  Motile organisms often use finite spatial perception of their surroundings to
navigate and search their habitats. Yet standard models of search are usually
based on purely local sensory information. To model how a finite perceptual
horizon affects ecological search, we propose a framework for optimal
navigation that combines concepts from random walks and optimal control theory.
We show that, while local strategies are optimal on asymptotically long and
short search times, finite perception yields faster convergence and increased
search efficiency over transient time scales relevant in biological systems.
The benefit of the finite horizon can be maintained by the searchers tuning
their response sensitivity to the length scale of the stimulant in the
environment, and is enhanced when the agents interact as a result of increased
consensus within subpopulations. Our framework sheds light on the role of
spatial perception and transients in search movement and collective sensing of
the environment.
