mutation - boston universitypeople.bu.edu/msoren/bi515_2014/lecture5.pdf · mutations ! point...
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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
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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
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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!
fA (1) = fA (0) 1−µ( )fA (t) = fA (0) 1−µ( )t
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0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 10,000 20,000 30,000 40,000 50,000
Time (t, in generations)
Allele
freq
uen
cy (pt )
10-4
10-5
10-6
10-7
Mutation in an Infinite Population
fA (t) = fA (0) 1−µ( )t
Mutation in an Infinite Population
v if mutations are reversible, the equilibrium allele frequency reflects the relative rates of forward and backward mutations
fA =µa→A
µa→A +µA→a
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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
v ~37% of individual alleles lost each generation, largely independent of Ne
€
1− 12N
#
$ %
&
' ( 2N
≈ e−1 = 0.368
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0.31
0.32
0.33
0.34
0.35
0.36
0.37
0.38
0 20 40 60 80 100
Population Size
Pro
bab
ilit
y t
hat α
1 is lo
st
Exact
Approximate
€
1− 12N
#
$ %
&
' ( 2N
≈ e−1 = 0.368
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
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Mutation vs. Fixation/Substitution
Average time to fixation/substitution
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Neutral Expectations…
v the rate of neutral evolution is independent of population size ² substitution rate (k) equals mutation rate
k = 2Nµ × 12N
= µ
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
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E d( ) = 2µt
Fate of New Mutations
Directional Selection
Neutral Drift
Balancing Selection