5 - Geometry of species distributions: random clustering and scale invariance

Summary

Introduction

Spatial biodiversity patterns are tightly related to the patterns of spatial distribution of individual species. It has been recognized that the spatial distribution of individuals is never random nor homogeneous within some well-defined clusters but is aggregated on many spatial scales: individuals form clusters which themselves are aggregated into larger clusters and so on. The most useful way to capture these patterns is with fractal geometry, which treats such patterns as self-similar sets (Kunin, 1998; Halley et al., 2004). Indeed, it has been shown that species spatial distribution is often close to fractal (Virkkala, 1993; Condit et al., 2000; Ulrich & Buszko, 2003) and that the assumption of fractality of species spatial distribution is appropriate for deriving multispecies macroecological patterns, namely the species–area relationship (Harte, Kinzig & Green, 1999; Šizling & Storch, 2004). By contrast, species sometimes reveal distributions that deviate from strict fractality (Hartley et al., 2004; He & Condit, this volume; Lennon et al., this volume). More importantly, although there are several ways in which fractal distributions could emerge (Halley et al., 2004), there is no strong biological reason why species spatial distribution should be exactly fractal, i.e. it is unclear which biological processes should produce fractal distribution.

Here we show that species spatial distributions which are very close to fractal can emerge from random processes leading to aggregation on several spatial scales. These processes have relatively straightforward biological interpretation and the spatial patterns they produce are in many parameters effectively undistinguishable from classical fractals.