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 proc esses. Recent studies have used increasingly complex neutral models that in corporate contagion and other constraints on random patterns, as well as us ing neutral landscapes as input to spatial simulation models. Here, I consi der a common mathematical framework based on spectral transforms that repre sents all neutral landscape models in terms of sets of spectral basis funct ions. Fractal and multi-fractal models are considered, as well as models wi th multiple scaling regions and anisotropy. All of the models considered ar e shown to be variations on a basic theme: a scaling relation between frequ ency and amplitude of spectral components. Two example landscapes examined showed long-range correlations (distances up to 1000 km) consistent with fr actal scaling.