There are limits to the navigational abilities of animals because they face sensory and computational constraints to what they can know and remember. In many situations, animals have to search for a goal or for food. Faced with these limitations and with the unpredictability of the world, animals have evolved very efficient strategies to search. Depending on the type, location, and distribution of targets, these strategies fall broadly into two categories: systematic and random search. Systematic search movements are employed in situations, in which animals have some information on the location of a target, for instance, when ants have been following path integration information on their return to nest (Figure 8a). When they do not find the nest entrance at the end of their home vector, ants begin searching for it by running along paths that describe ever-increasing loops centered on the location where the search began. This systematic search pattern is driven by the fact that the most likely location of the nest from the perspective of the returning ant is at the end of its home vector. Given that this home vector is associated with some uncertainty as to the direction and the distance at which the nest is to be found, the probability of finding the nest can be assumed to be distributed like a three-dimensional Gaussian around the endpoint of the home vector (Figure 8c). The probability would be highest close to that point and fall off with distance from it. At the beginning, then, search should be concentrated at that location, a process that decreases the probability that the nest is there and consequently increases the probability that it is located further away from the start location of the search. As search loops increase, the probability of finding the nest further out decreases and the probability at the start location becomes relatively higher again. The ant should thus repeatedly revisit this central location. An alternative to this strategy would be to search along a path spiraling out from the estimated nest location. However, if the perceptual horizon of an ant is limited, she is in danger of missing the nest and continuing on a spiral path would not allow her to correct that mistake. Interestingly, in ants which run off only part of their home vector, the subsequent search is not centered at the beginning of search, but leads further and further away in the direction of the home vector. Such biased search movements are thus still informed by the direction of the home vector and reflect the probability of finding the nest in this direction, but with ever-increasing uncertainty about

Figure 8 Systematic search in desert ants. (a) and (b) The 1-h-long search path of a desert ant that had been displaced before running off its home vector (see Figure 3b). The initial half-hour path is shown in (a) and the subsequent path in (b). Note the different scales. The area shown in (a) is marked gray in (b). The ant searches in ever-increasing loops, centered on the expected nest position at the intersection of the thick gray lines. (c) This systematic search pattern can be explained by considering that it is driven by the instantaneous probability distribution of finding the nest at the end of the home vector. The diagram shows the right part of a transect through a three-dimensional Gaussian distribution. Search is first concentrated at the center of the distribution close to the end of the home vector (A) and, consequently, the probability of finding the nest there decreases, which causes the probability at more distant parts of the distribution to become relatively higher (B). If search loops lead the searching agent further away from the center of the distribution, the probability of finding the nest decreases at these more peripheral parts of the distribution (D and E), leading to a relative increase of probability at the center of the distribution, which attracts the searching agent back. Modified from Wehner R and Srinivasan MV (1981) Searching behaviour of desert ants, genus Cataglyphis (Formicidae, Hymenoptera). Journal of Comparative Physiology 142: 315-338.

both the distance and the direction at which it could be found relative to the beginning of search.

In contrast to situations - like the one described above -where animals have some information on the location of targets, many foraging situations are different: prey or food items are often randomly distributed and their location may be hard to predict. In such a case, random, rather than systematic, search strategies are employed and have indeed been shown to be optimal for detecting randomly and sparsely distributed targets. The efficiency of random search movements is optimal, when the probability distribution of straight path lengths (between changes in movement direction) follows an inverse square power-law distribution. The foraging movements of so diverse animals as amoebas, bees, deer, and wandering albatrosses have all the characteristics of such optimized random search movements. They can also help animals find favorable conditions - like places with preferred temperature or moisture - that are extended in space. In such cases, random search movements are modified by environmental cues, which, for instance, trigger a decrease in the speed of movement and an increase in the size of turns whenever conditions become favorable. Both behavioral modifications tend to keep an animal within the range of favorable conditions.

The question of how animals orient in the world and what cues they have available to do so in an organized and systematic fashion can thus only be answered by understanding the specific ecology of information processing in each particular case. There are some universal constraints, like the ones imposed on vision by its closed-feedback nature, and like the ones that are imposed by the physical properties of the world, like in the case of cues providing robust compass information. But how much a given animal is confronted with such constraints depends on the particular habitat of an animal, its style of locomotion, its active space, and the tasks it has to solve. For most animals, we still know surprisingly little about these crucial aspects of their lives.

See also: Dispersal-Migration; Material and Metal Ecology; Optimal Foraging Theory; Optimal Foraging; Remote Sensing; Wireless Sensor Networks Enabling Ecoinformatics.

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