Optimal Lévy-flight foraging with cognition and memory

We propose a new foraging model based on the framework of random search with cognition and memory. We consider foraging to be a cognitive process of exploration to find sparse and revisitable targets in a finite landscape and use an exploration-return mechanism to mimic the spatial memory and returning be-haviours in foraging. We find that optimal Lévy-flight search strategies, charac-terised by a power-law step-size distribution P (l) ∝ l−µ, can emerge in this setting. The value of µ ∈ (1, 3) that maximises the search efficiency can shift substantially depending on two modelling parameters in the foraging process: the number of steps and the intensity of returning, which can represent a number of general internal or external hidden constraints in foraging. Our model provides a new understanding of the origin of Lévy-flight foraging as well as the substantial difference of the µ-values observed in empirical data, and therefore opens a new avenue for analysing trajectory and movement patterns of animals