{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T09:58:47Z","timestamp":1776074327111,"version":"3.50.1"},"reference-count":56,"publisher":"The Royal Society","issue":"237","license":[{"start":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T00:00:00Z","timestamp":1775606400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T00:00:00Z","timestamp":1775606400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000078","name":"Division of Materials Research","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000078","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000086","name":"Directorate for Mathematical and Physical Sciences","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000086","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,4,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>While living individuals frequently behave independently of one another, they can coordinate to form dynamic ordered groups. The functional forms of these interactions in experimental systems are often unclear and\/or complex. Despite the inherent complexity in experimental systems, the simplified interactions between active objects within the Vicsek model are sufficient to qualitatively reproduce some collective behaviours. This article aims to understand the simplified interactions between fish within experimental shoals by interpreting our experimental data, captured through video imaging, as Vicsek-type interactions. We find that Vicsek-type noise is controllable based on confinement, and a comparison with both metric and topological Vicsek models suggests that first-nearest-neighbour interactions best predict future fish orientations. These results promote our understanding of the interactions between fish.<\/jats:p>","DOI":"10.1098\/rsif.2026.0053","type":"journal-article","created":{"date-parts":[[2026,4,8]],"date-time":"2026-04-08T07:09:48Z","timestamp":1775632188000},"source":"Crossref","is-referenced-by-count":0,"title":["First-nearest neighbour interactions and Vicsek-type noise in shoals of\n                    <i>Paracheirodon axelrodi<\/i>\n                    fish"],"prefix":"10.1098","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0229-7429","authenticated-orcid":false,"given":"A. Pasha","family":"Tabatabai","sequence":"first","affiliation":[{"name":"California Polytechnic State University 1 , , ,","place":["San Luis Obispo, CA, USA"],"department":["Department of Physics"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joseph","family":"Chiu","sequence":"additional","affiliation":[{"name":"California Polytechnic State University 1 , , ,","place":["San Luis Obispo, CA, USA"],"department":["Department of Physics"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Karen","family":"Severson","sequence":"additional","affiliation":[{"name":"California Polytechnic State University 1 , , ,","place":["San Luis Obispo, CA, USA"],"department":["Department of Physics"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Gabriel","family":"Kuntz","sequence":"additional","affiliation":[{"name":"Seattle University 2 , , ,","place":["Seattle, WA, USA"],"department":["Department of Physics"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mitchell","family":"Rask","sequence":"additional","affiliation":[{"name":"Seattle University 2 , , ,","place":["Seattle, WA, USA"],"department":["Department of Physics"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"175","published-online":{"date-parts":[[2026,4,8]]},"reference":[{"key":"2026041305163134800_R1","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1002915","article-title":"Collective states, multistability and transitional behavior in schooling fish","volume":"9","author":"Tunstr\u00f8m","year":"2013","journal-title":"PLoS Comput. Biol."},{"key":"2026041305163134800_R2","doi-asserted-by":"crossref","DOI":"10.1038\/s41598-018-26037-9","article-title":"Collective gradient sensing in fish schools","volume":"8","author":"Puckett","year":"2018","journal-title":"Sci. Rep."},{"key":"2026041305163134800_R3","doi-asserted-by":"crossref","first-page":"12296","DOI":"10.1038\/s41598-024-63245-y","article-title":"Spatial confinement affects the heterogeneity and interactions between shoaling fish","volume":"14","author":"Kuntz","year":"2024","journal-title":"Sci. Rep."},{"key":"2026041305163134800_R4","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1146\/annurev-conmatphys-031113-133834","article-title":"Bird flocks as condensed matter","volume":"5","author":"Cavagna","year":"2014","journal-title":"Annu. Rev. Condens. Matter Phys."},{"key":"2026041305163134800_R5","doi-asserted-by":"crossref","first-page":"11865","DOI":"10.1073\/pnas.1005766107","article-title":"Scale-free correlations in starling flocks","volume":"107","author":"Cavagna","year":"2010","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"2026041305163134800_R6","doi-asserted-by":"crossref","first-page":"13626","DOI":"10.1073\/pnas.1001651107","article-title":"Collective motion and density fluctuations in bacterial colonies","volume":"107","author":"Zhang","year":"2010","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"2026041305163134800_R7","doi-asserted-by":"crossref","first-page":"1791","DOI":"10.1103\/PhysRevE.54.1791","article-title":"Formation of complex bacterial colonies via self-generated vortices","volume":"54","author":"Czir\u00f3k","year":"1996","journal-title":"Phys. Rev. E"},{"key":"2026041305163134800_R8","doi-asserted-by":"crossref","first-page":"7266","DOI":"10.1073\/pnas.1621469114","article-title":"Force generation by groups of migrating bacteria","volume":"114","author":"Sabass","year":"2017","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"2026041305163134800_R9","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.110.228701","article-title":"Collective motion of humans in mosh and circle pits at heavy metal concerts","volume":"110","author":"Silverberg","year":"2013","journal-title":"Phys. Rev. Lett."},{"key":"2026041305163134800_R10","doi-asserted-by":"crossref","first-page":"1232","DOI":"10.1073\/pnas.0711437105","article-title":"Interaction ruling animal collective behavior depends on topological rather than metric distance: evidence from a field study","volume":"105","author":"Ballerini","year":"2008","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"2026041305163134800_R11","doi-asserted-by":"crossref","first-page":"4690","DOI":"10.1073\/pnas.1420068112","article-title":"Revealing the hidden networks of interaction in mobile animal groups allows prediction of complex behavioral contagion","volume":"112","author":"Rosenthal","year":"2015","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"2026041305163134800_R12","doi-asserted-by":"crossref","first-page":"2862","DOI":"10.1016\/j.cub.2017.08.004","article-title":"Consistent individual differences drive collective behaviour and group functioning of schooling fish","volume":"27","author":"Jolles","year":"2017","journal-title":"Curr. Biol."},{"key":"2026041305163134800_R13","doi-asserted-by":"crossref","first-page":"488","DOI":"10.1038\/s41567-020-0787-y","article-title":"Noise-induced schooling of fish","volume":"16","author":"Jhawar","year":"2020","journal-title":"Nat. Phys."},{"key":"2026041305163134800_R14","doi-asserted-by":"crossref","first-page":"043209","DOI":"10.1088\/1742-5468\/accce7","article-title":"Non-reciprocal interactions spatially propagate fluctuations in a 2D Ising model","volume":"2023","author":"Seara","year":"2023","journal-title":"J. Stat. Mech."},{"key":"2026041305163134800_R15","doi-asserted-by":"crossref","first-page":"1773","DOI":"10.1016\/j.cub.2008.09.064","article-title":"Consensus decision making by fish","volume":"18","author":"Sumpter","year":"2008","journal-title":"Curr. Biol."},{"key":"2026041305163134800_R16","doi-asserted-by":"crossref","first-page":"715","DOI":"10.1098\/rsfs.2012.0026","article-title":"Spatially balanced topological interaction grants optimal cohesion in flocking models","volume":"2","author":"Camperi","year":"2012","journal-title":"Interface Focus"},{"key":"2026041305163134800_R17","doi-asserted-by":"crossref","first-page":"18720","DOI":"10.1073\/pnas.1107583108","article-title":"Inferring the structure and dynamics of interactions in schooling fish","volume":"108","author":"Katz","year":"2011","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"2026041305163134800_R18","doi-asserted-by":"crossref","first-page":"20190865","DOI":"10.1098\/rspb.2019.0865","article-title":"Local interactions and their group-level consequences in flocking jackdaws","volume":"286","author":"Ling","year":"2019","journal-title":"Proc. R. Soc. B"},{"key":"2026041305163134800_R19","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1002678","article-title":"Deciphering interactions in moving animal groups","volume":"8","author":"Gautrais","year":"2012","journal-title":"PLoS Comput. Biol."},{"key":"2026041305163134800_R20","doi-asserted-by":"crossref","DOI":"10.1103\/PRXLife.2.013008","article-title":"Geometrical structure of bifurcations during spatial decision-making","volume":"2","author":"Gorbonos","year":"2024","journal-title":"PRX Life"},{"key":"2026041305163134800_R21","doi-asserted-by":"crossref","DOI":"10.1073\/pnas.2102157118","article-title":"The geometry of decision-making in individuals and collectives","volume":"118","author":"Sridhar","year":"2021","journal-title":"Proc. Natl Acad. Sci. USA"},{"key":"2026041305163134800_R22","doi-asserted-by":"crossref","DOI":"10.1098\/rsos.240885","article-title":"Collective phases and long-term dynamics in a fish school model with burst-and-coast swimming","volume":"12","author":"Wang","year":"2025","journal-title":"R. Soc. Open Sci."},{"key":"2026041305163134800_R23","doi-asserted-by":"crossref","first-page":"1226","DOI":"10.1103\/PhysRevLett.75.1226","article-title":"Novel type of phase transition in a system of self-driven particles","volume":"75","author":"Vicsek","year":"1995","journal-title":"Phys. Rev. Lett."},{"key":"2026041305163134800_R24","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1140\/epjb\/e2008-00275-9","article-title":"Modeling collective motion: variations on the Vicsek model","volume":"64","author":"Chat\u00e9","year":"2008","journal-title":"Eur. Phys. J. B"},{"key":"2026041305163134800_R25","doi-asserted-by":"crossref","first-page":"2099","DOI":"10.1140\/epjst\/e2016-60066-8","article-title":"The physics of the Vicsek model","volume":"225","author":"Ginelli","year":"2016","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"2026041305163134800_R26","doi-asserted-by":"crossref","first-page":"30","DOI":"10.35459\/tbp.2022.000227","article-title":"Undergraduate tutorial for simulating flocking with the Vicsek model","volume":"4","author":"Tabatabai","year":"2023","journal-title":"Biophysicist"},{"key":"2026041305163134800_R27","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevE.77.046113","article-title":"Collective motion of self-propelled particles interacting without cohesion","volume":"77","author":"Chat\u00e9","year":"2008","journal-title":"Phys. Rev. E"},{"key":"2026041305163134800_R28","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1177\/1059712311426799","article-title":"Information transfer and antipredator maneuvers in schooling herring","volume":"20","author":"Marras","year":"2012","journal-title":"Adapt. Behav."},{"key":"2026041305163134800_R29","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevE.88.062724","article-title":"Collective behavior and predation success in a predator-prey model inspired by hunting bats","volume":"88","author":"Lin","year":"2013","journal-title":"Phys. Rev. E"},{"key":"2026041305163134800_R30","doi-asserted-by":"crossref","DOI":"10.1038\/srep04766","article-title":"Searching for effective forces in laboratory insect swarms","volume":"4","author":"Puckett","year":"2014","journal-title":"Sci. Rep."},{"key":"2026041305163134800_R31","doi-asserted-by":"crossref","first-page":"073042","DOI":"10.1088\/1367-2630\/18\/7\/073042","article-title":"Long-range acoustic interactions in insect swarms: an adaptive gravity model","volume":"18","author":"Gorbonos","year":"2016","journal-title":"New J. Phys."},{"key":"2026041305163134800_R32","doi-asserted-by":"crossref","first-page":"20170385","DOI":"10.1098\/rstb.2017.0385","article-title":"Inferring the rules of social interaction in migrating caribou","volume":"373","author":"Torney","year":"2018","journal-title":"Phil. Trans. R. Soc. B"},{"key":"2026041305163134800_R33","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.anbehav.2019.08.012","article-title":"Turbidity increases risk perception but constrains collective behaviour during foraging by fish shoals","volume":"156","author":"Chamberlain","year":"2019","journal-title":"Anim. Behav."},{"key":"2026041305163134800_R34","doi-asserted-by":"crossref","first-page":"120","DOI":"10.1007\/s00265-021-03060-x","article-title":"Water clarity affects collective behavior in two cyprinid fishes","volume":"75","author":"Michael","year":"2021","journal-title":"Behav. Ecol. Sociobiol."},{"key":"2026041305163134800_R35","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1009394","article-title":"Dominating lengthscales of zebrafish collective behaviour","volume":"18","author":"Yang","year":"2022","journal-title":"PLoS Comput. Biol."},{"key":"2026041305163134800_R36","doi-asserted-by":"crossref","first-page":"486","DOI":"10.1038\/s41592-022-01426-1","article-title":"SLEAP: a deep learning system for multi-animal pose tracking","volume":"19","author":"Pereira","year":"2022","journal-title":"Nat. Methods"},{"key":"2026041305163134800_R37","doi-asserted-by":"crossref","first-page":"708","DOI":"10.1016\/j.cub.2021.11.068","article-title":"Fish waves as emergent collective antipredator behavior","volume":"32","author":"Doran","year":"2022","journal-title":"Curr. Biol."},{"key":"2026041305163134800_R38","doi-asserted-by":"crossref","first-page":"016005","DOI":"10.1088\/1478-3975\/aca862","article-title":"Velocity correlations in jackdaw flocks in different ecological contexts","volume":"20","author":"O\u2019Coin","year":"2023","journal-title":"Phys. Biol."},{"key":"2026041305163134800_R39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1111\/oik.09202","article-title":"The effect of temperature on fish swimming and schooling is context dependent","volume":"2023","author":"Kuruvilla","year":"2023","journal-title":"Oikos"},{"key":"2026041305163134800_R40","doi-asserted-by":"crossref","DOI":"10.1002\/ece3.9958","article-title":"Increased water temperature and turbidity act independently to alter social behavior in guppies (Poecilia reticulata)","volume":"13","author":"Allibhai","year":"2023","journal-title":"Ecol. Evol."},{"key":"2026041305163134800_R41","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s42003-024-07267-2","article-title":"Collective anti-predator escape manoeuvres through optimal attack and avoidance strategies","volume":"7","author":"Bartashevich","year":"2024","journal-title":"Commun. Biol."},{"key":"2026041305163134800_R42","doi-asserted-by":"crossref","DOI":"10.7554\/eLife.64000","article-title":"TRex, a fast multi-animal tracking system with markerless identification, and 2D estimation of posture and visual fields","volume":"10","author":"Walter","year":"2021","journal-title":"eLife"},{"key":"2026041305163134800_R43","doi-asserted-by":"crossref","DOI":"10.1103\/PhysRevLett.105.168103","article-title":"Relevance of metric-free interactions in flocking phenomena","volume":"105","author":"Ginelli","year":"2010","journal-title":"Phys. Rev. Lett."},{"key":"2026041305163134800_R44","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pcbi.1003697","article-title":"Collective behaviour without collective order in wild swarms of midges","volume":"10","author":"Attanasi","year":"2014","journal-title":"PLoS Comput. Biol."},{"key":"2026041305163134800_R45","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1103\/nr7p-m4ff","article-title":"Experimental evidence of stress-induced critical state in schooling fish","volume":"3","author":"Lin","year":"2025","journal-title":"PRX Life"},{"key":"2026041305163134800_R46","doi-asserted-by":"crossref","DOI":"10.1038\/s42003-024-07322-y","article-title":"Non-invasive eye tracking and retinal view reconstruction in free swimming schooling fish","volume":"7","author":"Wu","year":"2024","journal-title":"Commun. Biol."},{"key":"2026041305163134800_R47","doi-asserted-by":"crossref","first-page":"045002","DOI":"10.1088\/1478-3975\/acd298","article-title":"A simple cognitive model explains movement decisions in zebrafish while following leaders","volume":"20","author":"Oscar","year":"2023","journal-title":"Phys. Biol."},{"key":"2026041305163134800_R48","doi-asserted-by":"crossref","DOI":"10.1063\/1.4974256","article-title":"Pattern, growth, and aging in aggregation kinetics of a Vicsek-like active matter model","volume":"146","author":"Das","year":"2017","journal-title":"J. Chem. Phys."},{"key":"2026041305163134800_R49","article-title":"Density-field structures in a few systems undergoing velocity ordering","author":"Das","year":"2025","journal-title":"arXiv."},{"key":"2026041305163134800_R50","doi-asserted-by":"crossref","DOI":"10.1140\/epje\/i2018-11653-4","article-title":"Active particle condensation by non-reciprocal and time-delayed interactions","volume":"41","author":"Durve","year":"2018","journal-title":"Eur. Phys. J. E"},{"key":"2026041305163134800_R51","doi-asserted-by":"crossref","first-page":"023144","DOI":"10.1103\/PhysRevResearch.7.023144","article-title":"Swarming transitions of self-propelled particles with anisotropic social interactions","volume":"7","author":"Gao","year":"2025","journal-title":"Phys. Rev. Res."},{"key":"2026041305163134800_R52","doi-asserted-by":"crossref","DOI":"10.1038\/s41467-024-48458-z","article-title":"Revealing the mechanism and function underlying pairwise temporal coupling in collective motion","volume":"15","author":"Amichay","year":"2024","journal-title":"Nat. Commun."},{"key":"2026041305163134800_R53","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1007\/BF00397518","article-title":"Schooling mackerel and herring choose neighbours of similar size","volume":"86","author":"Pitcher","year":"1985","journal-title":"Mar. Biol."},{"key":"2026041305163134800_R54","doi-asserted-by":"crossref","first-page":"1586","DOI":"10.2307\/2265553","article-title":"Phenotypic variability within and between fish shoals","volume":"77","author":"Krause","year":"1996","journal-title":"Ecology"},{"key":"2026041305163134800_R55","article-title":"Experimental trajectories of 25 Cardinal tetra in quasi-2D arenas of different radii","author":"Tabatabai","year":"2025"},{"key":"2026041305163134800_R56","article-title":"Supplementary material from \"First-Nearest Neighbor Interactions and Vicsek-Type Noise in Shoals of Paracheirodon axelrodi Fish. Figshare.","author":"Tabatabai","year":"2026"}],"container-title":["Journal of the Royal Society Interface"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/royalsocietypublishing.org\/rsif\/article-pdf\/doi\/10.1098\/rsif.2026.0053\/6131402\/rsif.2026.0053.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/royalsocietypublishing.org\/rsif\/article-pdf\/doi\/10.1098\/rsif.2026.0053\/6131402\/rsif.2026.0053.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T09:17:08Z","timestamp":1776071828000},"score":1,"resource":{"primary":{"URL":"https:\/\/royalsocietypublishing.org\/rsif\/article\/23\/237\/20260053\/481287\/First-nearest-neighbour-interactions-and-Vicsek"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,8]]},"references-count":56,"journal-issue":{"issue":"237","published-print":{"date-parts":[[2026,4,8]]}},"URL":"https:\/\/doi.org\/10.1098\/rsif.2026.0053","relation":{},"ISSN":["1742-5662"],"issn-type":[{"value":"1742-5662","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,8]]},"article-number":"20260053"}}