Multifractal analysis of neutral community spatial structure

Dead but not forgotten: complexity of Acropora palmata colonies increases with greater composition of dead coral

Coral reefs are highly biodiverse ecosystems that have declined due to natural and anthropogenic stressors. Researchers often attribute reef ecological processes to corals' complex structure, but effective conservation requires disentangling the contributions of coral versus reef structures. Many studies assessing the relationships between reef structure and ecological dynamics commonly use live coral as a proxy for reef complexity, disregarding the contribution of dead coral skeletons to reef habitat provision or other biogeochemical reef dynamics. This study aimed to assess the contribution of dead coral to reef complexity by examining structural variations in live and dead Acropora palmata colonies. We used photogrammetry to reconstruct digital elevation models (DEMs) and orthomosaics of the benthic region immediately surrounding 10 A. palmata colonies. These reconstructions were used to quantify structural metrics, including surface rugosity, fractal dimension, slope, planform curvature, and profile curvature, as a function of benthic composition (i.e., live A. palmata, dead A. palmata, or non-A. palmata substrate). The results revealed that dead coral maintained more varied profile curvatures and higher fractal dimensions than live or non-coral substrate. Conversely, A. palmata colonies with a higher proportion of live coral displayed more uniform structure, with lower fractal dimensions and less variability in profile curvature measures. Other metrics showed no significant difference among substrate types. These findings provide novel insights into the structural differences between live and dead coral, and an alternative perspective on the mechanisms driving the observed structural complexity on reefs. Overall, our results highlight the overlooked potential contributions of dead coral to reef habitat provision, ecological processes, and other biogeochemical reef dynamics, and could have important implications for coral reef conservation.

Seagrass macrofaunal abundance shows both multifractality and scale-invariant patchiness

Spatial patterns of abundance of the whole macrobenthic assemblage and of its 10 most numerous species were examined across hierarchically nested scales within a 0.85 ha area of intertidal seagrass in subtropical Moreton Bay, Queensland. Multifractality characterised the assemblage and all ten dominant species across those scales (c. 33, 130, 530 & 2115 m²), with patchiness of assemblage numbers and those of at least some dominants exhibiting scale-invariance. The system displayed several abundance peaks, 12% of stations accounting for 88% of total variance, with many individual dominants showing a series of non-overlapping 'hot-spots'. Scale invariance and multifractality occurred notwithstanding low levels of species interaction consequent on maintenance at very low density. This suggests that critical self-organisation cannot be responsible for such patterning. Contrary to received wisdom, coefficient β of Taylor's power-law cannot form an index of aggregation, although it does indicate direction of change in dispersion pattern with changing numbers.

mfSBA: Multifractal analysis of spatial patterns in ecological communities

Multifractals have been applied to characterize complex communities in a spatial context. They were developed for nonlinear systems and are particularly suited to capture multiplicative processes observed in ecological systems. Multifractals characterize variability in a scale-independent way within an experimental range. I have developed an open-source software package to estimate multifractals using a box-counting algorithm (available from https://github.com/lsaravia/mfsba and permanently available at doi: 10.5281/zenodo.8481). The software is specially designed for two dimensional (2D) images such as the ones obtained from remote sensing, but other 2D data types can also be analyzed. Additionally I developed a new metric to analyze MULTISPECIES SPATIAL PATTERNS WITH MULTIFRACTALS: spatial rank surface, which is included in the software.