Lecture 21 : Introduction to Neutral Theory and Phylogenetics

March 31, 2014

Last Time

Mutation introduction

Mutation-reversion equilibrium

Mutation and selection

Mutation and drift

Today Infinite alleles and stepwise mutation models

Introduction to neutral theory

Molecular clock

Introduction to phylogenetics

Exam

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?

Phylogenetics

Study of the evolutionary relationships among individuals, groups, or species

Relationships often represented as dichotomous branching tree

Extremely common approach for detecting and displaying relationships among genotypes

Important in evolution, systematics, and ecology (phylogeography)

A

BM

K

I

J

N

L

H

G

F

E

D

C

ZYXWVUT

PQ

SR

O

Ç

Evolution

Slide adapted from Marta Riutart

What is a phylogeny?

ZYXWVUT

PQ

SR

O

Ç Homology: similarity that is the result of inheritance from a common ancestor

Slide adapted from Marta Riutart

Phylogenetic Tree Terms

A B C D E F G H I J

ROOT

interior branches

node

terminal branches

Leaves, Operational Taxonomic Units (OTUs)

Slide adapted from Marta Riutart

Group, cluster, clade

Bacteria 1

Bacteria 3

Bacteria 2

Eukaryote 1

Eukaryote 4

Eukaryote 3

Eukaryote 2

Tree Topology

(Bacteria1,(Bacteria2,Bacteria3),(Eukaryote1,((Eukaryote2,Eukaryote3),Eukaryote4)))

Bacteria 1

Bacteria 3Bacteria 2

Eukaryote 1

Eukaryote 4Eukaryote 3

Eukaryote 2

Slide adapted from Marta Riutart

http://helix.biology.mcmaster.ca

How about these?

Are these trees different?

Rooted versus Unrooted Trees

archaea

archaea

archaea

eukaryote

eukaryote

eukaryote

eukaryote

Unrooted tree

Rooted by outgroup

bacteria outgroup

root

eukaryote

eukaryote

eukaryote

eukaryote

archaea

archaea

archaea

Monophyletic group

Monophyleticgroup

Slide adapted from Marta Riutart

D

C

B

AG

E

F

C

B

A

F

E

G

D

Rooting with D as outgroup

Slide adapted from Marta Riutart

D

C

B

AG

E

F

C

B

A

F

E

G

D

C

B

A

F

E

G

D

Now with C as outgroup

Which of these four trees is different?

Baum et al.