Spatial analyses for nonoverlapping objects with size variations and their application to coral communities

Spatial distributions of individuals are conventionally analysed by representing objects as dimensionless points, in which spatial statistics are based on centre-to-centre distances. However, if organisms expand without overlapping and show size variations, such as is the case for encrusting corals, interobject spacing is crucial for spatial associations where interactions occur. We introduced new pairwise statistics using minimum distances between objects and demonstrated their utility when examining encrusting coral community data. We also calculated the conventional point process statistics and the grid-based statistics to clarify the advantages and limitations of each spatial statistical method. For simplicity, coral colonies were approximated by disks in these demonstrations. Focusing on short-distance effects, the use of minimum distances revealed that almost all coral genera were aggregated at a scale of 1-25 cm. However, when fragmented colonies (ramets) were treated as a genet, a genet-level analysis indicated weak or no aggregation, suggesting that most corals were randomly distributed and that fragmentation was the primary cause of colony aggregations. In contrast, point process statistics showed larger aggregation scales, presumably because centre-to-centre distances included both intercolony spacing and colony sizes (radius). The grid-based statistics were able to quantify the patch (aggregation) scale of colonies, but the scale was strongly affected by the colony size. Our approach quantitatively showed repulsive effects between an aggressive genus and a competitively weak genus, while the grid-based statistics (covariance function) also showed repulsion although the spatial scale indicated from the statistics was not directly interpretable in terms of ecological meaning. The use of minimum distances together with previously proposed spatial statistics helped us to extend our understanding of the spatial patterns of nonoverlapping objects that vary in size and the associated specific scales.