Ostats - O-Stats, or Pairwise Community-Level Niche Overlap Statistics

O-statistics, or overlap statistics, measure the degree of community-level trait overlap. They are estimated by fitting nonparametric kernel density functions to each species’ trait distribution and calculating their areas of overlap. For instance, the median pairwise overlap for a community is calculated by first determining the overlap of each species pair in trait space, and then taking the median overlap of each species pair in a community. This median overlap value is called the O-statistic (O for overlap). The Ostats() function calculates separate univariate overlap statistics for each trait, while the Ostats_multivariate() function calculates a single multivariate overlap statistic for all traits. O-statistics can be evaluated against null models to obtain standardized effect sizes. 'Ostats' is part of the collaborative Macrosystems Biodiversity Project "Local- to continental-scale drivers of biodiversity across the National Ecological Observatory Network (NEON)." For more information on this project, see the Macrosystems Biodiversity Website (<https://neon-biodiversity.github.io/>). Calculation of O-statistics is described in Read et al. (2018) <doi:10.1111/ecog.03641>, and a teaching module for introducing the underlying biological concepts at an undergraduate level is described in Grady et al. (2018) <http://tiee.esa.org/vol/v14/issues/figure_sets/grady/abstract.html>.