Beyond Bt resistance of pests in the context of population dynamical complexity

Complexity in ecological systems often prevents long-term predictions about changes in population size and properties of the population dynamics. Mathematical modeling of such complex system behaviors can provide a rough idea of scenarios of the population dynamics. We use the reaction–diffusion model [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] to study the impact of pests resistant to toxins produced by genetically modified plants on the dynamics of the plant–insect system. Using genetically modified crops is an effective pest management tool for world-wide growers. However, there is a concern that pests may develop resistance to Bt toxins, which are a product of Bacillus thuringiensis genes introduced into genetically modified Bt plants. We show by computer simulations that the Bt plant–Bt-resistant insect dynamics resulting from the invasion of the Bt-resistant pests leads to variety of complex changes in the plant–insect biomass, which underlie the dependence of the Bt plant biomass on the duration of the insect reproduction period. We demonstrate that the plant and insect biomass can undergo both regular and irregular oscillations. We show that the character of such oscillations essentially depends on local insect fluxes resulting from inhomogeneous spatial distributions of the insects. In order to characterize the insect diffusion fluxes we introduce a new parameter, the diffusion number Dn. We show that the dependence between a value of Dn and regularity/irregularity of the plant–insect biomass oscillations is governed by a region in the model parameter space. In one of the regions the growth of the value of the diffusion number correlates with the transformation of regular oscillations into irregular ones, while in the neighboring region of the model parameter space the dependence between the character of the plant–insect oscillations and the value of the diffusion number Dn is more complex. The oscillations are irregular if the values of Dn are between 0.05 and 0.25. On either side of this interval the plant–insect oscillations are regular. The complex character of the response of the Bt crop–pest system to the invasion of Bt-resistant insects can lead to significant complications in attempts to regulate the system dynamics.