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Self-Organized Shape and Frontal Density of Fish Schools

机译：鱼群的自组织形状和额叶密度

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Models of swarming (based on avoidance, alignment and attraction) produce patterns of behaviour also seen in schools of fish. However, the significance of such similarities has been questioned, because some model assumptions are unrealistic [e.g. speed in most models is constant with random error, the perception is global and the size of the schools that have been studied is small (up to 128 individuals)]. This criticism also applies to our former model, in which we demonstrated the emergence of two patterns of spatial organization, i.e. oblong school form and high frontal density, which are supposed to function as protection against predators. In our new model we respond to this criticism by making the following improvements: individuals have a preferred 'cruise speed' from which they can deviate in order to avoid others or to catch up with them. Their range of perception is inversely related to density, with which we take into account that high density limits the perception of others that are further away. Swarm sizes range from 10 to 2000 individuals. The model is three-dimensional. Further, we show that the two spatial patterns (oblong shape and high frontal density) emerge by self-organization as a side-effect of coordination at two speeds (of two or four body lengths per second) for schools of sizes above 20. Our analysis of the model leads to the development of a new set of hypotheses. If empirical data confirm these hypotheses, then in a school of real fish these patterns may arise as a side-effect of their coordination in the same way as in the model.
机译：群聚模型（基于回避，对准和吸引）产生了行为模式，在鱼类群中也可以看到。但是，由于某些模型假设是不现实的，因此人们对这种相似性的重要性提出了质疑。在大多数模型中，速度是恒定的，并且具有随机误差，感知是全局的，所研究的学校规模很小（最多128个人）]。这种批评也适用于我们以前的模型，其中我们证明了空间组织的两种模式的出现，即长方形的学校形式和高额密度，它们被认为可以防止天敌。在我们的新模型中，我们通过以下改进来应对这种批评：个人具有偏爱的“巡航速度”，可以偏离这些速度以避免他人追赶或追赶他们。他们的感知范围与密度成反比，因此我们考虑到高密度会限制其他人的感知。群的大小从10到2000个人。该模型是三维的。此外，我们显示了对于20以上规模的学校，两种空间模式（长方形和高额叶密度）是通过自组织出现的，以两种速度（每秒两个或四个体长）的协调速度出现。对模型的分析导致了一组新的假设的发展。如果经验数据证实了这些假设，那么在一群真实的鱼类中，这些模式可能以与模型中相同的方式作为其协调的副作用而出现。

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