How Albatrosses, Sharks, and Bacteria Search for Food
Heavy-tailed distribution → occasional long jumps
Gaussian steps → uniform exploration
Lévy (orange) has power-law tail • Brownian (blue) is Gaussian
When food is sparse and randomly distributed, Lévy flights with μ ≈ 2 are mathematically OPTIMAL. The occasional long jumps let animals escape depleted areas. This beats Brownian motion which over-searches nearby regions. Natural selection favors Lévy searchers!
Viswanathan (1996) first claimed albatrosses use Lévy flights. Edwards (2007) disputed this with better statistics. But newer GPS data (2012) vindicated the original idea—albatrosses DO show Lévy patterns! The controversy pushed the science forward.
Sharks, bees, bacteria, T-cells, even human hunter-gatherers show Lévy-like patterns. When resources are scarce, animals switch from Brownian to Lévy search. Marine predators were tracked showing this behavior across 14 species and 12 million movements!
Unlike Gaussian distributions, power laws have "heavy tails"—extreme events aren't rare accidents but inherent features. Earthquakes, stock crashes, social media virality, and city sizes all follow power laws. Lévy flights connect random walks to this universal pattern!