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Global environmental change is challenging species with novel conditions, such that demographic and evolutionary trajectories of populations are often shaped by the exchange of organisms and alleles across landscapes. Current ecological theory predicts that random networks with dispersal shortcuts connecting distant sites can promote persistence when there is no capacity for evolution. Here, we show with an eco-evolutionary model that dispersal shortcuts across environmental gradients instead hinder persistence for populations that can evolve because long-distance migrants bring extreme trait values that are often maladaptive, short-circuiting the adaptive response of populations to directional change. Our results demonstrate that incorporating evolution and environmental heterogeneity fundamentally alters theoretical predictions regarding persistence in ecological networks., (© 2021 The Authors. Ecology published by Wiley Periodicals LLC on behalf of Ecological Society of America.)