Emergent dual scaling of riverine biodiversity

Abstract

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.

Keywords: freshwater; metacommunity; network theory; scaling law; species diversity.

Fig. 1.

(A and B) Theoretical branching networks generated under contrasting landscape scenarios. Branching river networks are depicted as a network of connected habitat patches, in which the number of habitat patches $N_p$ and branching probability $P_b$ dictate the ecosystem size and complexity ($N_p=30$ and $P_b=0.2,0.8$ in this example). Environmental conditions at headwaters (i.e., the most upstream patches) are drawn randomly from a normal distribution and propagate downstream with local environmental noise (Materials and Methods). Habitat patches are colored in proportion to environmental values (similar colors have similar environmental values). A and B show distinct landscape scenarios. Environmental variation at headwaters ${\sigma }_h$ exceeds the degree of local environmental noise ${\sigma }_l$ in A (${\sigma }_h=1,{\sigma }_l=0.01$), while the opposite is true in B (${\sigma }_h=0.01,{\sigma }_l=1$). (C) Example of intensively surveyed watersheds in Hokkaido, Japan (the red-colored watershed in D). Red dots indicate sampling sites for fish surveys. (D) Map of study regions (Left, Hokkaido, Japan; Right, Midwest, United States). Watersheds (i.e., metacommunities) are gray shaded in proportion to the number of sampling sites.

Fig. 2.

Qualitative match between theoretical predictions and empirical patterns in power law scaling of biodiversity. (A) Theoretical predictions. Ecosystem size (the number of habitat patches) scales $\gamma$ diversity through increased $\alpha$ or $\beta$ diversity across ecological scenarios. Lines and shades are loess curves fitted to simulated data and their 95% CIs. Each panel represents different ecological scenarios under which metacommunity dynamics were simulated. Rows represent different competition strength. Competition coefficients ($b_{ij}$) were varied randomly from 0 to 1.5 (Top, strong competition) or 0.75 (Bottom, weak competition). Columns represent different dispersal scenarios. Two dispersal parameters were chosen to simulate scenarios with long-distance (the rate parameter of an exponential dispersal kernel $\theta =0.10$) and short-distance dispersal ($\theta =1.0$). In this simulation, environmental variability among headwaters (i.e., the most upstream patches), which is expressed as the SD of a normal distribution (${\sigma }_h=1.0$), was greater than that of local environmental noise occurring at each habitat patch (${\sigma }_l=0.01$). Dispersal probability $p_d$ was 0.01 for all the scenarios. (B) Empirical observations. Observed biodiversity patterns match theoretical predictions of power law scaling along the axis of ecosystem size. Dots represent watershed replicates (i.e., metacommunities), and lines are predicted values from the robust regression models (solid: siginificant relationships; dashed: insignificant). The estimated slopes (i.e., the scaling exponents) were consistent across geographically distant regions with distinct fish fauna (Top: Hokkaido, Japan; Bottom: Midwest, United States).

Fig. 3.

Qualitative match between theoretical predictions and empirical patterns in power law scaling of biodiversity. (A) Theoretical predictions. Ecosystem complexity (branching probability) scales $\gamma$ diversity through increased $\alpha$ or $\beta$ diversity across ecological scenarios. Lines and shades are loess curves fitted to simulated data and their 95% CIs. Each panel represents different ecological scenarios under which metacommunity dynamics were simulated. Refer to Fig. 2 for details. (B) Empirical observations. Observed biodiversity patterns match theoretical predictions of power law scaling along the axis of ecosystem complexity. Dots represent watershed replicates (i.e., metacommunities), and solid lines are predicted values from the robust regression models. The estimated slopes (i.e., the scaling exponents) were consistent across geographically distant regions with distinct fish fauna (Top: Hokkaido, Japan; Bottom: Midwest, United States).