Neutral Theory and Genetic Drift

Drift and Variation

Illustrates population growth over time, from the Old Stone Age to modern times.
Significant events like the Black Death (the plague) are noted for their impact on population size.
The graph shows exponential population growth, especially in recent centuries.

The Neutral Theory explains the generation and evolution of variation as a combination of mutation and genetic drift.
Mutation adds variation over millions of years, eventually leading to equilibrium (N_e will approach N).

Much molecular variation is selectively neutral, or nearly so.
Neutral variation evolves primarily by drift, especially in small populations.
Neutral substitutions in a lineage occur at a constant rate.
Important limitations:
- Not all evolution proceeds by drift.
- Adaptations do not arise by drift.

Neutral substitutions in a lineage occur at a constant rate.
A graph shows the relationship between divergence time and substitutions per site (dS, dN, d_A).

The accumulation of character differences over time can be used to estimate divergence times.
Example: Comparison of genetic differences between species (Human, Dog, Carp, Shark).
Divergence times are estimated based on the fossil record (e.g., 70 Mya).
Percentage differences in a genetic sequence are calculated (e.g., Human vs. Dog: 16%).

The frequency of a new mutation affects the probability of it becoming fixed in a population.

Allele frequencies fluctuate randomly; one allele eventually becomes fixed (100%).
Population size affects the rate of allele frequency change.
The probability of allele A1 becoming fixed is equal to its initial frequency (p).
Populations with the same initial p will diverge; some will fix A1, others a different allele (1 – p).
Heterozygosity (H) decreases proportionally to the rate of drift.
In many isolated, initially identical populations, average p does not change, but H declines.
A new mutation will have a frequency of 1 / (2N), where N is the population size.
For new mutations that do become fixed, the average time to fixation is 4N generations.

Graphs illustrate allele frequency changes over generations in small (5 diploid individuals) and larger (100 diploid individuals) populations.
Smaller populations show more rapid and random fluctuations in allele frequencies.

The chance that any individual neutral mutation will become fixed is lower in a large population than in a small population.
However, there will be more mutations occurring in a large population due to the greater number of individuals.

Example: A population of 3 diploid individuals.
The frequency of a new mutant allele = 1 / (2N) = 1/6, meaning it has a 1/6 chance of becoming fixed.
Mutation rate is set at 1/gene copy/minute.
For new mutations that do become fixed, average time to fixation is 4N generations.

Example: A population of 1 diploid individual.
The frequency of a new mutant allele = 1 / (2N) = 1/2, meaning it has a 1/2 chance of becoming fixed.
Mutation rate is kept at 1/gene copy/minute.
For new mutations that do become fixed, average time to fixation is 4N generations.

The rate of fixation of new neutral alleles depends on the rate of neutral mutation.
It is the rate of neutral mutation.
In the example, the rate is 1/gene copy/minute.
The rate of fixation does not depend on population size.
New neutral mutations are more likely to become fixed in small populations than in large ones.
However, more new neutral alleles arise in large populations.

Time to fixation depends on population size, but the rate at which new mutations become fixed does not.

Analogy: Starting a bunch of runners every minute, all running at the same speed.

The accumulation of differences happens steadily, resulting in a molecular clock.
Formula: D = 2uOt, where:
- D = genetic distance
- u = mutation rate
- t = time

Another way to look at drift.
Eventually, one allele will become fixed and all others will go extinct.
Therefore, eventually only one copy of that one allele will remain, and all other copies will go extinct.

Illustrates the concept of gene trees in populations with different sizes (N = 6 and N = 12).
Time (in generations) back toward ancestors.

tca (time to the most recent common ancestor) = 156–250 kya (thousand years ago).
African/non-African split about 60 kya.
N_e (effective population size) estimated at 5–10k.
All non-Africans originated from a population of about 2000.

Graph showing mean heterozygosity in different geographic regions (Africa, Europe, Middle East, etc.).
Heterozygosity is plotted against the distance to Addis Ababa (km).