Rabbits protecting birds: Hypopredation and limitations of hyperpredation

► Hyperpredation: decrease in native prey after invasion of alternative prey. ► Here we investigate some limitations of hyperpredation using Cat-Rabbit-Bird models. ► (+,−) indirect effect between prey occurs when rabbits have high handling costs. ► This apparent predation results in hypopredation: increase in birds after invasion. ► Predator interference and competition can both increase and decrease hyperpredation.