Capturing the interaction types of two Bt toxins Cry1Ac and Cry2Ab on suppressing the cotton bollworm by using...

Transgenic crops are increasingly promoted for their practical effects on suppressing certain insect pests, but all transgenic crops are not equally successful. The insect pests can easily develop resistance against single Bacillus thuringiensis (Bt) toxin transgenic crops. Therefore, transgenic crops including two or more mixed Bt-toxins can solve this problem by delaying the resistance development and killing the majority of targeted pests before the evolution of resistance. It is important to test the controlling effects of transgenic crops including multiple mixed toxins on a particular insect pest. Previous research has checked the cross-resistance and interactions between Bt toxins Cry1Ac and Cry2Ab against one susceptible and four resistant strains of cotton bollworm. The results showed that independence was the main interaction type between two toxins for the susceptible strain, whereas synergism was the main interaction type for any one resistant strain. However, the optimal combinations of two toxins were not obtained. In the present study, we developed two multi-exponential equations (namely bi- and tri-exponential equations) to describe the combination effects of two Bt toxins. Importantly, the equations can provide predictions of combination effects of different continuous concentrations of two toxins. We compared these two multi-exponential equations with the generalized linear model (GLM) in describing the combination effects, and found that the bi- and tri-exponential equations are better than GLM. Moreover, the bi-exponential equation can also provide the optimal dose combinations for two toxins.