Accounting for imperfect observation and estimating true species distributions in modelling biological invasions

The documentation of biological invasions is often incomplete with records lagging behind the species’ actual spread to a spatio-temporally heterogeneous extent. Such imperfect observation bears the risk of underestimating the already realised distribution of the invading species, misguiding management efforts and misjudging potential future impacts. In this paper, we develop a hierarchical modelling framework which disentangles the determinants of the invasion and observation processes, models spatio-temporal heterogeneity in detection patterns, and infers the actual, yet partly undocumented distribution of the species at any particular time. We illustrate the model with a case study application to the invasion of common ragweed Ambrosia artemisiifolia in Austria. The invasion part of the model reconstructs the historical spread of this species across a grid of ∼ 6 × 6 km2 cells as driven by spatio-temporal variation in physical site conditions, propagule production, dispersal, and ‘background’ introductions from unknown sources. The observation part models the detection of the species’ occurrences based on heterogeneous sampling efforts, human population density, and estimated local invasion level. We fitted the hierarchical model using a Bayesian inference approach with parameters estimated by Markov chain Monte Carlo (MCMC). The actual spread of A. artemisiifolia concentrated on the climatically well-suited lowlands and was mainly driven by spatio-temporal propagule pressure from source cells with long-distance dispersal occurring rather frequently. Annual detection probabilities were estimated to vary between about 1 and up to 28%, depending mainly on sampling intensity. The model suggested that by 2005 about half of the actual distribution of the species was not yet documented. Our hierarchical model offers a flexible means to account for imperfect observation and spatio-temporal variability in detection efficiency. Inferences can be used to disentangle aspects of the invasion dynamics itself from patterns of data collection, develop improved future surveying schemes, and design more efficient invasion management strategies.