A Simple Spatial Method for Identifying Point Clusters by Neighbourhood Relationships

Neftalí Sillero

doi:10.3390/ecologies2030017

Abstract

Point events can be distributed regularly, randomly, or in clusters. A cluster of points is defined by the distance from which any point included in a cluster is farther from any other point outside the cluster. Many solutions and methods are possible to define clustering distance. I present here a simple method, nearest neighbour index clustering (NNIC), which separately identifies local clusters of points using only their neighbourhood relationships based on the nearest neighbour index (NNI). It computes a Delaunay triangulation among all points and calculates the length of each line, selecting the lines shorter than the expected nearest neighbour distance. The points intersecting the selected Delaunay lines are considered to belong to an independent cluster. I verified the performance of the NNIC method with a virtual and a real example. In the virtual example, I joined two sets of random point processes following a Poisson distribution and a Thomas cluster process. In the real example, I used a point process from the distribution of individuals of two species of Iberian lizards in a mountainous area. For both examples, I compared the results with those of the nearest neighbour cleaning (NNC) method. NNIC selected a different number of clustered points and clusters in each random set of point processes and included fewer points in clusters than the NNC method.

Highlights

How are events distributed across space? This is a very frequent question asked by researchers from many different disciplines, such as epidemiology [1], neurosciences [2], criminology [3], econometrics [4], agronomy [5], forestry [6], or ecology [7,8]
The nearest neighbour index (NNI) considers that a point process is clustered when the mean nearest neighbour distance is lower than the expected one
Ecologies 2021, 1, In the virtual example, nearest neighbour index clustering (NNIC) selected a different number of clustered points and clusters in each random set of point processes (Table S1)

Summary

Introduction

How are events distributed across space? This is a very frequent question asked by researchers from many different disciplines, such as epidemiology [1], neurosciences [2], criminology [3], econometrics [4], agronomy [5], forestry [6], or ecology [7,8]. It is important to know whether events are distributed regularly, randomly, or in clusters [9]. One famous example of the importance of analysing the distribution patterns of events is the epidemiological study performed by John Snow in 1854 [10]. He related the spatial location of water pumps with the incidence of cholera in London. The probabilities of finding events and empty areas are similar. The probability of finding a second event near the first one and of finding areas without events are very high but mutually exclusive

Methods

Results

Conclusion