A correlation of species and genetic diversity has been proposed but not uniformly supported. Large-scale DNA barcoding provides qualitatively novel data to test for correlations across hierarchical levels (genes, genealogies and species), and may help to unveil the underlying processes. Here we analyse sequence variation in communities of aquatic beetles across Europe (>5,000 individuals) to test for self-similarity of beta diversity patterns at multiple hierarchical levels. We show that community similarity at all levels decreases exponentially with geographic distance, and initial similarity is correlated with the lineage age, consistent with a molecular clock. Log-log correlations between lineage age, number of lineages, and range sizes, reveal a fractal geometry in time and space, indicating a spatio-temporal continuum of biodiversity across scales. Simulations show that these findings mirror dispersal-constrained models of haplotype distributions. These novel macroecological patterns may be explained by neutral evolutionary processes, acting continuously over time to produce multi-scale regularities of biodiversity.