School of Science and Technology, University of New England, Armidale, NSW, Australia.
School of Mathematical and Computing Science, Fiji National University, Suva, Fiji.
PLoS One. 2020 Dec 9;15(12):e0243631. doi: 10.1371/journal.pone.0243631. eCollection 2020.
Groups of animals coordinate remarkable, coherent, movement patterns during periods of collective motion. Such movement patterns include the toroidal mills seen in fish shoals, highly aligned parallel motion like that of flocks of migrating birds, and the swarming of insects. Since the 1970's a wide range of collective motion models have been studied that prescribe rules of interaction between individuals, and that are capable of generating emergent patterns that are visually similar to those seen in real animal group. This does not necessarily mean that real animals apply exactly the same interactions as those prescribed in models. In more recent work, researchers have sought to infer the rules of interaction of real animals directly from tracking data, by using a number of techniques, including averaging methods. In one of the simplest formulations, the averaging methods determine the mean changes in the components of the velocity of an individual over time as a function of the relative coordinates of group mates. The averaging methods can also be used to estimate other closely related quantities including the mean relative direction of motion of group mates as a function of their relative coordinates. Since these methods for extracting interaction rules and related quantities from trajectory data are relatively new, the accuracy of these methods has had limited inspection. In this paper, we examine the ability of an averaging method to reveal prescribed rules of interaction from data generated by two individual based models for collective motion. Our work suggests that an averaging method can capture the qualitative features of underlying interactions from trajectory data alone, including repulsion and attraction effects evident in changes in speed and direction of motion, and the presence of a blind zone. However, our work also illustrates that the output from a simple averaging method can be affected by emergent group level patterns of movement, and the sizes of the regions over which repulsion and attraction effects are apparent can be distorted depending on how individuals combine interactions with multiple group mates.
动物群体在集体运动期间协调出显著、连贯且协调一致的运动模式。这些运动模式包括鱼群中可见的环形磨坊状运动、候鸟群中高度一致的平行运动，以及昆虫的群集运动。自 20 世纪 70 年代以来，人们研究了广泛的集体运动模型，这些模型规定了个体之间的相互作用规则，并且能够产生与实际动物群体中观察到的视觉上相似的突发模式。这并不一定意味着实际动物完全应用了模型中规定的相同相互作用。在最近的研究中，研究人员试图通过使用多种技术，包括平均方法，直接从跟踪数据中推断真实动物的相互作用规则。在最简单的公式之一中，平均方法确定个体速度分量随时间的平均变化作为组内成员相对坐标的函数。平均方法还可用于估计其他密切相关的量，包括组内成员运动的平均相对方向作为其相对坐标的函数。由于这些从轨迹数据中提取相互作用规则和相关量的方法相对较新，因此这些方法的准确性受到了限制。在本文中，我们检验了一种平均方法从两种基于个体的集体运动模型生成的数据中提取预定相互作用规则的能力。我们的工作表明，平均方法可以仅从轨迹数据中捕获潜在相互作用的定性特征，包括速度和方向变化中明显的排斥和吸引效应，以及盲区的存在。然而，我们的工作还表明，简单平均方法的输出可能会受到突发的群体运动模式的影响，排斥和吸引效应明显的区域的大小可能会根据个体如何与多个群体成员结合相互作用而扭曲。
