Abstract
This paper considers some novel predictions of a mathematical model for a stagestructured insect species that undergoes diapause if faced with strong intra-specific competition among larvae. The model consists of a system of two delay differential equations with a state-dependent time delay of threshold type. When the model has an Allee effect, we show that diapause may cause extinction in some parameter regimes even where the initial population is high. We also demonstrate that the model can have diapause-induced periodic solutions that can arise even if the birth function is strictly increasing, a situation in which solutions for the constant delay case always converge to an equilibrium.