In recent years honey bee colonies have been experiencing increased loss of hives. One cause of hive loss is colony collapse disorder (CCD). Colony collapse disorder is characterised by a previously healthy hive having few or no adult bees but with food and brood still present. This occurs over several weeks. It is not known if there is an exact cause of CCD but rather it is thought to be the accumulation of multiple stressors placed on a hive. One of the stressors is the breakdown of thermoregulation inside the hive.
The bee life cycle begins with eggs that hatch into larvae that in turn pupae. The eggs, larvae and pupae together are known as brood. Pupal cells are capped off by adult bees (and so are known as capped brood) and they undergo change to develop into an adult bee. In order for this capped brood to develop correctly, the temperature within the hive must be regulated by the hive bees to ensure optimal development of the capped brood. Variations in the temperature, caused by the breakdown of thermoregulation, lead to suboptimal development in adults that emerge from capped brood. In particular, their brains and flight muscles are compromised. This later leads to these bees becoming inefficient foragers which also have shorter life spans.
In this thesis we aim to extend previous honey bee models with the inclusion of thermoregulatory stress. We will show that the inclusion of thermoregulatory stress produces an Allee effect. Furthermore, the analysis and simulations of our models show the importance of hive demography and the effects of changing climates on a hives’ survival. We use a delay differential equation (DDE) to model our systems. We give a brief introduction into the stability analysis of linear delay differential equations which is used to analyse the qualitative behaviour of our systems. Finally, we use ordinary differential equations to approximate the DDE model.