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Hopfe C, Ospina-Jara B, Schulze T, Tischer M, Morales D, Reinhartz V, Esfahani RE, Valderrama C, Pérez-Rigueiro J, Bleidorn C, Feldhaar H, Cabra-García J, Scheibel T. Impact of environmental factors on spider silk properties. Curr Biol 2024; 34:56-67.e5. [PMID: 38118450 DOI: 10.1016/j.cub.2023.11.043] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2023] [Revised: 10/11/2023] [Accepted: 11/20/2023] [Indexed: 12/22/2023]
Abstract
Spider orb webs have evolved to stop flying prey, fast and slow alike. One of the main web elements dissipating impact energy is the radial fibers, or major ampullate silks, which possess a toughness surpassing most man-made materials. Orb webs are extended phenotypes, and as such their architectural elements, including major ampullate silks, have been selected to optimize prey capture under the respective environmental conditions. In this study, we investigated the correlation of three landscape scales and three microhabitat characteristics with intrinsic silk properties (elastic modulus, yield stress, tensile strength, extensibility, and toughness) to understand underlying ecological patterns. For this purpose, we collected and mechanically tested major ampullate silks from 50 spider species inhabiting large altitudinal and climatic gradients in Colombia. Using regression analysis and model selection, we investigated the environmental drivers of inter- and intra-specific patterns of major ampullate silk properties, taking into account phylogenetic relatedness based on newly sequenced mitochondrial genomes. We found that the total amount of energy absorbed, i.e., toughness and tensile strength, is higher for fibers from species inhabiting regions where heavy rainfall is common. Interestingly, we observe the same general trend between individuals of the same species, stressing the importance of this environmental driver. We also observe a phylogenetic conservation in the relation of environmental variables with silk tensile strength and yield stress. In conclusion, the increase in major ampullate silk tensile strength and toughness may reflect an adaptation to prevent frequent rain damage to orb webs and the associated energetic loss.
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Affiliation(s)
- Charlotte Hopfe
- Department of Biomaterials, Universität Bayreuth, Prof.-Rüdiger-Bormann-Str. 1, Bayreuth 95447, Germany.
| | - Bryan Ospina-Jara
- Department of Biology, Universidad del Valle, Cl. 13 #100-00, Cali 760042, Colombia
| | - Thilo Schulze
- Department of Animal Evolution and Biodiversity, Georg-August-Universität Göttingen, Untere Karspüle 2, Göttingen 37073, Germany
| | - Marta Tischer
- Department of Animal Evolution and Biodiversity, Georg-August-Universität Göttingen, Untere Karspüle 2, Göttingen 37073, Germany
| | - Diego Morales
- Department of Biology, Universidad del Valle, Cl. 13 #100-00, Cali 760042, Colombia
| | - Vivien Reinhartz
- Department of Biomaterials, Universität Bayreuth, Prof.-Rüdiger-Bormann-Str. 1, Bayreuth 95447, Germany
| | - Rashin Eshghi Esfahani
- Department of Biomaterials, Universität Bayreuth, Prof.-Rüdiger-Bormann-Str. 1, Bayreuth 95447, Germany
| | - Carlos Valderrama
- Facultad de Ciencias, Universidad del Rosario, Cl. 12c #6-25, Bogotá 111711, Colombia
| | - José Pérez-Rigueiro
- Center for Biomedical Technology, Universidad Politécnica de Madrid, Crta. M40, Madrid 28223, Spain; Departamento de Ciencia de Materiales, ETSI Caminos, Canales y Puertos, Universidad Politécnica de Madrid, C/Prof. Aranguren 3, Madrid 28040, Spain; Biomedical Research Networking Center in Bioengineering Biomaterials and Nanomedicine (CIBER-BBN), Madrid 28029, Spain; Biomaterials and Regenerative Medicine Group, Instituto de Investigación Sanitaria del Hospital Clínico San Carlos (IdISSC), C/ Prof. Martín Lagos s/n, Madrid 28040, Spain
| | - Christoph Bleidorn
- Department of Animal Evolution and Biodiversity, Georg-August-Universität Göttingen, Untere Karspüle 2, Göttingen 37073, Germany
| | - Heike Feldhaar
- Department of Animal Ecology I, Bayreuth Center of Ecology and Environmental Research (BayCEER), Universität Bayreuth, Universitätsstraße 30, Bayreuth 95440, Germany
| | - Jimmy Cabra-García
- Department of Biology, Universidad del Valle, Cl. 13 #100-00, Cali 760042, Colombia
| | - Thomas Scheibel
- Department of Biomaterials, Universität Bayreuth, Prof.-Rüdiger-Bormann-Str. 1, Bayreuth 95447, Germany; Bayreuther Zentrum für Kolloide und Grenzflächen, Universität Bayreuth, Universitätsstraße 30, Bayreuth 95440, Germany; Bayreuther Materialzentrum, Universität Bayreuth, Universitätsstraße 30, Bayreuth 95440, Germany; Bayreuther Zentrum für Molekulare Biowissenschaften, Universität Bayreuth, Universitätsstraße 30, Bayreuth 95440, Germany; Bayrisches Polymerinstitut, Universität Bayreuth, Universitätsstraße 30, Bayreuth 95440, Germany.
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2
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Lin S, Chou N, Li G, Bao D, Wang G, Xie YM. A self-adapting woven net trap based on the evolution mechanism of orb-web topology. Acta Biomater 2024; 173:217-230. [PMID: 37981043 DOI: 10.1016/j.actbio.2023.11.016] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2023] [Revised: 11/06/2023] [Accepted: 11/09/2023] [Indexed: 11/21/2023]
Abstract
The development of structures that can adapt spontaneously to achieve desired functions in complex environments is crucial for new unmanned countermeasures, such as prey capture or net-recovery. Conventional structural optimization methods based on a singular net-like configuration may lead to functional limitations and fail to achieve specific objectives. In this study, we utilized an evolutionary algorithm that incorporated mechanical features and biological corrections to construct spider threads with advanced properties capable of efficient and reliable trapping behavior in arbitrary boundary conditions. We employed distinct thread types in different components, which achieved distinguished stiffness and strength that could not be accomplished by a single kind of thread. By assembling prestress reinforcement threads, we developed an orb-web-like trap that demonstrated effective trapping performance in experiments. The adaptive evolutionary method could be applied to design intelligent intercepting devices suited to particular functions and extreme environments, with wide application prospects in net-recovery system of UAV. STATEMENT OF SIGNIFICANCE: Structures that adapt spontaneously to perform desired functions in difficult environments are crucial for rising unmanned countermeasures. Conventional structural optimization methods based on a singular net-like configuration may lead to functional limitations and fail to achieve specific objectives. We used an evolutionary algorithm that combined mechanical features and biological corrections to create spider threads in arbitrary boundary circumstances in this work. The adaptive evolutionary method could be applied to design intelligent intercepting devices suited to particular functions and extreme environments, with wide application prospects in net-recovery system of UAV.
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Affiliation(s)
- Sen Lin
- State Key Laboratory of Advanced Design and Manufacturing Technology for Vehicle, College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China
| | - Nengzhuo Chou
- State Key Laboratory of Advanced Design and Manufacturing Technology for Vehicle, College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China
| | - Guangyao Li
- Shenzhen Automotive Research Institute (Shenzhen Research Institute of National, Engineering Laboratory for Electric Vehicles), Beijing Institute of Technology, Shenzhen, Guangdong 518118, China.
| | - Dingwen Bao
- Centre for Innovative Structures and Materials, School of Engineering, RMIT University, GPO Box 2476, Melbourne 3001, Australia; School of Architecture and Urban Design, RMIT University, GPO Box 2476, Melbourne 3001, Australia
| | - Guoping Wang
- School of Computer Science, Peking University, Beijing 100091, China
| | - Yi Min Xie
- Centre for Innovative Structures and Materials, School of Engineering, RMIT University, GPO Box 2476, Melbourne 3001, Australia
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3
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Han SI, Alicea-Serrano AM, Blackledge TA. Anchor threads can double the insect flight energy absorbed by spider orb webs. J Exp Biol 2023; 226:286587. [PMID: 36633333 PMCID: PMC10086537 DOI: 10.1242/jeb.245123] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2022] [Accepted: 12/20/2022] [Indexed: 01/13/2023]
Abstract
To successfully capture flying insect prey, a spider's orb web must withstand the energy of impact without the silk breaking. In this study, we examined the anchor threads: the silk lines that anchor the main capture area of the web to the surrounding environment. These anchor threads can account for a large portion of the web, yet are usually excluded from experiments and simulations. We compared projectile capture and kinetic energy absorption between webs with and without access to anchor threads. Webs with anchor threads captured significantly more projectiles and absorbed significantly more energy than those with constrained anchors. This is likely because the anchor threads increase web compliance, resulting in webs with the ability to catch high-energy flying insects without breaking. Anchor threads are one example of how different types of web architecture expand the range of possible prey capture strategies by enabling the web to withstand greater impacts.
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Affiliation(s)
- Sarah I Han
- The University of Akron, Biology Department, Akron, OH 44325, USA
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4
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Shin D, Cupertino A, de Jong MHJ, Steeneken PG, Bessa MA, Norte RA. Spiderweb Nanomechanical Resonators via Bayesian Optimization: Inspired by Nature and Guided by Machine Learning. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2022; 34:e2106248. [PMID: 34695265 DOI: 10.1002/adma.202106248] [Citation(s) in RCA: 12] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/10/2021] [Revised: 10/20/2021] [Indexed: 06/13/2023]
Abstract
From ultrasensitive detectors of fundamental forces to quantum networks and sensors, mechanical resonators are enabling next-generation technologies to operate in room-temperature environments. Currently, silicon nitride nanoresonators stand as a leading microchip platform in these advances by allowing for mechanical resonators whose motion is remarkably isolated from ambient thermal noise. However, to date, human intuition has remained the driving force behind design processes. Here, inspired by nature and guided by machine learning, a spiderweb nanomechanical resonator is developed that exhibits vibration modes, which are isolated from ambient thermal environments via a novel "torsional soft-clamping" mechanism discovered by the data-driven optimization algorithm. This bioinspired resonator is then fabricated, experimentally confirming a new paradigm in mechanics with quality factors above 1 billion in room-temperature environments. In contrast to other state-of-the-art resonators, this milestone is achieved with a compact design that does not require sub-micrometer lithographic features or complex phononic bandgaps, making it significantly easier and cheaper to manufacture at large scales. These results demonstrate the ability of machine learning to work in tandem with human intuition to augment creative possibilities and uncover new strategies in computing and nanotechnology.
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Affiliation(s)
- Dongil Shin
- Faculty of Mechanical, Maritime and Materials Engineering, Department of Materials Science and Engineering, Delft University of Technology, Delft, 2628 CD, The Netherlands
- Faculty of Mechanical, Maritime and Materials Engineering, Department of Precision and Microsystems Engineering, Delft University of Technology, Delft, 2628 CD, The Netherlands
| | - Andrea Cupertino
- Faculty of Mechanical, Maritime and Materials Engineering, Department of Precision and Microsystems Engineering, Delft University of Technology, Delft, 2628 CD, The Netherlands
| | - Matthijs H J de Jong
- Faculty of Mechanical, Maritime and Materials Engineering, Department of Precision and Microsystems Engineering, Delft University of Technology, Delft, 2628 CD, The Netherlands
- Faculty of Applied Sciences, Department of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2628 CD, The Netherlands
| | - Peter G Steeneken
- Faculty of Mechanical, Maritime and Materials Engineering, Department of Precision and Microsystems Engineering, Delft University of Technology, Delft, 2628 CD, The Netherlands
- Faculty of Applied Sciences, Department of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2628 CD, The Netherlands
| | - Miguel A Bessa
- Faculty of Mechanical, Maritime and Materials Engineering, Department of Materials Science and Engineering, Delft University of Technology, Delft, 2628 CD, The Netherlands
| | - Richard A Norte
- Faculty of Mechanical, Maritime and Materials Engineering, Department of Precision and Microsystems Engineering, Delft University of Technology, Delft, 2628 CD, The Netherlands
- Faculty of Applied Sciences, Department of Quantum Nanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Delft, 2628 CD, The Netherlands
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5
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Miller TE, Mortimer B. Control vs. Constraint: Understanding the Mechanisms of Vibration Transmission During Material-Bound Information Transfer. Front Ecol Evol 2020. [DOI: 10.3389/fevo.2020.587846] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Material-bound vibrations are ubiquitous in the environment and are widely used as an information source by animals, whether they are generated by biotic or abiotic sources. The process of vibration information transfer is subject to a wide range of physical constraints, especially during the vibration transmission phase. This is because vibrations must travel through materials in the environment and body of the animal before reaching embedded mechanosensors. Morphology therefore plays a key and often overlooked role in shaping information flow. Web-building spiders are ideal organisms for studying vibration information transfer due to the level of control they have over morphological traits, both within the web (environment) and body, which can give insights for bioinspired design. Here we investigate the mechanisms governing vibration information transfer, including the relative roles of constraints and control mechanisms. We review the known and theoretical contributions of morphological and behavioral traits to vibration transmission in these spiders, and propose an interdisciplinary framework for considering the effects of these traits from a biomechanical perspective. Whereas morphological traits act as a series of springs, dampers and masses arranged in a specific geometry to influence vibration transmission, behavioral traits influence these morphologies often over small timescales in response to changing conditions. We then explore the relative roles of constraints and control mechanisms in shaping the variation of these traits at various taxonomic levels. This analysis reveals the importance of morphology modification to gain control over vibration transmission to mitigate constraints and essentially promote information transfer. In particular, we hypothesize that morphological computation is used by spiders during vibration information transfer to reduce the amount of processing required by the central nervous system (CNS); a hypothesis that can be tested experimentally in the future. We can take inspiration from how spiders control vibration transmission and apply these insights to bioinspired engineering. In particular, the role of morphological computation for vibration control could open up potential developments for soft robots, which could use multi-scale vibration sensory systems inspired by spiders to quickly and efficiently adapt to changing environments.
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6
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Mortimer B, Soler A, Wilkins L, Vollrath F. Decoding the locational information in the orb web vibrations of Araneus diadematus and Zygiella x-notata. J R Soc Interface 2020; 16:20190201. [PMID: 31113332 DOI: 10.1098/rsif.2019.0201] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/03/2023] Open
Abstract
A spider's web is a multifunctional structure that captures prey and provides an information platform that transmits vibrational information. Many physical factors interact to influence web vibration and information content, from vibration source properties and input location, to web physical properties and geometry. The aim of the study was to test whether orb web vibration contains information about the location of the source of vibration. We used finite-element analysis model webs to control and vary major physical factors, investigating webs where spiders use a direct or remote monitoring strategy. When monitoring with eight sensors (legs) at the web centre, a comparison of longitudinal and transverse wave amplitude between the sensors gave sufficient information to determine source direction and distance, respectively. These localization cues were robust to changes in source amplitude, input angle and location, with increased accuracy at lower source amplitudes. When remotely monitoring the web using a single thread connected to the web's hub (a signal thread), we found that locational information was not available when the angle of the source input was unknown. Furthermore, a free sector and a stiff hub were physical mechanisms to aid information transfer, which provides insights for bioinspired fibre networks for sensing technologies.
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Affiliation(s)
- B Mortimer
- 1 Department of Zoology, University of Oxford , Oxford , UK.,2 School of Biological Sciences, University of Bristol , Bristol , UK
| | - A Soler
- 3 Department of Continuum Mechanics and Structural Analysis, Universidad Carlos III de Madrid , Madrid , Spain
| | - L Wilkins
- 1 Department of Zoology, University of Oxford , Oxford , UK
| | - F Vollrath
- 1 Department of Zoology, University of Oxford , Oxford , UK
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7
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Mortimer B, Soler A, Siviour CR, Vollrath F. Remote monitoring of vibrational information in spider webs. Naturwissenschaften 2018; 105:37. [PMID: 29789945 PMCID: PMC5978847 DOI: 10.1007/s00114-018-1561-1] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2018] [Revised: 05/02/2018] [Accepted: 05/07/2018] [Indexed: 01/21/2023]
Abstract
Spiders are fascinating model species to study information-acquisition strategies, with the web acting as an extension of the animal’s body. Here, we compare the strategies of two orb-weaving spiders that acquire information through vibrations transmitted and filtered in the web. Whereas Araneus diadematus monitors web vibration directly on the web, Zygiella x-notata uses a signal thread to remotely monitor web vibration from a retreat, which gives added protection. We assess the implications of these two information-acquisition strategies on the quality of vibration information transfer, using laser Doppler vibrometry to measure vibrations of real webs and finite element analysis in computer models of webs. We observed that the signal thread imposed no biologically relevant time penalty for vibration propagation. However, loss of energy (attenuation) was a cost associated with remote monitoring via a signal thread. The findings have implications for the biological use of vibrations by spiders, including the mechanisms to locate and discriminate between vibration sources. We show that orb-weaver spiders are fascinating examples of organisms that modify their physical environment to shape their information-acquisition strategy.
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Affiliation(s)
- B Mortimer
- Department of Zoology, University of Oxford, Oxford, UK. .,School of Biological Sciences, University of Bristol, Bristol, UK.
| | - A Soler
- Department Continuum Mechanics and Structural Analysis, Universidad Carlos III de Madrid, Madrid, Spain
| | - C R Siviour
- Department of Engineering Science, University of Oxford, Oxford, UK
| | - F Vollrath
- Department of Zoology, University of Oxford, Oxford, UK
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8
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Otto AW, Elias DO, Hatton RL. Modeling Transverse Vibration in Spider Webs Using Frequency-Based Dynamic Substructuring. DYNAMICS OF COUPLED STRUCTURES, VOLUME 4 2018. [DOI: 10.1007/978-3-319-74654-8_12] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
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9
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Mortimer B, Soler A, Siviour CR, Zaera R, Vollrath F. Tuning the instrument: sonic properties in the spider's web. J R Soc Interface 2017; 13:rsif.2016.0341. [PMID: 27605164 DOI: 10.1098/rsif.2016.0341] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2016] [Accepted: 08/10/2016] [Indexed: 11/12/2022] Open
Abstract
Spider orb webs are multifunctional, acting to absorb prey impact energy and transmit vibratory information to the spider. This paper explores the links between silk material properties, propagation of vibrations within webs and the ability of the spider to control and balance web function. Combining experimental and modelling approaches, we contrast transverse and longitudinal wave propagation in the web. It emerged that both transverse and longitudinal wave amplitude in the web can be adjusted through changes in web tension and dragline silk stiffness, i.e. properties that can be controlled by the spider. In particular, we propose that dragline silk supercontraction may have evolved as a control mechanism for these multifunctional fibres. The various degrees of active influence on web engineering reveals the extraordinary ability of spiders to shape the physical properties of their self-made materials and architectures to affect biological functionality, balancing trade-offs between structural and sensory functions.
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Affiliation(s)
- B Mortimer
- Department of Zoology, University of Oxford, Oxford, UK
| | - A Soler
- Department of Continuum Mechanics and Structural Analysis, Universidad Carlos III de Madrid, Madrid, Spain
| | - C R Siviour
- Department of Engineering Science, University of Oxford, Oxford, UK
| | - R Zaera
- Department of Continuum Mechanics and Structural Analysis, Universidad Carlos III de Madrid, Madrid, Spain
| | - F Vollrath
- Department of Zoology, University of Oxford, Oxford, UK
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10
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Tew N, Hesselberg T. The Effect of Wind Exposure on the Web Characteristics of a Tetragnathid Orb Spider. JOURNAL OF INSECT BEHAVIOR 2017; 30:273-286. [PMID: 28680193 PMCID: PMC5488162 DOI: 10.1007/s10905-017-9618-0] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Revised: 04/19/2017] [Accepted: 04/24/2017] [Indexed: 06/07/2023]
Abstract
Studies on spiders in their natural habitats are necessary for determining the full range of plasticity in their web-building behaviour. Plasticity in web design is hypothesised to be important for spiders building in habitats where environmental conditions cause considerable web damage. Here we compared web characteristics of the orb spider Metellina mengei (Araneae, Tetragnathidae) in two different forest habitats differing in their wind exposure. We found a notable lack of differences in web geometry, orientation and inclination between webs built along an exposed forest edge and those built inside the forest, despite marked differences in wind speed. This suggests that M. mengei did not exhibit web-building plasticity in response to wind in the field, contrasting with the findings of laboratory studies on other species of orb spiders. Instead, differences in prey capture and wind damage trade-offs between habitats may provide an explanation for our results, indicating that different species employ different strategies to cope with environmental constraints.
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Affiliation(s)
- Nicholas Tew
- Department of Zoology, University of Oxford, South Parks Road, Oxford, OX1 3PS UK
- Department of Life Sciences, Imperial College London, Buckhurst Road, Ascot, SL5 7PY UK
| | - Thomas Hesselberg
- Department of Zoology, University of Oxford, South Parks Road, Oxford, OX1 3PS UK
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11
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Soler A, Zaera R. The secondary frame in spider orb webs: the detail that makes the difference. Sci Rep 2016; 6:31265. [PMID: 27507613 PMCID: PMC4978998 DOI: 10.1038/srep31265] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2015] [Accepted: 06/29/2016] [Indexed: 11/09/2022] Open
Abstract
Spider orb webs are multifunctional structures, the main function of which is to dissipate the kinetic energy of the impacting prey, while minimizing structural damage. There is no single explanation for their remarkable strength and ductility. However, it is clear that topology is decisive in the structural performance upon impact, and the arrangement of the different silk threads in the web must also exert an effect. The aim of this study is to show how a slight variation in the geometry markedly affects the prey-capture ability of spider orb webs. The study is focused on the secondary frame, a thread interposed between radial and primary frame strands, the importance of which has not been examined until now. The simulation of the impact performance of webs using different lengths of the secondary frame clarifies its structural role, which has proven to be decisive. Furthermore, the study explains why secondary frame threads of moderate length, as commonly encountered, enable the capture of prey with higher energy without a marked increase in the volume of silk used.
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Affiliation(s)
- Alejandro Soler
- Universidad Carlos III de Madrid, Department of Continuum Mechanics and Structural Analysis, 28911 Leganés, Madrid, Spain
| | - Ramón Zaera
- Universidad Carlos III de Madrid, Department of Continuum Mechanics and Structural Analysis, 28911 Leganés, Madrid, Spain
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12
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13
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Affiliation(s)
- Samuel Zschokke
- Department of Environmental Sciences, Section of Conservation Biology; University of Basel; St. Johanns-Vorstadt 10 CH-4056 Basel Switzerland
| | - Kensuke Nakata
- Kyoto Women's University; Kitahiyoshi-cho 35 Higashiyama-ku Kyoto 605-8501 Japan
- Faculty of Human Environment; Nagasaki Institute of Applied Science; 536 Aba-machi Nagasaki 851-0193 Japan
- Tokyo Keizai University; Minami-machi 1-7-34 Kokubunji Tokyo 185-8502 Japan
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