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 SubstitutionAllele substitution/fixation: Process whereby one allelereplaces 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 : Probability that a mutant allele (A2) will be fixed in a population

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.

Fixation Probability

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

advantage or disadvantage, (Ne) effective population size.

P = [1 - e-(4Ne)sq ] / 1 - e-4(Ne)s

Kimura 1962

A1A1 A1A2 A2A2

1 1 + s 1 + 2sIf assume

Fixation Prob for A2

2s Fixation probability for small s (positive or negative)

1 - e-4(Ne)s

P = 2s Fixation probability for advantageous allele (positive s).

P =

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

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

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

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

advantage or disadvantage, (Ne) effective population size.

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

s = 0.01

Maruyama & Kimura (1974) showed:

S = -0.01 1658 yrs 1981 yrs

8000 yrs

1658 yrs

80,000 yrs

1981 yrs

Rate of Allele Substitution

K = 2N x 1/2N =

Depends upon: (2Nu) number of mutations arising at locus

per generation, and initial frequency of new allele (1/2N)

rate of substitution = rate of mutation!

under selection, K = 4 Nes

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/

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.

Under the neutral model an important balance is struck

Rate of loss ofgenetic variationby genetic drift

Rate of gain ofgenetic variationby mutation

~~

Although alleles comeand go, the level of geneticvariation remains the same.

Steady state frequency of heterozygotes H = 4Ne / 4Ne + 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 betweenheterozygosity at a locus and its rate of evolution.

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.

A A T C A C T

A T T G A C C

species 1allele

Each nucleotide substitution represents a unique allele fixation event that occurred in the past.

A A T G A C Tancestral allele species 2

allele

A T T G A C CGene 1 A

llel

e fr

equ

ency

Time

G T G G A T AGene 2 contemp. allele

1V

G A G G A T AGene 2 ancestral alleleLower rate of substitution,polymorphism

Causes of Variation in Substitution Rates

Rate of Substitution is determined by:

(1) Mutation rateAmong genesAmong gene regions

(2) Probability of fixationNeutral, advantageous, deleterious

Interpreting Variation in DNA sequences

How does natural selection modify neutral patterns?

Detecting Positive Selection Using WithinSpecies Data

KA/NA > KS/NS

# nonsyn. substitutionsnonsyn. site

# syn. substitutionssyn. 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

Genes that exhibit many interspecific differences will also have high levels of intraspecific polymorphism.

i.e.

NonsynonymousSynonymous

Fixed Differences Polymorphisms

212645%

2365.3%

•Only nonsynonymous mutations are adaptive•Synonymous mutations are neutral•Selectively adaptive (nonsynonymous) mutations more likely to be fixed.

nonsynonymous fixedsynonymous fixed

nonsynonymous polymorphismsynonymous polymorphism=

McDonald-Krietman Test

Assume:

G6PDH from D. melanogaster and D. simulans. Eanes et al. 1993

Neutral Prediction:

% nonsynonymous

Frequency

1.0

0

If most nonsynonymous substitutions are adaptive, thenthey will increase in frequency and be fixed more rapidlythan neutral alleles.

Time

As a result, they spend less time in a polymorphic state,therefore contribute less to within species polymorphism.

neutral allele

advantageous allele

NonsynonymousSynonymous

Fixed Differences Polymorphisms

71729%

2424.5%

Adh from D. melanogaster, D. simulans, and D. YakubaMacDonald and Kreitman 1991

% nonsynonymous

Another example (N = 6-12 alleles per species for the coding region.