Nearest Neighbor Methods for Testing Reflexivity and Species-Correspondence

TL;DR

This paper introduces new statistical tests based on nearest neighbor relationships to analyze spatial patterns, reflexivity, and species correspondence, with demonstrated effectiveness through simulations and ecological data application.

Contribution

It develops novel contingency tables and tests for reflexivity and species correspondence in spatial data, expanding the analytical tools for ecological pattern analysis.

Findings

New NN reflexivity contingency table (NN-RCT) effectively tests reflexivity.

Proposed species-correspondence test captures habitat specificity.

Methods show good empirical size and power in simulations.

Abstract

Nearest neighbor (NN) methods are employed for drawing inferences about spatial patterns of points from two or more classes. We consider Pielou's test of niche specificity which is defined using a contingency table based on the NN relationships between the data points. We demonstrate that Pielou's contingency table for niche specificity is actually more appropriate for testing reflexivity in NN structure, hence we call this table as NN reflexivity contingency table (NN-RCT) henceforth. We also derive an asymptotic approximation for the distribution of the entries of the NN-RCT and consider variants of Fisher's exact test on it. Moreover, we introduce a new test of class- or species-correspondence inspired by spatial niche/habitat specificity and the associated contingency table called species-correspondence contingency table (SCCT). We also determine the appropriate null hypotheses and the underlying conditions appropriate for these tests. We investigate the finite sample performance of the tests in terms of empirical size and power by extensive Monte Carlo simulations and the methods are illustrated on a real-life ecological data set.