Simulation of foraging behavior using a decision-making agent with Bayesian and inverse Bayesian inference: Temporal correlations and power laws in displacement patterns

Levy walks, random walks where the frequency of occurrence of a linear step length follows a power-law distribution, are found in the migratory behavior of organisms at various levels, from bacteria and T cells to humans. However, it has been pointed out that in human migratory behavior, the step length series may have temporal correlation (i.e., it is not random walk) and that there is some relationship between this time dependency and the fact that the frequency distribution of step length follows the power-law distribution. Furthermore, some large marine organisms have been found to switch between Levy and Brownian walks, wherein the frequency of occurrence of the step length is characterized by an exponential distribution (EP), depending on the difficulty of prey acquisition. However, as of now it has not been clarified how the aforementioned three phenomena arise: the positive correlation created in the step length series, the relation between the positive correlation of the step length series and the form of an individual’s step length distribution, and the switching between Levy and Brownian behavior depending on the abundance of prey. The purpose of this study is to simulate foraging behavior by three Bayesian decision-making agents: an agent simultaneously performing both knowledge learning and knowledge-based inference, an agent performing only learning, an agent performing only inference, and to analyze how the aforementioned three phenomena arise. The simulation results show that only the agent with both learning and inference has a mechanism that simultaneously causes all the phenomena. This suggests that simultaneous learning on prey distribution and inference based on the knowledge gained in exploratory behavior under incomplete information may be the key to the emergence of Levy walk-like patterns found in humans and marine organisms.