🧬 Moran Process Explorer

Three selection schemes — same N, same s, same start — different outcomes. Why?

100
0.10
0.002
0.30
10×
Scheme I — Offspring Copying
Scheme II — Mate Choice
Scheme III — Death

Scheme I — Offspring Copying

Gen: 0 p(A): 0.30 running
Two parents sampled uniformly. Which parent's allele is copied depends on fitness. Nonreversible for 3+ types.

Scheme II — Mate Choice

Gen: 0 p(A): 0.30 running
First parent random. Second parent biased by fitness, then neutral copying. Nonreversible for 3+ types.

Scheme III — Death

Gen: 0 p(A): 0.30 running
Who dies is biased against fitness (fitter = less likely to die). Then random reproduction. ✅ Reversible for any # of alleles.
Each scheme uses the same parameters. Differences are entirely from where selection acts. Schemes I & II: Nonreversible Scheme III: Reversible

How It Works

The Moran process is a finite-population model with overlapping generations — one birth and one death per timestep, keeping population size constant. This tool simulates 2 alleles (A and a) with relative fitness wA = 1 + s, wa = 1.

The three schemes are mathematically identical for neutral evolution (s = 0) but diverge under selection because selection placement changes the Markov chain's stationary distribution. Scheme III retains reversibility and a closed-form stationary distribution for any number of alleles; Schemes I and II become nonreversible when fitnesses are unequal and require computational methods.

Based on Braha & de Aguiar (2026), Selection Mechanisms, Stationary Distributions, and Reversibility in Multiallelic Moran Models, arXiv:2607.06732. 📝 Concept note