Imperfect comb construction reveals the architectural abilities of honeybees
03 Aug 2021-Proceedings of the National Academy of Sciences of the United States of America (National Academy of Sciences)-Vol. 118, Iss: 31
TL;DR: In this article, the authors used automated image analysis to extract the irregularities in natural comb building, and found 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.
Abstract: 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.
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TL;DR: In this paper , comparative methods have been used in bio-inspired design, and they have led to breakthroughs in studies on gecko-inspired adhesives and multifunctionality of butterfly wing scales.
Abstract: Biodiversity provides a massive library of ideas for bio-inspired design, but the sheer number of species to consider can be daunting. Current approaches for sifting through biodiversity to identify relevant biological models include searching for champion adapters that are particularly adept at solving a particular design challenge. While the champion adapter approach has benefits, it tends to focus on a narrow set of popular models while neglecting the majority of species. An alternative approach to bio-inspired design is the comparative method, which leverages biodiversity by drawing inspiration across a broad range of species. This approach uses methods in phylogenetics to map traits across evolutionary trees and compare trait variation to infer structure-function relationships. Although comparative methods have not been widely used in bio-inspired design, they have led to breakthroughs in studies on gecko-inspired adhesives and multifunctionality of butterfly wing scales. Here we outline how comparative methods can be used to complement existing approaches to bioinspired design, and we provide an example focused on bio-inspired lattices, including honeycomb and glass sponges. We demonstrate how comparative methods can lead to breakthroughs in bio-inspired applications as well as answer major questions in biology, which can strengthen collaborations with biologists and produce deeper insights into biological function.
8 citations
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TL;DR: Dong et al. as discussed by the authors showed that correct waggle dancing requires social learning and observed that the first dances of bees that could follow other dancers showed neither impairment. But they did not show that experience increased angle and direction accuracy, untutored bees were never able to recover accurate distance coding.
Abstract: Honey bees use a complex form of spatial referential communication. Their “waggle dance” communicates the direction, distance, and quality of a resource to nestmates by encoding celestial cues, retinal optic flow, and relative food value into motion and sound within the nest. We show that correct waggle dancing requires social learning. Bees without the opportunity to follow any dances before they first danced produced significantly more disordered dances with larger waggle angle divergence errors and encoded distance incorrectly. The former deficit improved with experience, but distance encoding was set for life. The first dances of bees that could follow other dancers showed neither impairment. Social learning, therefore, shapes honey bee signaling, as it does communication in human infants, birds, and multiple other vertebrate species. Description Learning to dance The honeybee waggle dance has long been recognized as a behavior that communicates information about resource location from a foraging worker to her nest mates. Dong et al. show that this complex dance is in part learned by young bees as they observe more experienced bees (see the Perspective by Chittka and Rossi). Specifically, bees that were not exposed to the dances of their older counterparts displayed more angle and distance errors than those that had a “tutor.” Although experience increased angle and direction accuracy, untutored bees were never able to recover accurate distance coding. Thus, as with birds, humans, and other social learning species, honeybees benefit from observing others of their kind that have experience. —SNV Honey bees use social signal learning to improve their ability to waggle dance, a complex example of nonhuman spatial referential communication.
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TL;DR: Using 4D X‐ray microscopy, this study shows how individual and groups of honeycomb cells are formed and contributes significantly to the comb's robust mechanical properties in all three dimensions.
Abstract: Honeycomb is one of nature's best engineered structures. Even though it has inspired several modern engineering structures, an understanding of the process by which the hexagonal cells are formed in 3D space is lacking. Previous studies on the structure of the honeycomb are based on either 2D microscopy or by direct visual observations. As a result, several critical features of its microstructure and the precise mechanisms of its growth are not well understood. Using 4D X‐ray microscopy, this study shows how individual and groups of honeycomb cells are formed. Cells grow additively from a corrugated central spine in a dynamic manner. The previously undocumented, corrugated spine contributes significantly to the comb's robust mechanical properties in all three dimensions. As cells grow, honey bees create a “coping,” which this study shows to be the location where new wax material is deposited behind where compaction and densification take place. This is exemplified by pores in the wax observed at the coping and alternating rear junctions between the comb cells that arise from the additive building technique and the highly efficient cell packing methodology, respectively. Additional mechanisms for growth and formation are discussed and described.
6 citations
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TL;DR: The authors argue that a pragmatic perspective of science, in which descriptive, mechanistic, and normative models and theories each play a distinct role in defining and bridging levels of abstraction, will facilitate neuroscientific practice.
Abstract: In recent years, the field of neuroscience has gone through rapid experimental advances and a significant increase in the use of quantitative and computational methods. This growth has created a need for clearer analyses of the theory and modeling approaches used in the field. This issue is particularly complex in neuroscience because the field studies phenomena that cross a wide range of scales and often require consideration at varying degrees of abstraction, from precise biophysical interactions to the computations they implement. We argue that a pragmatic perspective of science, in which descriptive, mechanistic, and normative models and theories each play a distinct role in defining and bridging levels of abstraction, will facilitate neuroscientific practice. This analysis leads to methodological suggestions, including selecting a level of abstraction that is appropriate for a given problem, identifying transfer functions to connect models and data, and the use of models themselves as a form of experiment.
5 citations
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TL;DR: Chittka et al. as mentioned in this paper show that bees also build various types of irregularly shaped and sized cells, for example when merging separate comb constructions, which raises the question of whether the bees' innate behavioral repertoire contains multiple different routines for each shape, whether bees plan ahead to insert optimal shapes, or whether such diversity of structures could be explained by simple rules.
Abstract: Perhaps the most magnificent animal building structure is the honeybee wax comb—a double-sided sheet of tessellated, near-horizontal hexagonal cells. The cells are built either side of a common backplane that forms a base for those to either side. This typically highly regular structure has been shown to be mathematically optimal to maximize storage space and stability while minimizing building material (1). However, Smith et al. (2) show that bees also build various types of irregularly shaped and sized cells, for example when merging separate comb constructions. This raises the question of whether the bees’ innate behavioral repertoire contains multiple different routines for each shape, whether bees plan ahead to insert optimal shapes, or whether such diversity of structures could be explained by simple rules.
The hexagonal grid structure of honeycomb, constructed by a leaderless collective of hundreds of bees, lends itself to speculation that a robotic, repetitive innate behavior routine must be at work. An analogy is the construction of a brick wall, where each new layer is built by adding new bricks in a staggered, one-over-two pattern. This can be efficiently achieved by a robot without the architect’s supervision (3). This concept—where the features of an existing structure are used to add the next element of the structure by a simple rule—is called stigmergy (4, 5). The perceived analogy between insect cells and bricks has led some social insect researchers to model comb construction as the simple process of fitting new, complete comb cells onto the existing structure (5).
However, a hexagonal cell is not an externally supplied prefabricated unit. Rather, the bee builds a cell using small specks of wax which are chewed, deposited, and sculpted into the walls (6) to form a hexagon of equal-length sides with internal angles of 120°. And this is not …
[↵][1]1To whom correspondence may be addressed. Email: l.chittka{at}qmul.ac.uk.
[1]: #xref-corresp-1-1
3 citations
References
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TL;DR: Copyright (©) 1999–2012 R Foundation for Statistical Computing; permission is granted to make and distribute verbatim copies of this manual provided the copyright notice and permission notice are preserved on all copies.
Abstract: Copyright (©) 1999–2012 R Foundation for Statistical Computing. Permission is granted to make and distribute verbatim copies of this manual provided the copyright notice and this permission notice are preserved on all copies. Permission is granted to copy and distribute modified versions of this manual under the conditions for verbatim copying, provided that the entire resulting derived work is distributed under the terms of a permission notice identical to this one. Permission is granted to copy and distribute translations of this manual into another language, under the above conditions for modified versions, except that this permission notice may be stated in a translation approved by the R Core Team.
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TL;DR: In this article, a model is described in an lmer call by a formula, in this case including both fixed-and random-effects terms, and the formula and data together determine a numerical representation of the model from which the profiled deviance or the profeatured REML criterion can be evaluated as a function of some of model parameters.
Abstract: Maximum likelihood or restricted maximum likelihood (REML) estimates of the parameters in linear mixed-effects models can be determined using the lmer function in the lme4 package for R. As for most model-fitting functions in R, the model is described in an lmer call by a formula, in this case including both fixed- and random-effects terms. The formula and data together determine a numerical representation of the model from which the profiled deviance or the profiled REML criterion can be evaluated as a function of some of the model parameters. The appropriate criterion is optimized, using one of the constrained optimization functions in R, to provide the parameter estimates. We describe the structure of the model, the steps in evaluating the profiled deviance or REML criterion, and the structure of classes or types that represents such a model. Sufficient detail is included to allow specialization of these structures by users who wish to write functions to fit specialized linear mixed models, such as models incorporating pedigrees or smoothing splines, that are not easily expressible in the formula language used by lmer.
50,607 citations
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TL;DR: This work determines the location and identity of every atom at a grain boundary and finds that different grains stitch together predominantly through pentagon–heptagon pairs, and reveals an unexpectedly small and intricate patchwork of grains connected by tilt boundaries.
Abstract: The properties of polycrystalline materials are often dominated by the size of their grains and by the atomic structure of their grain boundaries. These effects should be especially pronounced in two-dimensional materials, where even a line defect can divide and disrupt a crystal. These issues take on practical significance in graphene, which is a hexagonal, two-dimensional crystal of carbon atoms. Single-atom-thick graphene sheets can now be produced by chemical vapour deposition on scales of up to metres, making their polycrystallinity almost unavoidable. Theoretically, graphene grain boundaries are predicted to have distinct electronic, magnetic, chemical and mechanical properties that strongly depend on their atomic arrangement. Yet because of the five-order-of-magnitude size difference between grains and the atoms at grain boundaries, few experiments have fully explored the graphene grain structure. Here we use a combination of old and new transmission electron microscopy techniques to bridge these length scales. Using atomic-resolution imaging, we determine the location and identity of every atom at a grain boundary and find that different grains stitch together predominantly through pentagon-heptagon pairs. Rather than individually imaging the several billion atoms in each grain, we use diffraction-filtered imaging to rapidly map the location, orientation and shape of several hundred grains and boundaries, where only a handful have been previously reported. The resulting images reveal an unexpectedly small and intricate patchwork of grains connected by tilt boundaries. By correlating grain imaging with scanning probe and transport measurements, we show that these grain boundaries severely weaken the mechanical strength of graphene membranes but do not as drastically alter their electrical properties. These techniques open a new window for studies on the structure, properties and control of grains and grain boundaries in graphene and other two-dimensional materials.
1,824 citations
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TL;DR: Using atomistic calculations, graphene sheets with large-angle tilt boundaries that have a high density of defects are as strong as the pristine material and, unexpectedly, are much stronger than those with low-angle boundaries having fewer defects.
Abstract: Graphene in its pristine form is one of the strongest materials tested, but defects influence its strength. Using atomistic calculations, we find that, counter to standard reasoning, graphene sheets with large-angle tilt boundaries that have a high density of defects are as strong as the pristine material and, unexpectedly, are much stronger than those with low-angle boundaries having fewer defects. We show that this trend is not explained by continuum fracture models but can be understood by considering the critical bonds in the strained seven-membered carbon rings that lead to failure; the large-angle boundaries are stronger because they are able to better accommodate these strained rings. Our results provide guidelines for designing growth methods to obtain sheets with strengths close to that of pristine graphene.
767 citations