Optimal Lévy-flight foraging in a finite landscape

We present a simple model to study Lévy-flight foraging with a power-law step-size distribution [P(l) ∞ l-μ] in a finite landscape with countable targets. We find that different optimal foraging strategies characterized by a wide range of power-law exponent μopt, from ballistic motion (μopt → 1) to Lévy flight (1 < μopt < 3) to Brownian motion (μopt ≥ 3), may arise in adaptation to the interplay between the termination of foraging, which is regulated by the number of foraging steps, and the environmental context of the landscape, namely the landscape size and number of targets. We further demonstrate that stochastic returning can be another significant factor that affects the foraging efficiency and optimality of foraging strategy. Our study provides a new perspective on Lévy-flight foraging, opens new avenues for investigating the interaction between foraging dynamics and the environment and offers a realistic framework for analysing animal movement patterns from empirical data.