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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