 Read Chapter 7 sections 7.1 and 7.2. [You should read
7.3 and 7.4 to deepen your understanding of the topic, but I will not cover these topics in lecture].

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.

Continuous variation
 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 slide) or large (next slide) an individual has the darker/taller it will be and the continuous distribution results.

Continuous variation
 Examples in humans of traits that show continuous variation include height, intelligence, athletic ability, and skin color.

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 and the study of the genetic basis of quantitative traits is quantitative genetics.

Value of quantitative traits
 Quantitative traits determined by influence of (1) genes and (2) environment.
 The value of a quantitative traits such as height or fruit size 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.

Value of quantitative traits
 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.

Measuring Heritable Variation
 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.

Measuring Heritable Variation
 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.

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 (H 2 ). It defines the fraction of the total variance that is due to genetic causes.
 (Heritability is always a value 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) that can affect the phenotype and these effects are non-additive.

Measuring Heritable Variation
 To account for dominance and epistasis we break down the equation for P (value of the phenotype)
 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). [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.]

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

Measuring Heritable Variation
 Remember we defined broad sense heritability (H 2 ) as the proportion of total variance due to any form of genetic variation
 H 2 = Vg/Vg+Ve
 We similarly define narrow sense heritability h 2 as the proportion of variance due to additive genetic variance
 h 2 = 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 parents in a population.

 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.

 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)
 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 estimated heritability of bill depth as about 0.98.

 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 trait will depend on which phenotypes are being favored (see next slide).

Disruptive selection for bristle number in Drosophila

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.

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 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.

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=h 2 S
 R is predicted response to selection, h 2 is heritability, S is selection differential.

Effect of difference in heritability (h 2 ) on a population’s response to selection (R) with same selection differential (S).

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 (h 2 ).

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 the selection differential
(S) to be 5% (successfully pollinated plants 5% larger than population average).

Alpine skypilots and bumble bees
 Using her data Galen predicted response to selection
R.
 R=h 2 S
 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.