Global environmental change is affecting species distribution and their interactions with other species. In particular, the main drivers of environmental change strongly affect the strength of interspecific interactions with considerable consequences for biodiversity. However, extrapolating the effects observed on pair-wise interactions to entire ecological networks is challenging. Here we propose a framework to estimate the tolerance to changes in the strength of mutualistic interaction that species in mutualistic networks can sustain before becoming extinct. We identify the scenarios where generalist species can be the least tolerant. We show that the least tolerant species across different scenarios do not appear to have uniquely common characteristics. Species' tolerance is extremely sensitive to the direction of change in the strength of mutualistic interaction, as well as to the observed mutualistic trade-offs between the number of partners and the strength of the interactions.