Gene Pool Diorama: Mendel Crosses, Hardy-Weinberg, Drift and Island Migration Lab

Every figure carries two copies of a gene. Watch alleles pass from parents to children, drift by chance, get favoured by an environment, and travel between islands.

Live measurements

■ island 1 ■ island 2 ■ island 3 (frequency p of allele A, 0 to 1)

■ H within islands ■ H total ■ F_ST (axis 0 to 0.5)

Island	p(A)	AA/Aa/aa	H obs / 2pq	F_IS

Scenario and forces

Population N

Migration m

Mutation μ

Dominance h

Selection s, isl. 1

Selection s, isl. 2

Selection s, isl. 3

Start p, isl. 1

Start p, isl. 2

Start p, isl. 3

Speed2 gen/s

s > 0 favours allele A (AA fitness 1+s, Aa 1+hs, aa 1); s < 0 favours a. Changing the starting frequencies restarts the run; all other sliders act immediately.

Mendel cross lab

Parent 1

Parent 2

Offspring n100

Experiment: how fast does drift erase variation?

300 neutral populations per size start at p = 0.5 and run until one allele is lost.

Independent numerical checks

Check	Theory	Model

The science

Mendel. A diploid carries two alleles of a gene, A and a. Each parent passes on one of them at random, so crossing Aa × Aa gives AA : Aa : aa in the ratio 1 : 2 : 1 on average. In a finite sample the counts only approximate that ratio; the chi-square statistic χ² = Σ(O-E)²/E measures the scatter.

Hardy-Weinberg. In a large randomly mating population with allele frequency p (A) and q = 1-p, genotypes appear in proportions p² : 2pq : q², and without other forces p does not change. The table compares observed heterozygotes with 2pq through F_IS = 1 - H_obs/2pq.

Genetic drift. Each generation the 2N gene copies of the next generation are a random sample of the current ones. The variance of the change in p is pq/2N; heterozygosity decays as H_t = H₀(1-1/2N)^t, and a neutral allele eventually becomes fixed with probability equal to its starting frequency. Mean time to fixation or loss is about -4N[p ln p + q ln q] generations (diffusion approximation).

Selection. Genotype fitnesses are w_AA = 1+s, w_Aa = 1+hs, w_aa = 1. After selection the gamete frequency of A is (p²w_AA + pq w_Aa)/w̄ in a large population. Selection beats drift when |Ns| is clearly larger than 1. Kimura's diffusion result for a new additive (h = 1/2) mutation with starting frequency p is (1-e^-2Nsp)/(1-e^-2Ns).

Migration. In the island model a fraction m of each island's gametes comes from the other islands, so allele frequencies are pulled together; differences between islands shrink by the factor 1 - mk/(k-1) each generation (k = 3 islands). Differentiation is summarised by F_ST = (H_T - H_S)/H_T.

What is simplified. One gene with two alleles, discrete generations, random mating, equal and constant population sizes, no sexes, no linkage, no real genomics. Colours are a teaching device. Fitness values, migration rates and mutation rates are chosen to make the effects visible in minutes, not measured from any species (real mutation rates are of the order of 10^-8 to 10^-5 per gene copy per generation).

Checks on this page. Hardy-Weinberg proportions (200,000 offspring), neutral fixation probability, heterozygosity decay, Kimura's fixation probability, exact migration convergence and a separately written selection recursion. Stochastic checks use fixed random seeds and tolerances of roughly three standard errors.