As honeybees build their nests in preexisting tree cavities, they must deal with the presence of geometric constraints, resulting in nonregular hexagons and topological defects in the comb. In this work, we study how bees adapt to their environment in order to regulate the comb structure. Specifically, we identify the irregularities in honeycomb structure in the presence of various geometric frustrations. We 3D-print experimental frames with a variety of constraints imposed on the imprinted foundations. The combs constructed by the bees show clear evidence of recurring patterns in response to specific geometric frustrations on these starter frames. Furthermore, using an experimental-modeling framework, we demonstrate that these patterns can be successfully modeled and replicated through a simulated annealing process, in which the minimized potential is a variation of the Lennard-Jones potential that considers only first-neighbor interactions according to a Delaunay triangulation. Our simulation results not only confirm the connection between honeycomb structures and other crystal systems such as graphene, but also show that irregularities in the honeycomb structure can be explained as the result of analogous interactions between cells and their immediate surroundings, leading to emergent global order. Additionally, our computational model can be used as a first step to describe specific strategies that bees use to effectively solve geometric mismatches while minimizing cost of comb building.
more »
« less
Imperfect comb construction reveals the architectural abilities of honeybees
Honeybees are renowned for their perfectly hexagonal honeycomb, hailed as the pinnacle of biological architecture for its ability to maximize storage area while minimizing building material. However, in natural nests, workers must regularly transition between different cell sizes, merge inconsistent combs, and optimize construction in constrained geometries. These spatial obstacles pose challenges to workers building perfect hexagons, but it is unknown to what extent workers act as architects versus simple automatons during these irregular building scenarios. Using automated image analysis to extract the irregularities in natural comb building, we show that some building configurations are more difficult for the bees than others, and that workers overcome these challenges using a combination of building techniques, such as: intermediate-sized cells, regular motifs of irregular shapes, and gradual modifications of cell tilt. Remarkably, by anticipating these building challenges, workers achieve high-quality merges using limited local sensing, on par with analytical models that require global optimization. Unlike automatons building perfectly replicated hexagons, these building irregularities showcase the active role that workers take in shaping their nest and the true architectural abilities of honeybees.
more » « less- NSF-PAR ID:
- 10280102
- Publisher / Repository:
- Proceedings of the National Academy of Sciences
- Date Published:
- Journal Name:
- Proceedings of the National Academy of Sciences
- Volume:
- 118
- Issue:
- 31
- ISSN:
- 0027-8424
- Page Range / eLocation ID:
- Article No. e2103605118
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Khila, Abderrahman (Ed.)more » « less
The hexagonal cells built by honey bees and social wasps are an example of adaptive architecture; hexagons minimize material use, while maximizing storage space and structural stability. Hexagon building evolved independently in the bees and wasps, but in some species of both groups, the hexagonal cells are size dimorphic—small worker cells and large reproductive cells—which forces the builders to join differently sized hexagons together. This inherent tiling problem creates a unique opportunity to investigate how similar architectural challenges are solved across independent evolutionary origins. We investigated how 5 honey bee and 5 wasp species solved this problem by extracting per-cell metrics from 22,745 cells. Here, we show that all species used the same building techniques: intermediate-sized cells and pairs of non-hexagonal cells, which increase in frequency with increasing size dimorphism. We then derive a simple geometric model that explains and predicts the observed pairing of non-hexagonal cells and their rate of occurrence. Our results show that despite different building materials, comb configurations, and 179 million years of independent evolution, honey bees and social wasps have converged on the same solutions for the same architectural problems, thereby revealing fundamental building properties and evolutionary convergence in construction behavior.
-
more » « less
Plato envisioned Earth’s building blocks as cubes, a shape rarely found in nature. The solar system is littered, however, with distorted polyhedra—shards of rock and ice produced by ubiquitous fragmentation. We apply the theory of convex mosaics to show that the average geometry of natural two-dimensional (2D) fragments, from mud cracks to Earth’s tectonic plates, has two attractors: “Platonic” quadrangles and “Voronoi” hexagons. In three dimensions (3D), the Platonic attractor is dominant: Remarkably, the average shape of natural rock fragments is cuboid. When viewed through the lens of convex mosaics, natural fragments are indeed geometric shadows of Plato’s forms. Simulations show that generic binary breakup drives all mosaics toward the Platonic attractor, explaining the ubiquity of cuboid averages. Deviations from binary fracture produce more exotic patterns that are genetically linked to the formative stress field. We compute the universal pattern generator establishing this link, for 2D and 3D fragmentation.
-
Medical image segmentation is one of the most challenging tasks in medical image analysis and has been widely developed for many clinical applications. Most of the existing metrics have been first designed for natural images and then extended to medical images. While object surface plays an important role in medical segmentation and quantitative analysis i.e. analyze brain tumor surface, measure gray matter volume, most of the existing metrics are limited when it comes to analyzing the object surface, especially to tell about surface smoothness or roughness of a given volumetric object or to analyze the topological errors. In this paper, we first analysis both pros and cons of all existing medical image segmentation metrics, specially on volumetric data. We then propose an appropriate roughness index and roughness distance for medical image segmentation analysis and evaluation. Our proposed method addresses two kinds of segmentation errors, i.e. (i) topological errors on boundary/surface and (ii) irregularities on the boundary/surface. The contribution of this work is four-fold: (i) detect irregular spikes/holes on a surface, (ii) propose roughness index to measure surface roughness of a given object, (iii) propose a roughness distance to measure the distance of two boundaries/surfaces by utilizing the proposed roughness index and (iv) suggest an algorithm which helps to remove the irregular spikes/holes to smooth the surface. Our proposed roughness index and roughness distance are built upon the solid surface roughness parameter which has been successfully developed in the civil engineering.more » « less
-
more » « less
Abstract Host‐restricted lineages of gut bacteria often include many closely related strains, but this fine‐scale diversity is rarely investigated. The specialized gut symbiont
Snodgrassella alvi has codiversified with honeybees (Apis mellifera ) and bumblebees (Bombus ) for millions of years.Snodgrassella alvi strains are nearly identical for 16SrRNA gene sequences but have distinct gene repertoires potentially affecting host biology and community interactions. We examinedS. alvi strain diversity within and between hosts using deep sequencing both of a single‐copy coding gene (minD ) and of the V4 region of the 16SrRNA gene. We sampled workers from domestic and feralA. mellifera colonies and wild‐caughtBombus representing 14 species. Conventional analyses of community profiles, based on the V4 region of the 16SrRNA gene, failed to expose most strain variation. In contrast, theminD analysis revealed extensive strain variation within and between host species and individuals.Snodgrassella alvi strain diversity is significantly higher inA. mellifera than inBombus , supporting the hypothesis that colony founding by swarms of workers enables retention of more diversity than colony founding by a single queen. MostBombus individuals (72%) are dominated by a singleS. alvi strain, whereas mostA. mellifera (86%) possess multiple strains. NoS. alvi strains are shared betweenA. mellifera andBombus , indicating some host specificity. AmongBombus ‐restricted strains, some are restricted to a single host species or subgenus, while others occur in multiple subgenera. Findings demonstrate that strains diversify both within and between host species and can be highly specific or relatively generalized in their host associations.
