Modelling the Landmark Navigation Behavior of the Desert Ant Cataglyphis Technical Report

The snapshot model presented by Cartwright and Collett (1987, 1983) fails to explain the searching behavior of the desert ant Cataglyphis in asymmetrical landmark configurations. Whereas according to the snapshot model the ants should only search in the vicinity of the expected nest position, there are other pronounced peaks in the search density histograms at positions where the view resembles the snapshot, although the external orientation of the view in these positions differs from the orientation of the snapshot. This report presents an extension of the original snapshot model that reproduces this searching behavior of Cataglyphis qualitatively. The model is derived in three steps: First, the external compass information is excluded from the snapshot model and replaced by a deterministic search, where the current view is rotated until it optimally matches the snapshot. As a result of this modification, the single convergence point of the homing trajectories breaks up into multiple points at the locations also visited by the ants. Since the trajectories, depending on the starting point, always converge to only one of these convergence points whereas a single ant searches in all of them, the second step expands the model with a stochastic search that varies the rotation of the current view over time. This step yields multiple search peaks with equal height. In order to reproduce the observed preference of the ants for the right nest location, the third step reintroduces the compass into the model: the stochastic search now operates on a weighted superposition of the matching quality in dependence of the current view rotation and a measure describing the angular preference for the compass direction. 1 Original form of the snapshot model The model of landmark navigation in bees presented by Cartwright and Collett (1987, 1983) is based on the assumption, that the insect, before starting to forage, takes a snapshot of the surroundings at the nest — a panoramic view of the horizon that is stored relatively unprocessed in form of dark and bright sectors. Returning from the excursion, the insect continuously matches the current panoramic view with the stored snapshot to derive a vector pointing towards the nest. This is achieved by a simple disparity matching: For each (dark) landmark sector and (bright) gap sector in the snapshot, the nearest corresponding sector in the current view is determined. 1 Each pair of matched sectors contributes with two unit vectors to a total homing vector. The first vector is attached tangentially to the snapshot sector and points towards the sector in the current view; the second vector is radial to the snapshot sector and directed outwards, if the snapshot sector is larger than the sector in the current view and vice versa. All these contributions are weighted and summed up in a total homing vector; figure 1 visualizes the vector contributions at one point in the plane. A prerequisite of this matching is, though, that snapshot and current view are aligned in the same direction according to an external reference, i.e., the insect has to be equipped with some kind of compass. For Cataglyphis, this view is supported by Lingg and Wehner (1996). Figure 1: Vector contributions in the original snapshot model. Both the (dark) landmark sectors and the (bright) gap sectors contribute to the total homing vector. The 8 pairings of snapshot sectors (inner ring) and current view sectors (outer ring) yield 8 tangential and 8 radial unit vectors (partially zero), weighted 1:2 in this case. All vectors are attached to the middle of the corresponding snapshot sector. Their sum gives the total homing vector (red, originating in the middle, shortened in the diagram). The snapshot was taken in the nest position marked with the cross. As long as the landmark configuration is relatively simple, there is only one convergence point for all homing trajectories. At this point, the length of the total homing vector is zero. If the landmarks are still in the same configuration as stored in the snapshot, the total homing vector in the nest position vanishes as well as all contributing vectors, since current view and snapshot perfectly match in this location. If the landmark configuration changed in the mean time, there will still be points with zero total homing vector, whereas the contributing vectors can be non-zero, since a perfect match can not be achieved anymore; see figure 2. Figure 3 demonstrates the homing behavior predicted by the original snapshot model in form of vectors, trajectories and a grey-value plot of the length of the homing vectors. In the following, a slightly modified version of the snapshot model is used. In order to obtain a smooth change of the vectors with the position, the unit vector contributions are replaced by vectors with variable length, which is proportional to the angular disparity respectively the 2 Figure 2: Convergence point for a landmark configuration that was modified after the snapshot was taken (north-west landmark moved to the right). In the convergence point in the center of the contribution diagram only the vector sum becomes zero, but not the vector contributions themselves. angular difference in size between snapshot sector and current view sector; figure 4 presents a comparison. As can be seen in figure 5, the homing behavior is only slightly changed by this modification. As in the unit-vector model, both types of contributions are weighted equally; this weighting is used for all following experiments. 2 Modelling the homing behavior of Cataglyphis As revealed by current research (Susanne Åkesson, personal communication; see also Åkesson et al. (1998)) the desert ant Cataglyphis shows a homing behavior that can not be explained with the original snapshot model. For ‘asymmetrical’ landmark configurations (with respect to the nest position) like the one shown in figure 3, the ants search in the vicinity of all 4 positions where the view perfectly matches the snapshot as long as the orientation of the view is discarded; see figure 6. In contrast, in the model of Cartwright and Collett all trajectories will end at the expected nest position. Moreover, the ants’ trajectories give the impression of a stochastic search that randomly switches between the different candidate locations, whereas the snapshot model in its original form is purely deterministic. A third property of the ants searching pattern that a model should reproduce is the preference of the ants for the right nest location, visible in an increased height of this peak in a search density histogram. In the following, a modification of the snapshot model will be presented that qualitatively reproduces the homing behavior of Cataglyphis. The model regards the basic assumptions of the model by Cartwright and Collett: a snapshot is taken at the nest position and stored unprocessed in form of dark and bright sectors, and the computation of the homing vector from a current view and the snapshot is done in the same way by summing up contributing vectors (with the minor