Lecture 20: Introduction to Neutral TheoryNovember 5, 2012
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Classes related to Population Genetics/Genomics next semester:BIOL 493S SPTP: Next Generation Biology CRN 18190, 1 credit, Tues 13:00-13:50
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Mutation introductionMutation-reversion equilibriumMutation and selectionMutation and drift
Today Introduction to neutral theory Molecular clock Expectations for allele frequency
distributions under neutral theory
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()
211(
21
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:
21421
e
eq Nf
Ignoring μ2
144
e
ee N
NH
Remembering that H=1-f:
4Neμ is called the population mutation
rate, also referred to as θ
21 )1()
211(
21
t
eet f
NNf
141
eeq Nf
Ignoring 2μ
Expected Heterozygosity with Mutation-Drift Equilibrium under IAM
At equilibrium:
11
141
ee Nf
1
eH
Remembering that H = 1-f:
set 4Neμ = 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 lowFraser et al. 2004 PNAS 102: 1968
2
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?
144
e
ee N
NH
IAM:
)18(11
ee N
H
SMM:
Which should have higher produce He,the Infinite Alleles Model, or the
Stepwise Mutation Model, given equal Ne and μ?
144
e
ee N
NH
IAM:
)18(11
ee N
H
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 Stepwise
Why 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?
The main power of neutral theory is it provides a theoretical expectation for
genetic variation in the absence of selection.
Fate of Alleles in Mutation-Drift Balance
Time to fixation of a new mutation is much longer than time to loss
Generations from birth to
fixation
Time between fixation events
Fate of Alleles in Mutation-Drift-Selection Balance
Purifying Selection
Neutrality
Balancing Selection/Overdominance
Which case will have the most alleles on average
at any given time?What will this depend
upon?Highest HE?
Assume you take a sample of 100 alleles from a large (but finite) population in
mutation-drift equilibrium.
A.
Number of Observations of Allele
Num
ber o
f Alle
les
2
4
6
8
10
2 4 6 8 10
B.
2 4 6 8 10
C.
2 4 6 8 10
What is the expected distribution of allele frequencies in your sample under
neutrality and the Infinite Alleles Model?
Allele Frequency Distributions Neutral theory allows a
prediction of frequency distribution of alleles through process of birth and demise of alleles through time
Comparison of observed to expected distribution provides evidence of departure from Infinite Alleles model
Depends on f, effective population size, and mutation rate
Hartl and Clark 2007
Black: Predicted from Neutral Theory
White: Observed (hypothetical)
Ewens Sampling Formula
i
10
2
3
12
0
)(N
i ikE
3211)(
3
0
12
0
i
N
i iikE
.
Probability the i-th sampled allele is new given i alleles already sampled:
Probability of sampling a new allele on the first sample:
eH
1
Probability of observing a new allele after sampling one allele:
Probability of sampling a new allele on the third and fourth samples:
12...
211
N
Expected number of different alleles (k) in a sample of 2N alleles is:
Example: Expected number of alleles in a sample of 4:
eN4Population mutation rate: index of variability of population:
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