Relationships between food-web complexity and community persistence with varying fractions of adaptive prey (a–e; F=0.0, 0.25, 0.5, 0.75, 1.0) and adaptive rate (f–j; G=0.25, 0.025, 0.0025) in the cascade model. The other parameters are B=1, F=1 (f–j), G=0.25 (a–e), si=1, e=0.15, m=0.001–0.01, a=1. The patterns are qualitatively the same for the random model.