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Chapter 7 Quantitative Genetics 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].

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Quantitative Genetics Traits such as flower color in peas produce distinct phenotypes. Such discrete traits, which are determined by a single gene, are relatively rare. Most traits are determined by the effects of multiple genes (polygenic traits) and these show continuous variation in trait values.

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Complex traits vary continuously

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Continuous variation For example, grain color in winter wheat is determined by three genes at three loci each with two alleles.

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Additive effects of genes Genes affecting color of winter wheat interact in a straightforward way. They have additive genetic effects. Thus the phenotype is obtained by summing the effects of individual alleles. The more alleles for being dark (prev. slide) or large (next slide) an individual has, the darker/taller it will be. A continuous distribution results.

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Continuous variation Examples of humans traits that show continuous variation: height, intelligence, athletic ability, skin color.

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Quantitative traits For continuous traits we cannot assign individuals to discrete categories (e.g. tall or short). Instead we must measure them. Therefore, characters with continuously distributed phenotypes are called quantitative traits. Quantitative genetics is the study of the genetic basis of quantitative traits.

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Value of quantitative traits Quantitative traits determined by influence of (1) genes and (2) environment. The value of a quantitative trait such as height is determined by the organisms genes operating within their environment. Both the genes it inherited from its parents and the conditions under which it grows up affect an individuals height.

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Value of quantitative traits For a given individual the value of its phenotype (P) (e.g., a persons 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.

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Genetic and environmental influences create continuous distribution

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Measuring Heritable Variation Quantitative genetics 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.

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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.

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Measuring Heritable Variation Heritability is defined as the fraction of total phenotypic variation that is due to variation in genes

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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.)

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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 an individuals genotypic value G could be represented as the sum of individual gene effects.

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Measuring Heritable Variation However, interactions between alleles (dominance effects) and interactions between different genes (epistatic effects) can affect the phenotype and these effects are non-additive.

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Measuring Heritable Variation To account for dominance and epistasis we break down the equation for P (value of the phenotype) P = G +E Comonent 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

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Measuring Heritable Variation Similarly, assuming all 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 Only Va is directly operated on by natural selection. 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 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)

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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 parents 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. 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 slope of 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 its 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.

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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 estimated heritability of bill depth as about 0.98.

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

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Directional selection for oil content in corn

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Disruptive selection for bristle number in Drosophila

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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 and the effect of selection. To assess the effect of selection we have to measure differences in survival and reproductive success among individuals.

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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 members of a population breed and others dont 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.

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Selection Differential

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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 the simple formula: R=h 2 S R is predicted response to selection, h 2 is heritability, S is selection differential. R is the proportional (or if you multiply by 100, the percentage) change in a trait value.

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Effect of difference in heritability (h 2 ) on a populations response to selection (R) with same selection differential (S). Plots of parent offspring regressions for two populations. Intersection of axes is midpoint of parental (x-axis) and offspring (y-axis) trait values.

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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 (h 2 ).

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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 the selection differential (S) to be 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. R=h 2 S R=0.2*0.05 = 0.01 (low end estimate) R=1.0*0.05 = 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.