Optimal search strategies for hidden targets

TL;DR

This paper analyzes the efficiency of intermittent search strategies with active and ballistic phases, showing optimal durations scale with specific powers, aligning with experimental data across species.

Contribution

It provides an analytical framework for understanding optimal search durations in intermittent strategies, modeling perception as diffusion and matching empirical observations.

Findings

Optimal search efficiency occurs when motion phase durations scale as power 3/5 or 2/3 of search phases.

The model's predictions align with experimental data from various species.

Perception during search can be effectively modeled as a diffusive process.

Abstract

What is the fastest way of finding a randomly hidden target? This question of general relevance is of vital importance for foraging animals. Experimental observations reveal that the search behaviour of foragers is generally intermittent: active search phases randomly alternate with phases of fast ballistic motion. In this letter, we study the efficiency of this type of two states search strategies, by calculating analytically the mean first passage time at the target. We model the perception mecanism involved in the active search phase by a diffusive process. In this framework, we show that the search strategy is optimal when the average duration of "motion phases" varies like the power either 3/5 or 2/3 of the average duration of "search phases", depending on the regime. This scaling accounts for experimental data over a wide range of species, which suggests that the kinetics of search trajectories is a determining factor optimized by foragers and that the perception activity is adequately described by a diffusion process.