9/22/14 Mutation
v point mutations
²  synonymous (=silent)
²  non-synonymous (=replacement, missense)
²  nonsense (=premature stop codon)
v SNP (single nucleotide polymorphism)
v insertions, deletions
²  frameshift mutations
1 9/22/14 Mutations
v point mutations
²  synonymous (=silent)
²  non-synonymous (=replacement, missense)
²  nonsense (=premature stop codon)
v SNP (single nucleotide polymorphism)
v insertions, deletions
²  frameshift mutations
v chromosomal inversions, translocations
v repetitive elements
v transposable elements
Mutation Rates
v allozyme, per gene rates
² 10-4 to 10-6 per generation
v nucleotide rates
² nuclear ~10-9 per nucleotide per generation
²  47 billion new mutations in 7.2 billion
humans!
² mtDNA ~10-8 per nucleotide per generation
v microsatellite rates
² 10-2 to 10-5 per allele per generation
2 9/22/14 Hypothetical Distribution of Effects
Mutation in an Infinite Population
v start with old school approach
² mutations of allele A to allele a
² recall that pop gen theory was developed
before the structure of DNA was known
v recurrent mutation changes allele
frequency slowly!
f A (1) = f A (0) (1− µ )
f A (t) = f A (0) (1− µ )
t
3 9/22/14 Mutation in an Infinite Population
1
Allele frequency (pt)
0.9
0.8
0.7
0.6
f A (t) = f A (0) (1− µ )
0.5
0.4
t
10-4
10-5
10-6
10-7
0.3
0.2
0.1
0
0
10,000
20,000
30,000
40,000
50,000
Time (t, in generations)
Mutation in an Infinite Population
v if mutations are reversible, the equilibrium
allele frequency reflects the relative rates of
forward and backward mutations
fA =
µ a→A
µ a→A + µ A→a
4 9/22/14 Mutation and Genetic Drift
v a substantial fraction of alleles (lineages) will
be lost by chance each generation in a
random breeding population of finite size
v probability that allelei will be lost in a single
generation
2N
#
1 &
%1−
(
$ 2N '
≈ e−1 = 0.368
v ~37% of individual alleles lost each
generation, largely independent of Ne
€
5 9/22/14 α1 is lost
0.37
Probability that
0.38
0.35
0.36
0.34
0.33
2N
#
1 &
−1
%1−
( ≈ e = 0.368
$ 2N '
Exact
Approximate
0.32
0.31
€0
20
40
60
80
100
Population Size
Mutation and Genetic Drift
v eventually, only one of the original lineages
remains
v therefore, probability of fixation for a novel
mutation is 1/2N (average time to fixation =
4N generations) and the probability of loss
for a new mutation is (1-1/2N)
v except for very large populations, drift can
change allele frequencies much faster than
recurrent mutation
6 9/22/14 Mutation vs. Fixation/Substitution
Average time to fixation/substitution
7 9/22/14 Neutral Expectations…
v the rate of neutral evolution is independent
of population size
²  substitution rate (k) equals mutation rate
k = 2N µ ×
1
=µ
2N
Probability of Fixation & Rate of Evolution
v new mutations have a frequency of 1/(2N)
and therefore have a probability of
fixation of 1/(2N)
v new mutations become fixed at a rate
equal to µ (see previous slide)
² mutation rate equals “substitution” rate
² neutral rate is independent of population size!
v average time interval between fixation of
new mutations is 1/µ
8 9/22/14 E ( d ) = 2 µt
Fate of
New
Mutations
Directional
Selection
Neutral
Drift
Balancing
Selection
9