Using empirical and simulation approaches to quantify merits of rival measures of structural complexity in marine habitats

Ecosystem engineers often affect structural complexity of habitats. There are multiple methods of quantifying complexity, variously measuring topography, surface area, volume, fractal dimension, or rugosity. We compared eight methods, four employing the 3D modelling program 'Blender' to estimate total surface area, top surface area, their ratio, and interstitial volume; and four empirically measuring interstitial volume, fractals and two indices of rugosity. We compared these using seven metrics: 1) correlations among comparable measures; 2) consistency; 3) accuracy; 4) precision; 5) discrimination among configurations of objects; 6) discernment of complexities among zones on rocky shores; and 7) practicality. Of the eight methods, the virtual volumetric method, Blender interstitial volume, performed the best. Direct measurements of three-dimensional space related more closely to patterns in biodiversity than did measurements of two-dimensional space or indirect measures of complexity like fractals. Blender interstitial volume is thus the recommended means of measuring structural complexity of benthic environments