Graph-theoretic connectivity measures: what do they tell us about connectivity?

Graph-theoretic connectivity analyses have received much attention in connectivity evaluation during the last few years. Here, we explore the underlying conceptual differences of various graph-theoretic connectivity measures. Based on connectivity analyses from three reserve networks in forested landscapes in Central Finland, we illustrate how these conceptual differences cause inconsistent connectivity evaluations at both the landscape and patch level. Our results also illustrate how the characteristics of the networks (patch density) may affect the performance of the different measures. Many of the connectivity measures react to changes in habitat connectivity in an ecologically undesirable manner. Patch prioritisations based on a node removal analysis were sensitive to the connectivity measure they were based on. The patch prioritisations derived from different measures showed a disparity in terms of how much weight they put on patch size versus patch location and how they value patch location. Although graphs operate at the interface of structure and function, there is still much to do for incorporating the inferred ecological process into graph structures and analyses. If graph analyses are going to be used for real-world management and conservation purposes, a more thorough understanding of the caveats and justifications of the graph-theoretic connectivity measures will be needed.