The hidden spiral: systematic search and path integration in desert ants,Cataglyphis fortis

The main navigational mechanism used by foraging desert ants of the genus Cataglyphis is path integration (dead reckoning). Any such egocentric system of navigation is prone to cumulative navigational errors. Hence, while homing Cataglyphis might have reset its path integration system and yet not arrived at the start of its foraging excursion, the nest entrance. Then it resorts to piloting or performs a systematic search for the nest. The search pattern consists of a system of loops of ever increasing size centred about the origin, i.e. the start of the search. Here we show that underlying the system of loops is a spiral search programme that gets transformed into the observed pattern of loops by the ant's idiosyncratic path-integration algorithm. The ant starts to follow a spiral course, then breaks off this course and walks towards the centre, i.e. to what its path-integration system has computed to be the origin of the search. This reset episode is followed by another spiral course, which is terminated by the next reset, and so forth. After each reset, the spiral gets wider, so that the whole pattern expands. Futhermore, every now and then the spiral might change its sign. Computer simulations based on these simple rules lead to search patterns of the kind actually recorded in Cataglyphis ants. These patterns ensure that those parts of the area in which the target (nest entrance) is most likely to be located are searched most heavily; in other words: the search density profile is adapted to the probability density function of the target.