Two bacterial strains grow logistically on a shared nutrient supply and suppress each other via the competition coefficients α. Both populations are integrated forward with the explicit Euler method (dt = 0.1, 1000 steps):
dN1/dt = r1·N1·(K1 − N1 − α12·N2)/K1
dN2/dt = r2·N2·(K2 − N2 − α21·N1)/K2
Coexistence is stable when K1/α12 > K2 AND K2/α21 > K1 — geometrically, when the two nullclines cross so that each species inhibits itself more than it inhibits its rival. Otherwise one strain drives the other to competitive exclusion, or (when neither condition holds) the outcome depends on which strain started larger — the founder effect.