A bumble bee hovers near a cluster of brightly coloured flowers, foraging for nectar and pollen - resources that are vital not only for the colony's survival but also for pollinating crops.
Researchers at UBC Okanagan have created a mathematical model that captures something remarkable: how a bumblebee colony uses and manages its energy, and what that means for farmers, pollination and the future of sustainable agriculture.
Developed by doctoral student Pau Capera-Aragonès alongside Drs. Rebecca Tyson and Eric Foxall of UBC Okanagan's Department of Computer Science, Mathematics, Physics and Statistics , the model simulates the full energy budget of a bumblebee colony and how bees forage across a changing landscape.
The study introduces a new colony-level framework built on the principles of dynamic energy budget theory.
"The novelty is in treating the colony as a collective entity, not tracking individual bees. By modelling how the whole system allocates energy to survive, grow and reproduce, we can test how different environmental conditions influence long-term colony health," says Dr. Foxall.
The research was recently published in the Bulletin of Mathematical Biology .
The researchers also adapted the maximum entropy principle, a concept from physics, to estimate how bees distribute themselves across landscapes when foraging.
Rather than simulating every bee's behaviour, the model assumes bees spread out in ways that maximize energy gain while minimizing travel costs. "We're not saying this is a perfect prediction," notes Dr. Foxall, "but it's an efficient way to model typical spatial patterns under realistic constraints."
Findings with real-world relevance
While the model doesn't offer simple prescriptions, it highlights some critical design principles for supporting bee populations and, by extension, the pollination of many crops.
- Timing matters. An early-season mass bloom can lead to rapid colony expansion. But if resources disappear shortly afterward, the colony may collapse. Success isn't just about how much food is available, it's also about when.
- More isn't always better. If wildflower patches are too similar to crop flowers and located closer to the nest, bees may shift their focus away from the crops, reducing pollination where it's most needed.
- Diversity is key. Many crops provide plenty of nectar (sugar), but limited or unbalanced pollen (protein). "Flowers provide two kinds of food," explains Dr. Tyson. "Nectar gives them sugar, which is simple. But pollen provides protein, and that's much more complex." Different flowers offer different amino acid profiles, and most are not complete protein sources. Without dietary diversity, bees struggle to maintain healthy colonies.
"In some agricultural systems-like blueberry crops-the pollen lacks certain essential amino acids," Dr. Tyson adds. "That's where native wildflowers become especially valuable, because they help fill those nutritional gaps."
Even among wildflowers, quality varies. Dandelions, for example, are relatively low in protein.
"That's why we recommend planting a variety of wildflowers," says Dr. Tyson. "Preferably native species, because local bees are adapted to them. As long as you're planting for diversity, the patch will benefit pollinators."
A framework for learning and testing
The model strikes a balance between ecological detail and computational simplicity.
"You can plug in some basic assumptions and explore what causes a colony to thrive, or collapse. That's powerful," says Dr. Foxall.
While it wasn't built to produce location-specific recommendations, it offers a flexible testbed for exploring how landscape design can support pollination over time.
