Behavior-environment information loop drives sensory navigation

Navigation is a fundamental behavior for many species to locate resources in the sensory environment. This process requires coupling behavior to sensory cues. Here we propose an information-theoretic framework that quantifies this coupling using transfer entropy (TE). Specifically, TE from sensory inputs to behavior defines a "reactive" component and TE from behavior to sensory signal defines an "active" component that exploits correlation in the sensory environment. We analytically connect these microscopic flows to macroscopic performance—the steady flux up a sensory gradient—by showing that the geometric mean of active and reactive TE serves as a first-order predictor of drift. This heuristic is derived in a minimal Markov jump model with states defined by local environment (e.g. up/down gradient) and the animal's action (e.g. run/tumble). We apply the framework to experimentally measured trajectories from bacteria, worms, flies, and machine learning agents navigating sensory landscapes. Across datasets, the geometric mean of the two TE directions reliably predicts navigation efficiency, revealing a common behavioral-environment feedback structure in navigation. We conclude by outlining neural and biophysical mechanisms that could compute or exploit these information flows.