Informative and misinformative interactions in a school of fish

Abstract

It is generally accepted that, when moving in groups, animals process information to coordinate their motion. Recent studies have begun to apply rigorous methods based on Information Theory to quantify such distributed computation. Following this perspective, we use transfer entropy to quantify dynamic information flows locally in space and time across a school of fish during directional changes around a circular tank, i.e. U-turns. This analysis reveals peaks in information flows during collective U-turns and identifies two different flows: an informative flow (positive transfer entropy) based on fish that have already turned about fish that are turning, and a misinformative flow (negative transfer entropy) based on fish that have not turned yet about fish that are turning. We also reveal that the information flows are related to relative position and alignment between fish, and identify spatial patterns of information and misinformation cascades. This study offers several methodological contributions and we expect further application of these methodologies to reveal intricacies of self-organisation in other animal groups and active matter in general. * emanuele.crosato@sydney.edu.au arXiv:1705.01213v1 [q-bio.QM] 3 May 2017 Nagy et al. [55] used a variety of correlation functions to measure directional dependencies between the velocities of pairs of pigeons flying in flocks of up to ten individuals, reconstructing the leadership network of the flock. As has been shown later, this network does not correspond to the hierarchy between birds [56]. Information transfer has been extensively studied in flocks of starlings, by observing the propagation of direction changes across the flocks [20,19,2]. More recently, Rosenthal et al. [69] attempted to determine a communication structure of a school of fish during its collective evasion manoeuvres manifested through cascades of behavioural change. A functional mapping between sensory inputs and motor responses was inferred by tracking fish position and body posture, and calculating visual fields.Rather than consider semantic or pragmatic information, many contemporary studies employ rigorous information theoretic measures that quantify information as uncertainty reduction, following Shannon [24], in order to deal with the stochastic, continuous and noisy nature of intrinsic information processing in natural systems [28]. Distributed information processing is typically dissected into three primitive functions: the transmission, storage and modification of information [38]. Information dynamics is a recent framework characterising and measuring each of the primitives information-theoretically [49,41]. In viewing the state update dynamics of a random process as an information processing event, this framework performs an information regression in accounting for where the information to predict that state update can be found by an observer, first identifying predictive information from the past of the process as information storage, then predictive information from other sour...

Entropy balance and information processing in bipartite and nonbipartite composite systems

“…These conjectures have been formalized in the context of information dynamics [56], verifying the hypothesis that the collective memory within a swarm can be captured by active information storage, while the information cascades are captured by conditional transfer entropy [57,58]. This has been further verified for real biological groups, such as swarms of soldier crabs [59], schools of zebrafish responding to a robotic animal replica [60], pairs of bats [61], rummy-nose tetras (Hemigrammus rhodostomus) fish schools [62], and so on.…”

Finding continuity and discontinuity in fish schools via integrated information theory

“…In particular, with regard to the subject of this study, it is conceivable that the interactions of two-and three-fish groups may be different [35,36]. Many researchers, therefore, have considered information transfer (or causal relationships) among individuals in small groups [37,38,39]. The (local) transfer entropy is the preferred measure to use in this case [40,41,42,43,44,45].…”

“…The (local) transfer entropy is the preferred measure to use in this case [40,41,42,43,44,45]. For example, Crosato et al [39] showed that the transfer of misinformation happens in five-fish school when the whole school changes direction. Other studies suggest that active information storage can predict the timing when nontrivial information transfer happens [46,47].…”

Relating Complexities for the Reflexive Study of Complex Systems

“…Collective behaviors of fishes or birds are typical examples used to illustrate emergence and belong to the canonic examples of complex systems. We only begin to understand how these flows structure the system, and what are the spatial patterns of information transfer within a flock for example: [Crosato et al, 2017] introduce first empirical results with transfer entropy for fishes and lay the methodological basis of this kind of studies. Similarly, [Lecheval et al, 2018] show that nonlinear interaction between fishes are essential for the propagation of information in the school during a collective U-turn.…”