Abstract：
Interspecific interactions can influence species\' activity and movement patterns. In particular, species may avoid or attract each other through reactive responses in space and/or time. However, data and methods to study such reactive interactions have remained scarce and were generally limited to two interacting species. At this time, the deployment of camera traps opens new opportunities but adapted statistical techniques are still required to analyze interaction patterns with such data. We present the multivariate Hawkes process (MHP) and show how it can be used to analyze interactions between several species using camera trap data. Hawkes processes use flexible pairwise interaction functions, allowing us to consider asymmetries and variations over time when depicting reactive temporal interactions. After describing the theoretical foundations of the MHP, we outline how its framework can be used to study interspecific interactions with camera trap data. We design a simulation study to evaluate the performance of the MHP and of another existing method to infer interactions from camera trap-like data. We also use the MHP to infer reactive interactions from real camera trap data for five species from South African savannas (impala Aepyceros melampus, greater kudu Tragelaphus strepsiceros, lion Panthera leo, blue wildebeest Connochaetes taurinus and Burchell\'s zebra Equus quagga burchelli). The simulation study shows that the MHP can be used as a tool to benchmark other methods of interspecific interaction inference and that this model can reliably infer interactions when enough data are considered. The analysis of real data highlights evidence of predator avoidance by prey and herbivore-herbivore attraction. Lastly, we present the advantages and limits of the MHP and discuss how it can be improved to infer attraction/avoidance patterns more reliably. As camera traps are increasingly used, the multivariate Hawkes process provides a promising framework to decipher the complexity of interactions structuring ecological communities.
摘要：
种间相互作用可以影响物种的活动和运动模式。特别是,物种可以通过空间和/或时间上的反应性来避免或吸引彼此。然而,研究这种反应性相互作用的数据和方法仍然很少，并且通常仅限于两个相互作用的物种。此时,相机陷阱的部署开辟了新的机会，但仍需要采用适应的统计技术来分析与此类数据的交互模式。我们介绍了多元霍克斯过程（MHP），并展示了如何使用相机陷阱数据分析几个物种之间的相互作用。Hawkes过程使用灵活的成对交互功能，允许我们在描述反应性时间相互作用时考虑不对称性和随时间的变化。在描述了MHP的理论基础之后，我们概述了如何使用其框架来研究与相机陷阱数据的种间相互作用。我们设计了一个模拟研究来评估MHP的性能，以及另一种现有的方法来从相机陷阱状数据中推断相互作用。我们还使用MHP从真实的相机陷阱数据中推断出来自南非稀树草原（impalaAepycerosmelampus，大kuduTragelaphusstrepiceros，狮子PantheraLeo,蓝色角马Connochaetestaurinus和Burchell\的斑马马马马马夸加布尔切利）。模拟研究表明，MHP可以用作对其他种间相互作用推断方法进行基准测试的工具，并且当考虑足够的数据时，该模型可以可靠地推断相互作用。对真实数据的分析突出了捕食者被猎物和食草动物-食草动物吸引的证据。最后,我们介绍了MHP的优点和局限性，并讨论了如何对其进行改进以更可靠地推断吸引/回避模式。随着相机陷阱的使用越来越多，多元Hawkes过程提供了一个有希望的框架来破译构建生态群落的相互作用的复杂性。
