Ecological Modelling 186 (2005) 312–325 Quantifying spatial structure of volumetric neutral models Lee Anne Kirkpatrick a , John F. Weishampel b, ∗ a Liberal Studies Program, University of Central Florida, Orlando, FL 32816-2368, USA b Department of Biology, University of Central Florida, 4000 Central Florida Blvd, Orlando, FL 32816-2368, USA Received 11 June 2004; received in revised form 31 December 2004; accepted 7 January 2005 Available online 26 February 2005 Abstract Neutral models in landscape ecology that have been used as a framework to analyze actual landscapes have been largely planar. However, the natural world is greater than two dimensions; hence, many ecological structures, e.g., forest canopies or coral reefs, are better represented by topographies or tomographies. Because pattern and process or structure and function are intertwined, it becomes necessary to develop methods to quantify these complex architectures. With the advent of remote sensing technologies such as lidars and sonars, that permit structural mapping of some of these systems, volumetric data are becoming more prevalent. In this study, we developed a suite of binary voxel-based neutral models that possessed random, anisotropic, and hierarchical properties. We then evaluated the extent to which fractal-derived measurements, i.e., lacunarity, the simple fractal dimension, and multifractal spectra, were able to discern among the constructed model types at two different densities (p = 0.02 and p = 0.05). Multifractal analysis, where spectra were defined by three parameters, was shown to be the most sensitive to the differences among the neutral structures. Lacunarity, defined by a single parameter, was shown to be fairly useful in discerning the structures. The simple fractal dimension was found to have limited capability. To more fully assess the ability of these and additional pattern recognition methods, better representations of natural morphologies need to be developed and analyzed. © 2005 Elsevier B.V. All rights reserved. Keywords: Forest canopy; Lacunarity; Multifractal; Neutral landscape model; Three-dimensional architecture; Voxel “Distress not yourself if you cannot at first understand the deeper mysteries of Spaceland.” —A. Square a.k.a. E.A. Abbott (1884) in Flatland: A Romance of Many Dimensions ∗ Corresponding author. Tel.: +1 407 823 6623; fax: +1 407 823 5769. E-mail address: jweisham@mail.ucf.edu (J.F. Weishampel). 1. Introduction The role of neutral models, like that of the null hy- pothesis, has been to provide a standard by which to compare observations (Caswell, 1976; Taylor, 1979; Thomas and Foin, 1982; Gotelli and Graves, 1996). In the field of landscape ecology, the neutral landscape model (NLM), void of all biotic and abiotic factors thought to contribute to the landscape structure, de- 0304-3800/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.ecolmodel.2005.01.056