Wright-Fisher Model: Allele Frequency Drift (2D)

Population & Selection

Population size N (diploid) 100

Initial allele freq. p₀ 0.50

Selection coefficient s 0.10

Dominance h 0.50

Mutation rate μ 0.001

Replicate populations 15

Pace (generations/s) 4.0

Live Readout

Generation

Mean p (A)

–

Drift spread (σ)

–

Fixed pops

0/0

Deterministic p

–

Mean heterozyg.

–

How it works

Each replicate is a Wright–Fisher population of N diploid individuals carrying two alleles, A and a, at frequency p and q=1−p. Every generation applies three real evolutionary forces in sequence: selection (deterministic), mutation (deterministic), then finite-population sampling (stochastic drift):

w̄ = p²(1+s) + 2pq(1+hs) + q²
p_sel = [p²(1+s) + pq(1+hs)] / w̄
p_mut = p_sel(1−μ) + (1−p_sel)μ
k ~ Binomial(2N, p_mut);  p_next = k / 2N

The deterministic curve (dashed) is what a population would follow with N=∞ — no drift. Every real, finite replicate deviates from it because the binomial draw only samples 2N gametes: smaller N means a larger sampling variance each generation, so lines fan out faster and are more likely to hit p=0 (lost) or p=1 (fixed) even against selection.

Population size N — sets drift strength; theory predicts variance of the sampling step ≈ p(1−p)/2N per generation.
Selection coefficient s — fitness advantage of allele A homozygotes (1+s) over aa (1); negative s disfavours A.
Dominance h — heterozygote fitness is 1+hs; h=0.5 is additive, h=0 recessive A, h=1 dominant A.
Mutation rate μ — symmetric per-generation mutation between alleles; keeps p away from the absorbing boundaries.
Replicate populations — independent Wright–Fisher runs sharing the same parameters, so the spread between lines is the variance genetic drift alone contributes.

Replicate p(t) Deterministic (no drift) Genotype / distribution panes