Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework

Area of Science:

• Behavioral Ecology
• Cognitive Science
• Theoretical Biology

Background:

• Foraging path lengths in the wild often follow power law distributions.
• Lévy random walks are theoretically proposed as optimal for memoryless agents in sparse environments.
• The efficiency of such strategies for cognitively complex agents remains unclear.

Purpose of the Study:

• To develop a model explaining apparent power law path lengths in learning foragers.
• To investigate optimal exploration strategies for agents that build internal reward models with temporal discounting.
• To provide a theoretical framework for understanding spatial exploration in cognitively complex species.

Main Methods:

• Developed a computational model where agents learn spatial reward distributions, incorporating temporal discounting.
• Analyzed human spatial exploration data from a laboratory task with imposed time costs.
• Examined path length distributions from a dataset of free-ranging marine vertebrate movements.

Main Results:

• The model predicts hyperbolic path lengths, which approximate power laws, for agents with internal reward models and temporal discounting.
• Human search patterns systematically adapted to time costs, aligning with the model's predictions.
• Empirical data from marine vertebrates showed path length distributions well-described by the hyperbolic model.

Conclusions:

• Optimal exploration for cognitively complex foragers involves hyperbolic path lengths, not necessarily Lévy walks.
• Temporal discounting and internal reward modeling are key factors shaping exploration strategies.
• The proposed hyperbolic model offers a unified framework for understanding diverse animal and human foraging behaviors.