Allele-Frequency Dynamics: Selection, Dominance & Drift (2D)

Locus & Fitness

Initial allele freq. p₀ (A) 0.50

Selection coefficient s 0.20

Dominance h 1.00

Population & Drift

Population size N 500

Selection Regime Presets

Live Readout

Generation

p (freq. of A)

0.500

Mean fitness w̄

1.000

Fixation

—

AA / Aa / aa

25% / 50% / 25%

Equilibrium p*

—

How it works

One diploid, biallelic locus (A/a), discrete non-overlapping generations. Genotype frequencies start at Hardy–Weinberg proportions p²:2pq:q² and are recomputed from p every generation (random mating is assumed each round). Genotype fitnesses:

w(AA) = 1
w(Aa) = 1 − h·s
w(aa) = 1 − s

Mean population fitness and the exact discrete-generation allele-frequency recursion (Falconer & Mackay's standard one-locus selection model):

w̄  = p²·w(AA) + 2pq·w(Aa) + q²·w(aa)
p' = [ p²·w(AA) + pq·w(Aa) ] / w̄

With s>0 and h=1, A is fully favored and dominant → directional selection sweeps A to fixation (p→1). With h=0, A is recessive, so aa is hidden from selection while rare and selection is slow at first. With h<0 (heterozygote fitness exceeds both homozygotes — overdominance / heterozygote advantage), the recursion has a stable internal equilibrium at

p* = w(Aa) − w(aa)
     ───────────────────────────────
     2·w(Aa) − w(AA) − w(aa)

and any starting p converges to p* instead of fixing — real balancing selection, the same mechanism that keeps the sickle-cell allele at moderate frequency in malaria-endemic regions. With h>1 (heterozygote disadvantage / underdominance) that same point becomes an unstable threshold: populations starting above it fix A, below it fix a.

Drift, when enabled, replaces the deterministic p' with a binomial draw of 2N gametes at probability p' each generation (Wright–Fisher sampling) — small N makes the trajectory visibly noisy and can fix or lose an allele that selection alone would keep polymorphic; large N tracks the smooth deterministic curve.

Allele frequency p (this run) Deterministic p (no drift) Equilibrium p* (if stable)