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Redressing global patterns of biodiversity loss requires quantitative frameworks that can predict ecosystem collapse and inform restoration strategies. By applying a network-based dynamical approach to synthetic and real-world mutualistic ecosystems, we show that biodiversity recovery following collapse is maximized when extirpated species are reintroduced based solely on their total number of connections in the original interaction network. More complex network-based strategies that prioritize the reintroduction of species that improve ‘higher order’ topological features such as compartmentalization do not provide meaningful performance improvements. These results suggest that it is possible to design nearly optimal restoration strategies that maximize biodiversity recovery for data-poor ecosystems in order to ensure the delivery of critical natural services that fuel economic development, food security, and human health around the globe.