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# Exploring the Dynamics of Honeybee Mortality and Colony Collapse in Winter

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.

Figure 1. Comparison of temperature in the colony versus ambient temperature. When colony temperature surpasses a certain threshold, the entire colony collapses and dies.
“The key to surviving the winter is keeping the temperature in the hive high enough,” Rottschäfer said. “No new bees are produced during this time, so it’s important for both them and for us that they survive.” Existing studies of honeybees indicate that bees have no centralized mechanism, implying that they rely on a self-monitoring thermoregulation system that allows them to regulate their body temperatures and sense the ambient temperature around them. This mechanism consists of two processes. First, honeybees shiver with their flight muscles to produce heat when the colony falls below the preferred temperature. Second, bees adjust their positioning in the colony based on colony temperature. “If it’s too hot, they move towards a lower temperature” Rottschäfer said. “If it’s too cold, they move towards a higher temperature.” This is a form of thermotactic movement; although slightly different than chemotaxis, one can model bees’ motion with a type of chemotactic term.

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.”

Figure 2. Colonies with the highest population density at t=0 have the greatest chance of surviving the winter.
Rottschäfer then expanded her model to include the effect of mites that sicken bees, make them lethargic, and ultimately reduce their lifespan. The presence of enough mites affects honeybee mortality rates, as the mites do not die with their hosts — they simply move on to another bee.  She presented the collective results of her simulation with a graph depicting the sudden death of colonies with different population densities (see Figure 2). The schematic plots time on the horizontal axis and population density on the vertical axis, and indicates that a higher colony density at $$t=0$$ correlates with the increased likelihood of a colony making it to spring without dying off. Rottschäfer also experimented with other parameters—like ambient temperature or quantity of mites—which reconfirmed that honeybee populations die off more quickly in colder weather and in the presence of more mites.

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.

 Lina Sorg is the associate editor of SIAM News.