- changes in allele (or genotypic) frequencies
- changes in the frequency of phenotypes
- The connection: 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.
- 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 total fraction of phenotypic variation accounted for by genetic effects
- Some examples:
- 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
- The expected slope of the best linear fit of the value of a single parent on the mean value of their offspring is h
^{2}/2offspring mean = pop mean + ( h ^{2}/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 h
^{2}.offspring mean = pop mean + ( h ^{2}) ( midparent value - pop mean ) - Hence, h
^{2}= 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
- R = change in population mean (from one generation to the next)
- S = Mean selected parents - population mean
- S = 75-65 = 10
- R = h
^{2}* 10 - The new mean becomes 65 + h
^{2}*10 - Corr(Identical twins) = h
^{2}+ c^{2} - Corr(dizygotic twins) = h
^{2}/2 + c^{2} - Here c
^{2}measures the effects of shared environments - Method One:
- 2[ Corr(Identical twins) - Corr(dizygotic twins)]
- = 2 [ (h
^{2}+ c)^{2}- (h^{2}/2 + c^{2}) ] = h^{2}

- 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

Quantitative Genetics

* Copyright 1996. May not be reproduced for commerical purposes*

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

Suppose slope of midparent-offspring regression is .75.

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

**Monozygotic ** ( identical ) twins share all genes

**Dizygotic **( fraternal ) twins share only half their genes

** Key: Remove effect of shared environment c ^{2} **