title: Validating two-dimensional leadership models on three-dimensionally structured fish schools.
abstract: Identifying leader-follower interactions is crucial for understanding how a group decides where or when to move, and how this information is transferred between members. Although many animal groups have a three-dimensional structure, previous studies investigating leader-follower interactions have often ignored vertical information. This raises the question of whether commonly used two-dimensional leader-follower analyses can be used justifiably on groups that interact in three dimensions. To address this, we quantified the individual movements of banded tetra fish (Astyanax mexicanus) within shoals by computing the three-dimensional trajectories of all individuals using a stereo-camera technique. We used these data firstly to identify and compare leader-follower interactions in two and three dimensions, and secondly to analyse leadership with respect to an individual's spatial position in three dimensions. We show that for 95% of all pairwise interactions leadership identified through two-dimensional analysis matches that identified through three-dimensional analysis, and we reveal that fish attend to the same shoalmates for vertical information as they do for horizontal information. Our results therefore highlight that three-dimensional analyses are not always required to identify leader-follower relationships in species that move freely in three dimensions. We discuss our results in terms of the importance of taking species' sensory capacities into account when studying interaction networks within groups.
authors.affiliation: Department of Zoology , University of Oxford , Oxford OX1 3PS , UK.
authors.forename: Isobel
authors.identifier: 0000-0002-8305-8931
authors.initials: I
authors.lastname: Watts
authors.affiliation: Department of Zoology, University of Oxford, Oxford OX1 3PS, UK; Department of Collective Behaviour, Max Planck Institute for Ornithology, Konstanz, Germany; Department of Biology, University of Konstanz, Konstanz, Germany; MTA-ELTE Statistical and Biological Physics Research Group, Hungarian Academy of Sciences, Budapest, Hungary.
authors.forename: Máté
authors.initials: M
authors.lastname: Nagy
authors.affiliation: School of Computing , University of Leeds , Leeds LS2 9JT , UK.
authors.forename: Robert I
authors.initials: RI
authors.lastname: Holbrook
authors.affiliation: Department of Zoology , University of Oxford , Oxford OX1 3PS , UK.
authors.forename: Dora
authors.initials: D
authors.lastname: Biro
authors.affiliation: Department of Zoology , University of Oxford , Oxford OX1 3PS , UK.
authors.forename: Theresa
authors.initials: T
authors.lastname: Burt de Perera
keywords: Astyanax mexicanus; hierarchy; information flow; leadership; three-dimensional movement