Bayesian clustering of spatially distributed compositional data with application to the Great Barrier Reef

: The relative abundance of groups of species is often used in ecological surveys to estimate community composition, a metric that reflects patterns of commonness and rarity of biological assemblages. The focus of this paper is measurements of the abundances of four benthic groups (that live on the seafloor) at several reefs on Australia's Great Barrier Reef (GBR) gathered between 2012 and 2017. In this paper we develop a statistical model to find clusters of locations with similar composition. We examine the changes in clusters during a period impacted by an unprecedented sequence of extreme environmental disturbances. To achieve this, we propose a model that incorporates the geographical location of the data, accounting for the possibility that nearby reefs are similar in composition. This is accomplished with a Dirichlet mixture model and a Potts distribution on the cluster assignments. Non-availability of the normalised Potts distribution makes Bayesian inference a doubly-intractable task. To circumvent this additional inferential challenge, an approximate exchange algorithm is specified. The analysis of the 2012 data, collected before the weather disturbances, reveals four clusters. The four groups highlight the primary habitat patterns in the 2012 GBR, each with distinct ecological characteristics: (1) areas with above-average soft coral abundance, (2) sand-dominated regions commonly found in the central part, (3) southern reefs with a more balanced distribution of species, and (4) habitats dominated by algae and hard corals. Compared to subsequent surveys conducted after disturbances, there is evidence of a decline in the number of clusters and a simplification of reef composition at the regional scale.