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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.
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This content will become publicly available on March 21, 2026
Unifying spatial scaling laws of biodiversity and ecosystem stability
While both species richness and ecosystem stability increase with area, how these scaling patterns are linked remains unclear. Our theoretical and empirical analyses of plant and fish communities show that the spatial scaling of ecosystem stability is determined primarily by the scaling of species asynchrony, which is in turn driven by the scaling of species richness. In wetter regions, plant species richness and ecosystem stability both exhibit faster accumulation with area, implying potentially greater declines in biodiversity and stability following habitat loss. The decline in ecosystem stability after habitat loss can be delayed, creating a stability debt mirroring the extinction debt of species. By unifying two foundational scaling laws in ecology, our work underscores that ongoing biodiversity loss may destabilize ecosystems across spatial scales.
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- Award ID(s):
- 2224852
- PAR ID:
- 10656574
- Publisher / Repository:
- AAAS
- Date Published:
- Journal Name:
- Science
- Volume:
- 387
- Issue:
- 6740
- ISSN:
- 0036-8075
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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