Lévy walks derived from a Bayesian decision-making model in non-stationary environments
This work provides a computational explanation for the emergence of Lévy walks in biological decision-making, offering insights for researchers studying animal behavior and foraging strategies.
This paper investigates the origin of Lévy walks in biological migration patterns. The authors demonstrate through simulations that the introduction of learning and forgetting into Bayesian inference, leading to fluctuating confidence levels in non-stationary environments, results in Lévy-walk-like patterns, transforming universal Brownian walks into Lévy walks.
Lévy walks are found in the migratory behaviour patterns of various organisms, and the reason for this phenomenon has been much discussed. We use simulations to demonstrate that learning causes the changes in confidence level during decision-making in non-stationary environments, and results in Lévy-walk-like patterns. One inference algorithm involving confidence is Bayesian inference. We propose an algorithm that introduces the effects of learning and forgetting into Bayesian inference, and simulate an imitation game in which two decision-making agents incorporating the algorithm estimate each other's internal models from their opponent's observational data. For forgetting without learning, agent confidence levels remained low due to a lack of information on the counterpart and Brownian walks occurred for a wide range of forgetting rates. Conversely, when learning was introduced, high confidence levels occasionally occurred even at high forgetting rates, and Brownian walks universally became Lévy walks through a mixture of high- and low-confidence states.