Download Neutral theory 2: Neutral theory 1. Mutation 2. Polymorphism 3

Neutral theory 2:
Neutral theory
1. Mutation
2. Polymorphism
Neutral theory: connected these is a new (radical) way
3. Substitution
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Neutral theory of molecular evolution
Motoo Kimura:
• troubled by cost Haldane’s dilemma:
• 1 substitution every 300 generations
• troubled by Zukerkandl and Pauling’s (1965) molecular clock:
• 1 substitution every 2 years
Published a model of neutral evolution in 1968
Jack King and Thomas Jukes:
Independently arrived at same conclusion as Kimura
Published (1969) under the provocative title “Non-Darwinian evolution”
I cannot over emphasize how radical this idea was at that time.
Neutral theory of molecular evolution: elegant simplicity
k = rate of nucleotide substitution at a site per generation [year]
k = new mutations × probability of fixation
Number of new mutations = µ × 2Ne
Probability of fixation =
1
2Ne
Hence, the neutral rate is:
k =
µ × 2Ne × 1/2Ne
k =
µ
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Neutral theory of molecular evolution
Neutral theory: the rate of evolution is independent of effective population size
• mutation-drift equilibrium
• assumes (i) neutrality and (ii) constant mutation rate
• polymorphism is simply a phase of evolution (mutation, polymorphism and
substitution are not separate processes)
Evolution by natural selection: k = µ × 4Ne × s
• rate depends on mutation rate and population size and intensity of selection
Remember the genetic drift lecture…
If we run this simulation
long enough it will go to
fixation of loss; it just takes
much longer
• rate to fixation [under drift] slows with increasing in Ne
• ultimate fate is fixation or loss
• Larger Ne yield larger residence time of a polymorphism in a population
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Ne = 5000
Generations = 30
Generations = 50
Generations = 500
Generations = 1000
The average time to fixation is 4Ne generations
Time to fixation (t) of new alleles in populations with different effective sizes. Note that most new
mutations are lost from the population due to drift and those mutations are NOT shown. The time to
fixation (as an average) is longer in populations with large size.
Allele frequency
Ne = small
1
0
Allele frequency
t
1
Ne = large
0
t
A slice in time for each population is shown by a dotted vertical line (
). Note that at such a slice in time
the population with larger effective size is more polymorphic as compared with the smaller population.
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The average time between neutral substitutions is the reciprocal of µ
Mean time between mutation events (1/µ) is much shorter in the larger population because the number
of new mutations is on average = µ × 2Ne (for diploid organisms). The mutation rate (µ) is the same in
both populations, but numbers differ because of differences in population size.
Mutation event
Allele frequency
Ne = small
1
0
mean 1/µ
Allele frequency
Ne = large
1
0
mean 1/µ
The population attains an equilibrium substitution rate (k = µ)
k=µ
In words:
Large populations: high number of new mutants each generation (2Ne is
high) but probability of fixation is low (1/ 2Ne)
Small populations: lower number of new mutants each generation (2Ne is
lower), but each has a higher probability of fixation (1/ 2Ne is larger)
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The population attains an equilibrium substitution rate (k = µ)
At mutation-drift equilibrium the mutations rate is equal to the substitution rate and the effective
population size cancels out.
Allele frequency
Allele frequency
Ne = small: fewer mutations but they drift to fixation more often
1
0
1
Ne = large: more mutations, but few ultimately get fixed
0
Mutation that goes to fixation (same rate in both populations)
Mutation lost due to genetic drift
The population attains an equilibrium polymorphism
He = 4Neµ/(1+4Neµ)
this result assumes an “infinite alleles model”
θ = 4Neµ
population geneticists are obsessed with the θ parameter
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The population attains an equilibrium polymorphism
Expected equilibrium levels of heterozygosity at a locus as a
function of the parameter θ. Heterozygosity will be higher in
larger populations.
1
0.9
Heterozygosity (H)
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2
4
θ
6
8
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Neutral theory of molecular evolution
1.
The standing level of polymorphism is dependent on effective population size
2.
The rate of evolution is independent of effective population size
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Neutralist-selectionist debate
Neutralists and selectionists actually agree on many points:
• natural selection is ONLY explanation for adaptation
• most new mutations have fitness consequences
• most new mutations are deleterious and subject to purifying selection
• most new mutations are quickly removed from a population by selection
• morphological evolution is mainly driven by selective advantage
Early disagreements focused on genetic load verses selective neutrality:
“It is altogether unlikely that two genes would have identical
selective values under all the conditions under which they may
coexist in a population. … cases of neutral polymorphism do not
exist … it appears probable that random fixation is of negligible
evolutionary importance”
⎯Ernst Mayr
Neutralist-selectionist debate: an argument about proportions
Ne utral M ode l
Deleterious
Se le ctionis t M ode l
Neutral
Adaptive
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Misconceptions about neutral theory
There has been some confusion about what the neutral theory suggests, so it is worth trying to clear up some of
the misconceptions.
Myth 1: Only genes that are unimportant can undergo neutral mutations. [Neutral theory only asserts that
alternative alleles segregating at a locus are selectively equivalent. Such loci can, and do, encode genes that have important
functional roles.]
Myth 2: Neutral theory diminished the role of natural selection in adaptation. [To the contrary, neutralists and
selectionists both maintain that natural selection is the primary mechanism of adaptation, and that morphological evolution is
primarily driven by natural selection.]
Myth 3: Nucleotide or amino acid sites that undergo neutral substitutions are not subject to natural
selection. [Neutral theory does not preclude the possibility that adaptive mutations can occur at sites where neutral
mutations occur. Neutral theory only asserts that adaptive mutations will be much less frequent and will go to fixation much
more quickly; hence, most polymorphism observed in a population will be neutral.]
Myth 4: Neutral mutations have a selective coefficient of s = 0. [Because natural population sizes are finite, the
fate of mildly deleterious alleles can be fixed due to drift. See population genetic Topic 8 for a review.]
Myth 5: Neutral mutations are always neutral. [Neutral theory makes no assertions about the stability of the
environment. The selection coefficient will depend of the environment.]
Predictions of the neutral theory
1.
The level of within species genetic variation is determined by population size and
mutation rate, and is correlated with the level of sequence divergence between
species.
2.
The rate of gene evolution (substitution) is inversely related to the level of functional
constraint (purifying selection) acting on the gene. [this is macro-evolution]
3.
The pattern of base composition at neutral sites reflects mutational equilibrium.
4.
There is a constant rate of sequence evolution; i.e., a molecular clock.
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Genetic load and “hard selection”
We already encountered the notion of excess reproductive capacity of a
species. When excess individuals with the same fitness compete for finite
resources, the resulting mortality is unrelated to natural selection. This is
sometimes called “background mortality”.
Many models of genetic load were based on Hard Selection. Hard selection
refers to any selection-based mortality on top of the mortality that arises
when excess individuals have the same fitness; i.e., mortality in addition to
the background mortality.
All of Kimura’s and Haldane’s arguments concerning genetic load assumed
hard selection.
Genetic load and “hard selection”
A question that often comes up: What if we could substitute some of the genetic death for some of
the background mortality?
Soft selection is the term used to describe the situation when some selective deaths are substituted
for non-selective background mortality.
The consensus opinion is that natural selection in real populations reflects some mixture of hard
and soft selection. Hence, the initial models of genetic load and the cost of selection are thought to
overestimate the amount of genetic death. Hard and soft selection should be considered extreme
of a continuum, and natural selection is likely to represent some intermediate point along this
continuum.
Do we still need the neutral theory? We will return to this question later.
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hard and soft selection
Background: no selective death
120
100
Background
mortality when all
individuals have the
same fitness
80
60
40
20
0
1
2
Extreme soft selection
Mix of soft & hard selection
120
120
100
120
Only some selective
death is substituted
with background
mortality (50%); some
selective death is on
top of background
mortality (50%)
100
All selective death
is substituted with
background
mortality
80
60
40
80
60
40
20
20
0
0
1
2
Extreme hard selection
All selective death is
on top of background
mortality
100
80
60
40
20
0
1
2
1
2
Do we still need the neutral theory?
Let’s look at those predictions and see how they fit real data.
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