Bulletin of Mathematical Biology

, Volume 72, Issue 7, pp 1666–1695 | Cite as

Perverse Consequences of Infrequently Culling a Pest

  • Alan J. TerryEmail author
  • Stephen A. Gourley
Original Article


There are potentially many situations in which creatures will be subject to infrequent but regular culling. In terms of controlling crop pests, some farmers may only be able to afford to apply pesticides occasionally. Alternatively, pesticides may be applied only occasionally to limit their unwelcome side effects, which include pesticide resistance, chemical poisoning of agricultural workers, and environmental degradation. In terms of conservation, some species (such as the red deer in the UK) may be culled occasionally to maintain balances within their ecosystem. However, in this paper we discover, as the culmination of an exploration of adult-stage culling of a creature with juvenile and adult life stages, that, in certain circumstances, regular but infrequent culling will, perversely, increase the average population of the creature.

Pest control Impulsive adult culling Delay differential equation 


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Copyright information

© Society for Mathematical Biology 2009

Authors and Affiliations

  1. 1.Division of MathematicsUniversity of DundeeDundeeUK
  2. 2.Department of MathematicsUniversity of SurreyGuildfordUK

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