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： 河流以其类似分形的特性而闻名，这些特性导致了连接网络几何和大小的尺度定律的存在。 然而，这些几何关系可能并不一定能够捕捉到最直接影响生态过程（如生物多样性的产生和维持）的空间特征。 另一方面，连通性度量已被理论和实证研究证明会影响相关的大型生态结果。 因此，在本工作中，我们通过分析全球超过1000条河流获得的网络，建立了河流网络连通性随系统规模变化的规律。 具体而言，我们发现和谐中心性和介数中心性这两种网络连通性度量都表现出明显的幂律尺度变化。 随后，我们通过将最优渠道网络（OCN）模型拟合到每条真实河流上，创建了一个合成河流网络数据集，以询问OCN是否在连接性尺度定律方面与实证河流网络相同，OCN被广泛用于许多理论研究中表示河流。 我们发现实证和基于OCN的尺度定律之间有很好的一致性，这支持了OCN可以在基于网络的模型和分析中准确表示河流的观点。 最后，我们通过改变物种移动策略，从完美的最短路径导航到无偏随机游走，检验了连接性尺度定律的鲁棒性。 令人惊讶的是，我们发现随机游走移动破坏了和谐中心性的幂律尺度关系，但并未破坏介数中心性。 显示英文摘要

摘要： Rivers are well-known to exhibit fractal-like properties that lead to existence of scaling laws that link network geometry and size. However, these geometric relations might not necessarily capture the spatial features that most directly influence ecological processes such as the generation and maintenance of biodiversity. Connectivity metrics, on the other hand, have been shown both theoretically and empirically to influence relevant large-scale ecological outcomes. Therefore, in this work, we establish how river network connectivity scales with system size by analyzing networks obtained for more than 1000 rivers across the globe. Specifically, we found clear power-law scaling of both the Harmonic and Betweenness centrality network connectivity metrics. We then created a synthetic river network dataset by fitting an Optimal Channel Network (OCN) model to each real river, to ask if OCNs, which are widely used to represent rivers in many theoretical studies, exhibit the same connectivity scaling laws as empirical river networks. 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 by varying species movement strategies from perfect shortest-path navigation to unbiased random walks. Surprisingly, we found that random walk movement breaks the power-law scaling relationship for harmonic, but not for betweenness centrality.