On the Fractal Dimension of Ecotones among African Vascular Plants

Ecotones are transition zones of plant species compositional turnover, with inherent fractal characteristics corresponding to the shape of boundaries between adjacent bioregions. We characterize present-day ecotones of vascular plants across mainland sub-Saharan Africa and investigate environmental factors associated with their shapes. Specifically, we explore, (1) whether a fractal dimension is appropriate for characterizing the spatial patterns of ecotones, and (2) how the fractal dimensions of present-day ecotones may vary along latitudes and reflect other environmental contrasts between adjacent bioregions. Distributions of 23,189 vascular plant species were partitioned into bioregions across mainland sub-Saharan Africa according to the nonmetric multidimensional scaling (MDS) of Jaccard dissimilarity at 20 km resolution. The optimal number of clusters was determined using K-medoids and Clustering Large Applications (CLARA) algorithms, with the clustering validity evaluated using the silhouette coefficient. The present-day ecotones were then extracted as boundaries between adjacent bioregions, and their spatial patterns measured by the box-counting fractal dimension. Using generalized additive models (GAMs), we explained the variation of the fractal dimensions of present-day ecotones by the absolute differences in mean annual precipitation, mean annual temperature, bulk density, soil clay content, soil sand content, soil organic carbon, soil pH, topographic roughness, fire frequency, human footprint, geographic extent, and latitude, separately, between two adjacent bioregions. The MDS performed reasonably well (stress = 0.057), while CLARA succeeded in partitioning seven geographically distinct clusters (0.49 silhouette coefficient), from which 11 ecotones were identified, with eight characterized as true fractals but having low fractal dimensions (range: from 1.018 to 1.154). The GAM identified the difference in mean annual precipitation as significant (P = 0.02) for explaining the variation of the fractal dimensions of present-day ecotones with the difference in soil organic carbon near-significant (P = 0.07). The fractal dimensions also showed a moderate correlation with the difference in human footprint between adjacent bioregions (Spearman’s rho = 0.619), albeit not significant (P = 0.11). Overall, by spatially characterizing the present-day ecotones between different bioregions, we showed that the fractal dimension is an appropriate method for shape quantification and characterization of ecotones. We further highlighted key environmental factors that could explain the formation of present-day ecotones and thus the compositional turnover of vascular plant species across sub-Saharan Africa.