The recent rapid decline in global honey bee populations could have significant implications for ecological systems, economics and food security. No single cause of honey bee collapse has yet to be identified, although pesticides, mites and other pathogens have all been shown to have a sublethal effect. We present a model of a functioning bee hive and introduce external stress to investigate the impact on the regulatory processes of recruitment to the forager class, social inhibition and the laying rate of the queen. The model predicts that constant density-dependent stress acting through an Allee effect on the hive can result in sudden catastrophic switches in dynamical behaviour and the eventual collapse of the hive. The model proposes that around a critical point the hive undergoes a saddle-node bifurcation, and that a small increase in model parameters can have irreversible consequences for the entire hive. We predict that increased stress levels can be counteracted by a higher laying rate of the queen, lower levels of forager recruitment or lower levels of natural mortality of foragers, and that increasing social inhibition can not maintain the colony under high levels of stress. We lay the theoretical foundation for sudden honey bee collapse in order to facilitate further experimental and theoretical consideration.
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