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Spatiotemporal complexity in a predator--prey model with weak Allee effects
Modeling colony collapse disorder in honeybees as a contagion
1. | Departments of Mathematics and Curriculum & Instruction, University of Texas at Arlington, Box 19408, Arlington, TX 76019-0408, United States |
2. | Department of Mathematics, University of Texas at Arlington, Box 19408, Arlington, TX 76019-0408, United States |
References:
[1] |
G. Amdam, The hive bee to forager transition in honeybee colonies: The double repressor hypothesis, Journal of Theoretical Biology, 223 (2003), 451-464.
doi: 10.1016/S0022-5193(03)00121-8. |
[2] |
F. S. Bodenheimer, Studies in animal populations II. Seasonal population-trends in the honey-bee, Quat. Rev. Zool., 12 (1937), 406-425.
doi: 10.1086/394540. |
[3] |
CCD Steering Committee, Colony Collapse Disorder Progress Report, United States Department of Agriculture, June 2010. Retrieved 2013-08-28 from http://www.ars.usda.gov/is/br/ccd/ccdprogressreport2010.pdf. |
[4] |
D. Cramp, A Practical Manual of Beekeeping, How To Books, London, 2008. |
[5] |
B. Dahle, The role of Varroa destructor for honeybee colony losses in Norway, Journal of Apicultural Research, 49 (2010), 124-125.
doi: 10.3896/IBRA.1.49.1.26. |
[6] |
G. DeGrandi-Hoffman, S. A. Roth, G. L. Loper and E. H. Erickson, Jr., Beepop: A honeybee population dynamics simulation model, Ecological Modelling, 45 (1989), 133-150. |
[7] |
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous population, Journal of Mathematical Biology, 28 (1990), 365-382.
doi: 10.1007/BF00178324. |
[8] |
L. Dornberger, C. Mitchell, B. Hull, W. Ventura, H. Shopp, C. Kribs-Zaleta, H. Kojouharov and J. Grover, Death of the Bees: A Mathematical Model of Colony Collapse Disorder,, Technical Report 2012-12, (): 2012.
|
[9] |
H. J. Eberl, M. R. Frederick and P. G. Kevan, Importance of brood maintenance terms in simple models of the honeybee-Varroa destructor-acute bee paralysis virus complex, Electronic Journal of Differential Equations (EJDE) [electronic only] Conf. 19 (2010), 85-98. Available from: http://eudml.org/doc/232749. |
[10] |
N. Gallai, J. M. Salles, J. Settele and B. E. Vaissiere, Economic valuation of the vulnerability of world agriculture confronted with pollinator decline, Ecological Economics, 68 (2009), 810-821.
doi: 10.1016/j.ecolecon.2008.06.014. |
[11] |
M. Higes, R. Martin-Hernandez, C. Botias, E. G. Bailon, A. V. Gonzalez-Porto, How natural infection by Nosema ceranae causes honeybee colony collapse, Environmental Microbiology, 10 (2008), 2659-2669.
doi: 10.1111/j.1462-2920.2008.01687.x. |
[12] |
B. K. Hopkins, C. Herr and W. S. Sheppard, Sequential generations of honey bee (Apis mellifera) queens produced using cryopreserved semen, Reproduction, Fertility, and Development, 24 (2012), 1079-1083. |
[13] |
D. S. Khoury, Colony Collapse Disorder: Quantitative Models of Honey Bee Population Dynamics, Unpublished Thesis, School of Mathematics and Statistics, University of Sydney, Sydney, 2009. |
[14] |
D. S. Khoury, A. B. Barron and M. R. Myerscough, Modelling food and population dynamics in honey bee colonies, PLoS ONE, 8 (2013), e59084.
doi: 10.1371/journal.pone.0059084. |
[15] |
D. S. Khoury, M. R. Myerscough and A. B. Barron, A quantitative model of honey bee colony population dynamics, PLoS ONE, 6 (2011), e18491.
doi: 10.1371/journal.pone.0018491. |
[16] |
B. P. Oldroyd, What's killing American honeybees?, PLoS Biology, 5 (2007), e168.
doi: 10.1371/journal.pbio.0050168. |
[17] |
H. Özbek, Arılar ve İnsektisitler, Bees and insecticides, Uludag Bee Journal, 10 (2010), 85-95. |
[18] |
J. S. Pettis, E. M. Lichtenberg, M. Andree, J. Stitzinger and R. Rose, Crop pollination exposes honeybees to pesticides which alters their susceptibility to the gut pathogen, Nosema Ceranae, PLoS ONE, 8 (2013), e70182.
doi: 10.1371/journal.pone.0070182. |
[19] |
S. Russell, A. B. Barron and D. Harris, Dynamic modelling of honey bee (Apis mellifera) colony growth and failure, Ecological Modelling, 265 (2013), 158-169.
doi: 10.1016/j.ecolmodel.2013.06.005. |
[20] |
T. Schmickl and K. Crailsheim, HoPoMo: A model of honeybee intracolonial population dynamics and resource management, Ecological Modelling, 204 (2007), 219-245.
doi: 10.1016/j.ecolmodel.2007.01.001. |
[21] |
D. J. T. Sumpter and S. J. Martin, The dynamics of virus epidemics in Varroa-infested honey bee colonies, Journal of Animal Ecology, 73 (2004), 51-63. |
[22] |
S. Suryanarayanan and D. Kleinman, Be(e)coming experts: The controversy over insecticides in the honeybee colony collapse disorder, Social Studies Of Science (Sage Publications, Ltd.), 43 (2013), 215-240. |
[23] |
J. Traynor, Evaluating pollen production of plants, American Bee Journal, 141 (2001), 287-288. |
[24] |
U. S. Department of Agriculture (USDA) CCD Steering Committee, Colony Collapse Disorder Progress Report, USDA, 2010. Available from: http://www.ars.usda.gov/is/br/ccd/ccdprogressreport2010.pdf. |
[25] |
P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[26] |
D. VanEngelsdorp, J. Hayes Jr., R. M. Underwood and J. S. Pettis, A survey of honeybee colony losses in the United States, fall 2008 to spring 2009, Journal of Apicultural Research, 49 (2010), 7-14. |
[27] |
C. W. Whitfield, A-M. Cziko and G. E. Robinson, Gene expression profiles in the brain predict behavior in individual honey bees, Science, 302 (2003), 296-299.
doi: 10.1126/science.1086807. |
show all references
References:
[1] |
G. Amdam, The hive bee to forager transition in honeybee colonies: The double repressor hypothesis, Journal of Theoretical Biology, 223 (2003), 451-464.
doi: 10.1016/S0022-5193(03)00121-8. |
[2] |
F. S. Bodenheimer, Studies in animal populations II. Seasonal population-trends in the honey-bee, Quat. Rev. Zool., 12 (1937), 406-425.
doi: 10.1086/394540. |
[3] |
CCD Steering Committee, Colony Collapse Disorder Progress Report, United States Department of Agriculture, June 2010. Retrieved 2013-08-28 from http://www.ars.usda.gov/is/br/ccd/ccdprogressreport2010.pdf. |
[4] |
D. Cramp, A Practical Manual of Beekeeping, How To Books, London, 2008. |
[5] |
B. Dahle, The role of Varroa destructor for honeybee colony losses in Norway, Journal of Apicultural Research, 49 (2010), 124-125.
doi: 10.3896/IBRA.1.49.1.26. |
[6] |
G. DeGrandi-Hoffman, S. A. Roth, G. L. Loper and E. H. Erickson, Jr., Beepop: A honeybee population dynamics simulation model, Ecological Modelling, 45 (1989), 133-150. |
[7] |
O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous population, Journal of Mathematical Biology, 28 (1990), 365-382.
doi: 10.1007/BF00178324. |
[8] |
L. Dornberger, C. Mitchell, B. Hull, W. Ventura, H. Shopp, C. Kribs-Zaleta, H. Kojouharov and J. Grover, Death of the Bees: A Mathematical Model of Colony Collapse Disorder,, Technical Report 2012-12, (): 2012.
|
[9] |
H. J. Eberl, M. R. Frederick and P. G. Kevan, Importance of brood maintenance terms in simple models of the honeybee-Varroa destructor-acute bee paralysis virus complex, Electronic Journal of Differential Equations (EJDE) [electronic only] Conf. 19 (2010), 85-98. Available from: http://eudml.org/doc/232749. |
[10] |
N. Gallai, J. M. Salles, J. Settele and B. E. Vaissiere, Economic valuation of the vulnerability of world agriculture confronted with pollinator decline, Ecological Economics, 68 (2009), 810-821.
doi: 10.1016/j.ecolecon.2008.06.014. |
[11] |
M. Higes, R. Martin-Hernandez, C. Botias, E. G. Bailon, A. V. Gonzalez-Porto, How natural infection by Nosema ceranae causes honeybee colony collapse, Environmental Microbiology, 10 (2008), 2659-2669.
doi: 10.1111/j.1462-2920.2008.01687.x. |
[12] |
B. K. Hopkins, C. Herr and W. S. Sheppard, Sequential generations of honey bee (Apis mellifera) queens produced using cryopreserved semen, Reproduction, Fertility, and Development, 24 (2012), 1079-1083. |
[13] |
D. S. Khoury, Colony Collapse Disorder: Quantitative Models of Honey Bee Population Dynamics, Unpublished Thesis, School of Mathematics and Statistics, University of Sydney, Sydney, 2009. |
[14] |
D. S. Khoury, A. B. Barron and M. R. Myerscough, Modelling food and population dynamics in honey bee colonies, PLoS ONE, 8 (2013), e59084.
doi: 10.1371/journal.pone.0059084. |
[15] |
D. S. Khoury, M. R. Myerscough and A. B. Barron, A quantitative model of honey bee colony population dynamics, PLoS ONE, 6 (2011), e18491.
doi: 10.1371/journal.pone.0018491. |
[16] |
B. P. Oldroyd, What's killing American honeybees?, PLoS Biology, 5 (2007), e168.
doi: 10.1371/journal.pbio.0050168. |
[17] |
H. Özbek, Arılar ve İnsektisitler, Bees and insecticides, Uludag Bee Journal, 10 (2010), 85-95. |
[18] |
J. S. Pettis, E. M. Lichtenberg, M. Andree, J. Stitzinger and R. Rose, Crop pollination exposes honeybees to pesticides which alters their susceptibility to the gut pathogen, Nosema Ceranae, PLoS ONE, 8 (2013), e70182.
doi: 10.1371/journal.pone.0070182. |
[19] |
S. Russell, A. B. Barron and D. Harris, Dynamic modelling of honey bee (Apis mellifera) colony growth and failure, Ecological Modelling, 265 (2013), 158-169.
doi: 10.1016/j.ecolmodel.2013.06.005. |
[20] |
T. Schmickl and K. Crailsheim, HoPoMo: A model of honeybee intracolonial population dynamics and resource management, Ecological Modelling, 204 (2007), 219-245.
doi: 10.1016/j.ecolmodel.2007.01.001. |
[21] |
D. J. T. Sumpter and S. J. Martin, The dynamics of virus epidemics in Varroa-infested honey bee colonies, Journal of Animal Ecology, 73 (2004), 51-63. |
[22] |
S. Suryanarayanan and D. Kleinman, Be(e)coming experts: The controversy over insecticides in the honeybee colony collapse disorder, Social Studies Of Science (Sage Publications, Ltd.), 43 (2013), 215-240. |
[23] |
J. Traynor, Evaluating pollen production of plants, American Bee Journal, 141 (2001), 287-288. |
[24] |
U. S. Department of Agriculture (USDA) CCD Steering Committee, Colony Collapse Disorder Progress Report, USDA, 2010. Available from: http://www.ars.usda.gov/is/br/ccd/ccdprogressreport2010.pdf. |
[25] |
P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 29-48.
doi: 10.1016/S0025-5564(02)00108-6. |
[26] |
D. VanEngelsdorp, J. Hayes Jr., R. M. Underwood and J. S. Pettis, A survey of honeybee colony losses in the United States, fall 2008 to spring 2009, Journal of Apicultural Research, 49 (2010), 7-14. |
[27] |
C. W. Whitfield, A-M. Cziko and G. E. Robinson, Gene expression profiles in the brain predict behavior in individual honey bees, Science, 302 (2003), 296-299.
doi: 10.1126/science.1086807. |
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