# Wright–Fisher Population Drift & Allele Frequency Tutor

Simulate Wright–Fisher genetic drift across many replicate populations with mutation and selection. Visualize drift trajectories, the final-frequency distribution, heterozygosity decay Hₜ = H₀(1−1/2Nₑ)ᵗ, and run a Hardy–Weinberg chi-square test.

> Canonical page: https://elysiatools.com/en/tools/wright-fisher-population-drift-and-allele-frequency-tutor

- **Category:** Education

- **Keywords:** wright-fisher, genetic drift, allele frequency, fixation probability, heterozygosity, hardy-weinberg, population genetics, kimura, selection coefficient, mutation rate

## Overview

An interactive tutor for the Wright–Fisher model — the canonical null model of random genetic drift. Set a population size N (diploid 2N or haploid N gene copies), an initial allele frequency p₀, an optional mutation rate μ and selection coefficient s with dominant/recessive/additive dominance, then run many replicate populations in parallel. The tool plots every replicate trajectory, the distribution of final frequencies (showing how often A fixes vs is lost), the observed mean heterozygosity against the analytic decay Hₜ = H₀(1 − 1/(2Nₑ))ᵗ, and Kimura's theoretical fixation probability. Optionally paste genotype counts (AA/Aa/aa) to run a Hardy–Weinberg equilibrium chi-square test. Bridges the gap between a single Mendelian Punnett cross and the long-run population-level fate of an allele. Deterministic per seed.

## Inputs

- **Population size (N individuals)** (number)
- **Ploidy** (select)
- **Generations** (number)
- **Replicate populations** (number)
- **Initial frequency of allele A (p₀)** (number)
- **Mutation rate μ (per gene per generation)** (number)
- **Selection coefficient s (>0 favours A)** (number)
- **Dominance of A** (select)
- **Random seed (reproducibility)** (number)
- **Hardy–Weinberg test — AA count (optional)** (number): e.g. 36
- **Hardy–Weinberg test — Aa count (optional)** (number): e.g. 48
- **Hardy–Weinberg test — aa count (optional)** (number): e.g. 16

## When to use

- Explore how population size, ploidy, and starting allele frequency affect genetic drift.
- Compare neutral drift with mutation or selection favoring or opposing allele A.
- Test observed AA, Aa, and aa genotype counts against Hardy–Weinberg equilibrium.

## How it works

- Set population size N, diploid or haploid ploidy, number of generations, replicate populations, and initial allele frequency p₀.
- Optionally enter mutation rate μ, selection coefficient s, and dominant, recessive, or additive dominance for allele A.
- Run the simulation to view replicate trajectories, the final-frequency distribution, heterozygosity against the analytic decay curve, and fixation probability.
- Enter optional AA, Aa, and aa counts to run a Hardy–Weinberg equilibrium chi-square test; use a random seed to reproduce a simulation.

## Use cases

- Teach genetic drift, fixation, and loss of genetic variation in population genetics courses.
- Compare the effects of population size, initial frequency, mutation, and selection across repeated simulations.
- Evaluate whether observed genotype counts are consistent with Hardy–Weinberg equilibrium.

## Frequently asked questions

### What does the Wright–Fisher simulation show?

It shows allele-frequency trajectories across replicate populations, the distribution of final frequencies, heterozygosity decay, and fixation probability.

### What is the role of population size N?

N sets the number of individuals. In diploids, the model uses 2N gene copies; smaller populations generally show stronger random drift.

### Can I model natural selection and mutation?

Yes. Set mutation rate μ and selection coefficient s, then choose dominant, recessive, or additive dominance for allele A.

### What does a random seed do?

A seed makes the stochastic simulation deterministic, so the same settings and seed can reproduce the same result.

### How do I run the Hardy–Weinberg test?

Enter the observed counts for AA, Aa, and aa. The tool uses these genotype counts for a Hardy–Weinberg equilibrium chi-square test.

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