SIAM News Blog

Math Modeling Unveils the Threat of Parasites, Pesticides, and Seasonality Changes to Honeybees

By Jillian Kunze

Figure 1. Honeybees live in complex societies within hives throughout their life cycles. Figure courtesy of the Florida Division of Plant Industry, Florida Department of Agriculture and Consumer Services, and licensed under a Creative Commons Attribution 3.0 License.
Honeybees live in diverse, complex, and highly organized colonies containing three types of bees: a female queen, male drones, and female worker bees (see Figure 1). “Why are honeybees really important for humans?” Jun Chen of Arizona State University asked. “They’re pollinators, and pollinate 80 percent of crops.” Bees also produce honey and wax, which hold an enormous economic value. However, factors including climate change and pesticide exposure during pollination are threatening honeybee populations — and while some pesticides claim to be “bee safe,” beekeepers still report impacts to colonies after these chemicals are applied in nearby areas.

During a minisymposium presentation at the 2024 SIAM Conference on Mathematics of Planet Earth—which is taking place this week in Portland, Ore., concurrently with the 2024 SIAM Conference on the Life Sciences—Chen explained that the number of honeybee colonies in the U.S. fell by 30 percent between 1989 and 2008. People were quite concerned by this turn of events and began implementing measures to help honeybees, so populations have improved slightly since 2008. A number of influences still hamper honeybee flourishing, however, including varroa mites and other parasites as well as pesticides and climate change. Chen and her collaborators developed mathematical models to study the interactions between parasitism, seasonal effects, and pesticide exposure across the honeybee life cycle.

Varroa mites are parasites that cause bees to lose weight and impact their immune systems, which makes them more susceptible to viral diseases. Beekeepers generally treat colonies for mites in March and October, which is one way in which seasonality impacts honeybees. There is also the change in flowering plants that are available for pollination over the spring and summer. Worker bees alter their foraging behavior throughout the year, and tend to stay within the hive during winter months for warmth. The queen also lays more eggs during the summer, and does not lay any eggs during the colder months. “Everything always has this connection to seasonality,” Chen said — though global warming is throwing these seasonal connections out of alignment. 

Figure 2. Death rate of adult bees versus the concentration of fungicide in the pollen patties. Figure courtesy of Jun Chen.
“My research questions are first, how does seasonality affect parasitized honeybee colonies?” Chen said. “We can extend this to the effect of pesticides on honeybee colonies as well.” Chen presented a mathematical honeybee model that includes terms for the birth and death of bees and incorporates the effect of seasonality. As expected, the model shows that larger populations and higher baseline egg-laying rates help the colony survive. More intense changes between the seasons, however, can lead the population to collapse. 

Chen then parasitized the honeybee model with additional terms to account for the birth and death of the varroa mites. When examining the dynamics under a constant rate of egg laying, parasitism clearly has a negative impact. The length and intensity of seasons, in tandem with the timing of when the maximum egg-laying rate occurs, has a quite complex effect on the parasitized model. “We know that seasonality can have a negative or a positive influence, and can provide insights into the dynamics,” Chen said.

Next, Chen described an experiment in which she and her collaborators treated 40 bee colonies with four different levels of fungicide contained within patties of pollen (except for the untreated colonies that served as a control) and recorded data on the population and consumption levels. Their mathematical model of the system, which included the bee life cycle as well as the input of the pollen patties, fit well to the data. The experiment only took place over the course of five months, so it was not possible to fully explore the effects of seasonality, but it was still evident that environmental changes such as flowering plants affected the system.

Figure 3. The time at which the maximum egg laying rate occurs versus the concentration of fungicide in the pollen patties. Figure courtesy of Jun Chen.
At model equilibrium, the egg and adult populations have a linear relationship that depends on the ratio of adult and egg death rates. Furthermore, higher concentrations of the fungicides cause more deaths of adult bees (see Figure 2). “We find that adult mortality has a dose-dependent linear relationship,” Chen said. “We also find that the fungicides cause the time of the maximum egg-laying to change.” Fungicides shift the time of year at which the queen lays the highest number of eggs (see Figure 3); this shift, in combination with climate change, could worsen the situation for bees and lead to colony collapses. The model can also predict long-term dynamics, and indicates that both a high pesticide dose and low rate of egg laying will cause the colony to collapse.

Chen hopes that future research will investigate these interactions even further. Mathematical modeling can help researchers better understand the impact of overlapping factors on honeybee populations, and hopefully provide insights that will aid in their conservation.

Acknowledgements: Jun Chen acknowledges her collaborators Jennifer Fewell, Yun Kang, Jon Harrison, and Adrian Fisher II (all of Arizona State University) and Gloria DeGrandi-Hoffman (U.S. Department of Agriculture). She receives funding from the National Science Foundation, U.S. Department of Agriculture, Arizona State University, and James S. McDonnell Foundation.

  Jillian Kunze is the associate editor of SIAM News


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