MacArthur-Wilson theorem: S*=cP/(c+e); dS|₀=cP; dS|_P=−eP; τ=1/(c+e); c=e → P/2

Sympy-exact symbolic witness of the MacArthur-Wilson equilibrium identities. Setup: c (colonisation rate), e (extinction rate), P (source-pool size), S (island species number) — all positive symbols. Equilibrium: dS/dt = c·(P − S) − e·S…