标题： 河流网络中连通性度量的尺度化 显示英文标题

标题： Scaling of connectivity metrics in river networks

摘要： 河流表现出与几何和大小相关的标度定律有关的分形特性。最优河网（OCN）模型是一种数学上易于处理的河网表示，常用于理论研究，它基于河流的分形特性，因此能够再现几何标度定律。然而，纯粹的几何关系可能无法完全捕捉河流结构与物种运动策略之间的相互作用，而这种相互作用对于许多大规模生态过程最为相关。相反，连通性是一个结合了生境几何和个体运动的概念，已被理论和实证研究证明在广泛生态系统中影响相关的大型生态结果。在这里，我们分析了全球超过1000条主要河流（包括亚马逊河、密西西比河和尼罗河）的网络，以研究河流网络连通性指标如何随系统规模变化。具体而言，我们发现谐波中心性和介数中心性这两个网络连通性指标都呈现出明显的幂律标度。为了评估OCN能否捕捉这些经验连通性模式，我们通过将OCN模型拟合到每条真实河流来生成合成河网。我们发现经验数据与基于OCN的标度定律之间有很好的一致性，这支持了OCN能够在基于网络的模型和分析中准确表示河流的观点。最后，我们检查了连通性标度定律对从理想最短路径导航到次优随机路径导航的各种物种运动策略的鲁棒性。令人惊讶的是，我们发现随机导航会破坏谐波中心性的幂律标度关系，但不会破坏介数中心性的幂律标度关系。 显示英文摘要

摘要： Rivers exhibit fractal-like properties that are associated with scaling laws linking geometry and size. The optimal channel network (OCN) model, which is a mathematically tractable representation of river networks often used in theoretical studies, is based on the fractal properties of rivers and consequently reproduces geometric scaling laws. However, purely geometric relationships may not fully capture the interaction between river structure and species' movement strategies that is most relevant to many large-scale ecological processes. In contrast, connectivity, which is a concept that blends habitat geometry and individual movement, has been shown both theoretically and empirically to influence relevant large-scale ecological outcomes across a broad array of ecosystems. Here, we analyze networks from more than 1000 major rivers around the world, including the Amazon, Mississippi, and Nile, to investigate how river network connectivity metrics scale with system size. Specifically, we found clear power-law scaling of both the harmonic centrality and betweenness centrality network connectivity metrics. To assess the extent to which OCNs can capture these empirical connectivity patterns, we generated synthetic river networks by fitting an OCN model to each real river. We found excellent agreement between empirical and OCN-based scaling laws, supporting the notion that OCNs can accurately represent rivers in network-based models and analyses. Finally, we examined the robustness of the connectivity scaling laws to species movement strategies ranging from ideal shortest-path navigation to suboptimal random-path navigation. Surprisingly, we found that random navigation breaks the power-law scaling relationship for harmonic centrality, but not for betweenness centrality.