Transcript What is the rate of allele substitution?

Selectionist view: allele substitution and polymorphism
are determined by different, selective processes.
• Mutation yields advantageous
alleles that are driven to fixation by
positive natural selection.
• Two or more alleles are maintained
at a locus in a population by
balancing selection.
Neutralist view: allele substitution and polymorphism
are determined by the same evolutionary process.
•
Mutation provides a continual supply of new alleles.
Because many alleles are neutral
or effectively neutral, alleles
becomes fixed or lost from a
population as a result of
genetic drift.
•
Polymorphism is simply a snapshot of a continuous
process of mutational input and subsequent random
extinction or fixation of alleles.
Gene Substitution
Allele substitution/fixation: Process whereby one allele
replaces an existing allele.
• What is the probability of fixation for new alleles?
• How long does the process take (fixation time)?
• What is the rate of allele substitution?
Fixation
Probability
Fixation Probability
: Probability
that a mutant allele
(A
fixed in a population
2) will be
Depends
upon: (q) initial frequency of allele, (s) selective
advantage or disadvantage, (Ne) effective population size.
A 1A 1
1
Fixation Prob
for A2
A 1A 2
1+s
A 2A 2
1 + 2s
If assume
Kimura 1962
P = [1 - e-(4Ne)sq ] / 1 - e-4(Ne)s
When a new allele enters a population it has a frequency of 1/2N.
when s = 0:
P = q = 1/2N
Fixation probability for neutral allele.
2s
P=
1 - e-4(Ne)s
P = 2s
Fixation probability for small s (positive or negative)
Fixation probability for advantageous allele (positive s).
What is the probability of fixation for N = 1000 vs 10,000?
N = 1000
N = 10,000
s = 0.0
0.0005
0.00005
s = 0.01
0.02
0.02
s = - 0.001
0.00004
10 -20
Conditional Fixation
Time : mean
to fixation for
Conditional
Time time
to Fixation
mutants that will eventually be fixed in the population
Depends upon: (q) initial frequency of allele, (s) selective
advantage or disadvantage, (Ne) effective population size.
For new mutation (q = 1/2N):
Neutral allele
t = 4Ne generations
Kimura and Ohta, 1969
Advantageous
allele
t = (2/s) ln (2N) generations
What is the conditional fixation time for Ne = 1000 vs 10,000
if the organism in question has a generation time of 2 years?
Ne = 1000
Ne = 10,000
s = 0.0
8000 yrs
80,000 yrs
s = 0.01
1658 yrs
1981 yrs
Maruyama & Kimura (1974) showed:
S = -0.01
1658 yrs
1981 yrs
Rate of Allele Substitution
Depends upon: (2Nu) number of mutations arising at locus
per generation, and initial frequency of new allele (1/2N)
K = 2Nm x 1/2N = m
rate of substitution = rate of mutation!
under selection, K = 4 Nesm
Neutral Theory
There are several important results from the neutral theory.
1)
The probability that a new, neutral allele eventually becomes fixed is q (its
initial frequency).
2)
The average time to fixation of new, neutral alleles that are destined to be
fixed is 4Ne.
3) The rate that neutral mutations are fixed = mfixation/generation).
m is also the rate of mutation (e.g. substitutions/site/generation)
4) The average time between consecutive fixations = 1/m.
5) The rate of neutral evolution m depends upon neutral and effectively neutral
mutations.
Mootoo Kimura’s concept of neutralism is illustrated in the following
diagram from his original paper.
Mutation is constantly generating new alleles over the course of time. Most
of these mutations are eliminated immediately by purifying selection.
However neutral mutations result in novel alleles.
Mootoo Kimura’s concept of neutralism is illustrated in the following
diagram from his original paper.
However neutral theory predicts that the majority of these new neutral
alleles will have a short time to extinction.
Mootoo Kimura’s concept of neutralism is illustrated in the following
diagram from his original paper.
At a predictable period of time a new neutral mutation will appear that for
reasons largely associated with effective population size, become
established, and eventually fixed in the population. There is an extended
time required for these new neutral alleles to go to fixation.
Mootoo Kimura’s concept of neutralism is illustrated in the following
diagram from his original paper.
There is an extended time, proportional to 4Ne, required for these new
neutral alleles to go to fixation.
Mootoo Kimura’s concept of neutralism is illustrated in the following
diagram from his original paper.
The inverse of the rate of gene substitution is the mean time between two
consecutive substitutions.
Mootoo Kimura’s concept of neutralism is illustrated in the following
diagram from his original paper.
If we sampled the distribution of alleles at a large number of loci at any one
point in time, we would expect a large proportion of alleles to be very low in
frequency, a moderate proportion to have an intermediate frequency, and a
large proportion of alleles to be fixed.
Under the neutral model an important balance is struck
Rate of loss of
genetic variation
by genetic drift
Rate of gain of
genetic variation
by mutation
~~
Although alleles come
and go, the level of genetic
variation remains the same.
Steady state frequency of heterozygotes
H = 4Nem / 4Nem + 1
Because of two important consequences of
neutral evolution:
(1) steady rate of allele substitution
(2) equilibrium level of heterozygosity
We predict the following:
There should be a positive correlation between
heterozygosity at a locus and its rate of evolution.
Impact of the Neutral Theory of Molecular Evolution
Led to the recognition that genetic drift can not
be neglected when considering molecular evolution.
Established the concept that polymorphism within
populations and molecular evolution between species
are two facets of the same problem.
Neutral theory has become a starting point for analyses
of DNA sequences…..it serves as the null model.
Each nucleotide substitution represents a unique
allele fixation event that occurred in the past.
A A T G A C T
ancestral allele
species 1
allele
A A T C A C T
species 2
allele
A T T G A C C
Gene 1
Gene 2 ancestral allele
Gene 2 contemp. allele
A T T G A C C
G A G G A T A
G T G G A T A
1
V
Time
Lower rate of
substitution,
polymorphism
Causes of Variation in Substitution Rates
Rate of Substitution is determined by:
(1) Mutation rate
Among genes
Among gene regions
(2) Probability of fixation
Neutral, advantageous, deleterious
Interpreting Variation in DNA sequences
How does natural selection modify neutral patterns?
Detecting Positive Selection Using Within
Species Data
KA/NA >
# nonsyn. substitutions
nonsyn. site
>
KS/NS
# syn. substitutions
syn. site
Now we consider a more complicated approach……
involving polymorphism.
Testing the Neutral Mutation Hypothesis
The neutral theory predicts that
polymorphism within species is correlated positively
with fixed differences between species
i.e.
Genes that exhibit many interspecific differences will
also have high levels of intraspecific polymorphism.
McDonald-Krietman Test
Assume:
•Only nonsynonymous mutations are adaptive
•Synonymous mutations are neutral
•Selectively adaptive (nonsynonymous) mutations
more likely to be fixed.
Neutral Prediction:
nonsynonymous fixed
synonymous fixed
=
nonsynonymous polymorphism
synonymous polymorphism
Fixed Differences
Nonsynonymous
Synonymous
% nonsynonymous
21
26
45%
Polymorphisms
2
36
5.3%
G6PDH from D. melanogaster and D. simulans. Eanes et al. 1993
If most nonsynonymous substitutions are adaptive, then
they will increase in frequency and be fixed more rapidly
than neutral alleles.
1.0
advantageous allele
Frequency
neutral allele
0
Time
As a result, they spend less time in a polymorphic state,
therefore contribute less to within species polymorphism.
Another example (N = 6-12 alleles per species for
the coding region.
Fixed Differences
Nonsynonymous
Synonymous
% nonsynonymous
7
17
29%
Polymorphisms
2
42
4.5%
Adh from D. melanogaster, D. simulans, and D. Yakuba
MacDonald and Kreitman 1991