Moran Process — Genetic Drift & Fixation

Stochastic Population Genetics: Allele Frequency Trajectories & Fixation Probability

Population Parameters

Population size N: 30 Initial A alleles k: 5 Fitness advantage r: 1.00 Mutation rate u: 0.000 Number of runs: 10 Running...

Moran process: Discrete-time stochastic model. At each step: select one individual proportional to fitness to reproduce, select one uniformly to die. Population size N is fixed.
Fixation probability (Moran 1958): For a single mutant with fitness r in neutral background (r=1) population: π = 1/N. With selection: π = (1−1/r)/(1−1/rᴺ). For r→1: π=1/N (neutral).
Fixation time: Neutral conditioned on fixation: ⟨T_fix|fix⟩ = −2N·[k·ln(k/N) + (N−k)·ln(1−k/N)] / (N-1).
Genetic drift dominates for small N; selection dominates when r·N >> 1. The effective population size N_e sets the balance.