BIO 370 Lecture Notes - Lecture 14: Allele Frequency, Mutation Rate, Mutation
Mutation
We will start with the simplifying assumption that mutation is the only evolutionary force at
work, and ask what happens to allele frequencies under mutation alone.
Given alleles A1 and A2, and A1 mutates to A2 at the rate m, and A2 mutates to A1 at the rate n.
If the starting frequency of A1 is p, then
- p will be increased by qn over one generation
- p will be decreased by pm over one generation.
If the frequency of A1 alleles lost by mutation to A2 is pm, and the frequency of A1 alleles gained
by mutation from A2 is qn, then:
p’ = p – pm + qn
where p’ is the seod geeatio alue of p.
p’ = p – pm + qn
= p(1 – m) + qn
= p(1 – m) + (1 – p)n
p’ = p(1 – m) + (1 – p)n
With only mutation, the A1 allele will eventually reach equilibrium, p*. At that point, the allele
frequency p’ i oe geeatio is uhaged fo p in the previous generation and, therefore,
p = p’ = p*. Substituting p* for both p and p’ i the aoe euatio:
p’ = p(1 – m) + (1 – p)n
p* = p*(1 – m) + (1 – p*)n
Solving for p* we get:
find more resources at oneclass.com
find more resources at oneclass.com
p* = n/(m + n)
Correspondingly:
q* = m/(m + n)
The equilibrium frequency of A1
is equal to the mutation rate TO A1
divided by the sum of mutation rates
TO and FROM A1.
The equilibrium frequency of A2
is equal to the mutation rate TO A2
divided by the sum of mutation rates
TO and FROM A2.
If p* = n/(m + n) and q* = m/(m + n), and if mutation is the only evolutionary force at work,
THEN
the equilibrium frequencies of two alleles of the same locus can be determined directly from
the mutation rates.
Stable equilibrium (reaches a point and stays there, not at 0 or 1)
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
We will start with the simplifying assumption that mutation is the only evolutionary force at work, and ask what happens to allele frequencies under mutation alone. Given alleles a1 and a2, and a1 mutates to a2 at the rate m, and a2 mutates to a1 at the rate n. P will be increased by qn over one generation. P will be decreased by pm over one generation. If the starting frequency of a1 is p, then. With only mutation, the a1 allele will eventually reach equilibrium, p*. At that point, the allele frequency p" i(cid:374) o(cid:374)e ge(cid:374)e(cid:396)atio(cid:374) is u(cid:374)(cid:272)ha(cid:374)ged f(cid:396)o(cid:373) p in the previous generation and, therefore, p = p" = p*. Substituting p* for both p and p" i(cid:374) the a(cid:271)o(cid:448)e e(cid:395)uatio(cid:374): p" = p(1 m) + (1 p)n p* = p*(1 m) + (1 p*)n. Solving for p* we get: p* = n/(m + n)
