The ubiquity of scale-free mobility in nature, as observed in systems ranging from microorganisms to fishing boats, has stimulated a number of foraging theories and individual-based random search models. Here, we unveil an essential yet unexplored property of multiple-scale motion, which relates to the stability of entire populations. We use Lotka–Volterra models to predict that foragers diffusing normally tend to go extinct in fragile fragmented ecosystems, whereas their populations become resilient to degraded conditions and have maximized abundances when individuals perform scale-free Lévy flights. Our analytical and simulated results shift the scope of multiple-scale foraging from the individual level to the scales of collective phenomena that are of primary interest in conservation biology.
Lévy flight movements prevent extinctions and maximize population abundances in fragile Lotka–Volterra systems
Teodoro Dannemann, Denis Boyer and Octavio Miramontes
PNAS March 26, 2018. 201719889; published ahead of print March 26, 2018. https://doi.org/10.1073/pnas.1719889115