Perverse Consequences of Infrequently Culling a Pest

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.

[1]  Y. Kuang Delay Differential Equations: With Applications in Population Dynamics , 2012 .

[2]  L. Gut,et al.  Codling moth management and chemical ecology. , 2008, Annual review of entomology.

[3]  P. Epstein Is global warming harmful to health? , 2000, Scientific American.

[4]  I. East,et al.  Vaccination against Lucilia cuprina: The causative agent of sheep blowfly strike , 1993, Immunology and cell biology.

[5]  Stephen A. Gourley,et al.  Extinction Criteria in Stage-Structured Population Models with Impulsive Culling , 2006, SIAM J. Appl. Math..

[6]  V M Trenkel,et al.  Exploring red deer culling strategies using a population-specific calibrated management model. , 2001, Journal of environmental management.

[7]  B. Shulgin,et al.  Pulse vaccination strategy in the SIR epidemic model , 1998, Bulletin of mathematical biology.

[8]  S. P. Blythe,et al.  Nicholson's blowflies revisited , 1980, Nature.

[9]  Alan J. Terry Impulsive adult culling of a tropical pest with a stage-structured life cycle , 2010 .

[10]  K. Cooke,et al.  Interaction of maturation delay and nonlinear birth in population and epidemic models , 1999, Journal of mathematical biology.

[11]  A. Nicholson An outline of the dynamics of animal populations. , 1954 .

[12]  G. Gettinby,et al.  Positive and negative effects of widespread badger culling on tuberculosis in cattle , 2006, Nature.

[13]  K. Cooke,et al.  Interaction of maturation delay and nonlinear birth in population and epidemic models , 1999 .

[14]  A. Dixon,et al.  Aphid Ecology An optimization approach , 1985, Springer Netherlands.

[15]  J. A.,et al.  The Self-Adjustment of Populations to Change , 2008 .

[16]  Jianhong Wu,et al.  Eradicating vector-borne diseases via age-structured culling , 2007, Journal of mathematical biology.

[17]  K. Kim,et al.  Boll Weevil (Anthonomus grandis Boheman) (Coleoptera: Curculionidae) Dispersal in the Southern United States: Evidence from Mitochondrial DNA Variation , 2004 .

[18]  G. Tyler Miller,et al.  Sustaining the Earth , 2008 .

[19]  Richard Shine,et al.  Invasion and the evolution of speed in toads , 2006, Nature.

[20]  Pejman Rohani,et al.  Dynamics of infectious diseases and pulse vaccination: Teasing apart the embedded resonance effects , 2006 .

[21]  D. Gubler,et al.  Resurgent vector-borne diseases as a global health problem. , 1998, Emerging infectious diseases.

[22]  Horst R. Thieme,et al.  Mathematics in Population Biology , 2003 .

[23]  K. Deimling Nonlinear functional analysis , 1985 .

[24]  R. Shine,et al.  Assessing the Potential Impact of Cane Toads on Australian Snakes , 2003 .

[25]  J. V. van Loon,et al.  Attraction of Colorado Potato Beetle to Herbivore-Damaged Plants During Herbivory and After Its Termination , 1997, Journal of Chemical Ecology.

[26]  S. Pimm,et al.  Culling and the dynamics of the Kruger National Park African elephant population , 1999 .

[27]  W. Ricker Stock and Recruitment , 1954 .

[28]  Xiao-Qiang Zhao,et al.  Dynamical systems in population biology , 2003 .

[29]  R. Frutos,et al.  Insect Pathogens as Biological Control Agents: Do They Have a Future? , 2001 .

[30]  William E. Ricker Handbook of computations for biological statistics of fish populations , 1960 .

[31]  Hal L. Smith,et al.  Monotone Dynamical Systems: An Introduction To The Theory Of Competitive And Cooperative Systems (Mathematical Surveys And Monographs) By Hal L. Smith , 1995 .