A prevailing paradigm suggests that species richness increases with area in a decelerating way. This ubiquitous power law scaling, the species-area relationship, has formed the foundation of many conservation strategies. In spatially complex ecosystems, however, the area may not be the sole dimension to scale biodiversity patterns because the scale-invariant complexity of fractal ecosystem structure may drive ecological dynamics in space. Here, we use theory and analysis of extensive fish community data from two distinct geographic regions to show that riverine biodiversity follows a robust scaling law along the two orthogonal dimensions of ecosystem size and complexity (i.e., the dual scaling law). In river networks, the recurrent merging of various tributaries forms fractal branching systems, where the prevalence of branching (ecosystem complexity) represents a macroscale control of the ecosystem's habitat heterogeneity. In the meantime, ecosystem size dictates metacommunity size and total habitat diversity, two factors regulating biodiversity in nature. Our theory predicted that, regardless of simulated species' traits, larger and more branched "complex" networks support greater species richness due to increased space and environmental heterogeneity. The relationships were linear on logarithmic axes, indicating power law scaling by ecosystem size and complexity. In support of this theoretical prediction, the power laws have consistently emerged in riverine fish communities across the study regions (Hokkaido Island in Japan and the midwestern United States) despite hosting different fauna with distinct evolutionary histories. The emergence of dual scaling law may be a pervasive property of branching networks with important implications for biodiversity conservation.
