Daftari Katherine, Mayo Michael L, Lemasson Bertrand H, Biedenbach James M, Pilkiewicz Kevin R
Department of Mathematics, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, USA.
U.S. Army Engineer Research and Development Center, 3909 Halls Ferry Road, Vicksburg, MS 39180, USA.
Entropy (Basel). 2024 Sep 10;26(9):775. doi: 10.3390/e26090775.
Leader-follower modalities and other asymmetric interactions that drive the collective motion of organisms are often quantified using information theory metrics like transfer or causation entropy. These metrics are difficult to accurately evaluate without a much larger number of data than is typically available from a time series of animal trajectories collected in the field or from experiments. In this paper, we use a generalized leader-follower model to argue that the time-separated mutual information between two organism positions can serve as an alternative metric for capturing asymmetric correlations that is much less data intensive and more accurately estimated by popular -nearest neighbor algorithms than transfer entropy. Our model predicts a local maximum of this mutual information at a time separation value corresponding to the fundamental reaction timescale of the follower organism. We confirm this prediction by analyzing time series trajectories recorded for a pair of golden shiner fish circling an annular tank.
引导-跟随模式以及驱动生物体集体运动的其他不对称相互作用，通常使用诸如转移熵或因果熵等信息论指标来量化。如果没有比从野外收集的动物轨迹时间序列或实验中通常可获得的数据多得多的数据，这些指标很难准确评估。在本文中，我们使用一个广义的引导-跟随模型来论证，两个生物体位置之间的时间分离互信息可以作为一种替代指标，用于捕捉不对称相关性，它所需的数据量要少得多，并且比转移熵更能通过流行的最近邻算法准确估计。我们的模型预测，在与跟随生物体的基本反应时间尺度相对应的时间分离值处，这种互信息会出现局部最大值。我们通过分析一对围绕环形水箱游动的金色闪光鱼的时间序列轨迹来证实这一预测。
