Deriving spatially-explicit beta diversity metrics from spatially-implicit, plot-based data
Knowledge of species distributions across a landscape can shed light on the processes structuring ecological communities and provide insight into conservation interventions to protect species from human impacts. Given data on the locations of individual organisms at known coordinates in space, a species' spatial pattern is often described using spatially-explicit, two-point metrics, such as Ripley's K or the O-ring statistic, that describe the conditional presence or abundance of the species at one location given its known presence or abundance at a second location. While these metrics are particularly useful for describing beta diversity and species turnover, the coordinate data on individual locations that are generally used to fit these functions may be difficult and expensive to collect. Here I demonstrate that it is also possible to fit these spatial point pattern metrics using spatially-implicit, one-point data on counts of the abundance of a species in disjoint plots or cells of different areas. This method is general and numerical and does not depend on assumptions regarding the processes that generate the spatial pattern.
This procedure is shown to accurately capture the shape of the O-ring statistic for 591 tree species across two tropical and one temperate forest. The approach is shown to exhibit biases, however, in the presence of range restriction, predicting an overly steep slope for the O-ring metric. These equations are then applied to explore the spatially-explicit patterns that are compatible with the spatially-implicit predictions of maximum entropy theories in ecology, finding that at least one existing theory predicts a spatial pattern that is very unlikely to exist in the field. This method can be applied broadly to the study of point processes and has particular importance for the characterization of beta diversity and species turnover in spatial ecology.