O ■ Example: Suppose A₁ mutates to A2 at rate 0.005, but A2A2 homozygous recessives are 50% less fit (s = 0.5) than either A1A1 or A₁A2. What are the expected equilibrial abundances of A₁ and A2? μ = 0.005 S = 0.5 ● ● (pl/s) ● p*= 1-sqrt(u/s) = 1-sqrt(0.005/0.5) = 0.9 q* = sqrt(u/s) = sqrt(0.005/0.5) = 0.1 Question: Suppose A₁ mutates to A2 at rate 0.01, but A2A2 homozygous recessives are 40% less fit (s = 0.4) than either A1A1 or A₁A2. What are the expected equilibrial abundances of A₁ and A2?

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O
Mutation-selection
balance
Suppose that one allele A₁ mutates to another allele A2 at some rate, μ.
Suppose as well that A₁ is dominant over A2 such that A₁A1 and A₁A2 both
have the same fitness, but that individuals that are homozygous recessive
(A2A2) for the mutant allele A2 are less fit than the dominant genotype by
some amount s, the selection coefficient. In this case, A2 mutant alleles come
into the population at rate µ, and are removed from the population only
when the show up in homozygous genotypes. The gory mathematical proof
can be found in Box 7.8, which tells us that:
O
■
Example: Suppose A₁ mutates to A2 at rate 0.005, but A₂A2 homozygous
recessives are 50% less fit (s = 0.5) than either A₁A1 or A₁A2. What are the
expected equilibrial abundances of A₁ and A2?
μ = 0.005
S = 0.5
p* = 1-sqrt(µ/s) = 1-sqrt(0.005/0.5) = 0.9
= sqrt(µ/s) = sqrt(0.005/0.5) = 0.1
●
*
p = = 1-sqrt(µ/s)
q* = sqrt(μ/s)
●
Question: Suppose A₁ mutates to A2 at rate 0.01, but A₂A2 homozygous
recessives are 40% less fit (s = 0.4) than either A₁A1 or A1A2. What are the
expected equilibrial abundances of A₁ and A₂?
8
Transcribed Image Text:O Mutation-selection balance Suppose that one allele A₁ mutates to another allele A2 at some rate, μ. Suppose as well that A₁ is dominant over A2 such that A₁A1 and A₁A2 both have the same fitness, but that individuals that are homozygous recessive (A2A2) for the mutant allele A2 are less fit than the dominant genotype by some amount s, the selection coefficient. In this case, A2 mutant alleles come into the population at rate µ, and are removed from the population only when the show up in homozygous genotypes. The gory mathematical proof can be found in Box 7.8, which tells us that: O ■ Example: Suppose A₁ mutates to A2 at rate 0.005, but A₂A2 homozygous recessives are 50% less fit (s = 0.5) than either A₁A1 or A₁A2. What are the expected equilibrial abundances of A₁ and A2? μ = 0.005 S = 0.5 p* = 1-sqrt(µ/s) = 1-sqrt(0.005/0.5) = 0.9 = sqrt(µ/s) = sqrt(0.005/0.5) = 0.1 ● * p = = 1-sqrt(µ/s) q* = sqrt(μ/s) ● Question: Suppose A₁ mutates to A2 at rate 0.01, but A₂A2 homozygous recessives are 40% less fit (s = 0.4) than either A₁A1 or A1A2. What are the expected equilibrial abundances of A₁ and A₂? 8
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