You might've heard that honey bees perform a waggle dance inside the hive to communicate the location of food sources to their sisters. What I didn't know at the start of this project is that honey bees also have a fairly sophisticated resource storage strategy. A global pattern of cell allocation emerges from the individual actions of many bees. Our project extends a model proposed by Scott Camazine and coauthors by presenting biologically relevant and realistic rules that individual bees could follow in order to both develop and maintain the observed pattern. Here I'll give a brief overview of the problem and our work. For a complete review of the literature, check out the arXiv preprint or the accepted version at JTB.
There are a couple of questions that can be asked about this pattern. The first one that comes to my mind is "why?". Is there some kind of evolutionary advantage to this pattern? There's some evidence that there is. Brood develop better at specific, constant temperatures, and honey storage on the outer parts of the comb act as a sort of thermal reservoir. Pollen is most frequently used to feed brood, and so there is an efficiency advantage to having it located near its consumers. But in general, I think fleshing out this question is best left to trained biologists.
The question applied mathematicians can help make headway on is "how?". How does this collection of ostensibly individually simple creatures together create such a interesting pattern? They could each have a master blueprint in their mind which they implement. Or they could each follow some simple rules that just happen to result in the creation of the cell allocation pattern.
Scott Camazine and coauthors proposed a short list of simple rules that worker bees and the queen might follow. They showed that even this simple collection of rules was sufficient to develop the pattern. Our team found that using just these rules there is a gradual degradation of the cohesiveness of the pattern over time. As brood hatch and vacate their cells, these former nursery cells were repurposed as honey and/or pollen storage cells, and eventually the pattern was lost.
One of our main contributions was to propose an extension of Camazine's rules that avoided pattern degradation. In particular, we show that if the queen's movement is slightly skewed towards the center of the comb (perhaps by thermal gradients), then the pattern can be retained indefinitely.
Our other contribution was to introduce two metrics that track the quality cell allocation over time. This allows us to quantitatively compare different models of bee behavior. We found that the two major components of a good cell allocation scheme were strong brood clumping and a clear pollen ring; if these two conditions were met, then the pattern would qualitatively match the ideal cell allocation pattern.
We also performed sensitivity analysis on the parameters of the model in order to better understand what was driving these differences. These could tell a story that would be a post in itself.
I'd like to thank my coauthors, especially Katie Montovan, for their hard work on this project. It's hard to imagine that she and I started this project 4 years ago this summer while on IGERT fellowships.