Panoramic pictures: image difference distribution
We quantified the alteration of the visual panorama created by the different displacements of the landmark (Figure 2). Across multiple positions, we recorded and compared panoramic images taken with the landmark either in the training position (reference scenery) or displaced (test scenery) (see Additional file 1). The panoramic image difference between reference and test scenery across the field can then be calculated [32]. At first, the landmark was shifted into a distant area (roughly 100 m away). The picture comparisons revealed high image differences between the training and distant test field. Indeed, even in front of the landmark, a great part of the panoramic view is very different from that found at an equivalent position on the training field. Within the training area, removing the landmark does not significantly alter the view at the beginning of the route but results in high image differences near the nest position (Figure 2A). Indeed, the visual area covered by the landmark (or here, absence of landmark) is negligible at the feeder but increases as a tangent function as one approaches the nest (Figure 1, see also Additional file 1). Similarly, shifting the landmark by 16° or 32° does not significantly alter the view at the beginning of the route but creates high image differences at the real nest position.
The 16° displacement creates a region of high image difference in the area opposite to the displaced landmark. This results in a valley of lower image differences between the feeder and the landmark. Within this valley, a zone of higher mismatch is located around 7-8 m on the way towards the 16° displaced landmark (Figure 2B). The presence of this latter zone of mismatch is easily explained. As one moves from the feeder towards the displaced landmark, the image differences result from two competing factors: the landmark and the rest of the panorama. As a result of moving away from the training direction, the perceived distant panorama (i.e., all the scenery except the landmark) becomes more and more altered, thus steadily increasing the mismatch. The landmark, however, matches its target counterpart perfectly, and although very small at the beginning of the route (filling < 5% of the azimuth), it increases in size sharply with distance, thereby minimizing the global mismatch. In combining landmark and panorama, the panoramic image differences grows as an ant travels from the feeder towards the landmark until a point of maximum mismatch (around 7-8 m along the feeder nest axis), beyond which the increasing size of the matching landmark diminishes the global mismatch (Figure 2B).
It is important to emphasise that the distributions of image differences presented here are not intended to model a particular homing strategy such as matching gradient descent, but simply allowed us to quantify the modification of the panoramic scenery the ants were subjected to during the tests. Whatever the actual process involved, any guidance strategy based on panoramic input should lead to disrupted behaviour if the global scenery is too much altered. Therefore, if ants are guided by panoramic views, they should not be able to reach the nest position in any of the tests conditions, as all of them present substantial panoramic image differences around the nest location. With 16° displacements of the landmark, however, the ants may end up searching in front of the displaced landmark, but their approaching route should then be altered while crossing the hill of high mismatch located at around 7-8 m.
Panoramic pictures: rotational image difference
Panoramic images can be rotated until they produce the best matching to the reference image. Here, rotational IDFs (i.e., Image Difference as a Function of the rotation) presented often two distinct best choices for matching (Figure 3A). One choice (distant panorama choice) was generally obtained while facing the same direction as during training, because the distant panoramas of both images overlap well. The other choice (landmark choice) was generally obtained while facing roughly towards the displaced landmark, because the landmarks of both images are superimposed.
At the beginning of the route, the 'distant panorama choice' provides a better matching value than the 'landmark choice' (Figure 3B, C) because the landmark appears very small and the distant panorama covers most of the view. However, as one travels towards the nest, the apparent size of the landmark increases and the part of the field of view covered by the distant panorama decreases. Therefore, the 'landmark choice' matching quality grows and the 'distant panorama choice' decreases in importance. Ants travelling towards their nest in the training direction may thus suddenly switch in orientation when the image difference along the 'distant panorama choice' becomes too bad or when the 'landmark choice' direction becomes better. Such a switch towards the landmark direction does not imply that the ant is now attending to the landmark, but just that the panoramic image difference is lower while facing in that new direction. Ants may also 'hesitate' between the two directions when they provide equivalent matching quality, leading potentially to wiggling paths for that part of the route (see examples Figure 4G).
Interestingly, a side difference arises in the 16° conditions. When the landmark is displaced to the left, facing the landmark becomes the best matching rotation at earlier locations than when the landmark is displaced to the right (Figure 3B). Some ants might thus continue to walk in the training direction longer when the landmark is displaced to the right.
Following purely the strategy of walking in the best matching direction should nonetheless lead the ant to the displaced landmark in the 16° condition (Figure 3B) and to the nest or the landmark in the 32° condition (Figure 3C). However, the actual image difference value of the selected direction might be important too. Ants might stop following the best matching direction if the image difference is considered too high (Figure 2 displays the distribution of the actual best matching values).
Ant responses: control condition
Ants homing from the feeder were captured just before reaching their nest in front of the landmark, and released again at the feeder location. When the landmark was left at its original position, the ants ran their route home again readily (Figure 4A) showing that they were guided by the perceived scenery and were not affected by potentially conflicting information provided by their path integrator. However, changing either the presence or the position of the landmark affected homing performance adversely, showing that the ants were affected by such alteration of the scenery.
Ant responses: distant area, 32° displacements and removal of the landmark
When the landmark was translated to a distant area presenting an unfamiliar panorama, the ants released at 10 m (i.e., fictive feeder) or 2 m in front of the fictive nest engaged immediately in a search pattern at the release point and none of them (0 out of 16 and 0 out of 15 respectively) went searching at the fictive nest relative to the landmark (Figure 4B).
On the training field, with the landmark removed (Figure 4C) or displaced by 32° (Figure 4D), the ants tended to run a first relatively straight segment but then displayed a U-turn on average half way from the nest and started searching. None of these ants (No-landmark: 0 out of 23; Left and Right 32° displacements: 0 out of 31) found the nest or reached the fictive nest in front of the displaced landmark (within 3 min). Interestingly, the approaches were on average centred along the feeder-nest axis in the no-landmark condition, but were a little bit skewed towards the displaced landmark in the 32° condition (Additional file 2). The searches appeared centred on the first U-turn, but, interestingly, showed a larger spread than the searches displayed on the distant area (Additional file 2).
Ant responses: 16° displacements of the landmark
With a smaller displacement of the landmark (16°), the ants displayed different behaviours, which we categorised into 3 groups (Figure 4E, F, G). Some ants (13 out 49) never reached the nest or searched for it in front of the displaced landmark (Figure 4E). The others (36 out of 49 individuals) eventually aimed at the landmark and displayed a dense search for the nest in front of it (Figure 4F, G). Determining whether (Figure 4F, G) or not (Figure 4E) an ant searched at the goal proved completely unambiguous, as two independent judges could agree completely: the 'nest-search' pattern would suddenly get much denser and the ants would not leave the area in front of the landmark for several minutes.
The 36 ants that searched for the nest (i.e., dense nest-search) in front of the landmark were categorised in two groups depending on whether or not they displayed U-turns while approaching the landmark. U-turns consisted of more than a sharp turn, but also the stipulation that the ant walk back in a direction at least 113 degrees away from the training direction (i.e., went at least 20 cm down along the Y axis within 50 cm of travel). As a result, an ant could display very sharp turns to the left and to the right without being considered as displaying U-turns.
Around half of these ants (19 out of 36) displayed at least one U-turn before reaching the displaced landmark (Figure 4F), a much higher proportion than in the control group returning under training conditions (Fisher's exact test: 19/36 vs. 1/25, odds ratio 25.56, p < 0.0001). Interestingly, their first U-turns were not located randomly along the route (Chi-square against random distribution across categories of 1 m: χ2 = 30, df = 9, p < 0.0001) but occurred mostly between 7 m and 8 m away from the feeder (first U-turn average distance from the feeder ± sd: 7.43 ± 1.48 m) (Figure 2B yellow crosses, Figure 4F).
The other half (17 out of 36) approached the landmark without displaying any U-turns. The first U-turn of these 17 individuals occurred right in front of the landmark (Figure 2B blue crosses, Figure 4G) and, rather than showing uncertainty en route, corresponds to the beginning of the characteristic dense search for the nest entrance. However, a closer look at the approach of those individuals revealed an increasing tortuosity that reaches its maximum around 7 to 8 m away from the feeder, a pattern that was not observed in the control group (ANOVA groups*distances: n = 17+25, F = 9.008, p = 0.0001; between groups: F = 12.971, p = 0.0009) (Figure 5).
Overall, even though most ants searched for the nest in front of the 16°-displaced landmark, its displacement notably affected their approach. Their paths were more tortuous than in the control condition: wiggles and U-turns were strongest around 7 to 8 m away from the feeder.
Path tortuosity and compass direction
To test whether or not this degradation was due to the fact that the ants in the 16° condition were led in a slightly different compass direction than during training, we focused on individuals that displayed long segments oriented towards the displaced landmark. Some ant paths (17 out of 48) presented a neat transition in the direction of travel, with a first segment oriented towards the nest and a second segment oriented towards the landmark (see Additional file 3 for examples). The switch in direction occurred on average around 5 m away from the feeder (average distance from the feeder ± sd: 5.1 ± 1.3 m). Around half of those ants (8 out of 17) displayed a first U-turn while approaching the landmark. Those first U-turns did not occur immediately after the switch towards the landmark as it would be expected if the path disruption was due to the new compass direction of travel, but several meters thereafter (average distance between switch and first Uturn ± sd: 3.8 ± 0.9 m), that is, around 7-8 m away from the feeder (average distance of the first U-turns from the feeder ± sd: 7.9 ± 1.1 m).
Other ants (8 out of 48) headed towards the 16°-displaced landmark from the start (see Additional file 3 for examples). Although the direction of travel was similarly oriented towards the landmark all along their approach (heading direction: paired sample t test: 0-4 meter vs. 4-8 meter, t = -0.508, p = 0.627), the tortuosity of their paths increased significantly in the second half of the journey (tortuosity: paired sample t test: 0-4 meter vs. 4-8 meter, t = -4.635, p = 0.002) and half of them (4 out of 8) also displayed a first U-turn after 5 m of travel towards the landmark (first U-turn average distance from the feeder ± sd: 6.5 ± 1.3).
Overall, ants were not equally perturbed everywhere along their way towards the landmark. Their paths were disrupted mostly around 7 m away from the feeder, independently of the ant's compass direction of travel. It seems therefore unlikely that the observed degradation of the path results from a discrepancy between the landmark direction and a memorised celestial compass information.
Side differences
In both 16° and 32° conditions, displacing the landmark to the left or to the right had different effects on the ants' first U-turn location. In 16° conditions, U-turn location differences appeared along the x-axis. When the landmark was displaced to the right, U-turns occurred closer to the feeder-nest axis and further away from the landmark side than when the landmark was displaced to the left (t-test independent samples (values mirrored for one side): t = 4.254, p = 0.0002). Remarkably, such a difference was predicted by the panoramic image comparisons (see "rotational matching of panoramic views"). Along the y-axis, the distribution of first U-turns were similar on average (t-test independent samples: t = 1.587, p = 0.1234) but were more spread in the 16°Right condition (Levene's test: F = 6.376, p = 0.0170).
With 32° displacement of the landmark, no side differences in U-turns distribution appeared along the x-axis (t-test independent samples: t = -1.208, p = 0.2368). Along the y-axis, however, U-turns occurred significantly earlier (t-test independent samples: t = 14.047, p < 0.0001) and were significantly more scattered (Levene's test: F = 6.128, p = 0.0190) when the landmark was displaced to the right.