Reproduction Number and Asymptotic Stability for the Dynamics of a Honey Bee Colony with Continuous Age Structure

A Multi-Scale Model of Disease Transfer in Honey Bee Colonies

Inter-colony disease transfer poses a serious hurdle to successfully managing healthy honeybee colonies. In this study, we build a multi-scale model of two interacting honey bee colonies. The model considers the effects of forager and drone drift, guarding behaviour, and resource robbing of dying colonies on the spread of disease between colonies. Our results show that when drifting is high, disease can spread rapidly between colonies, that guarding behaviour needs to be particularly efficient to be effective, and that for dense apiaries drifting is of greater concern than robbing. We show that while disease can put an individual colony at greater risk, drifting can help less the burden of disease in a colony. We posit some evolutionary questions that come from this study that can be addressed with this model.

The effects of diploid male production on honey bee colony evolution and survival

The order Hymenoptera includes most of the eusocial species on the planet. Correlated is the fact that many of the social species within the order are haplodiploid and use complementary sex determination (CSD) to determine the sex of offspring. CSD is the mechanism by why single sex alleles within an organism result in male development (haploid) and mismatched sex alleles develop into females (diploids). Related to this is the production of diploid males: fertilized eggs with matched sex alleles which develop as male instead of female. Honey bees are no exception to this, and as their numbers continue to suffer globally and their genetic diversity lowers, the effects of diploid male production (DMP) may pose an increased risk to the survival of bee colonies. In the present study, we develop a model for diploid male production in a honey bee colony and show that with ample resources, this phenomena has little effect on a colony's health, but there is a limit to the sustainability of a colony suffering from diploid male production. We use our model to show that there were likely no great evolutionary pressures against CSD and DMP in wild honey bees as its effects on colony health in the wild would have been negligible but increased environmental hazards such as pesticides and monoculture crops increase the effects of DMP on colony health.

Thermal efficiency extends distance and variety for honeybee foragers: analysis of the energetics of nectar collection and desiccation by Apis mellifera

The desiccation of nectar to produce honey by honeybees ( Apis mellifera L.) is an energy-intensive process, as it involves a quasi-isothermal change in the concentration of sugars from typically 20 to 80% by vaporization (honey ripening). This analysis creates mathematical models for: the collected nectar to honey ratio; energy recovery ratio; honey energy margin; and the break-even distance, which includes the factors of nectar concentration and the distance to the nectar from the nest; energetics of desiccation and a new factor, thermal energy efficiency (TEE) of nectar desiccation. These models show a significant proportion of delivered energy in the nectar must be used in desiccation, and that there is a strong connection between TEE and nest lumped thermal conductance with colony behaviour. They show the connection between TEE and honeybee colony success, or failure, in the rate of return, in terms of distance or quality of foraging. Consequently, TEE is a key parameter in honeybee populations and foraging modelling. For bee keeping, it quantifies the summer benefits of a key hive design parameter, hive thermal conductance and gives a sound theoretical basis for improving honey yields, as seen in expanded polystyrene hives.