The sandpile drove itself critical with no tuned knob. Does the same happen in EVOLUTION — does an ecosystem self-organize to a critical state, and does extinction come in scale-free bursts?
▶ Launch the interactive simulationRun the Bak–Sneppen model: a ring of N=256 species each with a fitness f∈[0,1]; each step the LEAST-fit species and its two ring neighbours go extinct and are replaced by fresh random fitnesses. With no tuned parameter, accumulate the stationary fitness histogram and measure the self-organized threshold f_c two ways — the half-height edge of the histogram, and 2⟨f⟩−1 (the stationary fitnesses are ≈uniform on [f_c,1]).
self-organized criticality with no knob: the fitnesses pile up above a sharp threshold f_c ≈ 0.667 (the 1-D nearest-neighbour Bak–Sneppen value), and evolution proceeds by PUNCTUATED EQUILIBRIUM — long calm spells above f_c broken by sudden scale-free 'coevolutionary avalanches' of extinctions (the same SOC signature as the sandpile, here as mass-extinction bursts). f_c is a precise numerical (not closed-form) value; the finite-N live estimate carries a small finite-size correction