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Multiple-scale mobility is ubiquitous in nature and has become instrumentalfor understanding and modeling animal foraging behavior. However, the impact ofindividual movements on the long-term stability of populations remains largelyunexplored. We analyze deterministic and stochastic Lotka Volterra systems,where mobile predators consume scarce resources (prey) confined in patches. Infragile systems (that is, those unfavorable to species coexistence), thepredator species has a maximized abundance and is resilient to degraded preyconditions when individual mobility is multiple scaled. Within the L\'evyflight model, highly superdiffusive foragers rarely encounter prey patches andgo extinct, whereas normally diffusing foragers tend to proliferate withinpatches, causing extinctions by overexploitation. L\'evy flights ofintermediate index allow a sustainable balance between patch exploitation andregeneration over wide ranges of demographic rates. Our analytical andsimulated results can explain field observations and suggest that scale-freerandom movements are an important mechanism by which entire populations adaptto scarcity in fragmented ecosystems.

L\'evy flight movements prevent extinctions and maximize population abundances in fragile Lotka Volterra systems