Notes for Lecture #6: Quantitative Genetics

Copyright 1996. May not be reproduced for commerical purposes

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Genotypes versus phenotypes

• changes in allele (or genotypic) frequencies
• changes in the frequency of phenotypes
• The connection: continuous characters

The nature of continuous characters

• Fisher (1918) building on the work of plant breeders (1900's - 1910) suggested the polygenetic model.
• Many characters have a large number of loci underlying them.
• The variation, coupled with environmental variation generates a continuous distribution of character values.

For 10 loci of equal effect, with p = 0.5,

z = g + e

• phenotypic value (z) = genetic value (g) + environmental value (e)
• Nature versus nurture: how much of the resemblance is due to shared genetic values (shared g values) and how much due to shared environmental values (shared e values) ?

The concept of heritability

• The total fraction of phenotypic variation accounted for by genetic effects
• Some examples:

Estimating heritability: parent-offspring regressions

• Idea: if there is some genetic basis to the character, then offspring should resemble their parents
• Galton: one measure of this is to regress parents on offspring
• Fisher (1918) connected these methods of resemblance between relatives from the biometricians with mendelian models of genetics

Galton' s data on human height

• The expected slope of the best linear fit of the value of a single parent on the mean value of their offspring is h2/2

offspring mean = pop mean + ( h2/2 ) ( parent value - pop mean )

• The expected slope of the midparental value (average of the two parents) on the mean value of their offspring is h2.

offspring mean = pop mean + ( h2 ) ( midparent value - pop mean )

Example

Suppose slope of midparent-offspring regression is .75.

• Hence, h2 = 0.75.

• If a parent is 10 units below the mean, then the average value of its offspring is (.75/2)*10 = 3.75 units below the mean

• Suppose the average value of both parents is 20 units above the mean. Then the average value of their offspring is 0.75*20 = 15 units above the mean

Response to Selection

R = h2 S

• R = change in population mean (from one generation to the next)

• S = Mean selected parents - population mean

Example

If height in reproducting parents is 75 inches, while the population average is 65,

• S = 75-65 = 10

• R = h2* 10

• The new mean becomes 65 + h2*10

Sib analysis

Monozygotic ( identical ) twins share all genes

Dizygotic ( fraternal ) twins share only half their genes

Correlations between sibs

• Corr(Identical twins) = h2 + c 2

• Corr(dizygotic twins) = h2/2 + c 2

• Here c2 measures the effects of shared environments

Estimating h2 from sibs

Key: Remove effect of shared environment c2

• Method One:

• 2[ Corr(Identical twins) - Corr(dizygotic twins)]
• = 2 [ (h2 + c)2- (h2/2 + c2) ] = h2

• Method two: Examine twins separated at birth

• Removes shared environmental effects (c = 0)

• If genetic basis, corr(Iden twins) = 2corr(dizygotic twins) > 0

• A related way to look at this: Suppose the frequency of a trait in the population is 0.10, while the frequency in separated identical twins is 0.20 --- this suggests a genetic basis.

• However, suppose frequency in separated dizygotic twins is also 0.20, which is not consistent with a genetic basis, as we expect monozygotic frequency to be higher than dizygotic frequency