Beyond Least-Cost Paths: An Effective-Resistance Approach for Identifying Potentially Critical Patches in Urban Ecological Networks

The identification of key ecological patches is fundamental to the construction of ecological security patterns. The current Probability of Connectivity (PC) index and its associated delta (dPC) rely on least-cost path distances and assume that species disperse along a single optimal path, which may underestimate the ecological value of patches that act as multipath hubs. This study proposed computing the PC and dPC indices based on effective resistance from circuit theory. Using NetworkX, we obtained global effective resistance from adjacent-patch resistance, replaced least-cost path distance as the distance metric, and recalibrated the dispersal constant. To evaluate the method, we used a tree network (7 nodes, 6 edges), a cyclic network (8 nodes, 10 edges), and 640 random networks. In the tree network, the optimized method yielded the same ranking as the traditional method, confirming the computational consistency expected in a tree. In the cyclic network, the two methods diverged: Patch 8, whose connector was essentially zero under the conventional method, rose to the largest connector value (15.42%) and climbed from fifth to third place. Across the random networks, the two methods agreed in tree networks and diverged increasingly with topological redundancy. The effective-resistance method therefore makes visible a connector role that the single-path framework cannot detect and should be used to complement, rather than replace, the least-cost method; whether the identified patches are ecologically more critical, however, remains to be confirmed by empirical dispersal data.