Lecture 19 : Mutation, Selection, and Neutral Theory

November 2, 2015

Last Time

Mutation introduction

Mutation-reversion equilibrium

Mutation and drift

Today

Mutation and selection

Introduction to neutral theory

Exam

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

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)

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 eukaryotesG

enic

Fra

ction

(%)

Genome Size (x109 bp)

What is the probability of a mutation hitting a coding region in humans? Assumptions?

Lynch (2007) Origins of Genome

Architecture

Composition of the Human Genome

Classical-Balance Fisher focused on the dynamics of allelic forms of genes,

importance of selection in determining variation: argued that selection would quickly homogenize populations (Classical view)

Wright focused more on processes of genetic drift and gene flow, argued that diversity was likely to be quite high (Balance view)

Problem: no way to accurately assess level of genetic variation in populations! Morphological traits hide variation, or exaggerate it.

Molecular Markers Emergence of enzyme electrophoresis in mid 1960’s

revolutionized population genetics

Revealed unexpectedly high levels of genetic variation in natural populations

Classical school was wrong: purifying selection does not predominate

Initially tried to explain with Balancing Selection

Deleterious homozygotes create too much fitness burden

22

211 qspsi

mi for m loci

The rise of Neutral Theory Abundant genetic variation exists, but perhaps not driven by

balancing or diversifying selection: selectionists find a new foe: Neutralists!

Neutral Theory (1968): most genetic mutations are neutral with respect to each other

Deleterious mutations quickly eliminated

Advantageous mutations extremely rare

Most observed variation is selectively neutral

Drift predominates when s<1/(2N)

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

4Neμ often symbolized by Θ

Equilibrium Heterozygosity under IAM

Frequencies of individual alleles are constantly changing

Balance between loss and gain is maintained

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

Stepwise Mutation Model Do all loci conform to Infinite Alleles Model?

Are mutations from one state to another equally probable?

Consider microsatellite loci: small insertions/deletions more likely than large ones?

14

4

e

ee N

NH

IAM:

)18(

11

ee

NH

SMM:

Which should have higher produce He,the Infinite Alleles Model, or the Stepwise Mutation Model, given equal Ne and μ?

14

4

e

ee N

NH

IAM:

)18(

11

ee

NH

SMM:

Plug numbers into the equations to see how they behave. e.g, for Neμ = 1, He = 0.66 for SMM and 0.8 for IAM

Expected Heterozygosity Under Neutrality Direct assessment of neutral

theory based on expected heterozygosity if neutrality predominates (based on a given mutation model)

Allozymes show lower heterozygosity than expected under strict neutrality

Why?

Avise 2004

Observed

1

eH

Neutral Expectations and Microsatellite Evolution

Comparison of Neμ (Θ) for 216 microsatellites on human X chromosome versus 5048 autosomal loci

Only 3 X chromosomes for every 4 autosomes in the population

Ne of X expected to be 25% less than Ne of autosomes:

θX/θA=0.75

AutosomesX

X chromosome

Correct model for microsatellite evolution is a combination of IAM

and StepwiseWhy is Θ higher for autosomes?

Observed ratio of ΘX/ΘA was 0.8 for Infinite Alleles Model and 0.71 for Stepwise model

Sequence Evolution

DNA or protein sequences in different taxa trace back to a common ancestral sequence

Divergence of neutral loci is a function of the combination of mutation and fixation by genetic drift

Sequence differences are an index of time since divergence

Molecular Clock If neutrality prevails, nucleotide divergence between two sequences should be

a function entirely of mutation rate

1

t

Expected Time Until Fixation of a New Mutation:

Since μ is number of substitutions per unit time

Time since divergence should therefore be the reciprocal of the estimated mutation rate

Probability of creation of new

alleles

Probability of fixation of new

alleles

Variation in Molecular Clock If neutrality prevails, nucleotide divergence between two sequences should

be a function entirely of mutation rate

So why are rates of substitution so different for different classes of genes?

Exam 2 Results: 86.8% Avg, 9.8% Std Dev.