Moran fixation probability:
π(k) = (1 − r⁻ᵏ) / (1 − r⁻ᴺ)
where r = 1+s (fitness ratio)
Neutral drift (s=0): π = k/N — a single mutant has probability exactly 1/N of taking over.
Key insight: Even strongly beneficial mutations (s>0) are usually LOST by drift when rare. Only ~2s fraction survives when N is large — the "cost of rarity."
Green = fixation, red = extinction