Honeybee Swarm Decision-Making: Dance Recruitment and Quorum Sensing on a Map

What you see. A honeybee swarm hangs from a branch while a few scouts look for a new home. Each scout flies out to a nest site, judges it, returns and dances for it; the better she judges the site the more dance circuits she performs, so more bees follow her. When enough bees are at one site at the same moment the swarm has decided (Thomas Seeley, Honeybee Democracy, 2010; Seeley and Visscher 2004).

The model. A scout is always in one of seven states: on the cluster, flying out, at the site, flying back, dancing, flying to the winner, arrived. Flight is at 7 m/s, so a trip takes d / v each way plus a fixed inspection time at the site. After the first visit she dances C = 100 q circuits of 1.5 s each (q = site quality from 0 to 1, a single number that stands for cavity volume, entrance size, dryness and height); on each later return the dance is shorter by the dance decay, and when it reaches zero she either retires to the cluster or keeps visiting without dancing. A bee watching the cluster is recruited to site i at the rate κ ni / (1 + n / ns), where ni is the number of bees now dancing for site i; unemployed scouts also discover a random site on their own. The vote is counted at the site: when Q bees are at one site at the same moment, that site wins.

Why it works. A better site is not recruited to because anyone compares: it simply holds dancers longer, so it has more dancers at any moment, so it recruits faster (positive feedback), while the decay of every dance makes unsupported sites fade (negative feedback). A larger quorum waits for more evidence: accuracy rises and speed falls, which is the speed-accuracy trade-off in the third graph (30 fresh swarms for every quorum value, recomputed when you change a setting). A far site is visited less often per hour, so it needs a larger quality advantage: try the preset “Best site is far away”.

Honest simplifications. The numbers are illustrative: real swarms have thousands of bees, take hours to days to decide, have 20 to 30 scouts at the site as a quorum, and scouts also use piping signals, shaking signals and the dance direction and distance, none of which are modelled here (the coloured line is only a picture of the dance's direction code). Quality is one number; rates (κ, discovery rate, retirement chance) are tuned for a decision in tens of simulated minutes, not measured. Bees, trees and sites are drawn far larger than life and the swarm is not to scale. Time runs faster than real time (time-lapse slider). Random numbers are seeded, so a run repeats exactly.

Checks. (1) Every scout is in exactly one state at all times and the positions stay finite; after the vote all scouts head for the winner. (2) One scout's round trip equals 2d/v plus the inspection time and her dance lasts C × 1.5 s (exact kinematics, independent of the stochastic part). (3) Two identical sites win 50 % each within three standard errors over 200 swarms (no hidden bias). (4) The better of two equally distant sites wins clearly more than half of 200 swarms. All four run on the page when it loads.