Abstract
There is growing public concern that pests may develop resistance to Bt toxins produced by genetically modified Bt plants. We develop and analyse a conceptual reaction-diffusion model of the agricultural ecosystem, to simulate the Bt-resistant insect massive invasion when the insect fecundity rate is limited by the number of females rather than by the mating frequency. We show by computer simulations that reproduction of Bt-resistant pests is a factor that significantly affects the Bt plant biomass under the Bt-resistant pest invasion. We demonstrate that periodical Bt plant sowing can lead to both regular and irregular oscillations in Bt plant and Bt-resistant insect biomass. The character of the oscillations (regular or irregular) is shown to be dependent on local insect fluxes, which are characterised by the diffusion number Ξ. The oscillations are irregular if Ξ ≥ 0.02, but otherwise the oscillations of the plant and insect biomass are regular.
This work was partially supported by ISTC, DFG, RFBR, NSF Biocomplexity Program, and by the University of California Agricultural Experiment Station. We are thankful to the anonymous referees for helpful suggestions.
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References
Alstad, D. N., Andow, D. A. (1995) Managing the evolution of insect resistance to transgenic plants. Science 268, 1894–1896.
Armstrong, C.L., Parker, G.B., Pershing, J.C., Brown, S.M., Sanders, P.R., Duncan, D.R., Stone, T., Dean, D.A., DeBoer, D. L., Hart, J., Howe, A.R., Morrish, F. M., Pajeau, M. E., Petersen, W. L., Reich, B.J., Rodriguez, R., Santino, C. G., Sato, S.I., Schuler, W., Sims, S.R., Stehling, S., Tarochione, L. J., Fromm, M. E. (1995) Field evaluation of European corn borer control in progeny of 173 transgenic corn evens expressing an insecticidal protein from Bacillus thuringiensis. Crop Sci. 35, 550–557.
Bazykin, A. D. (1969) A model of the dynamics of a species size, and the problem of coexistence of closely related species. Journal of General Biology 30, 259–264.
Bazykin, A. D. (2004) Nonlinear Dynamics of Interacting Populations. Moscow, Izhevsk: ICS.
Frutos, R., Rang, C, Royer, M. (1999) Managing resistance to plants producing Bacillus thuringiensis toxins. Crit. Rev. Biotechnol. 19, 227–276.
Groot, A.T., Dicke, M. (2002) Insect-resistant transgenic plants in a multi-trophic context. Plant J. 31, 387–406.
Gould, F. (1998) Sustainability of transgenic insecticidal cultivars: integrating pest genetics and ecology. Annu. Rev. Entomol. 43, 701–726.
Hillier, J.G., Birch, A.N.E. (2002) A Bt-trophic mathematical model for pest adaptation to a resistant crop. J. Theor. Biol. 215, 305–319.
Janmaat, A.F., Meyers, J. (2003) Rapid evolution and the cost of resistance to Bacillus thuringiensis in greenhouse populations of cabbage loopers, Trichoplusia ni. Proc. R. Soc. Lond. B Biol. Sci. 270, 2263–2270.
Kolmogorov, A., Petrovskii, I., Piskunov, S. (1937) Étude de l’equation de la diffusion avec croissance de la quantité de mattière et son application à un problème biologique. Bull. Univ. Moscou, Serie Int. (Section A) 1, 1–25.
Kot, M. (2001) Elements of Mathematical Ecology. Cambridge: Cambridge University.
Lewis, W.J., van Lenteren, J.C., Phatak, S.C., Tumlinson, J.H. (1998) A total system approach to sustainable pest management. Proc. Natl Acad. Sci. USA 94, 12243–12248.
Lotka, A. J. (1925) Elements of Physical Biology. Baltimore: Williams and Wilkins.
Malchow, H., Petrovskii, S. V., Medvinsky, A. B. (2001) Pattern formation in models of plankton dynamics. Oceanologica Acta 24, 479–487.
Medvinsky, A.B., Gonik, M. M., Li, B.-L., Malchow, H. (2007) Beyond Bt resistance of pests in the context of population dynamics complexity. Ecological Complexity 4, 201–211.
Medvinsky, A. B., Gonik, M. M., Li, B.-L., Velkov, V. V., Malchow, H. (2006) Invasion of pests resistant to Bt toxin can lead to inherent non-uniqueness in genetically modified Bt-plant dynamics: mathematical modeling. J. Theor. Biol. 242, 539–546.
Medvinsky, A.B., Gonik, M.M., Velkov, V. V., Li, B.-L., Malchow, H. (2005) Modeling invasion of pests resistant to Bt toxins produced by genetically modified plants: recessive vs. dominant invaders. Natural Resource Modeling 18, 347–362.
Medvinsky, A.B., Morozov, A.Y., Velkov, V. V., Li, B.-L., Sokolov, M.S., Malchow, H. (2004) Modeling the invasion of recessive Bt-resistant insects: an impact on transgenic plants. J. Theor. Biol. 231, 121–127.
Medvinsky, A.B., Petrovskii, S.V., Tikhonova, LA., Malchow, H., Li, B.-L. (2002) Spatiotemporal complexity of plankton and fish dynamics. SIAM Review 44, 311–370.
Medvinsky, A.B., Tikhonova, I. A., Petrovskii, S.V., Malchow, H., Venturino, E. (2001) Chaos and order in spatially structured plankton dynamics. A theoretical study. In: Nonlinear Dynamics in the Life and Social Sciences (ed. by W. Sulis and I. Trofimova). Amsterdam, Berlin, Oxford, Tokyo, Washington: IOS.
Petrovskii, S. V., Li, B.-L. (2006) Exactly Solvable Models of Biological Invasion. Boca Raton: Chapman & Hall/CRC.
Rajamohan, F., Lee, M. K., Dean, D.H. (1998) Bacillus thuringiensis insecticidal protein: molecular mode of action. Prog. Nucl. Res. Mol. Biol. 60, 1–23.
Scott, S.E., Wilkinson, M.J. (1998) Transgene risk is low. Nature 393, 320.
Storer, N.P., Peck, S.L., Gould, F., van Duyn, J. W., Kennedy, G.G. (2003) Spatial processes in the evolution of resistance in Helicoverpa zea (Lepidoptera: Noctiudae) to Bt transgenic corn and cotton in a mixed agroecosystem: a biology-rich stochastic simulation model. J. Econ. Entomol. 96, 156–172.
Tabashnik, B. E. (1994) Evolution of resistance to Bacillus thuringiensis. Annu. Rev. Entomol. 39, 47–49.
Tabashnik, B.E., Carriere, Y., Dennehy, T.J., Morin, S., Sisterson, M.S., Roush, R. T., Shelton, A. M., Zhao, J.-Z. (2003) Insect resistance to transgenic Bt crops: Lessons from the laboratory and the field. J. Econ. Entomol. 96, 1031–1038.
Tabashnik, B.E., Cushing, N.L., Finson, N., Johnson, M.W. (1990) Field development of resistance to Bacillus thuringiensis in diamondback moth (Lepidoptera: Plutellidae). J. Econ. Entomol. 83, 1671–1676.
Tabashnik, B.E., Patin, A.L., Dennehy, T.J., Liu, Y.B., Carriere, Y., Sims, M.A., Antilla, L. (2000) Frequency of resistance to Bacillus thuringiensis in field populations of pink bollworm. Proc. Natl Acad. Sci. USA 97, 12980–12984.
Velkov, V. V., Medvinsky, A.B., Sokolov, M.S., Marchenko, A.I. (2005) Will transgenic plants adversely affect environment? J. Biosciences 30, 515–548.
Volterra, V. (1926) Fluctuations in the abundance of a species considered mathematically. Nature 118, 558–560.
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Medvinsky, A.B., Gonik, M.M., Tyutyunov, Y.V., Li, BL., Rusakov, A.V., Malchow, H. (2008). Insecticidal Bt Crops Under Massive Bt-resistant Pest Invasion: Mathematical Simulation. In: Hosking, R.J., Venturino, E. (eds) Aspects of Mathematical Modelling. Mathematics and Biosciences in Interaction. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8591-0_5
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