Bayesian image restoration models for combining expert knowledge on recording activity with species distribution data

Biological atlases are, for many species, the only source of information on their distribution over large geographical areas, and are widely used to inform models of the environmental distribution of species. Such data are not collected using standardized survey techniques, however, and spatial variations in coverage (the relative extent or completeness of records) may lead to variations in the probability that the species will be recorded at locations where it is present (the "recording probability"). If spatial patterns in recording probabilities are correlated with key environmental variables, then biased estimates of the relationships between environmental variables and species distributions may be obtained. We outline a general statistical framework for modelling the environmental distribution of species using, known as Bayesian Image Restoration (BIR). BIR can be used in combination with any species distribution model, but in addition allows us to account for spatial heterogeneity in recording probabilities by utilizing expert knowledge on spatial patterns in coverage. We illustrate the methodology by applying it to maps of the recorded distribution of two plant species in Germany, taken from the German atlas of vascular plants. We find that estimated spatial patterns in recording probabilities for both species are correlated with key environmental variables. Consequently, different relationships between the probability of presence of a species and environmental variables were obtained when the species distribution models were parameterised within a BIR framework. Care must be taken in the application of BIR, since the resulting inferences can depend strongly upon the modelling assumptions that are adopted. Nevertheless, we conclude that BIR has the potential to make better use of uncertain information on species distributions than conventional methods, and can be used to formally investigate the robustness of inferences on the environmental distribution of species to assumptions concerning spatial patterns in recording probabilities