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 (such traits are called polygenic traits) and
these show continuous variation in trait values.
Complex traits vary continuously. For example, grain color in winter wheat is determined by three genes
at three loci each with two alleles.
Additive effects of genes
The genes affecting color of winter wheat interact in a particularly straightforward way. They have
additive genetic effects. This means that the phenotype for an individual is obtained just by summing
the effects of individual alleles. For example, the more alleles for being dark (previous image) or large
(next image) that an individual has, the darker/taller it will be and the continuous distribution results.
Examples in humans of traits that show continuous variation include height, intelligence, athletic ability,
and skin color.
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 and
the study of the genetic basis of quantitative traits is quantitative genetics.
Quantitative genetics is the study of the genetic basis of quantitative traits.
Value of quantitative traits. Quantitative traits are determined by influence of (1) genes and (2)
environment. The value of a quantitative trait such as an individual’s height or running speed is
determined by the organism’s genes operating within their environment. The size an organism grows is
affected not only by the genes it inherited from its parents, but the conditions under which it grow up.
For a given individual the value of its phenotype (P) (e.g., the weight of a tomato in grams, a person’s
height in cm) 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.
Genetic and environmental influences together (above) create a continuous distribution.
Measuring Heritable Variation
It is impossible to consider an individual and decide how much of a trait value to assign to genes or
environment. Therefore, the quantitative genetics approach takes a population view and tracks
variation in phenotype and whether this variation has a genetic basis. Variation in a sample is measured
using a statistic called the variance. The variance measures how different individuals are from the mean
and estimates 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 Vp is phenotypic variance, Vg is variance due to genotypic effects and Ve is
variance due to environmental effects.
Heritability measures what fraction of variation is due to variation in genes and what fraction is due to
variation in environment.
Heritability is defined as the fraction of total phenotypic variation that is due to variation in genes
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 value between 0 and 1.)
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) that can affect the phenotype and these effects
are non-additive.
To account for dominance and epistasis we break down the equation for P (value of the phenotype)
P = G +E
Component G (genetic effects) is the sum of three subcomponents – A [additive component], D
[dominance component] and I [epistatic or interaction component].
G=A+D+I
So, therefore, P = A + D + I + E
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
Breaking down the variances allows us to produce a simple expression for how a phenotypic trait
changes over time in response to selection.
Importantly, only one component of variation 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). [E.g. a recessive allele
only exerts its effect on a phenotype when it is homozygous. If a dominant allele is present the recessive
allele is not expressed.] Va however exerts the same effect regardless of the genetic background.
Therefore, its effects are always visible to selection.
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
variance
h2 = Va/(Va + Vd + Vi + Ve)
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 parents in a population.
It turns out that narrow sense heritability (h2) is easy to measure. It turns out to be the slope of a linear
regression between the average phenotype of the two parents and the phenotype of the offspring. We
can assess this relationship using a scatter plot. To do this we 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. A slope of zero
indicates most variation in individuals is due to variation in the environments they grew up in. If the
offspring strongly resemble their parents then the slope of the best fit line will be close to 1. Most traits
in most populations fall somewhere in the middle; with the offspring showing a moderate resemblance
to their parents.
When estimating heritability it’s important to remember parents and offspring share an environment.
We need to make sure there is no correlation between the environments experienced by parents and
their offspring. This requires cross-fostering experiments to randomize environmental effects.
Smith and Dhondt (1980) studied heritability of beak size in Song Sparrows. In their experiment they
moved eggs and young to nests of foster parents. Then they compared the resulting chicks beak
dimensions to the beak dimensions of their parents and foster parents.
Smith and Dhondt estimated heritability of bill depth as about 0.98.
Evolutionary response to selection.
Once we know the sources of variation in a quantitative trait we can study how it evolves. If selection
favors certain values of a trait then we expect the population to evolve in response. The effect on the
distribution of the values of the trait will depend on which phenotypes are being favored (see next
image).
Directional selection results in one extreme of the distribution being favored and the population
evolves over time in that direction. Disruptive selection results in selection against the middle of the
distribution so that the extremes are favored. Examples of directional selection are frequently referred
to in text books as they show change in a population, which is what most people think of as evolution.
However, in reality, most selection results in keeping things as they are now. This is stabilizing selection
in which individuals with average trait values are favored and extremes are selected against. This makes
sense if you remember that all organisms living today have been shaped by millions of years of evolution
and, hence, are very well adapted to their environments. It stands to reason then that the average
phenotype is an excellent fit to the environment and any deviation from that will tend to make an
organism less well adapted and be selected against. Thus, the commonest form of selection we see in
nature is stabilizing selection.
Evolutionary response to selection
To quantify the amount and direction of change in a trait value from one generation to the next (i.e.
how a trait evolves) we need to quantify heritability [as we’ve done] and the effect of selection.
We need to be able to measure differences in survival and reproductive success among individuals to
assess the effect of selection. To do this we need to be able to quantify the difference between
winners and losers in whatever trait we are interested in. This is strength of selection.
If some members of a population breed and others don’t and you compare the 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.
[In the diagram above what is called S and described as the strength of selection is the selection
differential.]
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.
Knowing heritability and selection differential we can predict evolutionary response to selection (R).
Given by the simple formula: R=h2S. R is the predicted response to selection, h2 is heritability, S is
selection differential.
R is the proportional (or if you multiply by 100, the percentage) change in a trait value.
Diagram above shows the effect of different values of narrow sense heritability on R the response to
selection. The bigger h2 is the greater the resulting value of R.
Effect of difference in heritability (h2) on a population’s response to selection (R) with same selection
differential (S). Plots of parent offspring regressions for two populations. The intersection of axes is the
midpoint of parental (x-axis) and offspring (y-axis) trait values.
Alpine skypilots and bumble bees
Alpine skypilot is a perennial wildflower found in the Rocky Mountains. Populations at timberline and
tundra differed in size. Tundra flowers about 12% larger in diameter. Timberline flowers are pollinated
by many insects, but tundra only by bees. Bees known to be more attracted to larger flowers.
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%.
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).
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.
Galen correlated number of surviving young with flower size of parent. She estimated the selection
differential (S) to be 5% (successfully pollinated plants were 5% larger than population average). 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)
Thus, we expect a 1-5% increase in flower size per generation.
Therefore, the difference we see between populations in flower size is plausibly due to
bumblebee selection pressure.