Metapopulation stability in branching river networks

Intraspecific population diversity (specifically, spatial asynchrony of population dynamics) is an essential component of metapopulation stability and persistence in nature. In 2D systems, theory predicts that metapopulation stability should increase with ecosystem size (or habitat network size): Larger ecosystems will harbor more diverse subpopulations with more stable aggregate dynamics. However, current theories developed in simplified landscapes may be inadequate to predict emergent properties of branching ecosystems, an overlooked but widespread habitat geometry. Here, we combine theory and analyses of a unique long-term dataset to show that a scale-invariant characteristic of fractal river networks, branching complexity (measured as branching probability), stabilizes watershed metapopulations. In riverine systems, each branch (i.e., tributary) exhibits distinctive ecological dynamics, and confluences serve as "merging" points of those branches. Hence, increased levels of branching complexity should confer a greater likelihood of integrating asynchronous dynamics over the landscape. We theoretically revealed that the stabilizing effect of branching complexity is a consequence of purely probabilistic processes in natural conditions, where within-branch synchrony exceeds among-branch synchrony. Contrary to current theories developed in 2D systems, metapopulation size (a variable closely related to ecosystem size) had vague effects on metapopulation stability. These theoretical predictions were supported by 18-y observations of fish populations across 31 watersheds: Our cross-watershed comparisons revealed consistent stabilizing effects of branching complexity on metapopulations of very different riverine fishes. A strong association between branching complexity and metapopulation stability is likely to be a pervasive feature of branching networks that strongly affects species persistence during rapid environmental changes.