title: Bistability induced by generalist natural enemies can reverse pest invasions.
abstract: 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.
authors.affiliation: LMPT, UMR CNRS 7350, Université François-Rabelais de Tours, 37200, Tours, France. sten.madec@lmpt.univ-tours.fr.
authors.forename: Sten
authors.initials: S
authors.lastname: Madec
authors.affiliation: IRBI, UMR CNRS 7261, Université François-Rabelais de Tours, 37200, Tours, France.|Institut Universitaire de France, Paris, France.
authors.forename: Jérôme
authors.initials: J
authors.lastname: Casas
authors.affiliation: LMPT, UMR CNRS 7350, Université François-Rabelais de Tours, 37200, Tours, France.
authors.forename: Guy
authors.initials: G
authors.lastname: Barles
authors.affiliation: IRBI, UMR CNRS 7261, Université François-Rabelais de Tours, 37200, Tours, France.
authors.forename: Christelle
authors.initials: C
authors.lastname: Suppo
mesh_terms: D000818:Animals; D058865:Introduced Species; D008954:Models, Biological; D010571:Pest Control; D011157:Population Dynamics; D011235:Predatory Behavior
keywords: Biological control; Generalist predator; Invasion process; Long time dynamics; Prey–predator interaction; Reaction diffusion system; Traveling wave