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2014, 11(3): 511-521. doi: 10.3934/mbe.2014.11.511

Optimal sterile insect release for area-wide integrated pest management in a density regulated pest population

1. 

Department of Mathematics and Statistics, Utah State University, Logan, UT 84322, United States

Received  January 2013 Revised  June 2013 Published  January 2014

To determine optimal sterile insect release policies in area-wide integrated pest management is a challenge that users of this pest control method inevitably confront. In this note we provide approximations to best policies of release through the use of simulated annealing. The discrete time model for the population dynamics includes the effects of sterile insect release and density dependence in the pest population. Spatial movement is introduced through integrodifference equations, which allow the use of the stochastic search in cases where movement is described through arbitrary dispersal kernels. As a byproduct of the computations, an assessment of appropriate control zone sizes is possible.
Citation: Luis F. Gordillo. Optimal sterile insect release for area-wide integrated pest management in a density regulated pest population. Mathematical Biosciences & Engineering, 2014, 11 (3) : 511-521. doi: 10.3934/mbe.2014.11.511
References:
[1]

A. Bakri, K. Mehta and D. R. Lance, Sterilizing insects with ionizing radiation,, in Sterile Insect Technique. Principles and Practice in Area-Wide Integrated Pest Management (eds. V. A. Dyck, (2005), 233.  doi: 10.1007/1-4020-4051-2_9.  Google Scholar

[2]

H. J. Barclay, The sterile release method with unequal male competitive ability,, Ecological Modelling, 15 (1982), 251.  doi: 10.1016/0304-3800(82)90029-1.  Google Scholar

[3]

H. J. Barclay, Modelling the effects of aggregation on the efficiency of insect pest control,, Researches on Population Ecology, 34 (1992), 131.  doi: 10.1007/BF02513526.  Google Scholar

[4]

H. J. Barclay, Modeling incomplete sterility in a sterile release program: interactions with other factors,, Researches on Population Ecology, 43 (2001), 197.  doi: 10.1007/s10144-001-8183-7.  Google Scholar

[5]

H. J. Barclay, Mathematical models for the use of sterile insects,, in Sterile Insect Technique. Principles and Practice in Area-Wide Integrated Pest Management (eds. V. A. Dyck, (2005), 147.  doi: 10.1007/1-4020-4051-2_6.  Google Scholar

[6]

H. J. Barclay and M. Mackauer, The sterile insect release method for pest control: a density-dependent model,, Environmental Entomology, 9 (1980), 810.   Google Scholar

[7]

H. J. Barclay, R. Matlock, S. Gilchrist, D. M. Suckling, J. Reyes, W. R. Enkerlin and M. J. B. Vreysen, A conceptual model for assessing the minimum size area for an area-wide integrated pest management program,, International Journal of Agronomy, 2011 (4093).  doi: 10.1155/2011/409328.  Google Scholar

[8]

W. G. Costello and H. M. Taylor, Mathematical models of the sterile male technique of insect control,, in Mathematical Analysis of Decision Problems in Ecology (eds. A. Charnes and W. R. Lynn). Lecture Notes in Biomathematics, 5 (1975), 318.  doi: 10.1007/978-3-642-80924-8_12.  Google Scholar

[9]

F. Courchamp, L. Berec and J. Gascoigne, Allee Effects in Ecology and Conservation,, Oxford University Press, (2008).  doi: 10.1093/acprof:oso/9780198570301.001.0001.  Google Scholar

[10]

W. Danthanarayana, Population Ecology of the Light Brown Apple Moth, Epiphyas postvittana (Lepidoptera: Tortricidae),, Journal of Animal Ecology, 52 (1983), 1.  doi: 10.2307/4585.  Google Scholar

[11]

W. R. Enkerlin, Impact of fruit fly control programmes using the sterile insect technique,, in Sterile Insect Technique. Principles and Practice in Area-Wide Integrated Pest Management (eds. V. A. Dyck, (2005), 651.  doi: 10.1007/1-4020-4051-2_25.  Google Scholar

[12]

W. Enkerlin, Guidance for packing, shipping, holding and release of sterile flies in area-wide fruit fly control programmes,, Joint FAO/IAEA progamme of nuclear techniques in food and agriculture. Food and Agriculture Organization of the United Nations, (2007).   Google Scholar

[13]

O. Häggström, Finite Markov Chains and Algorithmic Applications,, Cambridge University Press, (2003).  doi: 10.1017/CBO9780511613586.  Google Scholar

[14]

K. Klassen and C. F. Curtis, History of the sterile insect technique,, in Sterile Insect Technique. Principles and Practice in Area-Wide Integrated Pest Management (eds. V. A. Dyck, (2005), 3.  doi: 10.1007/1-4020-4051-2_1.  Google Scholar

[15]

E. F. Knipling, Possibilities of insect control or eradication through the use of sexually sterile males,, Journal of Economic Entomology, 48 (1953), 459.   Google Scholar

[16]

M. Kot, M. A. Lewis and P. van den Driessche, Dispersal data and the spread of invading organisms,, Ecology, 77 (1996), 2027.  doi: 10.2307/2265698.  Google Scholar

[17]

M. F. L'Annunziata, Radioactivity: Introduction and History,, Elsevier, (2007).   Google Scholar

[18]

M. A. Lewis and P. van den Driessche, Waves of extinction from sterile insect release,, Mathematical Biosciences, 116 (1993), 221.  doi: 10.1016/0025-5564(93)90067-K.  Google Scholar

[19]

J. D. Mumford J.D., Applications of benefit/cost analysis to insect pest control using the sterile insect technique,, in Sterile Insect Technique. Principles and Practice in Area-Wide Integrated Pest Management (eds. V. A. Dyck, (2005), 481.   Google Scholar

[20]

M. G. Neubert, M. Kot and M. A. Lewis, Dispersal and pattern formation in a discrete-time predator-prey model,, Theoretical Population Biology, 48 (1995), 7.   Google Scholar

[21]

S. L. Peck and J. Bouyer, Mathematical modeling, spatial complexity, and critical decisions in Tsetse control,, Journal of Economic Entomology, 105 (2012), 1477.  doi: 10.1603/EC12067.  Google Scholar

[22]

T. Prout, The joint effects of the release of sterile males and immigration of fertilized females on a density regulated population,, Theoretical Population Biology, 13 (1978), 40.  doi: 10.1016/0040-5809(78)90035-7.  Google Scholar

[23]

D. Suckling, J. F. Brunner, G. M. Burnip and J. T. S. Walker, Dispersal of Epiphyas postvittana (Walker) and Planotortrix octo Dugdale (Lepidoptera: Tortricidae) at a Canterbury, New Zealand orchard,, New Zealand Journal of Crop and Horticultural Science, 22 (1994), 225.   Google Scholar

[24]

R. A. J. Taylor, The relationship between density and distance of dispersing insects,, Ecological Entomology, 3 (1978), 63.  doi: 10.1111/j.1365-2311.1978.tb00903.x.  Google Scholar

[25]

G. M. Viswanathan, M. G. E. da Luz, E. P. Raposo, H. E. Stanley, The Physics of Foraging,, Cambridge University Press, (2011).   Google Scholar

[26]

M-H Wang, M. Kot and M. G. Neubert, Integrodifference equations, Allee effects, and invasions,, Journal of Mathematical Biology, 44 (2002), 150.  doi: 10.1007/s002850100116.  Google Scholar

[27]

T. Yamanaka and A. M. Liebhold, Spatially implicit approaches to understand the manipulation of mating success for insect invasion management,, Population Ecology, 51 (2009), 427.  doi: 10.1007/s10144-009-0155-3.  Google Scholar

show all references

References:
[1]

A. Bakri, K. Mehta and D. R. Lance, Sterilizing insects with ionizing radiation,, in Sterile Insect Technique. Principles and Practice in Area-Wide Integrated Pest Management (eds. V. A. Dyck, (2005), 233.  doi: 10.1007/1-4020-4051-2_9.  Google Scholar

[2]

H. J. Barclay, The sterile release method with unequal male competitive ability,, Ecological Modelling, 15 (1982), 251.  doi: 10.1016/0304-3800(82)90029-1.  Google Scholar

[3]

H. J. Barclay, Modelling the effects of aggregation on the efficiency of insect pest control,, Researches on Population Ecology, 34 (1992), 131.  doi: 10.1007/BF02513526.  Google Scholar

[4]

H. J. Barclay, Modeling incomplete sterility in a sterile release program: interactions with other factors,, Researches on Population Ecology, 43 (2001), 197.  doi: 10.1007/s10144-001-8183-7.  Google Scholar

[5]

H. J. Barclay, Mathematical models for the use of sterile insects,, in Sterile Insect Technique. Principles and Practice in Area-Wide Integrated Pest Management (eds. V. A. Dyck, (2005), 147.  doi: 10.1007/1-4020-4051-2_6.  Google Scholar

[6]

H. J. Barclay and M. Mackauer, The sterile insect release method for pest control: a density-dependent model,, Environmental Entomology, 9 (1980), 810.   Google Scholar

[7]

H. J. Barclay, R. Matlock, S. Gilchrist, D. M. Suckling, J. Reyes, W. R. Enkerlin and M. J. B. Vreysen, A conceptual model for assessing the minimum size area for an area-wide integrated pest management program,, International Journal of Agronomy, 2011 (4093).  doi: 10.1155/2011/409328.  Google Scholar

[8]

W. G. Costello and H. M. Taylor, Mathematical models of the sterile male technique of insect control,, in Mathematical Analysis of Decision Problems in Ecology (eds. A. Charnes and W. R. Lynn). Lecture Notes in Biomathematics, 5 (1975), 318.  doi: 10.1007/978-3-642-80924-8_12.  Google Scholar

[9]

F. Courchamp, L. Berec and J. Gascoigne, Allee Effects in Ecology and Conservation,, Oxford University Press, (2008).  doi: 10.1093/acprof:oso/9780198570301.001.0001.  Google Scholar

[10]

W. Danthanarayana, Population Ecology of the Light Brown Apple Moth, Epiphyas postvittana (Lepidoptera: Tortricidae),, Journal of Animal Ecology, 52 (1983), 1.  doi: 10.2307/4585.  Google Scholar

[11]

W. R. Enkerlin, Impact of fruit fly control programmes using the sterile insect technique,, in Sterile Insect Technique. Principles and Practice in Area-Wide Integrated Pest Management (eds. V. A. Dyck, (2005), 651.  doi: 10.1007/1-4020-4051-2_25.  Google Scholar

[12]

W. Enkerlin, Guidance for packing, shipping, holding and release of sterile flies in area-wide fruit fly control programmes,, Joint FAO/IAEA progamme of nuclear techniques in food and agriculture. Food and Agriculture Organization of the United Nations, (2007).   Google Scholar

[13]

O. Häggström, Finite Markov Chains and Algorithmic Applications,, Cambridge University Press, (2003).  doi: 10.1017/CBO9780511613586.  Google Scholar

[14]

K. Klassen and C. F. Curtis, History of the sterile insect technique,, in Sterile Insect Technique. Principles and Practice in Area-Wide Integrated Pest Management (eds. V. A. Dyck, (2005), 3.  doi: 10.1007/1-4020-4051-2_1.  Google Scholar

[15]

E. F. Knipling, Possibilities of insect control or eradication through the use of sexually sterile males,, Journal of Economic Entomology, 48 (1953), 459.   Google Scholar

[16]

M. Kot, M. A. Lewis and P. van den Driessche, Dispersal data and the spread of invading organisms,, Ecology, 77 (1996), 2027.  doi: 10.2307/2265698.  Google Scholar

[17]

M. F. L'Annunziata, Radioactivity: Introduction and History,, Elsevier, (2007).   Google Scholar

[18]

M. A. Lewis and P. van den Driessche, Waves of extinction from sterile insect release,, Mathematical Biosciences, 116 (1993), 221.  doi: 10.1016/0025-5564(93)90067-K.  Google Scholar

[19]

J. D. Mumford J.D., Applications of benefit/cost analysis to insect pest control using the sterile insect technique,, in Sterile Insect Technique. Principles and Practice in Area-Wide Integrated Pest Management (eds. V. A. Dyck, (2005), 481.   Google Scholar

[20]

M. G. Neubert, M. Kot and M. A. Lewis, Dispersal and pattern formation in a discrete-time predator-prey model,, Theoretical Population Biology, 48 (1995), 7.   Google Scholar

[21]

S. L. Peck and J. Bouyer, Mathematical modeling, spatial complexity, and critical decisions in Tsetse control,, Journal of Economic Entomology, 105 (2012), 1477.  doi: 10.1603/EC12067.  Google Scholar

[22]

T. Prout, The joint effects of the release of sterile males and immigration of fertilized females on a density regulated population,, Theoretical Population Biology, 13 (1978), 40.  doi: 10.1016/0040-5809(78)90035-7.  Google Scholar

[23]

D. Suckling, J. F. Brunner, G. M. Burnip and J. T. S. Walker, Dispersal of Epiphyas postvittana (Walker) and Planotortrix octo Dugdale (Lepidoptera: Tortricidae) at a Canterbury, New Zealand orchard,, New Zealand Journal of Crop and Horticultural Science, 22 (1994), 225.   Google Scholar

[24]

R. A. J. Taylor, The relationship between density and distance of dispersing insects,, Ecological Entomology, 3 (1978), 63.  doi: 10.1111/j.1365-2311.1978.tb00903.x.  Google Scholar

[25]

G. M. Viswanathan, M. G. E. da Luz, E. P. Raposo, H. E. Stanley, The Physics of Foraging,, Cambridge University Press, (2011).   Google Scholar

[26]

M-H Wang, M. Kot and M. G. Neubert, Integrodifference equations, Allee effects, and invasions,, Journal of Mathematical Biology, 44 (2002), 150.  doi: 10.1007/s002850100116.  Google Scholar

[27]

T. Yamanaka and A. M. Liebhold, Spatially implicit approaches to understand the manipulation of mating success for insect invasion management,, Population Ecology, 51 (2009), 427.  doi: 10.1007/s10144-009-0155-3.  Google Scholar

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