Wright-Fisher Genetic Drift

The Wright–Fisher Model

The Wright–Fisher model describes how allele frequencies change over time in finite populations due to random sampling of gametes (genetic drift). It's the foundation of population genetics theory.

Model Assumptions

• Discrete generations: Non-overlapping generations with synchronous reproduction
• Fixed population size: Constant N diploid individuals (2N gene copies)
• Random mating: All individuals have equal probability of reproducing
• Binomial sampling: Each new generation is a random sample of 2N alleles from the previous generation

Key Concepts

• Genetic drift: Random fluctuations in allele frequency due to finite population size. Stronger in smaller populations.
• Fixation: When an allele reaches frequency 1.0 (all individuals carry it). The probability of fixation for a neutral allele equals its initial frequency.
• Loss: When an allele reaches frequency 0.0 (completely eliminated from the population).
• Time to fixation: On average, 4N generations for a neutral allele starting at 50% frequency.

Variance in Allele Frequency

For a neutral allele at frequency p, the variance in frequency after one generation is:

Var(p) = p(1-p) / (2N)

This shows that drift is strongest when:

• Population size N is small (variance increases as N decreases)
• Allele frequency is intermediate (maximum variance at p = 0.5)

Selection vs. Drift

When selection is present, the deterministic force of selection competes with stochastic drift. If |s| >> 1/(2N), selection dominates. If |s| << 1/(2N), drift dominates. This determines whether evolution is primarily adaptive or random.

Effective Population Size

Real populations often have effective population sizes (N~e~) much smaller than census size due to variation in offspring number, sex ratios, and overlapping generations. For conservation, N~e~ > 50 prevents inbreeding depression, while N~e~ > 500 maintains adaptive potential.