Lecture 20 : Mutation
March 28, 2014
Last Time
u Exam (to be returned Monday or
Wednesday)
u Effects of population structure,
admixture, selection, and mutation on LD
u Admixture calculation (now corrected
online)
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 7.5 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
Question:
Do most mutations cause reduced
fitness?
Why or why not?
Relative Abundance of Mutation Types
Most mutations are
neutral or ‘Nearly
Neutral’
A smaller fraction are
lethal or slightly
deleterious (reducing
fitness)
A small minority are
advantageous
Types of Mutations (Polymorphisms)
Synonymous versus
Nonsynonymous SNP
First and second position
SNP often changes
amino acid
 UCA, UCU, UCG, and UCC
all code for Serine
Third position SNP often
synonymous
Majority of positions are
nonsynonymous
Not all amino acid
changes affect fitness:
allozymes
Nuclear Genome Size
Size of nuclear genomes
varies tremendously
among organisms
Weak association with
organismal complexity,
especially within
kingdoms
Arabidopsis thaliana
Poplar
Rice
Maize
Barley
Hexaploid wheat
Fritillaria (lilly family)
120 Mbp
460 Mbp
450 Mbp
2,500 Mbp
5,000 Mbp
16,000 Mbp
>87,000 Mbp
Noncoding DNA accounts for majority of
genome in many eukaryotes
Intergenic space is larger
Transposable element insertions (Alu in humans)
Genic Fraction (%)
Noncoding DNA accounts for majority of
genome in many eukaryotes
Genome Size (x109 bp)
Intron Size Partly Accounts for Genome Size
Differences
log(number of introns)
Aparicio et al. 2002, Science 297:1301
Human: 3500 Mbp
Fugu: 365 Mbp
Intron Size (bp)
What is the probability of a mutation hitting a coding
region in humans? Assumptions?
Composition of the Human Genome
Lynch (2007)
Origins of
Genome
Architecture
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)
Mutation-Selection Balance
Equilibrium occurs when creation of mutant allele is balanced by
selection against that allele
For a recessive mutation:
2
sq p
qs  
2
1  sq
At equilibrium:
2
qmu  qs  0
q eq 
2

s
qmu  p
qeq 
sq p
p 
2
1  sq

s
assuming: 1-sq21
What is the equilibrium allele frequency of a
recessive lethal with no mutation in a large
(but finite) population?
What happens with increased forward mutation rate
from wild-type allele?
How about reduced selection?
qeq 

s
Balance Between Mutation and Selection
Recessive lethal allele with s=0.2 and μ=10-5
Muller’s Ratchet
Deleterious mutations accumulate in haploid or asexual lineages
Driving force for evolution of recombination and sex
Mutation-Selection Balance with Dominance
Dominance exposes alleles to selection, and therefore acts to
decrease equilibrium allele frequencies
qeq 

for h>>0
hs
Complete Dominance of A2:
qeq 

s
Recessive Case:
qeq 

s
Which qeq is larger?
Why?
Effect of dominance and selection on allele frequency in
mutation-selection balance (μ=10-5)
Drastic effect of
dominance on
equilibrium
frequencies of
deleterious alleles
Exposure to selection
in heterozygotes
recessive case
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
 7.14x10
542
If all mutations are equally probable, what is the chance
of getting same mutation twice?