Lecture 18 : Mutation

October 30, 2015

Last Time Exam to be returned Monday. Answer

key is posted

Effects of population structure, admixture, selection, and mutation on LD

Admixture calculation

Selective sweeps

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 17 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

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 LeuThr Tyr Leu LeuACC TACC TAAT TTG CTGT TTG CTG

ReversionACC TACC TGGT TTG T TTG CTG Thr CTG Thr PhePhe Leu Leu Leu LeuC GC GACC TACC TCCT TTG CTG Thr T TTG CTG Thr

SerSer Leu Leu Leu Leu

A CA C

ACC TACC TTTT TTG CTG Thr T TTG CTG 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:

)( qq

)(

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)

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

21)(

Nqu

211)(

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?

Fate of Alleles in Mutation-Drift Balance

Time to fixation of a new mutation is much longer than time to loss

Npu

21)(

Nqu

211)(

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

Mutation & Mating Simulation1. 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.

xApoorva Margo

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.