韦伯定律与动物群体的稳定性
Weber's law based perception and the stability of animal groups
摘要：
群体生活的动物形成群体和羊群，尽管个体内部运动，但仍然保持凝聚力。这是可能的，因为单个组成员重复地调整其位置和运动以响应其他组成员的位置和运动。在这里，我们开发了一个理论方法来解决这个问题，什么一般功能-如果有的话-的基础上的相互作用规则，调解组的稳定性，在所有物种的动物？我们这样做，考虑如何的空间组织的一组将在完全没有相互作用的变化。如果没有相互作用，一个群体就会以一种可以很容易地用菲克扩散方程描述的方式分散。因此，我们可以解决的逆理论问题，找到个人水平的相互作用所需的反应，以抵消扩散和保持集团的稳定性。我们表明，个人层面的响应邻居密度的形式韦伯定律（一个“普遍”的法律，描述所有物种的动物的感觉系统的功能）的结果在一个“反扩散”长期在组的水平。在短时间尺度上，这种反扩散以一种让人想起图像处理中的图像去模糊方法的方式恢复初始组配置。我们还表明，任何非均匀的，空间密度分布可以保存随着时间的推移，如果个人的运动模式的形式的韦伯定律的反应。韦伯定律描述了感知系统的基本功能。我们的研究表明，这也是一个必要的-但不是充分的-在稳定的动物群体的集体互动的功能。
英文摘要：
Group living animals form aggregations and flocks that remain cohesive in spite of internal movements of individuals. This is possible because individual group members repeatedly adjust their position and motion in response to the position and motion of other group members. Here we develop a theoretical approach to address the question, what general features -- if any -- underlie the interaction rules that mediate group stability in animals of all species? We do so by considering how the spatial organisation of a group would change in the complete absence of interactions. Without interactions, a group would disperse in a way that can be easily characterised in terms of Fick's diffusion equations. We can hence address the inverse theoretical problem of finding the individual-level interaction responses that are required to counterbalance diffusion and to preserve group stability. We show that an individual-level response to neighbour densities in the form of Weber's law (a 'universal' law describing the functioning of the sensory systems of animals of all species) results in an 'anti-diffusion' term at the group level. On short time scales, this anti-diffusion restores the initial group configuration in a way which is reminiscent of methods for image deblurring in image processing. We also show that any non-homogeneous, spatial density distribution can be preserved over time if individual movement patterns have the form of a Weber's law response. Weber's law describes the fundamental functioning of perceptual systems. Our study indicates that it is also a necessary -- but not sufficient -- feature of collective interactions in stable animal groups.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
