Post on 17-Dec-2015
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.