# Searching behaviour of desert ants, genus*Cataglyphis* (Formicidae, Hymenoptera)

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## Summary

- 1.
If a homing ant (

*Cataglyphis bicolor*,*C. albicans*) gets lost, it does not perform a random walk but adopts a stereotyped search strategy. During its search the ant performs a number of loops of ever-increasing size, starting and ending at the origin and pointing at different azimuthal directions. This strategy ensures that the centre area where the nest is most likely to be, is investigated most extensively. - 2.
After one hour of continuous search the ant's search paths cover an area of about 10

^{4}m^{2}. Nevertheless, the system of loops performed during this time is precisely centred around the origin. The ant's searching density does not depend on the azimuthal direction around the origin but only on the distance from the origin. It rapidly decreases with increasing distance. - 3.
The ant's searching pattern can be characterized by two functions: the

*d/t*-function correlating distance (*d*) with time (*t*), and the*α/t*-function correlating azimuthal direction (*α*) with time. If fixes of the ant's position are taken every 10 s, the vectors pointing from the origin to successive fixes change their lengths*d*systematically (α/t-function) and their directions*α*randomly (α/t-function). What is especially characteristic of the ant's searching pattern is the oscillating*d/t*-function which clearly demonstrates that the searching ant repeatedly returns to the origin, even after it has walked, within one hour, along a search trajectory of more than 1 km (the latter number refers to*C. albicans-A*). The ant's walking speed does not change within a search time of 1 h. - 4.
The distribution of changes in direction between successive segments of a search path,

*β*, is usually unimodal with a mean of 0°, if complete search paths are considered. Nevertheless, within smaller periods of time, especially during the initial portions of the search the integrated angle*β*may continuously change in the same direction. Such portions of the search crudely resemble a spiral which alternately expands and contracts. - 5.
Although all 3 species of

*Cataglyphis*studied in this paper adopt the same general search strategy, there are some differences in the fine structure of the search:*C. albicans-A*departs further from the origin than any other species, and performs the most rapid turns. The tendency towards spiralling is most pronounced in*C. albicans-B.* - 6.
An efficient searching strategy is formulated, based on purely theoretical grounds. It is assumed that when the search begins the probability density function (PDF) for the location of the nest is Gaussian in two dimensions (a priori PDF). It is further assumed that the ant can never be

*completely*certain that a given area has been fully explored, so that it is only the*probability*of encountering the nest within a certain region that decreases as the time spent in searching this region increases. Thus, the most promising region to search is specified by an a posteriori PDF which takes the ant's past performance into account. - 7.
A computer model is presented that searches in optimum fashion, as proposed above. In the model, motion of the ant is characterized in terms of radial and tangential components, with the tangential component varying randomly and the radial component varying according to the a posteriori PDF. The model successfully describes what the ants are actually doing (e.g., compare Figs. 17 and 18 with Fig. 3, Figs. 19 and 20 with Figs. 8–10, and Fig. 21a and b with Figs. 4 and 5), indicating that the searching behaviour of

*Cataglyphis*is geared to find the nest as quickly as possible.

## Keywords

Probability Density Function Probability Density Function Tangential Component Searching Behaviour Azimuthal Direction## Abbreviation

*PDF*probability density function

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