Quantifying spatial structure of volumetric neutral models

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.