Graduate School of Sciences and Technology for Innovation, Yamaguchi University, Ube, Yamaguchi, Japan.
Department of Mathematical Sciences, Kwansei Gakuin University, Sanda, Hyogo, Japan.
PLoS One. 2018 Oct 24;13(10):e0205353. doi: 10.1371/journal.pone.0205353. eCollection 2018.
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.
蜜蜂筑巢由规则排列的六边形圆柱组成。在蜂巢建造的第一阶段，它们先建造出一个四足结构的线性序列，作为蜂巢的基础。然而，考虑到它们的生理限制，目前还不清楚蜜蜂是如何产生最初的图案的。在这里，为了试图理解蜂巢建造的机制，我们提出了一个基于主体的模型，即附着-挖掘模型，其中工蜂被分为分泌和附着蜡的附着者，以及切除附着蜡的挖掘者。该模型假设工蜂本能地避免在蜡块的薄弱部分挖掘。然后，我们进行了二维（2D）模拟，展示了三脚架模式如何可以看作是四足结构在平面上的投影。模拟结果表明，三脚架模式的出现是由于附着者和挖掘者之间的竞争造成的。随着时间的推移，各向同性的蜡生长导致三脚架在平面上连接。由于均匀变宽的结构与天然蜂巢不匹配，我们采用各向异性的蜡生长来获得线性排列的构建三脚架，这表明各向异性是蜂巢建造第一阶段的一个重要因素。从我们的模拟结果可以得出结论，蜜蜂在蜂巢建造的第一阶段利用自组织来实现复杂性。预计我们的研究结果将为了解如何在层次结构中实现复杂性提供一些启示。
