Validating two-dimensional leadership models on three-dimensionally structured fish schools

Isobel Watts,Máté Nagy,Dora Biro,Theresa Burt De Perera,Robert I Holbrook

doi:10.1098/rsos.160804

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.

Highlights

Important information about the environment, such as the location of predators or resources, can be acquired by and transmitted through a group of individuals responding to the position, orientation and speed of nearby neighbours [1]
The fish schools moved in three-dimensional space (figure 2; electronic supplementary material, figures S2 and S3 with a mean distance from the bottom of the tank of 232 mm (±87 mm s.d.) and had a threedimensional structure with a mean school height across the six shoals of 144 mm (±43 mm s.d.)
By resolving pairwise interactions for high-resolution three-dimensional movement data in fish schools, we have demonstrated that two-dimensional leadership analyses can correctly identify leader–follower interactions in three dimensions

Summary

Introduction

Important information about the environment, such as the location of predators or resources, can be acquired by and transmitted through a group of individuals responding to the position, orientation and speed of nearby neighbours [1]. Previous studies have used leader–follower interactions to reveal that robust, transitive leadership hierarchies underlie collective decision-making in homing pigeon (Columba livia) flocks [9,10,11,12] and medaka fish (Oryzias latipes) schools [13], as well as the direction of information transfer within golden shiner (Notemigonus crysoleucas) schools [3]. These studies are based on animals that move freely in three dimensions, yet the analyses used are restricted to two dimensions—the horizontal planes. It is unknown whether vertical and horizontal information are transferred in similar ways and whether leaders that emerge when only considering horizontal information are identified as leaders when considering information from all three dimensions

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Conclusion