Bistability induced by generalist natural enemies can reverse pest invasions
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Analytical modeling of predator–prey systems has shown that specialist natural enemies can slow, stop and even reverse pest invasions, assuming that the prey population displays a strong Allee effect in its growth. We aimed to formalize the conditions in which spatial biological control can be achieved by generalists, through an analytical approach based on reaction–diffusion equations. Using comparison principles, we obtain sufficient conditions for control and for invasion, based on scalar bistable partial differential equations. The ability of generalist predators to control prey populations with logistic growth lies in the bistable dynamics of the coupled system, rather than in the bistability of prey-only dynamics as observed for specialist predators attacking prey populations displaying Allee effects. As a consequence, prey control is predicted to be possible when space is considered in additional situations other than those identified without considering space. The reverse situation is also possible. None of these considerations apply to spatial predator–prey systems with specialist natural enemies.
KeywordsReaction diffusion system Long time dynamics Traveling wave Invasion process Biological control Prey–predator interaction Generalist predator
Mathematics Subject Classification35B40 35K57 92D25 92D40 92B99
The authors would like to thank the two anonymous reviewers for their valuable comments and suggestions to improve the quality of this manuscript.
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