Invasive species are regularly claimed as the second threat to biodiversity. To apply a relevant response to the potential consequences associated with invasions (e.g., emphasize management efforts to prevent new colonization or to eradicate the species in places where it has already settled), it is essential to understand invasion mechanisms and dynamics. Quantifying and understanding what influences rates of spatial spread is a key research area for invasion theory. In this paper, we develop a model to account for occupancy dynamics of an invasive species. Our model extends existing models to accommodate several elements of invasive processes; we chose the framework of hierarchical modeling to assess site occupancy status during an invasion. First, we explicitly accounted for spatial structure and how distance among sites and position relative to one another affect the invasion spread. In particular, we accounted for the possibility of directional propagation and provided a way of estimating the direction of this possible spread. Second, we considered the influence of local density on site occupancy. Third, we decided to split the colonization process into two subprocesses, initial colonization and recolonization, which may be ground-breaking because these subprocesses may exhibit different relationships with environmental variations (such as density variation) or colonization history (e.g., initial colonization might facilitate further colonization events). Finally, our model incorporates imperfection in detection, which might be a source of substantial bias in estimating population parameters.
We focused on the case of the Eurasian Collared-Dove (Streptopelia decaocto) and its invasion of the United States since its introduction in the early 1980s, using data from the North American BBS (Breeding Bird Survey). The Eurasian Collared-Dove is one of the most successful invasive species, at least among terrestrial vertebrates. Our model provided estimation of the spread direction consistent with empirical observations. Site persistence probability exhibits a quadratic response to density. We also succeeded at detecting differences in the relationship between density and initial colonization vs. recolonization probabilities. We provide a map of sites that may be colonized in the future as an example of possible practical application of our work.