1. Understanding how animal movements change across space and time is a fundamental question in ecology. While classical analyses of trajectories give insightful descriptors of spatial patterns, a satisfying method for assessing the temporal succession of such patterns is lacking.
2. Network analyses are increasingly used to capture properties of complex animal trajectories in simple graphical metrics. Here, building on this approach, we introduce a method that incorporates time into movement network analyses based on temporal sequences of network motifs.
3. We illustrate our method using four example trajectories (bumblebee, black kite, roe deer, wolf) collected with different technologies (harmonic radar, platform terminal transmitter, global positioning system). First, we transformed each trajectory into a spatial network by defining the animal's coordinates as nodes and movements in between as edges. Second, we extracted temporal sequences of network motifs from each movement network and compared the resulting behavioural profiles to topological features of the original trajectory. Finally, we compared each sequence of motifs with simulated Brownian and Lévy random motions to statistically determine differences between trajectories and classical movement models.
4. Our analysis of the temporal sequences of network motifs in individual movement networks revealed successions of spatial patterns corresponding to changes in behavioural modes that can be attributed to specific spatio‐temporal events of each animal trajectory. Future applications of our method to multi‐layered movement and social network analysis yield considerable promises for extending the study of complex movement patterns at the population level.

中文翻译：

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动物运动网络中的时间模式分析

1. 了解动物运动如何随时间和空间变化是生态学中的一个基本问题。尽管对轨迹的经典分析给出了空间模式的深刻描述，但仍缺乏一种令人满意的方法来评估这种模式的时间顺序。
2. 网络分析越来越多地用于以简单的图形指标捕获复杂动物轨迹的属性。在此，在此方法的基础上，我们介绍了一种基于网络主题的时间序列将时间纳入运动网络分析的方法。
3. 我们使用四个示例轨迹（大黄蜂，黑鸢，ro，狼）用不同技术（谐波雷达，平台终端发射器，全球定位系统）收集了示例方法来说明我们的方法。首先，我们通过将动物的坐标定义为节点并将其间的运动定义为边缘，将每个轨迹转换为空间网络。其次，我们从每个运动网络中提取了网络主题的时间序列，并将所得的行为特征与原始轨迹的拓扑特征进行了比较。最后，我们将图案的每个序列与模拟的Brownian和Lévy随机运动进行比较，以统计确定轨迹与经典运动模型之间的差异。
4. 我们对单个运动网络中网络主题的时间序列的分析表明，与行为模式的变化相对应的空间模式的连续性可以归因于每种动物轨迹的特定时空事件。我们的方法在多层运动和社交网络分析中的未来应用为扩展对人口层面复杂运动模式的研究提供了可观的前景。