Testing biodiversity using inhomogeneous summary statistics

TL;DR

This paper evaluates McGill's biodiversity axioms using inhomogeneous spatial point pattern statistics, addressing limitations of previous stationary assumptions to better understand species distribution patterns.

Contribution

It introduces inhomogeneous summary statistics to test key biodiversity axioms, improving analysis accuracy for spatially varying ecological data.

Findings

Confirmed clustering of same species individuals.

Supported independence of different species.

Demonstrated effectiveness of inhomogeneous statistics in ecological analysis.

Abstract

McGill's theory of biodiversity 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. Over the past decade, classical point pattern analyses have been employed to verify these axioms based on the false assumption of stationarity. In this paper, we use inhomogeneous versions of the classical summary statistics for spatial point patterns to assess the validity of McGill's first and third axioms for data obtained from a 50 hectare plot on Barro Colorado Island.