Optimization of brownian search strategies

Abstract

What are the simplest search strategies that lead an animal to a particular target, what are their limitations, and what changes can be made to develop more effective strategies? To answer these question a class of search strategies was examined that require an animal to have only a minimal capacity for spatial orientation; the effectiveness of such strategies in solving the following basic search problem was determined. The animal begins its search at a distance r _o (starting distance) from a spatially fixed target. It detects the target when it has approached it to within a certain distance a (the detection radius). The analysed class of search strategies has the following characteristics: C1. The animal uses the same search strategy in all regions it enters. Therefore it needs no information as to the actual location of the target. C2. Its search strategy is constant in time. The animal has only to detect whether it has reached the target or not. C3. Once the animal has chosen a direction, it continues in that direction for a certain distance. This is the only way in which the preceding parts of the search affect the animal's decision as to the direction in which it will search next. In the long term the animal's movement directions are independent, with no preference for any particular direction. Despite their extreme simplicity in application these “Brownian” search strategies are remarkably successful (Fig. 1). Indeed, if the search is continued long enough the target is certain to be found. The success of the search depends in part on the search duration (Fig. 2) or the search-path length S, the starting distance and the detection radius. On the other hand, an animal can have a decisive influence on its degree of success simply by adjusting the frequency with which it changes its walking direction to match its sensory abilities. That is, a not-too-short Brownian search (S≫r _o) is most successful when the searching animal, between the points at which it changes direction, walks approximately straight for a distance equal to the detection radius (Figs. 3 and 4). A further increase in search effectiveness is possible only by turning to another class of search strategies. These, however, demand that the animal either have more information about the position of its target at the beginning of the search or be able to organize its search behavior even over fairly long periods of time.