Spectral representation of neutral landscapes

Pattern in ecological landscapes is often the result of different processes operating at different scales. Neutral landscape models were introduced in landscape ecology to differentiate patterns that are the result of simple random processes from patterns that arise from more complex ecological processes. Recent studies have used increasingly complex neutral models that incorporate contagion and other constraints on random patterns, as well as using neutral landscapes as input to spatial simulation models. Here, I consider a common mathematical framework based on spectral transforms that represents all neutral landscape models in terms of sets of spectral basis functions. Fractal and multi-fractal models are considered, as well as models with multiple scaling regions and anisotropy. All of the models considered are shown to be variations on a basic theme: a scaling relation between frequency and amplitude of spectral components. Two example landscapes examined showed long-range correlations (distances up to 1000 km) consistent with fractal scaling.