Moran Process — Evolutionary Fixation

Birth-Death Dynamics in a Finite Population: Drift vs Selection
Population N30
Fitness r2.0
Initial mutants k1
Runs100
ρ (theory) = — ρ (empirical) = — Neutral drift 1/N = — Fix time ⟨τ⟩ = —
Moran process: at each step, one individual reproduces proportional to fitness, one dies randomly. Fixation probability for k initial mutants with relative fitness r: ρ = (1 − r^{−k}) / (1 − r^{−N}). For k=1: ρ = (1−1/r)/(1−1/rᴺ). Neutral (r=1): ρ = k/N (pure drift). Strong selection r→∞: ρ → 1 − r^{−k}. Fixation time scales as N log N for neutral, N/ln(r) for strong selection.