Moran Process — Neutral Drift & Fixation

Moran process (Moran 1958): At each step, one individual reproduces proportional to fitness, and one random individual dies. For a mutant with relative fitness r in population N:

Fixation probability: ρ = (1 − 1/r) / (1 − 1/rᴺ) [Nowak 2006]. For neutral drift (r=1): ρ = k/N (initial mutant count / population size).

Conditional fixation time (neutral): ⟨T|fix⟩ ∝ N² generations. This is a continuous-time Markov chain — the Wright-Fisher model is its discrete-time cousin. The histogram (right) shows fixation times across the ensemble. Increase r to see selection accelerate fixation; neutral drift (r=1) shows the slowest random walk to absorption.