Using likelihood to test for Lévy flight search patterns and for general power-law distributions in nature

Abstract

1. Ecologists are obtaining ever-increasing amounts of data concerning animal movement. A movement strategy that has been concluded for a broad variety of animals is that of Lévy flights, which are random walks whose step lengths come from probability distributions with heavy power-law tails. 2. The exponent that parameterizes the power-law tail, denoted μ, has repeatedly been found to be within the Lévy range of 1 < μ ≤ 3. Here, we use Monte Carlo simulations to show that the methods used to infer the value of μ are inaccurate. 3. The widely used method of simply logarithmically transforming a standard histogram of movement lengths has been shown elsewhere to be problematic. Here, we further demonstrate how poor it is, and show that it actually biases estimates of μ towards the Lévy range of 1