Oceanic islands harbor high levels of endemism, making them conservation priorities, yet their ecosystems are especially vulnerable to anthropogenic disturbance, particularly biological invasions. Assessing the impacts of introduced species is especially challenging when they establish mutualistic interactions with native taxa, as occurs in plant-pollinator systems, creating complex networks shaped by both mutualistic and competitive interactions. In this context, mathematical models represent an invaluable tool to investigate how the introduction (or removal) of an alien species cascades through interaction networks. Here, we propose a process-based mathematical model that captures plant-pollinator dynamics mediated by reward resources. We apply the model to empirical networks, collected over two years on two islands of the Galapagos archipelago, including both native and non-native species. By simulating the removal of plants, pollinators, or both, we quantitatively assess how invasions influence native communities. Our results reveal pronounced heterogeneity in the net effect of introduced species, whose presence can generate both positive and negative outcomes for native taxa. The model further disentangles direct from indirect interactions, showing how cascading effects through the network can substantially alter community responses. Additionally, we highlight the importance of co-invasions, where multiple non-native species reinforce each other’s persistence and impact.  Although further calibration is required for direct management applications, our quantitative framework underscores that the consequences of biological invasions cannot be understood in isolation but must be evaluated at the community level to capture the full complexity of ecological interactions.