11: Genetic Drift

Path of evolution

Neither directed, deterministic, nor predictable.

Erratic pattern of change.

Random environmental shifts.

Individual reproduction

Diploid sexually-reproducing organisms are the basic source of randomness.

Two sources of randomness that cause allele frequency changes are number of offspring and meiosis.

Wright-Fisher (WF) model

Model of genetic drift; focuses on alleles in a population.

Assumptions:

• No selection.

• No recombination.

• No mutations.

• No introgression (gene flow / migration).

• No population structure.

• Panmictic population.

• Non-overlapping generations.

If these assumptions are violated, then it is evidence that certain forces (of evolution) exist and allows us to make some predictions.

Genetic drift

The random (stochastic) change in allele frequencies from one generation to the next due to chance.

Factors of allele frequency change

Population size:

• Increased (large) → not likely to be lost or fixed.

• Decreased (small) → likely to be lost or fixed.

Number of generations:

• Increased (more) → likely to be lost or fixed.

• Decreased (fewer) → not likely to be lost or fixed.

Starting frequency of allele:

• Increased (higher) → likely to be fixed (100% present in population).

• Decreased (lower) → likely to be lost (disappears completely).

Rate of genetic drift

Rate of drift is determined by the variance in fitness.

Under the Wright-Fisher model, fitness (W) = 1.

The greater the variance in individual fitness, the faster the rate (and jumps) of random drift.

Types of fitness (drift)

Darwinian W = number of offspring × survivability.

Gene W = number of copies in the next generation.

Allele W = number copies in next generation / number copies in present generation.

Genotype W = Darwinian fitness of an individual.

Absolute W = number of offspring produced.

Relative W = W₁ / W₂ (ratio of fitness between two populations).

Allele frequency variance equations

Under WF model: allele frequency = pq / 2N.

In general: allele frequency = vpq / 2N.

p = allele 1; q = allele 2; v = variance in fitness (width of graph).

q = 1 — p

Effective population size (N_e)

Size of an idealized population that experiences genetic drift at the same rate as the actual (observed) population.

Does not equal the number of individual (nominal population size).

Tries to fit the WF model to a natural population to examine drift in allele frequencies.

Drift is dependent on effective population size (N_e); the lower the N_e, the higher (more erratic) the genetic drift.

Coalescence

A model of how alleles sampled from a population may have originated from a common ancestor.

Coalescence at the common ancestor takes, on average, 2N_e generations to find.

Large populations have a lower coalescence rate, as it is harder to find a common ancestor (which is typically much higher up on the phylogenetic tree).

Coalescence rate (equation)

Rate = 1 / 2N_e

Rate with fitness variance = v / 2N_e

Higher variance correlates with a higher coalescence rate.

Neutral divergence

Most evolutionary changes occur at the molecular level, and most of the variation within and between species are due to random genetic drift of mutant alleles that are selectively neutral.

The rate of neutral divergence equals the mutation rate; provided that mutations are neutral, the rate at which pairs of genes diverge is equal to the total rate of mutation.

Theory that most of the genetic variation in populations is the result of mutation and genetic drift, not natural selection (variation is neutral and does not affect fitness).

MRCA equation

Most recent common ancestor of two species lived t generations ago.

• There are 2t generations during which mutations can occur (two species).

• Mutation rate is m (per gene per generation).

• The two genes will differ by 2mt mutations.

If those mutations are neutral, the rate at which pairs of genes diverge is equal to the total rate of mutation.

Variation between populations ##

Two genes from two separate species will differ by 2N_em mutations.

Neutral variation is determined by mutation-drift balance.

Nucleotide diversity (𝜋)

Mutation-drift balance determines neutral variation.

𝜋 = 4N_em = 𝜃 _{[under neutrality]}

𝜃 measures the relative rates of mutation and random drift, and hence determines the balance between them.