In this paper, we aim to determine which properties of a three-dimensional path are stored and available to recall in desert ants, Cataglyphis fortis, by comparing their behavior in three different training paradigms. The most conspicuous result is the close similarity of the ants' behavior after ramp and Λ training, while the flat training resulted in a different behavior. These differences enable us to identify some features of the ants' orientation mechanism when confronted with a three-dimensional itinerary. Furthermore, the results from experiment 3, which specifically tested the ants' orientation pertaining to a vertical vector component, do not provide supportive evidence for a 3-D path integrator.
Desert ants do not completely discard information about descents and ascents
Earlier experiments had shown that Cataglyphis ants are able to compute ground distances when walking on slopes [16,17] and to correctly incorporate this information into their path integration module [18]. A first simple hypothesis, which is fully compatible with these earlier results, would be that the ant's path integrator operates exclusively in 2-D, and that the animals have no further access to information about the 3-D structure of their environment after having corrected the walking distance to ground distance. The expectation under this hypothesis is that upon encountering slopes, ants should show similar behavior after flat and ramp training. The data, however, are clearly not consistent with this expectation. The proportion of ants that descended or ascended on one of the test ramps in Homebound and Outbound tests, respectively, differed strongly between flat trained and ramp trained animals (Figure 2A and 5A).
When considering only those animals that chose to descend or ascend in Homebound and Outbound tests, the distance that was walked on ramps provides additional, independent evidence for the different effects of the training paradigms (Figures 2B and 5B): Not only did fewer ants step onto ramps after flat training, but those flat trained ants that actually did, covered significantly shorter distances before deciding to turn around. We conclude from the observed differences in ascent and descent lengths, respectively, that the animals had access to stored information about either the elevated position of the food source, or the presence of a slope along the way. We therefore reject hypothesis A of an exclusively two-dimensional representation as the basis of the desert ants' path integration mechanism.
The percentages of flat trained animals that did not turn around immediately after stepping onto a ramp may appear large at first glance: 30 % chose to descend in the Homebound test, and ~20 % chose to ascend in the Outbound test, although the experiment's test runs marked the animals' very first exposure to a ramp. However, the short actual distances that these animals walked on ramps before turning around (Figures 2B and 5B) suggest that these tentative trips onto the ramps can probably be interpreted as explorative behavior.
The global vector does not extend into the third dimension
The ability to perform path integration in the horizontal plane enables desert ants to walk back to their starting point on a direct, straight path, irrespective of the meanderings of the preceding outbound route [2-4]. If such a home vector extended into the third dimension (Hypothesis C), ants that were trained according to the Λ paradigm should behave like flat trained ants: eventually, the upward and downward slope cancel out in respect to the resulting vector, which is identical to that of the flat training setup. Hence, after Λ training, ants should be as reluctant as after flat training to climb down on their way home or climb up during an outbound excursion to the food source. In both cases, choosing a ramp would result in a deviation from the direction of their home-bound and food-bound vectors, respectively. Contrary to this prediction, the behavior of ants that had participated in the Λ training was strikingly different from those in the flat training, and closely resembled that of ants after ramp training (Figures 2 and 5).
The most stringent argument against a true 3-D vector (Hypothesis C) results from experiment 3, in which we tried to specifically influence the vertical component of the global vector. There was no indication whatsoever that the enforced descents had induced a (negative) vertical component of the vector – as would be postulated for a true 3-D vector. We therefore conclude that the global vector that leads desert ants back to their point of origin in the plane is essentially two-dimensional. If a walked trajectory includes a vertical component, this aspect is not accurately included into the ants' path integrator, although a correction of walking distance to ground distance takes place [16-18]. Information about ascents and descents seems to be stored as separate information about an ant's trajectory. The hypothesis of a global vector that extends to all three dimensions of space, as outlined in the introduction (Hypothesis C), is therefore rendered highly unlikely.
Missing hills
What happens when desert ants encounter an ascent, or a hill, during repeated visits to a feeder, and are then transferred to a channel without such features? If they have stored the occurrence of such a "hill" in a general, unspecific way, its nonappearance should have an influence on the ants' search behavior. The absence of learnt visual landmarks leads to a general undershooting in the ants' homebound run [27]. Similarly, the "flat control" tests after ramp and Λ training resulted in an early onset of the ants' search for the nest entrance (Figure 4). That the ants in fact searched for the nest, and not for the "hill", can be seen by the inclusion of a training paradigm where the ramp was located at 9 m distance from the nest, instead of the usual 5.2 m distance. In the case of a search for the hill, the search distribution for the ramp at 9 m should be expected to be farther away from the position of the nest. This is not the case.
We see these results also as additional evidence that desert ants to not possess a path integrator that is operative in all three dimensions. In the case of such a mechanism employing a 3-D global vector, we would expect that at least a portion of tested animals after Λ training would welcome the opportunity to walk straight along their global vector back to the nest, and search at its correct ground distance. This is clearly not the case, with only two out of 38 animals reaching the nest position before turning around for the first time.
What remains open is the question why the search distributions of the two ramp training situations on one hand, and those after Λ training on the other, also differ from each other. Possibly, the reason for Λ training resulting in the strongest undershooting is because here an ascent and a descent were missing, or perhaps this "hill" was visually more conspicuous and was therefore a more obvious visual landmark than the descent in ramp training.
How do our findings of truncated homebound runs fit in with the results reported by Wohlgemuth et al. [16], where such an undershooting of walked distances did not occur? In her experiments, ants were trained to walk over a continuous series of hills and tested in a flat channel, or vice versa. One possible explanation is that, owing to the great discrepancy between the itinerary that was on offer during training and the subsequent test, the majority of ants exclusively relied on their global vector to find the nest. It is worth noting though that several ants in Wohlgemuth's experiments initiated their search for the nest almost immediately after being released, without running off their home vector first. In our experiment, only one ascent (in ramp training), or an ascent and a descent (in Λ training) were encountered, and the difference between the training and test situation was consequently smaller. Under these circumstances, the ants may have also tried to orientate by using these ramps as landmarks. The non-appearance of landmarks has been shown to initiate a truncation in homebound runs [27]. However, it is worth noting that even severe changes to the ants' visual environment do not prompt a reset of the path integrator, which instead is running continuously [28,29].
Ascents and descents are not stored with their respective distances from defined points in the ants' environment
A possible way to accurately navigate between a central place (i.e. the nest) and a food source could be to extend the two-dimensional global vector to the third dimension by associating commands to climb up or down with specific values of the home vector (Hypothesis B). This would make sense especially in situations and environments in which it makes a difference where one chooses to ascend or descend – e.g. if a food source was located on a tree, and a specific trunk had to be climbed in order to reach it. In short, this means that an ant would have to remember at which exact distance from the nest (or the food source) it made a turn in the vertical dimension, and re-execute such a vertical change of direction in subsequent runs. Under this assumption, we expected in our experimental setup that after ramp training, one test ramp would be preferred, namely the ramp that was located at the same position as the ramp during the preceding training (marked by a black arrow in Figures 3 and 6). This should result in a non uniform distribution of descent/ascent frequencies with a peak at that respective ramp. The data are not in accord with this expectation for ramp trained Cataglyphis fortis. Neither on homebound runs nor on outbound runs did this ramp attract more descents/ascents than the other available ramps (Figures 3B, 6B). The only ramp preference of statistical relevance was for ramp No. 6 in the Homebound test, i.e. the first ramp encountered on the homebound path after ramp training. Neither the ramp training nor the Λ training (Figures 3C, 6C) give any indication for a strong preference of the test ramp located at the training distance. The inclusion of shorter descents/ascents into the analysis (Additional files 1 and 2), which can be interpreted as initial (but not final) decisions for a ramp, did not change this picture. The observation that ramp and Λ trained ants more readily walk on the first ramp they encounter in the Homebound test, but not the Outbound test, may reflect a general preference for descents. In a different experiment we conducted, ants were able to choose at one point on their way home to either ascend or descend. After all three training paradigms, the ants showed a strong preference for the downward ramp (unpublished data). One reason for this could be that the descending ramp offers unhindered vision in the forward direction during the approach of the ramp.
Hence, our results do not corroborate the hypothesis of an orientation mechanism that links commands to climb up or down to specific values of the path integrator (Hypothesis B), although such a coupling of local vectors to the overall state of the ant's path integrator has been recently demonstrated for U-turns in a flat channel [19].
Ants do not follow the trained sequence of ascents and descents
So far, we found no evidence that ants employ a global 3-D vector when navigating in landscapes of three-dimensional formation, or that "up" and "down" commands are linked to specific states of their home vector. But how accurate is their representation of their environment with respect to the third dimension at all?
Is, for example, a hill on the ant's way recalled as the sequence of climbing up first and climbing down second? The Λ training simulates such a hill. If, in the subsequent test, the ant can choose between a straight continuation of its path and a descent, it should avoid descending on a ramp (because a preceding ascent is lacking), and continue walking horizontally – provided that it had stored the sequence of ascents and descents. In the Homebound test, however, Λ trained ants did the opposite and eagerly climbed down the offered ramps in larger numbers than after flat training (Figure 2A), with most animals covering the full length of the ramps (Figure 2B). Their behavior corresponded fully to that of ramp trained individuals. The lack of hesitation in their descents was remarkable, especially when viewed in comparison with the cautious behavior of flat trained ants, where most tested individuals soon turned around on any downward ramp that they encountered (Figure 2B). It appears that desert ants do accept any slope if they had encountered slopes before, but do not expect them to appear in the sequence as they were encountered during training. This behavior is also in accord with the hypothesis that after ramp or Λ training, a slope triggers an ant to descend, but without regard of the context within which the slope is encountered.
Are ascents and descents local vectors themselves?
It is conceivable that stepping onto a ramp prompted the ant to follow a trained local vector leading up or down, respectively. Cues that could invoke such a local vector could be the change in proprioceptive input, caused by the changed position relative to the force of gravity, the sudden tilting of the horizon and other celestial cues, or a combination of both. Visual landmarks are known to elicit local vectors, irrespective of the status of the global vector. The Australian desert ant Melophorus bagoti has been shown to initiate a learned sequence of local vectors upon encountering a known landmark panorama, irrespective of the current state of its path integrator [30]. Further experiments will have to show if such local ascent/descent vectors actually exist, what properties of descents or ascents (e.g. length and slope angle) they encompass, and how they are linked to the 2-D path integrator.
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