Order and Flexibility in the Motion of Fish Schools

Inada, Yuki; Kawachi, Keiji

doi:10.1006/jtbi.2001.2449

Cited by 128 publications

(124 citation statements)

References 39 publications

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“…To date, most other zone-based models implicitly assume that the alignment force is equal in magnitude to the attraction/repulsion force (Aoki 1982, Huth & Wissel 1990, Hiramatsu et al 2000, Inada & Kawachi 2002. As we have shown in this paper, alignment forces that are high relative to attraction/repulsion forces are likely to produce schools that have artificially high and invariable alignment (Figs.…”

Section: Discussionmentioning

confidence: 67%

Individual behavior and emergent properties of fish schools: a comparison of observation and theory

Viscido¹,

Parrish²,

Grünbaum³

2004

Mar. Ecol. Prog. Ser.

179

148

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Polarity, group velocity, and inter-individual spacing are characteristics of fish schools that strongly affect individual school members. However, these characteristics are group-level 'emergent properties': collective outcomes of behavioral interactions among members, not under direct control of any single member. The relationships between members' behaviors and the emergent group properties they produce are complex and poorly understood. In this study, we quantified 3D trajectories of all individual fish within 4-and 8-fish populations of Danio aequipinnatus, using stereo videography and a computerized tracking algorithm. We compared group polarity, group speed, and mean nearest-neighbor distances of schools within these populations to a simulation model that explored how fish responded to attraction/repulsion, alignment and random forces. Real fish exhibited a high degree of temporal variability in both polarity and group speed. Polarity and speed of simulated schools depended very strongly on the strength of the alignment force. Time-averaged polarity of real fish schools was most similar to simulated schools when alignment force was 1 to 5% of the attraction/repulsion force. For both real and simulated fish, a clear relationship existed between group speed and polarity: polarized groups were faster than non-polarized groups. We propose a multi-dimensional state space where several emergent property statistics are represented along the axes, and suggest certain 'preferred' ranges of state space within which animal groups tend to localize, and in which they can sustain distinct types of regular architecture.

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Section: Discussionmentioning

confidence: 67%

Individual behavior and emergent properties of fish schools: a comparison of observation and theory

Viscido¹,

Parrish²,

Grünbaum³

2004

Mar. Ecol. Prog. Ser.

179

148

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“…ref. 30). The minima of the effective potential correspond to the stable branch (black) and the maxima correspond to the unstable branch (gray).…”

Section: Discussionmentioning

confidence: 99%

Coarse-grained analysis of stochasticity-induced switching between collective motion states

Kolpas¹,

Moehlis

Kevrekidis

2007

Proc. Natl. Acad. Sci. U.S.A.

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A single animal group can display different types of collective motion at different times. For a one-dimensional individual-based model of self-organizing group formation, we show that repeated switching between distinct ordered collective states can occur entirely because of stochastic effects. We introduce a framework for the coarse-grained, computer-assisted analysis of such stochasticity-induced switching in animal groups. This involves the characterization of the behavior of the system with a single dynamically meaningful ''coarse observable'' whose dynamics are described by an effective Fokker-Planck equation. A ''lifting'' procedure is presented, which enables efficient estimation of the necessary macroscopic quantities for this description through short bursts of appropriately initialized computations. This leads to the construction of an effective potential, which is used to locate metastable collective states, and their parametric dependence, as well as estimate mean switching times.F ish, birds, and honey bees, as well as many other animal groups, display collective types of motion such as schooling, flocking, and swarming (1, 2). A single animal group can display different types of collective motion at different times, with Ͻ1 day of residence time in each state (3). Although such transitions could be due to changing behavioral rules or environmental factors, they also can occur entirely due to stochastic effects, as will be demonstrated for the model considered in this paper.One class of biologically motivated, individual-based models for group formation, frequently used for schooling fish, abstracts animal behavior by placing zones around individuals in which they respond to others through repulsion, alignment, and/or attraction (4-11). In the three-dimensional model of Couzin et al. (10), long-time steady-state computations revealed four different types of stable collective motion in different parameter regions: swarm, torus, dynamic parallel, and highly parallel. It was also shown that by changing the quantitative features of the behavioral rules (increasing or decreasing the radius of alignment), the collective state of the school could be changed.In ref. 10, stochasticity is incorporated by adding a small deviation to the heading of each individual obtained from the deterministic evolution algorithm. Our simulations show that if one instead considers relatively rare but substantial variations, namely that there is a small probability of each individual changing its direction substantially from that obtained from the deterministic algorithm, then for certain parameter regions multiple successive transitions between the torus and the dynamic parallel state can occur. See supporting information (SI) Fig. 7.In this paper, we study a one-dimensional individual-based model for group formation with stochasticity included along the lines of the variation described above. This system exhibits repeated stochasticity-induced switching between distinct ordered collective motion states. This switching appe...

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“…In particular, given any matrix K ∈ R 3×3 , the coefficients of its characteristic polynomial λ 3 − tr(K)λ 2 + 1 2 [(trK) 2 − tr(K 2 )]λ − det(K) (here det(·) is the determinant operator) are invariant to similarity transformations and are polynomial functions of the entries of K, hence smooth. So we will use these coefficients to parametrize K * /SO (3), and explicitly define the projection map π SO(3) as follows:…”

Section: (C) Decomposition Of Inertia Tensor Transformationsmentioning

confidence: 99%

Geometric decompositions of collective motion

Mischiati

Krishnaprasad

2017

Proc. R. Soc. A.

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Collective motion in nature is a captivating phenomenon. Revealing the underlying mechanisms, which are of biological and theoretical interest, will require empirical data, modelling and analysis techniques. Here, we contribute a geometric viewpoint, yielding a novel method of analysing movement. Snapshots of collective motion are portrayed as tangent vectors on configuration space, with length determined by the total kinetic energy. Using the geometry of fibre bundles and connections, this portrait is split into orthogonal components each tangential to a lower dimensional manifold derived from configuration space. The resulting decomposition, when interleaved with classical shape space construction, is categorized into a family of kinematic modes-including rigid translations, rigid rotations, inertia tensor transformations, expansions and compressions. Snapshots of empirical data from natural collectives can be allocated to these modes and weighted by fractions of total kinetic energy. Such quantitative measures can provide insight into the variation of the driving goals of a collective, as illustrated by applying these methods to a publicly available dataset of pigeon flocking. The geometric framework may also be profitably employed in the control of artificial systems of interacting agents such as robots.

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Order and Flexibility in the Motion of Fish Schools

Cited by 128 publications

References 39 publications

Individual behavior and emergent properties of fish schools: a comparison of observation and theory

Individual behavior and emergent properties of fish schools: a comparison of observation and theory

Coarse-grained analysis of stochasticity-induced switching between collective motion states

Geometric decompositions of collective motion

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