1 Quantitative Inheritance - Pt.2 Chapter 8. 2 Offspring- parent regression for height in humans (and why it’s called regression) (Fig. 8.11d)

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Quantitative Inheritance - Pt.2

Chapter 8

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Offspring-parent regression for height in humans (and why it’s called regression) (Fig. 8.11d)

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Assumptions of offpring-parent regression as an estimate of heritability

• The most important assumption being made in these analyses is that the only cause of resemblance between offspring and parents is shared genes

• This assumption may be violated if parents and offspring share the same environment and if environment has strong effects on the trait

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“Cross-fostering” and heritability of beak length in song sparrows (Fig. 8.12) - 1

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“Cross-fostering” and heritability of beak length in song sparrows (Fig. 8.12) - 2

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Estimating heritability from twin studies (Fig. 8.14)

If heritability is high both monzygotic and dizygotic twins should resemble each other, but monzygotic twins should resemble each other more closely than dizygotic twins (because the former share all their genes, while the latter share only half their genes)

If heritability is low, then neither type of twin should show close resemblance

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The heritability (H2 ?) of “general cognitive ability” as measured in a study of Swedish twins is about 0.62 (Fig. 8.1c)

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Estimating heritability from crosses between inbred lines:Corolla height in longflower tobacco (see Fig. 8.3)

• F1 individuals all have same heterozygous genotype. Therefore F1 variance = VE

• F2 individuals have variable genotypes (homozygotes and heterozygotes). Therefore, F2 variance = VG + VE

• VG = (F2 variance) minus (F1 variance)

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Measuring the strength of directional selection (Fig. 8.15)Selection for increased tail length in mice

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Selection differential and selection gradient

• The directional selection differential, S, is the difference between the mean phenotype of the selected parents (t* in the previous slide), and the mean phenotype of the entire population from which the parents were selected (t “bar” in the previous slide). It allows us to predict the evolutionary response of a population to selection.

• The selection gradient is the relationship between relative fitness and the phenotypic value. It shows how strongly phenotypic variation affects fitness.

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Two-trait analysis of selection on Geospiza fortis on Daphne Major during the drought of 1976-77 (Fig. 8.16)

Beak widthF

itnes

s

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Two-trait analysis of antipredator defenses in garter snakes (Brodie 1992)

For striped snakes, the best survival strategy is straight-line escape.

For unstriped or spotted snakes, the best survival strategy is to reverse direction many times

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The evolutionary response to directional selection

• Evolutionary response (in generation t + 1) to a directional selection episode (in generation t), R = h2S

• R is the change in the mean phenotype of the population over one (or more) generation(s)

• Note: if h2 = 0, the population will not evolve

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Response to directional selection, R = h2S

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Response to selection for increased tail-length in mice

• Di Masso et al. (1991) selected for longer tails in mice for 18 consecutive generations.

• Average tail length increased by about 10%– This is a rather modest selection response– It suggests that the heritability of tail length in this population of

mice was low, or that the intensity of selection, S, was low, or both.

– A selection response, R, indicates that a trait is heritable, h2 = R/S, and that there is additive genetic variance for the trait (in this case tail length)

– Closer analysis showed that long-tailed mice had more vertebrae in their tails (28 vs. 26-27 in controls)

– Therefore, what was actually heritable (had additive genetic variance) was number of tail vertebrae

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Selection response in Geospiza fortis, revisited

From the figure at left, R = 9.7 - 8.9 = 0.8 mm

Average beak depth of the survivors of the drought was ~ 10.1 mm: S = 10.1 - 8.9 = 1.1 mm

Therefore, the realized heritability of beak length is:

h2 = R/S = 0.8/1.1 = 0.73

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Heritability and natural selection on flower size in alpine skypilots (Candace Galen 1989, 1996)

• A perennial Rocky Mountain wildflower• Flowers are about 12% larger in tundra populations vs.

timberline populations• Tundra populations are pollinated almost exclusively by

bumblebees• Timberline populations are pollinated by a variety of

insects• Questions:

1) Is flower size in skypilots heritable?2) Do bumblebees select for larger flowers?

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Is flower size in skypilots heritable?

• Offspring- single parent regression– Measure diameters of 144 parents from small-flowered timberline

population

– Collect seeds from parents and germinate 617 seedlings in laboratory

– Transplant seedlings to random locations in same habitat as parents

– Measure flower size in 58 surviving offspring seven years later

• The estimate of heritability was h2 = 1, but this has low precision. With more confidence, Galen concluded that 0.2 ≤ h2 ≤ 1

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Estimating the heritability of flower size in alpline skypilots (Fig. 8.20)

The slope of the regression line is about 0.5Since this is offspring - single parent regression, h2 = twice the slope, or about 1.0

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Do bumblebees select for larger flowers?

• Large screen-enclosed cage at study site with 98 transplanted skypilots + bumblebees (but no other pollinators)

• Measured flowers and later collected seeds• Germinated seeds in lab then planted seedlings at random

locations in natural habitat• Six years later counted all the surviving offspring (=

fitness) that had been produced by each of the original caged parents

• Calculated selection gradient on parents (relative fitness vs flower size)

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The selection gradient on flower size in alpine skypilots (Fig. 8.21)

The slope of the line (the selection gradient) is about 0.13

This corresponds to a selection differential, S = 5%

(S = VP x selection gradient)

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Response to selection on flower size in alpine skypilots

• Using the relationship R = h2S, and an estimate of S = 5%, the single-generation response to selection would be 1% (h2 = 0.2) to 5% (h2 = 1.0)

• Therefore, it would not take very many generations for selection by bumblebees to produce the 12% difference in flower size seen between tundra and timberline populations of skypilots

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Selection on flower size in alpine sky pilots – two questions

• How do we know that bumblebees are doing the selecting? Maybe plants with bigger flowers produce more offspring even without bumblebees– Galen (1989) previously documented that plants with

larger flowers attract more bumblebees and plants that attract more bumblebees produce more seeds

– Experimental controls: when plants are hand pollinated or pollinated by other insects, there is no relationship between flower size and fitness

• If bumblebees are constantly selecting for larger flowers, why aren’t flowers getting bigger and bigger?

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Modes of selection(Fig. 8.23)

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Modes of selection and genetic variance

• Long-term directional phenotypic selection tends to reduce phenotypic and genetic variance (it results in fixation of alleles, as in our one-locus genetic models of selection)

• Long-term stabilizing selection also tends to reduce phenotypic and genetic variance (it is not like single-locus overdominant selection, which tends to preserve genetic variation)

• Disruptive selection increases phenotypic variance in the short-term. However, it is generally thought to be uncommon because it will be unstable in a random mating population (similar to single-locus underdominance), or will favor reproductive isolation between alternative phenotypes

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Stabilizing selection on gall size in a gall-making fly(Weis and Abramson, 1986)

• Fly larva (Eurosta solidaginis) induces host plant goldenrod (Solidago altissima) to make a gall, inside of which the larva develops

• Parasitic wasps attack fly larvae in small galls• Birds eat larvae in large galls• Larvae in medium size galls have highest survival

rate

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Stabilizing selection on a gall-making fly (Fig. 8.24)

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Disruptive selection on beak size in the black-bellied seed

cracker (Smith 1993) (Fig. 8.25)

• Adult birds have either large or small beaks

• Birds in the two groups specialize on different kinds of seeds

• Figure shows survival of juveniles in relation to beak size

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Misunderstanding and misusing quantitative genetics – 1• h2 = 0 means only that none of the phenotypic variation among

individuals is due to genetic differences among individuals• h2 = 0 does not mean that genes do not “determine” the phenotype• To understand this, consider the example that we have used of

inheritance of corolla height in longflower tobacco• In a true-breeding (homozygous) parental line, all individuals have the

same genotype and the heritability of corolla height is zero within that parental line

• However, the experiment also demonstrates that corolla length is under genetic “control” and that the parental lines have genes that influence corolla height– The two parental lines have consistently different corolla heights when

grown in the same environment– The F2 plants have increased phenotypic variance relative to the

genetically uniform F1 and the homozygous and genetically uniform parental lines

– Starting with the F2, subsequent generations show a response to selection

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Corolla height in longflower tobacco (Fig. 8.3)

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Misunderstanding and misusing quantitative genetics – 2

• Estimates of genetic variance and heritability apply only to the group or population in which they are made

• Knowing that a trait has high heritability tells us nothing about the causes of differences in mean phenotypes between groups or populations

• Several studies indicate that the heritability of IQ score is ≥ 0.30• On comparable IQ tests, Japanese children score, on average, about 10

points higher than white Americans• Are Japanese genetically “smarter” than Americans?• What other factors might explain the difference in average IQ scores?• Can you design an experiment to test your hypothesis?• Aside from the obvious ethical issues, what problems might such an

experiment encounter?

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All of the difference in average plant height between these two genetically identical “populations” of Achillea is due to environmenal effects (Clausen, Keck and Heisey) (Fig. 8.26)

Mather is in the foothills of the Sierra Nevada mountains

Stanford is low altitude and near the Pacific coast

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Populations of Achillea at different elevations are genetically different - but the direction of difference depends on the

elevation of the “common garden” (Fig. 8.29)

Our conclusion about which population is genetically “programmed” to have plants with more stems will depend on where we chose to do the experiment.This is an example of genotype by environment interaction