Smooth Alien Species Invasion Model with Random and Time-Varying Effects

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.