Moran process: At each step, one individual reproduces proportional to fitness, one dies randomly. The mutant (fitness r=1+s) competes with wildtype (fitness 1). Fixation probability: ρ = (1−r⁻¹)/(1−r⁻ᴺ) for a single mutant (k=1). Under pure drift (s=0): ρ = 1/N — even beneficial mutations mostly go extinct! Mean fixation time: conditioned on fixation ~ N ln N for neutral, faster for beneficial. The top panel shows individual trajectories; bottom shows ρ vs initial frequency compared to theory.