A population model for diapausing multivoltine insects under asymmetric cannibalism

Pupa-eating cannibalism occurs naturally in several insect species. Byasa alcinous is a multivoltine species of Red-bodied Swallowtail butterfly found in East Asia, which diapauses as pupa over the winter and whose larvae cannibalize eggs and pupae. We investigate the effects on population dynamics of increasing the asymmetric cannibalistic attack rate of a general insect species in different environmental conditions. We do this by theoretically formulating a generalized system of univoltine and bivoltine larvae over two generations in the spring and summer months. We predict that a lack of resources over the summer can force the population to become entirely univoltine, unless the second-generation bivoltine larvae increase their cannibalistic attack rate, and consume the diapausing pupae from the first generation. The model shows that under extreme environmental conditions, the persistence of univoltine larvae is favoured when faced with the threat of extinction. The model also predicts the conditions for the coexistence of both univoltine and bivoltine larvae, and the degree to which they can both coexist, which decreases as the resource in the second generation increases. This work provides the grounding for future theoretical and experimental consideration of the role of cannibalism in determining insect voltinism.