere in the
middle with offspring showing moderate resemblance
to parents.
 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.
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.
Berthold and Pullido study
 Berthold and Pullido studied the heritability of
migratory restlessness in European Blackcaps.
 Berthold and Pullido estimated heritability of
migratory restlessness as about 0.453.
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 of monozygotic [“identical” twins i.e.
derived from splitting of one egg] and 130 pairs of
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.
Selection differential and response
to selection
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 whatever trait we are interested
in. 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).
 This term is derived from selective breeding trials.
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.
Evolutionary response to selection
 Knowing heritability and selection differential we
can predict evolutionary response to selection (R).
 Given by formula: R=h2S
 R is predicted response to selection, h2 is
heritability, S is selection differential.
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.