Lecture 45: Population Genetics VI:
Interaction of Selection and Drift
(version 31 July 2002)
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Interactions of Drift and Selection
In a finite population,
- an allele favored by selection can still become lost
- an allele selected against can still become fixed.
How often do these respective events occur (i.e., when does drift overpower the
effects of selection and vise-versa?)
Kimura's expression
Motto Kimura (1957, 1964) showed that for an allele with the simple fitnesses
of 1: 1+ s : 1+2s for the genotypes aa: Aa: AA, that
the probability of fixation, U(p), that allele A is
fixed given it starts at allele frequency p, is given by
Of greatest interest is that probability that an allele introduced as
a single copy, so that p = 1/(2N). Here, Kimura's expression simplifies
Key points:
- Drift dominates selection when 4 N | s | << 1, as here U(p) = p.
- Even a selectively-favored allele has a low chance (2s) of becoming fixed
Example
Consider an allele with s = 0.01 in three different populations:
- For N = 10
- p = 1/20 = 0.05, while U(p) = 0.06
- For N = 100
- p = 1/200 = 0.005, while U(p) = 0.02
- For N = 1000
- p = 1/20 = 0.0005, while U(p) = 0.02
Lecture 46