Analysing and mapping species range dynamics using occupancy models

Aim: Our aims are: (1) to highlight the power of dynamic occupancy models for analysing species range dynamics while accounting for imperfect detection; (2) to emphasize the flexibility to model effects of environmental covariates in the dynamics parameters (extinction and colonization probability); and (3) to illustrate the development of predictive maps of range dynamics by projecting estimated probabilities of occupancy, local extinction and colonization. Location: Switzerland. Methods: We used data from the Swiss breeding bird survey to model the Swiss range dynamics of the European crossbill (Loxia curvirostra) from 2000 to 2007. Within-season replicate surveys at each 1 km 2 sample unit allowed us to fit dynamic occupancy models that account for imperfect detection, and thus estimate the following processes underlying the observed range dynamics: local extinction, colonization and detection. For comparison, we also fitted a model variant where detection was assumed to be perfect. Results: All model parameters were affected by elevation, forest cover and elevation-by-forest cover interactions and exhibited substantial annual variation. Detection probability varied seasonally and among years, highlighting the need for its estimation. Projecting parameter estimates in environmental or geographical space is a powerful means of understanding what the model is telling about covariate relationships. Geographical maps were substantially different between the model where detection was estimated and that where it was not, emphasizing the importance of accounting for imperfect detection in studies of range dynamics, even for high-quality data. Main conclusions: The study of species range dynamics is among the most exciting avenues for species distribution modelling. Dynamic occupancy models offer a robust framework for doing so, by accounting for imperfect detection and directly modelling the effects of covariates on the parameters that govern distributional change. Mapping parameter estimates modelled by spatially indexed covariates is an under-used way to gain insights into dynamic species distributions.