Beyond planar: fish schools adopt ladder formations in 3D

Abstract The coordinated movement of fish schools has long captivated researchers studying animal collective behavior. Classical literature from Weihs and Lighthill suggests that fish schools should favor planar diamond formations to increase hydrodynamic efficiency, inspiring a large body of work r...

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Main Authors: Hungtang Ko, Abigail Girma, Yangfan Zhang, Yu Pan, George Lauder, Radhika Nagpal
Format: Article
Language:English
Published: Nature Portfolio 2025-06-01
Series:Scientific Reports
Online Access:https://doi.org/10.1038/s41598-025-06150-2
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author Hungtang Ko
Abigail Girma
Yangfan Zhang
Yu Pan
George Lauder
Radhika Nagpal
author_facet Hungtang Ko
Abigail Girma
Yangfan Zhang
Yu Pan
George Lauder
Radhika Nagpal
author_sort Hungtang Ko
collection DOAJ
description Abstract The coordinated movement of fish schools has long captivated researchers studying animal collective behavior. Classical literature from Weihs and Lighthill suggests that fish schools should favor planar diamond formations to increase hydrodynamic efficiency, inspiring a large body of work ranging from fluid simulations to hydrofoil experiments. However, whether fish schools actually adopt and maintain this idealized formation remains debated and unresolved. When fish schools are free to self-organize in three dimensions, what formations do they prefer? By tracking polarized schools of giant danios (Devario aequipinnatus) swimming continuously for ten hours, we demonstrate that fish rarely stay in a horizontal plane, and even more rarely, in the classical diamond formation. Of all fish pairs within four body-lengths from each other, only 25.2% were in the same plane. Of these, 54.6% were inline, 30.0% were staggered, and 15.4% were side-by-side. The diamond formation was observed in less than 0.1% of all frames. Notably, a vertical “ladder formation” emerged as the most probable formation for schooling giant danios, appearing in 79% of all fish pairs, and it elongated at higher swimming speeds. These findings highlight the dynamic and three-dimensional nature of fish schools and suggest that hydrodynamic benefits may be obtained without maintaining fixed formations. This research provides a foundation for future studies that examine the hydrodynamics and control of underwater collectives in 3D formations.
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publishDate 2025-06-01
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spelling doaj-art-2f0dd413b50e4bee8a916888397e99682025-08-20T03:31:45ZengNature PortfolioScientific Reports2045-23222025-06-0115111210.1038/s41598-025-06150-2Beyond planar: fish schools adopt ladder formations in 3DHungtang Ko0Abigail Girma1Yangfan Zhang2Yu Pan3George Lauder4Radhika Nagpal5Department of Mechanical and Aerospace Engineering, Princeton UniversityDepartment of Electrical and Computer Engineering, Princeton UniversityDepartment of Organismic & Evolutionary Biology, Harvard UniversityDepartment of Organismic & Evolutionary Biology, Harvard UniversityDepartment of Organismic & Evolutionary Biology, Harvard UniversityDepartment of Mechanical and Aerospace Engineering, Princeton UniversityAbstract The coordinated movement of fish schools has long captivated researchers studying animal collective behavior. Classical literature from Weihs and Lighthill suggests that fish schools should favor planar diamond formations to increase hydrodynamic efficiency, inspiring a large body of work ranging from fluid simulations to hydrofoil experiments. However, whether fish schools actually adopt and maintain this idealized formation remains debated and unresolved. When fish schools are free to self-organize in three dimensions, what formations do they prefer? By tracking polarized schools of giant danios (Devario aequipinnatus) swimming continuously for ten hours, we demonstrate that fish rarely stay in a horizontal plane, and even more rarely, in the classical diamond formation. Of all fish pairs within four body-lengths from each other, only 25.2% were in the same plane. Of these, 54.6% were inline, 30.0% were staggered, and 15.4% were side-by-side. The diamond formation was observed in less than 0.1% of all frames. Notably, a vertical “ladder formation” emerged as the most probable formation for schooling giant danios, appearing in 79% of all fish pairs, and it elongated at higher swimming speeds. These findings highlight the dynamic and three-dimensional nature of fish schools and suggest that hydrodynamic benefits may be obtained without maintaining fixed formations. This research provides a foundation for future studies that examine the hydrodynamics and control of underwater collectives in 3D formations.https://doi.org/10.1038/s41598-025-06150-2
spellingShingle Hungtang Ko
Abigail Girma
Yangfan Zhang
Yu Pan
George Lauder
Radhika Nagpal
Beyond planar: fish schools adopt ladder formations in 3D
Scientific Reports
title Beyond planar: fish schools adopt ladder formations in 3D
title_full Beyond planar: fish schools adopt ladder formations in 3D
title_fullStr Beyond planar: fish schools adopt ladder formations in 3D
title_full_unstemmed Beyond planar: fish schools adopt ladder formations in 3D
title_short Beyond planar: fish schools adopt ladder formations in 3D
title_sort beyond planar fish schools adopt ladder formations in 3d
url https://doi.org/10.1038/s41598-025-06150-2
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