Mixed additive modelling of global alien species co-invasions of plants and insects

Abstract Alien species refer to non-native species introduced into an ecosystem, potentially causing harm to the environment, economy, or human health. Presence of confounding factors has so far prevented a comprehensive picture of relative importance of various drivers of such invasions. In this article, we aim to develop and apply a general mixed additive relational event model (REM) to describe the pattern of global invasions of alien species. An alien species invasion can be seen as a relational event, where the species—sender—reaches a region—receiver—at a specific time in history. We consider the First Record Database and focus on co-invasions by insects and plants between 1880 and 2005. REM aims to describe underlying hazard of each sender–receiver pair. Besides potentially time-varying, exogenous, and endogenous covariates, our mixed additive REM incorporates time-varying and random effects. Our efficient inference procedure relies on case–control sampling, yielding the same likelihood as that of a degenerate logistic regression. Resulting computational efficiency means that complex models for large dynamic networks can be estimated in seconds on a standard computer. We also present a framework for testing the goodness-of-fit of REMs via cumulative martingale-residuals. Implementation is performed through R package mgcv.