By Lina Sorg
Global honeybee populations are declining at a troubling rate. Scientists attribute this continued drop to a variety of phenomena, including industrial agriculture, colony collapse disorder, parasitic/pathogenic infections, and climate change. Given that one-third of our food production depends on bee pollination, a continued decline could have deadly effects on agricultural practices. Honeybee colonies are particularly vulnerable during the winter, when both outside temperatures and colony temperatures drop well below the bees’ preferred temperature of 30 degrees Celsius. When colony temperature surpasses a certain threshold, the entire colony dies off (see Figure 1). During a minisymposium presentation at the 2019 SIAM Conference on Applications of Dynamical Systems, currently taking place in Snowbird, Utah, Vivi Rottschäfer of Leiden University examined thermoregulation in honeybee colonies to better understand the consequences of honeybee mortality in the winter.
Rottschäfer’s model for thermotactic movement includes variables for temperature and density, incorporates the presence of diffusion, and accounts for heat production from the bees’ shivering flight muscles. This is a generalized Keller-Segel model based on James Watmough and Scott Camazine’s 1995 work. Rather than analyze a three-dimensional structure, Rottschäfer examines a cross-section of the cluster of bees in a honeycomb. “We take a cross-section through the middle, with axis 0 as the middle of the beehive,” she said. The boundary conditions are thus symmetric.
Model analysis distinguished two states of honeybee colonies: (i) one in which the colony size is above a critical population number, thus allowing the bees to maintain a core temperature above the temperature threshold, and (ii) one in which the colony’s core temperature drops below the critical threshold, thus increasing bee mortality and ultimately resulting in sudden death of the colony. “If the ambient temperature is lower, the critical total bee concentration must be higher,” Rottschäfer said.
Next she included mortality in the model, as this factor specifically explores the reason for honeybee death. Rottschäfer explained that bees have to work quite hard if the local temperature is low. Honeybees can only work about 30 minutes at a time before they have to rest. When they reach their work limit, they move towards higher temperatures at colony’s core and are replaced in the cooler parts by other bees; this is called the refresh rate. “If the total bee population is low, they have to work harder because they have to work more often,” Rottschäfer said. “If the temperature is high enough, they don’t have to work and there’s no influence on mortality.”
In light of these results, Rottschäfer wondered whether scientists can actively help colonies survive the winter. At this point she had only examined the cross-section of one honeycomb, when in reality multiple combs comprise a colony. So she decided to look at two combs with the potential for interaction. If the core temperature dips below the critical threshold in one comb, all of those bees move to the other comb. This observation reveals a potential means of human interference. “It might be an option to put two colonies together towards the end of winter,” Rottschäfer said. “But we still need to look into this in much more detail.”
Ultimately, Rottschäfer’s model reveals that the density of honeybees populating a colony is crucial to that colony’s survival through the winter. In the future, she hopes to analyze multiple honeycombs rather than just one or two, and study the relationship between pre-winter colony size and colony collapse. Possessing a better understanding of winter colony collapse can help researchers better comprehend the consequences of collapse, preserve colonies, and prevent further loss of worldwide honeybee populations.