Synchronization unveils the organization of ecological networks with positive and negative interactions

Network science has helped to understand the organization principles of the interactions among the constituents of large complex systems. However, recently, the high resolution of the data sets collected has allowed to capture the different types of interactions coexisting within the same system. A particularly important example is that of systems with positive and negative interactions, a usual feature appearing in social, neural, and ecological systems. The interplay of links of opposite sign presents natural difficulties for generalizing typical concepts and tools applied to unsigned networks and, moreover, poses some questions intrinsic to the signed nature of the network, such as how are negative interactions balanced by positive ones so to allow the coexistence and survival of competitors/foes within the same system? Here, we show that synchronization phenomenon is an ideal benchmark for uncovering such balance and, as a byproduct, to assess which nodes play a critical role in the overall organization of the system. We illustrate our findings with the analysis of synthetic and real ecological networks in which facilitation and competitive interactions coexist.