Spatial variance in abundance and occupancy of corals across broad geographic scales

Species assemblages vary in structure due to a wide variety of processes operating at ecological and much broader biogeographical scales. Cross-scale studies of assemblage structure are necessary to fully understand this variability. Here, we evaluate the abundance and occupancy patterns of hierarchically sampled coral assemblages in three habitats (reef flat, crest, and slope) and five regions (Indonesia, Papua New Guinea, the Solomon Islands, American Samoa, and the Society Islands) across the west-central Pacific Ocean. Specifically, we compare two alternative models that unify spatial variance and occupancy via the negative binomial distribution. The first assumes a power-law scaling between the mean and variance of abundance; the second assumes a quadratic variance-mean relationship and a constant abundance-invariant aggregation parameter. Surprisingly, the well-established power-law model performs worse than the model assuming abundance-invariant aggregation, for both variance-mean and occupancy-abundance relationships. We also find strong evidence for regional and habitat variation in these relationships and in the levels of aggregation estimated by the abundance-invariant aggregation model. Among habitats, corals on reef flats exhibited lower occupancy and higher levels of aggregation compared to reef crests and slopes. Among regions, low occupancy and high aggregation were most pronounced across all habitats in American Samoa. These patterns may be related to habitat and regional differences in disturbance and recovery processes. Our results suggest that the spatial scaling of abundance and occupancy is sensitive to processes operating among these habitats and at regional scales. However, the consistency of these relationships across species within assemblages suggests that a theoretical unification of spatial variance and occupancy patterns is indeed possible.