Mapping species distributions in one dimension by non-homogeneous hidden Markov models: the case of freshwater pearl mussels in the River Dee

The investigation of species distributions in rivers involves data which are inherently sequential and unlikely to be fully independent. To take these characteristics into account, we develop a Bayesian hierarchical model for mapping the distribution of freshwater pearl mussels in the River Dee (Scotland). At the top of the hierarchy the likelihood is used to describe the sequence of sites in which mussels were observed or not. Given that false observations can occur, and that “not observed” means both that the species was not present and that it was not observed, a Markov prior is introduced at the second level of the hierarchy to represent the sequence of sites in which mussels are estimated to occur. The Markov prior allows modelling the spatial dependency between neighbouring sites. A third level in the hierarchy is given by the representation of the transition probabilities of the Markov chain in terms of site-specific explanatory variables, through a logistic regression. The selection of the explanatory variables which influence the Markov process is performed by means of a simulation-based procedure, in the complex case of association between covariates. Four features were found to be associated with reduced chance of finding a local mussel population: tributaries, bridges, dredging, and waste water treatment works. These results complement the results of a previous study, providing new evidence for the causes of the deterioration of a highly threatened species.