Recognizing and valuing the full range of ecosystem services, and the need for managing ecosystems accordingly, is a top priority in both ecological research and management. The world has already experienced several catastrophic events where ecosystem services have been lost, with far-reaching consequences for humans. However, even though specific species are providing the services, these species are always incorporated in a larger network interacting with numerous other species. As such, disturbance of a single species in the system has the potential to reverberate through the network and cause other, possibly distantly connected, species to go extinct, with implications for the system’s ecosystem service provisioning. Simultaneously, ecosystems are facing threats, of varying severity for different species. Here we present a method based on Bayesian networks for analyzing how threats posed to a complex system of interacting species affect ecosystem service delivery. We showcase this by using a dataset from the Baltic sea food web that includes interacting species, set of specific threats affecting them and a set of ecosystem services they provide. Our results show that negative effects of certain threats percolates widely in the ecosystem and are causing extensive damage to ecosystem service delivery. Our methods highlight the importance of accounting for the network structure in ecosystem service management.