Decomposing the heterogeneity of species distributions into multiple scales: a hierarchical framework for large-scale count surveys


E. Bellier, Biostatistics and Spatial Processes, INRA Avignon, Domaine Saint-Paul, Site Agroparc, FR-84914 Avignon Cedex 9, France. E-mail:


We introduce a novel spatially explicit framework for decomposing species distributions into multiple scales from count data. These kinds of data are usually positively skewed, have non-normal distributions and are spatially autocorrelated. To analyse such data, we propose a hierarchical model that takes into account the observation process and explicitly deals with spatial autocorrelation. The latent variable is the product of a positive trend representing the non-constant mean of the species distribution and of a stationary positive spatial field representing the variance of the spatial density of the species distribution. Then, the different scales of emergent structures of the distribution of the population in space are modelled from the latent density of the species distribution using multi-scale variogram models. Multi-scale kriging is used to map the spatial patterns previously identified by the multi-scale models. We show how our framework yields robust and precise estimates of the relevant scales both for spatial count data simulated from well-defined models, and in a real case-study based on seabird count data (the common guillemot Uria aalge) provided by large-scale aerial surveys of the Bay of Biscay (France) performed over a winter. Our stochastic simulation study provides guidelines on the expected uncertainties of the scales estimates. Our results indicate that the spatial structure of the common guillemot can be modelled as a three-level hierarchical system composed of a very broad-scale pattern (∼ 200 km) with a stable location over time that might be environmentally controlled, a broad-scale pattern (∼ 50 km) with a variable shape and location, that might be related to shifts in prey distribution, and a fine-scale pattern (∼ 10 km) with a rather stable shape and location, that might be controlled by behavioural processes. Our framework enables the development of robust, scale-dependent hypotheses regarding the potential ecological processes that control species distributions.