Geometrical multiscale tortuosity of desert ant walking trajectories.

Desert ants stand out as some of the most intriguing insect navigators, having captured the attention of scientists for decades. This includes the structure of walking trajectories during goal approach and search behaviour for the nest and familiar feeding sites. We analyse such trajectories with regard to changes in walking direction. The directional change of the ants is quantified, i.e. an angle θ between trajectory increments of a given arclength λ is computed. This was done for different length scales λ, according to our goal of analysing desert ant path characteristics with respect to length scale. (i) Varying λ through more than two orders of magnitude demonstrated Brownian motion characteristics typical of the random walk component of search behaviour. Unexpectedly, this random walk component was also present in - supposedly rather linear - approach trajectories. (ii) There were small but notable deviations from a uniform angle distribution that is characteristic of random walks. This was true for specific search situations, mostly close to the (virtual) goal position. (iii) Experience with a feeder position resulted in straighter approaches and more focussed searches, which was also true for nest searches, albeit to lesser extents. Taken together, these results both verify and extend previous studies on desert ant path characteristics. Of particular interest are the ubiquitous Brownian motion signatures and specific deviations thereof close to the goal position, indicative of unexpectedly structured search behaviour.