Emergent dual scaling of riverine biodiversity

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.

Ecologists have long sought to understand the general drivers of biodiversity. One of the most robust empirical generalizations in ecology is the positive relationship between species richness and area, that is, the species–area relationship (the SAR) (1). In 1921, Arrhenius (2) formulated the SAR as a power law S=cAz, an equation currently known as the Arrhenius SAR (S is the number of species observed in a given geographic area A, c the constant, and z the scaling exponent). Since then, the spatial scaling of species richness has been observed in many taxonomic groups (3). The SAR is ubiquitous because multiple mechanisms produce an apparently similar pattern. Larger ecosystems typically support more diverse metacommunities due to increased habitat diversity (4), larger metacommunity size (5), and/or enhanced colonization dynamics (6). Importantly, the SAR provides the foundation for global conservation efforts (7–9). For example, conservation ecologists have used SAR estimates to design marine and terrestrial protected areas (7, 8), which currently encompass more than 30 million km² globally (10).Many ecosystems, however, possess a complex spatial structure that cannot be represented by area—a dimension referred to as scale-invariant complexity (11, 12). Such complexity is evident in branching ecosystems, including rivers, trees, and mountain ranges, to name just a few (12). Geomorphic or biological processes generate a pronounced self-similarity in complex branching patterns such that the part and the whole look alike (12). Even though the branching structure is independent of spatial scale, it forms a physical template that dictates habitat diversity and dispersal corridors for living organisms (13). Limited but accumulating evidence suggests that classical metapopulation and metacommunity theories cannot predict ecological dynamics driven by branching structure (14–16), and this recognition has led to recent developments of spatial theories devoted to complex branching ecosystems (17). For example, these studies have highlighted key roles of branching structure in driving local biodiversity patterns, such as increased species richness at merging points of branches (18). However, most research has explored the consequences of branching complexity for local community structure (19) or has relied solely on theoretical arguments with limited replications of branching architecture (20). At present, we lack a comprehensive evaluation of how branching complexity scales biodiversity patterns at the metacommunity level. Filling this knowledge gap may provide common ground for achieving successful conservation in spatially complex ecosystems, where accelerated species loss threatens the delivery of ecosystem services (21).Here, we propose a unified framework of ecosystem size and complexity in scaling biodiversity patterns in rivers—a prime example of complex branching ecosystems. Individual streams and rivers flow through different landscapes with distinct geological and climatic backgrounds, serving as a spatial unit of unique in-stream environments (16, 22–27). The recurrent merging of diverse tributaries ultimately forms a fluvial network with fractal branching patterns (12). As such, the complexity of branching structure, which we define here as the probability of branching per unit river distance (24, 28), may represent a macroscale control of the ecosystem’s habitat heterogeneity (habitat diversity per unit area) (13, 23, 24). Meanwhile, ecosystem size (watershed area) should determine the metacommunity size and total habitat diversity (area times heterogeneity), two factors that regulate biodiversity at the metacommunity level (4, 5). Hence, riverine biodiversity may manifest scaling laws along the two orthogonal dimensions of branching networks. We call this the dual scaling hypothesis of biodiversity.The present study combines theory and analysis of extensive community data from two different regions of the globe to show that multiple ecological pathways converge to the emergence of dual diversity scaling. Specifically, watershed-scale species richness (γ diversity) followed power laws with ecosystem size A and branching probability Pb as γ=cAξ1Pbξ2 (ξ1 and ξ2 are the scaling exponents) regardless of ecological contexts. However, contributing factors of increased γ diversity—either enhanced local species richness (α diversity) and/or spatial variation of species composition (β diversity)—depended on constituent species’ characteristics. Our findings suggest that the dual scaling law is a pervasive yet overlooked feature of complex ecosystems with important implications for biodiversity conservation.