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

Cooperative acceleration of task performance: foraging behavior of interacting multi-robots system

The effect of population size and number of influential neighbors on the emergent properties of fish schools

The main benefit of the oblong shape of schools of fish is supposed to be the protection against predation. Models of self-organised travelling groups have shown that this shape may arise as a side effect of the avoidance of collisions with group members. These models were developed for schools of fish in open water, whereas the oblong shape of schools of real fish has mostly been observed in schools in tanks. Therefore, it is not known how school shape in a tank originates neither in models nor in real fish. To find out what causes this shape, we use the combination of a theoretical and an empirical study. We test the predictions produced by our earlier models regarding the effect of school size on the school shape both in a model of self-organised schooling in a tank and empirically. Empirically, we study the 3D positions of all individuals in the schools of 10‐60 real mullets (Chelon labrosus). We calculate for each individual its distance to its nearest neighbour and its velocity and we measure per school its length and width. The relation between school shape and size in the model and in the real mullets supports our prediction and thus supports the hypothesis that school shape may be emergent from the avoidance of collisions during coordinated travelling.

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Emergence of Oblong School Shape: Models and Empirical Data of Fish

The emergence of collective strategies in a prey-predator system is studied. We use the term "collective" in the sense of the collective motion of defense or attack often found in behaviors of animal grotips. In our prey-predator system, both prey and predators move around on a two-dimensional plane, interacting by playing a game; predators can score by touching the backside of a prey. Thresholds are assumed for the scores of both prey and predators. The species with the higher scores can reproduce more, and that with the lower scores will be diminished. As a result, strategies as collective motions are observed; these consist of rotating cluster motions, line formations, disordered but one-way marching, and random swarming. In particular, the strategy of random swarming encourages symbiosis in the sense that it is associated with a low extinction probability for the whole system.

Emergence of collective strategies in a prey-predator game model

The behaviour of a fish school is considered an interesting phenomenon because a fish school behaves differently in various situations. The paper considers a fish school as an autonomous decentralized system and constructs a mathematical model for the autonomous decentralized mechanism. Simulation results show that, by varying the quantity of information exchange among members in school, the present model describes fish behaviour not only for a school with fixed configuration but also for that with variable form. Furthermore, a remarkable difference in fish trajectory is found between the two schools.

A simulation study on autonomous decentralized mechanism in fish behaviour model

A Simulation Study on Schooling Mechanism in Fish Behavior

How does Fish School Change Form?:A Hypothesis from Simulation Study

In this paper the schooling behaviour of fish in a water tank is investigated. A mathematical model is presented for the schooling mechanism offish. A water tank experiment is carried out by leaving five small fish in a small tank which is only a few centimetres deep. By using this observation data, the unknown parameters of the model are estimated. Then the model obtained is used to simulate schooling behaviour in a tank. In this simulation, two cases are considered. In the first case the simulation is carried out without considering any random factors. Some deterministic behaviours of fish school are shown. In the second case random variables are added to the model. We examine school trajectory, school size, speeds of individuals and their correlations and distributions. Simulation results are compared with the results obtained from observation data.

Mohammad Ali Doustari

Papers

A simulation study on autonomous decentralized mechanism in fish behaviour model

A Simulation Study on Schooling Mechanism in Fish Behavior

How does Fish School Change Form?:A Hypothesis from Simulation Study

A simulation study on schooling behaviour of fish in a water tank

How does Fish School Change Form