The power of 3D fractal dimensions for comparative shape and structural complexity analyses of irregularly shaped organisms

1. The increasing interest in 3D morphological approaches for addressing evolutionary and ecological questions has driven the need for reliable, efficient, and easily accessible methods for shape quantification and complexity characterization. This applies in particular to irregularly shaped organisms, such as stony corals, which are challenging to study using traditional morphometric analyses. 2. A potential approach to assess shape and spatial complexity of 3D documented organisms are 3D fractal dimension analyses that combine information from various spatial scales, thus enabling a holistic shape quantification. Therefore, the latest 3D scanning technology and fractal dimension analyses were used to test the performance of this novel combination of methods for quantifying inter- and intraspecific differences in shape and spatial complexity of highly irregularly shaped organisms. As model taxa, six widespread species of stony corals were used, belonging to the genera Acropora, Pocillopora and Porites. First, high-resolution shape models of coral colonies were generated using 3D structured light scanning. Then the univariate fractal dimension D and the multivariate multiscale fractal dimension as well as two traditional univariate morphological measures (surface-volume ratio and rugosity) were calculated. Finally all parameters were tested for significant interspecific and intraspecific differences, and the discriminative power of the two fractal dimension and the two traditional measures were assessed. 3. The results show that 3D shape analyses based on fractal dimensions can be used to quantify both inter- and intraspecific variations in irregularly shaped organisms such as corals. Compared to traditional methods, fractal dimensions performed at least as good at the interspecific level and considerably better at the intraspecific level. 4. This study demonstrates that 3D fractal dimension analyses are an efficient and easily applicable method for shape quantification and complexity characterization of irregularly shaped organisms, such as stony corals. Given the specific properties of fractal dimensions, they may either serve as an alternative complexity measure or as an additional characteristic for studying irregularly shaped organisms. Ultimately, fractal dimensions may provide a more integrative understanding of morphological variation within an ecological and evolutionary context, and could open up new opportunities for semi-automatic or automatic species determination based on 3D morphological images.