Self-organization at the first stage of honeycomb construction: Analysis of an attachment-excavation model.

Honeybees construct nests that consist of regularly arrayed hexagonal cylinders. In the first stage of honeycomb construction, they build a linear sequence of tetrapod structures that form the basis of the comb. However, considering their physiological limitations, it is unknown how honeybees produce that initial pattern. Herein, in an attempt to understand the mechanisms of honeycomb construction, we propose an agent-based model, the attachment-excavation model, in which worker honeybees are classified into attachers who secrete and attach wax, and excavators who excise the attached wax. The model assumes that workers instinctively refrain from digging through the thin parts of a wax cluster. We then conduct two-dimensional (2D) simulations that show how a tripod pattern can be seen as a projection of tetrapods onto a plane. The simulation results show that the tripod pattern emerges due to competition between the attachers and excavators. As time advances, the isotropic wax growth causes the tripods to connect planarly. Because the homogeneously broadened structures do not match that of a natural comb, we employ anisotropic wax growth to obtain a linear sequence of constructed tripods, thus suggesting that anisotropy is a significant contributor to the first stage of honeycomb construction. From our simulation results, we conclude that honeybees utilize self-organization to achieve complexity during the first stage of honeycomb construction. It is anticipated that the results of our study will provide insights into how complexity can be achieved within a hierarchy.