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

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

A model comparison reveals dynamic social information drives the movements of humbug damselfish (Dascyllus aruanus)

Animals make use a range of social information to inform their movement decisions. One common movement rule, found across many different species, is that the probability that an individual moves to an area increases with the number of conspecifics there. However, in many cases, it remains unclear what social cues produce this and other similar movement rules. Here, we investigate what cues are used by damselfish (Dascyllus aruanus) when repeatedly crossing back and forth between two coral patches in an experimental arena. We find that an individual's decision to move is best predicted by the recent movements of conspecifics either to or from that individual's current habitat. Rather than actively seeking attachment to a larger group, individuals are instead prioritizing highly local and dynamic information with very limited spatial and temporal ranges. By reanalyzing data in which the same species crossed for the first time to a new coral patch, we show that the individuals use static cues in this case. This suggests that these fish alter their information usage according to the structure and familiarity of their environment by using stable information when moving to a novel area and localized dynamic information when moving between familiar areas

Superfluid transport of information in turning flocks of starlings

Collective decision-making in biological systems requires all individuals in the group to go through a behavioural change of state. During this transition, the efficiency of information transport is a key factor to prevent cohesion loss and preserve robustness. The precise mechanism by which natural groups achieve such efficiency, though, is currently not fully understood. Here, we present an experimental study of starling flocks performing collective turns in the field. We find that the information to change direction propagates across the flock linearly in time with negligible attenuation, hence keeping group decoherence to a minimum. This result contrasts with current theories of collective motion, which predict a slower and dissipative transport of directional information. We propose a novel theory whose cornerstone is the existence of a conserved spin current generated by the gauge symmetry of the system. The theory turns out to be mathematically identical to that of superfluid transport in liquid helium and it explains the dissipationless propagating mode observed in turning flocks. Superfluidity also provides a quantitative expression for the speed of propagation of the information, according to which transport must be swifter the stronger the group's orientational order. This prediction is verified by the data. We argue that the link between strong order and efficient decision-making required by superfluidity may be the adaptive drive for the high degree of behavioural polarization observed in many living groups. The mathematical equivalence between superfluid liquids and turning flocks is a compelling demonstration of the far-reaching consequences of symmetry and conservation laws across different natural systems

Collective response to perturbations in a data-driven fish school model

22 pages, 9 figures and 3 videos in the supplementary materialInternational audienceFish schools are able to display a rich variety of collective states and behav-ioural responses when they are confronted by threats. However, a school's response to perturbations may be different depending on the nature of its collective state. Here we use a previously developed data-driven fish school model to investigate how the school responds to perturbations depending on its different collective states, we measure its susceptibility to such perturbations, and exploit its relation with the intrinsic fluctuations in the school. In particular, we study how a single or a small number of perturbing individuals whose attraction and alignment parameters are different from those of the main population affect the long-term behaviour of a school. We find that the responsiveness of the school to the perturbations is maximum near the transition region between milling and schooling states where the school exhibits multistability and regularly shifts between these two states. It is also in this region that the susceptibility, and hence the fluctuations, of the polarization order parameter is maximal. We also find that a significant school's response to a perturbation only happens below a certain threshold of the noise to social interactions ratio

From behavioural analyses to models of collective motion in fish schools

International audienceFish schooling is a phenomenon of long lasting interest in ethology and ecology, widely spread across taxa and ecological contexts, and which has attracted much interest from statistical physics and theoretical biology as a case of self-organized behaviour. One topic of intense interest is the search of the peculiar and specific behavioural mechanisms at stake at the individual level and from which the school properties emerges. This is fundamental for understanding how selective pressure acting at individual level promotes adaptive properties of schools and in trying to disambiguate functional properties from non-adaptive epiphenomena. Decades of studies on collective motion by means of individual-based modelling have allowed a qualitative understanding of the selforganization processes leading to collective properties at school level, and provided insight to the behavioural mechanisms that result in coordinated motion. Here we emphasize a set of paradigmatic modelling assumptions whose validity remains unclear, both from a behavioural point of view and in terms of quantitative agreement between model outcome and empirical data. We advocate for a specific and biologically oriented re-examination of these assumptions through experimentally-based behavioural analysis and modelling

Swarming, schooling, milling: phase diagram of a data-driven fish school model

International audienceWe determine the basic phase diagram of the fish school model derived from data by Gautrais et al (2012 PLoS Comput. Biol. 8 e1002678), exploring its parameter space beyond the parameter values determined experimentally on groups of barred flagtails (Kuhlia mugil) swimming in a shallow tank. A modified model is studied alongside the original one, in which an additional frontal preference is introduced in the stimulus/response function to account for the angular weighting of interactions. Our study, mostly limited to groups of moderate size (in the order of 100 individuals), focused not only on the transition to schooling induced by increasing the swimming speed, but also on the conditions under which a school can exhibit milling dynamics and the corresponding behavioural transitions. We show the existence of a transition region between milling and schooling, in which the school exhibits multistability and intermittence between schooling and milling for the same combination of individual parameters. We also show that milling does not occur for arbitrarily large groups, mainly due to a distance dependence interaction of the model and information propagation delays in the school, which cause conflicting reactions for large groups. We finally discuss the biological significance of our findings, especially the dependence of behavioural transitions on social interactions, which were reported by Gautrais et al to be adaptive in the experimental conditions