A simple mathematical model using centred loops and random perturbations accurately reconstructs search patterns observed in desert ants

Abstract

This paper describes a new mathematical model that is based on centred loops to reconstruct the “Systematic Search” behaviour of Cataglyphis desert ants. The notable advantage of this model is the combination of simplicity, efficiency and performance. All model input is kept to a minimum, using only parameters that previous research has shown to be available to the animals at all times: distance from the origin, direction of the last step and home vector. Outbound and inbound search paths are being combined into loops that return to the origin, sampling this area more intensely. A stochastic element is added by random perturbations during the next step, mimicking unsystematic errors during the process of path integration and yielding the typical search patterns observed in Cataglyphis desert ants. The model output is compared to runs observed in the field.

Analysis of aligning active local searchers orbiting around their common home position

“…The same approximation is done in the expression for the N sens (r, β, t) in Eq. (17). The latter drops together with the density N ρ(r , β , t) πr 2 sens ≈ N sens (r, β, t) in Eq.…”

“…During the path integration the searcher is always aware of the direction towards the home without having knowledge about the distance. An alternative interesting model was recently proposed by Waldner and Merkle [17]. It considers a central harmonic force and recovers beautiful rosette like trajectories around the home which have been reported several times for dessert ants [2,10,11,15].…”

“…In [26] we have calculated the period as well as the precession. We mention, that a similar model was introduced by Waldner and Merkle [17] who computed similar trajectories.…”

“…For these animals and possibly for many others too, homing behavior is found during foraging. Especially, the various structured spatial patterns at which the entities move during their search and return have received a lot of interest and have been computed [14][15][16][17]. Typically such trajectories begin at the home.…”

Vector calibration in Australian desert ants, Melophorus bagoti: Effects of a delay after the acquisition of vector information

“…Learned landmark cues, when they are present (Collett, ; Narendra, Si, Sulikowski, & Cheng, ; Schultheiss et al, ; Wehner, Michel, & Antonsen, ), help to correct the accumulated error, and systematic search (Müller & Wehner, ; Narendra, ; Schultheiss & Cheng, ; Wehner, ; Wehner & Srinivasan, ) serves as a backup mechanism. In systematic search, the navigator travels in loops around the starting point of search (Waldner & Merkle, ), with the loops increasing in size as the search runs on (Schultheiss, Cheng, & Reynolds, ).…”