Phys. Rev. E (in the press); preprint at http://arxiv.org/abs/1611.07575
How does a swarm of honeybees (pictured) decide on the best site for its nest? To find the answer — or at least part of it — Andreagiovanni Reina and colleagues cast the problem into a mathematical model.
The authors described the situation with a set of coupled differential equations, in which the time-dependent variables are the subpopulations of bees committed to different nest sites, and the remaining set of uncommitted bees. The system contains various parameters, such as the commitment and abandonment rates of subpopulations, describing spontaneous transitions of individual bees. Interactive transitions are accounted for as well: 'recruitment' (positive feedback of scout bees to uncommitted bees, via the waggle dance) and 'cross-inhibition' (negative feedback, in the form of stop-signals, to bees committed to another option).
Reina et al. identified the ratio between interaction and spontaneous transitions as a key control parameter — its biological meaning being the prospensity of scout bees to deliver signals. A high ratio helps to resolve decision deadlocks, if there is a choice between nests of equal quality, but low values worsen decision accuracy.
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Verberck, B. Honeybee house-hunt. Nature Phys 13, 529 (2017). https://doi.org/10.1038/nphys4173