Abstract
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.
Footnotes
↵* adam.gosztolai{at}unige.ch
↵† m.barahona{at}imperial.ac.uk
A summary of the changes is as follows: 1) We have rewritten the setup of the Keller-Segel model (old Eq. (3)) for general dimensions. 2) Our derivation of the ON model (old Eqs. (4) - (11)) is valid in any dimension d without changes. 3) We have extended the estimates of the optimal time horizon in Section III (old Eqs. (18) - (20)) to d > 1 for a symmetric multivariate Gaussian profile S1. The revised Eq. (20) shows that the diffusive component of the random walk depends on the dimension d, while the ballistic component remains the same. We added the simulations for d = 2 in Figure 3 to illustrate how (20) and (21) allows us to estimate the optimal time horizon in 2D. 4) We have extended the rescaling procedure in Section IV for general dimension d for a symmetric Gaussian profile, and we have added a discussion of the effect of the dimension on the rescaling. 5) We have added simulations of the interacting case in 2D (Section V)