Change in frequency of the unbanded allele (q) as a function of q for island populations.

Equilibrium points

a) Strong selection for q, little migration of pp, pq.

Gene SubstitutionAllele substitution/fixation: Process whereby one allelereplaces an existing allele.

•What is the probability?

•How long does the process take?

•What is the rate of allele substitution?

Fixation Probability : Probability that a mutant allele (A2) will be fixed in a population

Fixation Probability

Depends upon: (q) initial frequency of allele, (s) selective

advantage or disadvantage, (Ne) effective population size.

What is the probability of fixation for N = 1000 vs 10,000?N = 1000 N = 10,000

s = 0.0

s = 0.01

s = - 0.001

0.0005

0.02

0.00004

0.00005

0.02

10 -20

Note: Probabilities are derived under a 1 locus, 2 allele model

Conditional Fixation Time : mean time to fixation formutants that will eventually be fixed in the population

t = 4Ne generations

Kimura and Ohta, 1969

Neutral allele

Advantageousallele

t = (2/s) ln(2N) generations

Conditional Time to Fixation or Loss

Depends upon: (q) initial frequency of allele and (N) population size.

For new mutation (q=1/2N):

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

s = 0.01

s = - 0.01

8000 yrs

1658 yrs

1658 yrs

80,000 yrs

1981 yrs

1981 yrs

Note: The vast majority of deleterious alleles will be lost; thisdescribes 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!

Time to fixationneutral allele

Time to extinction

Ne = 1000 Ne = 10,000

Assume: Ne=N, 2 gen/yr

30 yrs

8000 yrs

38 yrs

80,000 yrs

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 TheoryThere 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 = fixation/generation).

is also the rate of mutation (e.g. substitutions/site/generation)

4) The average time between consecutive fixations = 1/

and 1/= generation/fixation.

5) The rate of neutral evolution 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 notbe neglected when considering molecular evolution.

Established the concept that polymorphism withinpopulations and molecular evolution between speciesare two facets of the same problem.

Neutral theory has become a starting point for analysesof DNA sequences…..it serves as the null model.