Mathematical analysis of the honeybee waggle dance.

A honeybee informs her nestmates of the location of a flower by doing a waggle dance. The waggle dance encodes both the direction of and distance to the flower from the hive. To reveal how the waggle dance benefits the colony, we created a Markov model of bee foraging behavior and performed simulation experiments by incorporating the biological parameters that we obtained from our own observations of real bees as well as from the literature. When two feeders were each placed 400 m away from the hive in different directions, a virtual colony in which honeybees danced and correctly transferred information (a normal, real bee colony) made significantly greater numbers of successful visits to the feeders compared to a colony with inaccurate information transfer. Howerer, when five feeders were each located 400 m from the hive, the inaccurate information transfer colony performed better than the normal colony. These results suggest that dancing's ability to communicate accurate information depends on the number of feeders. Furthermore, because non-dancing colonies always made significantly fewer visits than those two colonies, we concluded that dancing behavior is beneficial for hives' ability to visit food sources.