A species that, coming from a source population, appears in a new environment where it was not present before is named alien. Due to the harm it poses to biodiversity and the expenses associated with its control, the phenomenon of alien species invasions is currently under careful examination. Although the presence of a considerable literature on the subject, the formulation of a dedicated statistical model has been deemed essential. The objective is to overcome current computational constraints while also correctly accounting for the dynamics behind the spread of alien species. A first record can be seen as a relational event, where the species (the sender) reaches a region (the receiver) for the first time in a certain year. As a result, whenever an alien species is introduced, the relational event graph adds a time-stamped edge. Besides potentially time-varying exogenous and endogenous covariates, our smooth relational event model (REM) also incorporates time-varying and random effects to explain the invasion rate. Particularly, we aim to track temporal variations in impacts' direction and magnitude of the ecological, socioeconomic, historical, and cultural forces at work. Network structures of particular interest (such as species' co-invasion affinity) are inspected as well. Our inference procedure relies on case-control sampling, yielding the same likelihood as that of a logistic regression. Due to the smooth nature of the incorporated effects, we may fit a generalised additive model where random effects are also estimated as 0-dimensional splines. The consequent computational advantage makes it possible to simultaneously examine many taxonomies. We explore how vascular plants and insects behave together. The goodness of fit of the smooth REM may be evaluated by means of test statistics computed as region-specific sums of martingale-residuals.

翻译：源自源种群并出现在先前不存在的新环境中的物种被称为外来物种。由于其危害生物多样性并带来高昂控制成本，外来物种入侵现象目前正受到密切关注。尽管已有大量文献涉及该课题，但构建专用统计模型仍被视为必要。其目标是在正确解释外来物种传播动态的同时，克服当前计算条件的限制。首次记录可视为一个关系事件，即某物种（发送者）在某一年首次到达某个区域（接收者）。因此，每当有外来物种被引入时，关系事件图会增加一个带有时间戳的边。除可能具有时变性的外生和内生协变量外，我们的光滑关系事件模型还纳入了时变效应和随机效应来解释入侵速率。具体而言，我们旨在追踪生态、社会经济、历史和文化因素作用的方向与强度随时间的变化。我们同时考察了特别关注的网络结构（如物种共侵染亲和性）。推理过程采用病例对照抽样，其似然函数与逻辑回归相同。由于所纳入效应的光滑性，我们可以拟合广义可加模型，其中随机效应也被估计为0维样条。由此带来的计算优势使得同时研究多个分类群成为可能。我们探讨了维管植物与昆虫的协同行为。光滑关系事件模型的拟合优度可通过基于区域特定鞅残差之和的检验统计量进行评估。