Change in frequency of the unbanded
allele (q) as a function of q for island populations.
a) Strong selection for q,
little migration of pp, pq.
Equilibrium points
Gene Substitution
Allele substitution/fixation: Process whereby one allele
replaces an existing allele.
•What is the probability?
•How long does the process take?
•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.
Note: Probabilities are derived under a 1 locus, 2 allele model
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
time toor
fixation
Conditional
Time: mean
to Fixation
Loss for
mutants that will eventually be fixed in the population
Depends upon: (q) initial frequency of allele and (N) 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 varmit 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
s = - 0.01
1658 yrs
1981 yrs
Note: The vast majority of deleterious alleles will be lost; this
describes the time for those that are ultimately fixed.
The average conditional time to extinction of a neutral allele
= (2Ne/N)ln(2N) generations
Much shorter time than time to fixation!
neutral
allele
Time to fixation
Time to extinction
Ne = 1000
Ne = 10,000
8000 yrs
80,000 yrs
30 yrs
38 yrs
Assume: Ne=N, 2 gen/yr
A long time is required for a neutral allele to be fixed. A
short time is required for a new neutral allele to go to
extinction.
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.
and 1/m= generation/fixation.
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.
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.