Many fish exhibit rheotaxis, a behavior in which fish orient themselves relative to flow. Rheotaxis confers many benefits, including energetic cost savings and interception of drifting prey. Despite the fact that most species of fish school during at least some portion of their life, little is known about the importance of rheotactic behavior to schooling fish and, conversely, how the presence of nearby conspecifics affects rheotactic behavior. Understanding how rheotaxis is modified by social factors is thus of ecological importance. Here we present a mathematical model in the form of an all-to-all, coupled-oscillator framework over the non-Euclidean space of fish orientations to model group rheotactic behavior. Individuals in the model measure the orientation of their neighbors and the flow direction relative to their own orientation. These measures are corrupted by sensory noise. We study the effect of sensory noise and group size on internal (i.e., within the school) and external (i.e., with the flow) disagreement in orientation. We find that under noisy environmental conditions, increased group size improves rheotaxis. Results of this study have implications for understanding animal behavior, as well as for potential applications in bio-inspired engineering.

中文翻译：

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在具有感觉噪声的耦合相模型中，流变性性能随着基团大小的增加而增加：噪声和基团大小对流变性的影响。

许多鱼表现出流趋性，即鱼相对于水流定向的行为。趋向性带来许多好处，包括节省能源成本和拦截漂流的猎物。尽管事实上大多数鱼类至少在其生命的某个阶段会形成群体，但人们对于流策略行为对于鱼群的重要性以及附近同种动物的存在如何影响流策略行为的重要性知之甚少。因此，了解社会因素如何改变趋变性具有生态重要性。在这里，我们提出了一个数学模型，其形式是在鱼类方向的非欧几里得空间上的全对全耦合振荡器框架，以模拟群体流变行为。模型中的个体测量其邻居的方向以及相对于其自身方向的流动方向。这些措施会被感官噪音破坏。我们研究感官噪音和群体规模对内部（即学校内部）和外部（即流动）方向分歧的影响。我们发现，在嘈杂的环境条件下，增加群体规模可以改善流变性。这项研究的结果对于理解动物行为以及仿生工程的潜在应用具有重要意义。