Animal Search Strategies: A Quantitative Random-Walk Analysis

Recent advances in spatial ecology have improved our understanding of the role of large-scale animal movements.However, an unsolved problem concerns the inherent stochasticity involved in many animal search displacements and its possible adaptive value.When animals have no information about where targets (i.e., resource patches, mates, etc.) are located, different random search strategies may provide different chances to find them.Assuming random-walk models as a necessary tool to understand how animals face such environmental uncertainty, we analyze the statistical differences between two random-walk models commonly used to fit animal movement data, the Le ´vy walks and the correlated random walks, and we quantify their efficiencies (i.e., the number of targets found in relation to total displacement) within a random search context.Correlated random-walk properties (i.e., scale-finite correlations) may be interpreted as the by-product of locally scanning mechanisms.Le ´vy walks, instead, have fundamental properties (i.e., super-diffusivity and scale invariance) that allow a higher efficiency in random search scenarios.Specific biological mechanisms related to how animals punctuate their movement with sudden reorientations in a random search would be sufficient to sustain Le ´vy walk properties.Furthermore, we investigate a new model (the Le ´vy-modulated correlated random walk) that combines the properties of correlated and Le ´vy walks.This model shows that Le ´vy walk properties are robust to any behavioral mechanism providing short-range correlations in the walk.We propose that some animals may have evolved the ability of performing Le ´vy walks as adaptive strategies in order to face search uncertainties.