No evidence for fractal scaling in canopy surfaces across a diverse range of forest types

Abstract

Abstract Canopy structural complexity is a key emergent property of forest ecosystems that directly relates to their ability to store carbon, cycle water and nutrients, and provide habitat for biodiversity. However, we lack a general framework for quantifying the structural complexity of forest canopies, and it remains to be seen if there are simple rules that explain the huge variation in canopy structure that we observe across the world's forests. A leading candidate for characterizing differences in structural complexity among forest ecosystems are fractal scaling laws, or measures of statistical self‐similarity. If forest canopies were fractal in nature, their structural attributes could be distilled into a single coefficient—their fractal dimension—which could then be used to directly compare structural differences within and across biomes. To test this idea, we used airborne laser scanning (ALS) data acquired across nine landscapes in Australia that span a huge environmental gradient and include everything from dry shrublands, tropical savannas, dense rainforests, to 90 m tall Mountain Ash forests. Using the ALS data, we built high‐resolution 3D canopy height models of each landscape so that we could quantify how closely they followed fractal scaling laws, based on a comprehensive set of fractal dimension estimators. Across all ecosystem types, fractal scaling assumptions were consistently violated, with clear and systematic differences between real‐world forest canopies and simulated fractal surfaces. However, deviations from fractality did vary predictably among sites, with forests in less arid environments, dominated by tall trees with large crowns, exhibiting a higher degree of self‐similarity across scales. Synthesis: Our study conclusively shows that canopy surfaces are not fractal beyond the scale of individual tree crowns. Nevertheless, we still observed ecologically meaningful and generalisable patterns in forest structure across scales, which closely reflect biophysical and physiological constraints on tree size and architecture. These patterns point the way towards a more general framework for characterizing ecological complexity.