Abstract

Toxic plants have been used for years in agriculture to control major crop pests. However, the continuous exposure of targeted pests to toxins dramatically increases the rate of resistance evolution (Gassman et al. in Annu Rev Entomol 54:147–163, 2009a ; Tabashnik et al. Nat Biotechnol 26:199–202, 2008 ). To prevent or delay resistance, non toxic host plants can be used as refuges. Our study considers spatial and temporal refuges that are respectively implemented concurrently or alternatively a toxic crop. A conceptual model based on impulsive differential equations is proposed to describe the dynamics of the susceptible and resistant pest populations over time. The mathematical study enlightens threshold values of the proportion of the spatial refuge and key parameters that should help to understand evolution of pest resistance to toxic crop.