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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. 

Abstract AimClimate variability threatens to destabilize production in many ecosystems. Asynchronous species dynamics may buffer against such variability when a decrease in performance by some species is offset by an increase in performance of others. However, high climatic variability can eliminate species through stochastic extinctions or cause similar stress responses among species that reduce buffering. Local conditions, such as soil nutrients, can also alter production stability directly or by influencing asynchrony. We test these hypotheses using a globally distributed sampling experiment. LocationGrasslands in North America, Europe and Australia. Time periodAnnual surveys over 5 year intervals occurring between 2007 and 2014. Major taxa studiedHerbaceous plants. MethodsWe sampled annually the per species cover and aboveground community biomass [net primary productivity (NPP)], plus soil chemical properties, in 29 grasslands. We tested how soil conditions, combined with variability in precipitation and temperature, affect species richness, asynchrony and temporal stability of primary productivity. We used bivariate relationships and structural equation modelling to examine proximate and ultimate relationships. ResultsClimate variability strongly predicted asynchrony, whereas NPP stability was more related to soil conditions. Species richness was structured by both climate variability and soils and, in turn, increased asynchrony. Variability in temperature and precipitation caused a unimodal asynchrony response, with asynchrony being lowest at low and high climate variability. Climate impacted stability indirectly, through its effect on asynchrony, with stability increasing at higher asynchrony owing to lower inter‐annual variability in NPP. Soil conditions had no detectable effect on asynchrony but increased stability by increasing the mean NPP, especially when soil organic matter was high. Main conclusionsWe found globally consistent evidence that climate modulates species asynchrony but that the direct effect on stability is low relative to local soil conditions. Nonetheless, our observed unimodal responses to variability in temperature and precipitation suggest asynchrony thresholds, beyond which there are detectable destabilizing impacts of climate on primary productivity.