Population Genetics and Gene Flow Simulator

Two-Island Population

Population size (N per island) 80

Migration rate m 0.05

Selection s (favors allele A) 0.00

Generations / sec 2

Generation

p — island 1

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p — island 2

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p = frequency of allele A (teal). The two islands start at opposite extremes; watch gene flow pull them together while drift and selection pull them apart.

How it works

Each island runs a Wright-Fisher model of a single two-allele locus. Every generation, selection first reweights each island's allele frequency toward whichever allele has higher relative fitness, migration then blends a fraction of each island's frequency with its neighbour's, and finally a finite population is resampled by binomial draw — the source of genetic drift.

p_sel = p(1+s) / (1 + s·p)
p_mig,1 = (1-m)·p_sel,1 + m·p_sel,2
p_mig,2 = (1-m)·p_sel,2 + m·p_sel,1
p_next = Binomial(N, p_mig) / N

Population size (N) — smaller islands drift harder: even a neutral allele (s = 0) randomly fixes or is lost in a few dozen generations.
Migration rate (m) — the gene-flow term. Even a trickle of migrants per generation (m ≈ 1/N) is usually enough to keep the two islands from diverging, a classic result of population genetics.
Selection s — a positive value gives allele A a survival/reproduction edge on both islands, pulling both toward fixation for A regardless of migration; a negative value favors allele a instead.
Generations / sec — how fast the simulated clock advances; slow it down to watch an individual generation's sampling step.

Real-world relevance: this balance between drift, selection and gene flow explains why isolated populations (island endemics, mountain-valley populations, human founder groups like the Ashkenazi Jewish or Finnish populations) accumulate distinctive allele frequencies, while well-connected populations stay genetically homogeneous even under local selection pressure.

Allele A Allele a Migrant in transit

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