Journal of Mathematical Biology

, Volume 75, Issue 3, pp 543–575 | Cite as

Bistability induced by generalist natural enemies can reverse pest invasions

  • Sten Madec
  • Jérôme Casas
  • Guy Barles
  • Christelle Suppo


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.


Reaction diffusion system Long time dynamics Traveling wave Invasion process Biological control Prey–predator interaction Generalist predator 

Mathematics Subject Classification

35B40 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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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Sten Madec
    • 1
  • Jérôme Casas
    • 2
    • 3
  • Guy Barles
    • 1
  • Christelle Suppo
    • 2
  1. 1.LMPT, UMR CNRS 7350Université François-Rabelais de ToursToursFrance
  2. 2.IRBI, UMR CNRS 7261Université François-Rabelais de ToursToursFrance
  3. 3.Institut Universitaire de FranceParisFrance

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