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The presence in ecological communities of unfeasible species interactions, termed forbidden links, due to physiological or morphological exploitation barriers has been long debated, but little direct evidence has been found. Forbidden links are likely to make ecological communities less robust to species extinctions, stressing the need to assess their prevalence. Here, we used a dataset of plant-hummingbird interactions, coupled with a Bayesian hierarchical model, to assess the importance of exploitation barriers in determining species interactions. We found evidence for exploitation barriers between flowers and hummingbirds across the 32 studied communities, however, the proportion of forbidden links changed drastically among communities, because of changes in trait distributions. The higher the proportion of forbidden links, the more they decreased network robustness, because of constraints on interaction rewiring. Our results suggest that exploitation barriers are not rare in plant-hummingbird communities and have the potential to limit the rescue of species experiencing partner extinction.