Using math to figure out how bees make group decisions

Honeybees have a queen, of course, but she doesn't issue royal decrees. Instead, bees rely on each other to gather information about the environment to inform decisions.

Likewise, the ideal hive contains a healthy mix of risk-takers and risk-avoiders under normal conditions and benefits from having more risk-avoiders in lean times when foraging becomes especially dicey. This enables the entire collective to capitalize on resources when improved conditions permit, researchers found. 

Having risk-takers venturing out in all conditions also lets the rest of the hive quickly know when conditions improve and risk-averse individuals can safely resume their foraging.

The study was published in the journal PNAS.

Lead author and University of Cincinnati Assistant Professor Hyunjoong Kim has used probability models to study other aspects of animal foraging behavior. For this project, researchers used math principles such as the Bellman Equation, Markov decision process, large deviation theory and Monte Carlo simulations.

“I always liked honeybees,” Kim said. “That’s how I started to think about the collective behavior problems through mathematics. How does a collective make a decision?”

Titled “Daring few, patient many,” the paper describes the most advantageous division of labor for animals that live in leaderless collectives, particularly honeybees.

Kim worked with Zachary Kilpatrick in the Department of Applied Mathematics at the University of Colorado-Boulder and Kresimir Josic, a mathematical biologist at the University of Houston.

“An efficient division of labor in a collective doesn’t require that anyone is in charge,” Josic said. “Rather, if each individual follows a private rule, a decentralized group can perform as well as one with an omniscient coordinator.”

Researchers said to achieve similar results, small groups must take more risks than bigger groups with more resources.

“Surprisingly, we show that a society that increases 10 times in size does not need nearly 10 times the number of risk-takers to reap the same benefits,” he said. “But this only holds if the society is well connected and the information that adventurers provide is shared.”

Kilpatrick said desert ants, harvester ants and honeybees all have shown to behave in the way that their model describes.

“Red harvester ants lose water every time they forage in the desert and gain it back from seeds, so they cut foraging on hot, dry days to conserve water,” he said. “The harsher the conditions, the fewer ants they send out.”

In honeybee hives, only a small fraction of scouts initially fan out to look for good sources of pollen and nectar. Upon its return, a scout will perform a “waggle dance” that tells other members of the hive the direction, distance and quality of the flowers discovered. Kilpatrick said when it’s time to look for a new home, the hive relies on even fewer scouts to choose the best real estate.

Animals live in a dynamic environment that is always changing. And they have to react quickly to those changing conditions, Kim said.

“In a static environment, you see the group becoming more risk averse. If the environment changes randomly, the group becomes more homogenous,” he said.

Researchers said it would be interesting to put their findings to the test in field experiments.

The study was supported with grants from the Charles Phelps Taft Research Center and the National Science Foundation.

“Math is fun,” Kim said. “It can help you solve interesting problems.”

Featured image at top: UC Assistant Professor Hyunjoong Kim is using math to unlock the strategies behind group decisionmaking. Photo/Peggy Greb/USDA