The analysis of the dynamics of interaction networks (i.e. trophic webs) better capture the state of ecosystem facing a perturbation than individual species dynamics could. We propose a framework that examines network robustness to a given perturbation at the local (species), mesoscale (species directly linked together) and global (network) level, based on traits and the topology of the network. Using the Celtic Sea as an example, we showed that the network was the least robust to the simulated loss of forage taxa and the most exposed taxa to fishing pressure, indicating conservation priority could be focused on these taxa. However estimating the sensitivity to fishing at the taxa ‘level was insufficient to predict the robustness of the network. The network appeared relatively robust to the simulated loss of the most central taxa, suggesting that mesoscale metrics such as centrality, although widely used, are not always adapted to prioritize species conservation.