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Lecture 18 : Mutation
October 30, 2015
Last Time
u Exam to be returned Monday. Answer key
is posted
u Effects of population structure,
admixture, selection, and mutation on LD
u Admixture calculation
u Selective sweeps
Today
Mutation introduction
Mutation-reversion equilibrium
Mutation and selection
What Controls Genetic Diversity Within
Populations?
4 major evolutionary forces
Mutation
Drift
+
-
Diversity
+/Selection
+
Migration
Mutation
Primary driver of genetic diversity
Main source of new variants within a reproductively
isolated species
Mutation often ignored because rates assumed to be
extremely low relative to magnitude of other effects
Accumulation of mutations in population primarily a
function of drift and selection PLUS rate of backmutation
Mutation rates are tough to estimate!
Spontaneous mutation rates
Schlager and Dickie (1967) tracked
spontaneous mutation at 5 loci controlling
coat color in 17 million house mice
Forward > Backward mutation
http://jaxmice.jax.org
http://www.gsc.riken.go.jp
Mutation Rates can Vary Tremendously Among Loci
Length mutations occur much more frequently than point
mutations in repetitive regions
Microsatellite mutation rates as high as 10-2
Source: SilkSatDB
Reverse Mutations
Most mutations are “reversible” such that original allele can
be reconstituted
Probability of reversion is generally lower than probability of
mutation to a new state
Possible States for Second Mutation at a Locus
Thr Tyr Leu Leu
ACC TAT TTG CTG
Reversion
A
C
ACC TCT TTG CTG Thr
Ser Leu Leu
C
T
ACC TTT TTG CTG Thr
Cys Leu Leu
ACC TGT TTG CTG Thr
C
G
Phe Leu Leu
Allele Frequency Change Through Time
With no back-mutation:
p1  p0  p0
 (1   ) p0
pt  (1   ) p0
t
How long would it take to reduce A1 allele frequency by 50% if
μ=10-5?
Two-Allele System with Forward and Reverse Mutation
A1
µ
ν
A2
where μ is forward mutation rate, and ν is reverse mutation rate
Expected change in mutant allele:
q  p q
Allele Frequency Change Driven By Mutation
q  p q
q    q(   )
Equilibrium between forward and reverse mutations:
qe 

(   )
pe 

(   )
Allele Frequency Change Through Time with Reverse
mutation
Allele Frequency (p)
Reverse Mutation (ν)
Forward Mutation (µ)
Mutant Alleles (q)
Equilibrium Occurs between Forward and Reverse
Mutation
Is this equilibrium stable or unstable?
qe 

(   )
μ=10-5
Forward
mutation 10-5
Lower rate of
reverse
mutation
means higher
qeq
Mutation-Reversion Equilibrium
pe 

(   )
where µ=forward mutation rate (0.00001)
and ν is reverse mutation rate (0.000005)
What if the population is not infinite?
Fate of Alleles in Mutation-Drift Balance
p=frequency of new
mutant allele in small
population
Time to fixation of a new
mutation is much longer than
time to loss
1
u ( p) 
2N
An equilibrium occurs between
creation of new mutants, and
loss by drift
1
u (q)  1 
2N
u(p) is probability of fixation
u(q) is probability of loss
Infinite Alleles Model (Crow and Kimura Model)
Each mutation creates a completely new allele
Alleles are lost by drift and gained by mutation: a balance occurs
Is this realistic?
Average human protein contains about 300 amino acids (900
nucleotides)
Number of possible mutant forms of a gene:
n4
900
 7.14 x10
542
If all mutations are equally probable, what is the chance
of getting same mutation twice?
Fate of Alleles in Mutation-Drift Balance
p=frequency of new
mutant allele in small
population
Time to fixation of a new
mutation is much longer than
time to loss
1
u ( p) 
2N
An equilibrium occurs between
creation of new mutants, and
loss by drift
1
u (q)  1 
2N
u(p) is probability of fixation
u(q) is probability of loss
Mutation & Mating Simulation
1. Select two gametes from the gamete
pool (brown is wild=type,
green=mutant
2. Find a mate using the Excel sheet
(e.g., see below)
3. Pass a random allele down to each of
2 offspring. One of these offspring
will become you for the next
generation.
4. Mutate an offspring allele if indicated
by the Excel sheet by choosing a new
random allele from the pool (cup of
candy) (rate = 1x10-2)
5. Repeat for the next generation.
Apoorva
Margo
x
Results of Mutation & Mating Simulation
The forward mutation rate was quite high (1x10-2), and the reverse mutation rate was
at least an order of magnitude lower (based on the freqency of brown M&M’s in the
mutant pool), so the frequency of mutant alleles increased fairly dramatically even
with substantial potential for genetic drift.