We discuss recent methodological developments in inhomogeneous summary statistics and envelope testing and study their applications in the field of spatial point pattern analysis. Specifically, we use these methods to test McGill’s theory of biodiversity. This theory is based upon three axioms: individuals of the same species cluster together, many rare species co-exist with a few common ones and individuals of different species grow independently of each other. We assess the validity of the first and third axioms for data obtained from a 50 hectare plot on Barro Colorado Island.
- Clustering within species
- ndependence between species
- Inhomogeneous summary statistics
- Spatial point pattern
- Rank and global envelope tests