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Lecture 19 : Mutation
November 2, 2012
Last Time
Human origins
Human population structure
Signatures of selection in human populations
Neanderthals, Denisovans and Homo sapiens
Today
Mutation introduction
Mutation-reversion equilibrium
Mutation and selection
What Controls Genetic Diversity Within Populations?
4 major evolutionary forces
Diversity
Mutation+
Drift-
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 back-mutation
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://www.gsc.riken.go.jphttp://jaxmice.jax.org
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?
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)
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
Synonymous versus Nonsynonymous SNP
Nuclear Genome Size Size of nuclear genomes
varies tremendously among organisms
Weak association with organismal complexity, especially within kingdoms
Arabidopsis thaliana 120 MbpPoplar 460 MbpRice 450 Mbp Maize 2,500
Mbp Barley 5,000
MbpHexaploid wheat 16,000
MbpFritillaria (lilly family) >87,000
Mbp
Noncoding DNA accounts for majority of genome in many
eukaryotes
Intergenic space is larger
Transposable element insertions (Alu in humans)
Noncoding DNA accounts for majority of genome in many
eukaryotesG
enic
Fra
ctio
n (%
)
Genome Size (x109 bp)
Intron Size Partly Accounts for Genome Size Differences
Fugu: 365 Mbp
Human: 3500 Mbp
log(
num
ber
of in
tron
s)
Intron Size (bp)
Aparicio et al. 2002, Science 297:1301
What is the probability of a mutation hitting a coding region?
Lynch (2007) Origins of Genome
Architecture
Composition of the Human Genome
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 LocusThr Tyr Leu LeuThr Tyr Leu LeuACC TACC TAAT TTG CTGT TTG CTG
Reversion ACC TACC TGGT TTG T TTG CTG CTG
Thr Thr PhePhe Leu Leu Leu LeuC GC GACC TACC TCCT TTG T TTG CTG Thr CTG Thr SerSer Leu Leu Leu Leu
A CA C
ACC TACC TTTT TTG CTG T TTG CTG Thr Thr CysCys Leu Leu Leu Leu
C TC T
Allele Frequency Change Through Time
001 ppp
With no back-mutation:
0)1( p
0)1( pp tt
How long would it take to reduce A1 allele frequency by 50% if μ=10-5?
Two-Allele System with Forward and Reverse Mutation
where μ is forward mutation rate, and ν is reverse mutation rate
A1 A2 µ
ν
qpq Expected change in mutant allele:
Allele Frequency Change Driven By Mutation
Equilibrium between forward and reverse mutations:
)(
eq )(
ep
qpq
Allele Frequency Change Through Time with Reverse mutation
Forward Mutation (µ)
Reverse Mutation (ν)
Allele Frequency (p)
Mutant Alleles (q)
Equilibrium Occurs between Forward and Reverse Mutation
Forward mutation 10-5
Lower rate of reverse mutation means higher qeq
)(
eqIs this equilibrium stable or unstable?
μ=10-5
Mutation-Reversion Equilibrium
)(
ep
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:
pqmu
0 smu qq
At equilibrium:
2
2
1 sq
psqp
sqeq
sqeq
2
2
2
1 sq
psqqs
assuming: 1-sq21
sqeq
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?
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
hsqeq
for h>>0
Complete Dominance of A2:
sqeq
sqeq
Recessive Case:
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
Time to fixation of a new mutation is much longer than time to loss
Npu
2
1)(
Nqu
2
11)(
u(p) is probability of fixationu(q) is probability of loss
An equilibrium occurs between creation of new mutants, and loss by drift
p=frequency of new mutant
allele in small population
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:542900 1014.74 xn
If all mutations are equally probable, what is the chance of getting same
mutation twice?
Infinite Alleles Model (IAM: Crow and Kimura Model)
Homozygosity will be a function of mutation and probability of fixation of new mutants
21 )1()
2
11(
2
1
t
eet f
NNf
Probability of sampling same
allele twice
Probability of sampling two
alleles identical by descent due to
inbreeding in ancestors
Probability neither allele
mutates
Expected Heterozygosity with Mutation-Drift Equilibrium under IAM
At equilibrium ft = ft-1=feq
Previous equation reduces to:
214
21
e
eq Nf
Ignoring μ2
14
4
e
ee N
NH
Remembering that H=1-f:
4Neμ is called the population mutation
rate
21 )1()
2
11(
2
1
t
eet f
NNf
14
1
eeq Nf
Ignoring 2μ
Equilibrium Heterozygosity under IAM
Frequencies of individual alleles are constantly changing
Balance between loss and gain is maintained
14
4
e
ee N
NH
4Neμ>>1: mutation predominates, new mutants persist, H is high
4Neμ<<1: drift dominates: new mutants quickly eliminated, H is low
Effects of Population Size on Expected Heterozgyosity Under Infinite Alleles Model (μ=10-5)
Rapid approach to equilibrium in small populations
Higher heterozygosity with less drift