Search efficiency of biased migration towards stationary or moving targets in heterogeneously structured environments

摘要

Efficient search acts as a strong selective force in biological systems ranging from cellular populations topredator-prey systems. The search processes commonly involve finding a stationary or mobile target within aheterogeneously structured environment where obstacles limit migration. An open generic question is whetherrandom or directionally biased motions or a combination of both provide an optimal search efficiency and howthat depends on the motility and density of targets and obstacles. To address this question, we develop a simplemodel that involves a random walker searching for its targets in a heterogeneous medium of bond percolationsquare lattice and used mean first passage time () as an indication of average search time. Our analysis revealsa dual effect of directional bias on the minimum value of . For a homogeneous medium, directionality alwaysdecreases and a pure directional migration (a ballistic motion) serves as the optimized strategy, while for aheterogeneous environment, we find that the optimized strategy involves a combination of directed and randommigrations. The relative contribution of these modes is determined by the density of obstacles and motility oftargets. Existence of randomness and motility of targets add to the efficiency of search. Our study reveals genericand simple rules that govern search efficiency. Our findings might find application in a number of areas includingimmunology, cell biology, ecology, and robotics.