Neutral Theory and Genetic Drift

Drift and Variation

• Drift applies only to neutral variation.
• Drift reduces variation.
• Mutation counteracts drift by introducing new variation.

World Population Growth Through History

• 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.

Neutral Theory

• 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).

Neutral Theory: Key Points

• 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 and Divergence Time

• 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).

Molecular Clock

• 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%).

Frequency of New Mutations

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

Drift Generalizations

• 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.

Allele Frequency and Population Size

• 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.

Fixation of Neutral Mutations

• 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.

Population Size and Mutation Rate

• 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.

Population Size and Mutation Rate (Small Population)

• 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.

Rate of Fixation

• 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

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

Runners Analogy

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

Time to Fixation: Small vs. Large Population

• Illustrates the time to fixation in small and large populations.

Result of Neutral Alleles

• Neutral alleles are substituted at a constant rate.
• Differences arise steadily, on average.
• The population becomes fixed for an allele.

Molecular Clock (Revisited)

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

Heterozygosity

• Decreases with drift.
• Lower in small Ne than in large Ne.

Coalescence Theory

• 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.

Drift and Gene Trees

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

Modern Humans

• 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.

Mean Heterozygosity

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