A new centrality index designed for multilayer networks

Abstract

Since its inception, the keystone species concept has become a central theoretical framework in ecology. Among many approaches, keystones have been operationalized in natural and human environments using centrality metrics applied to monolayer networks. Despite the great success of this approach, as species make several types of interactions, recent studies on keystones moved from monolayer to multilayer networks. To help fulfil the need for a centrality metric designed for multilayer networks, here we introduce Gnorm. We tested the performance of our new metric using in silico data in addition to an empirical data set of frugivory and nectarivory interactions between bats and plants in the Neotropics. A comparison between the results obtained with different random and scale-free networks demonstrates the performance of our new metric. First, a modularity analysis based on the multilayer version of the Louvain algorithm enables the modules to be composed of nodes from different layers. Second, by setting the coupling parameter ((Formula presented.)) and the resolution parameter ((Formula presented.)), module identity changes gradually, from single- to multiple-node modules and from mono- to multilayer composition. Third, we check the number of modules from different layers to which a node belongs (G) at different levels of (Formula presented.) and (Formula presented.). Finally, by observing how average G decreases with (Formula presented.) and (Formula presented.), it is possible to calculate Gnorm and detect which nodes are most resistant to change in these two parameters. Those resistant nodes are identified as central in the multilayer structure. After applying this new analysis to the bat–plant network, we observed that it identified a different set of potential keystone species compared to previous analyses performed separately for each layer or the aggregated network. In conclusion, our new metric opens a new way of operationalizing the keystone species concept in multilayer networks. It may help identify keystone species involved in different interaction types.