In the Positive Control, after some quick scans near the centre of the goniometer, foragers of both nests walked paths that were straight and nest-directed, displaying little meandering. These characteristics together suggest competent navigation, whether due to scene familiarity, or access to vector and visual compass information. In the Front Condition, foragers reacted to the panoramic view change, with most ants meandering until they found their way around the blockage on either on the right or left side. In the Back Condition, displaced foragers looked around at the Start and also turned back to look along the route, thus decreasing path straightness, but their initial headings were mostly nest-oriented. In the Lower Condition, most of the foragers came out from the goniometer centre and performed scans, and a number of them showed meandering with scanning along their route, decreasing path straightness. In the Upper Condition, foragers performed more meandering near the goniometer centre and some of them performed a systematic search with scans along their route, but the ants’ initial headings were mostly nest-oriented. In the Terrestrial Condition, foragers performed some scans around the goniometer centre and then showed straight-line orientation in random directions. Conversely, when we blocked the canopy information but left the surrounding view open, most of the foragers showed the navigational pattern of the Positive Control ants, suggesting little impact of the missing canopy information. Finally, in the Negative Control Condition, when we blocked all of the visual information, foragers performed scans with meandering throughout their slow, circuitous journeys in scattered directions. Formal inferential statistical analyses support these impressions. Overall, we found that blocking the front view, the lower elevations, and the entire terrestrial surround had the biggest adverse effects on initial orientation. The initial heading orientations of ants in these conditions were uniformly distributed. With the front or the lower portion of the view blocked, ants also scanned more at the start and along the route and took longer to exit the goniometer. With the entire terrestrial surround blocked, the ants were, surprisingly to us, quick in exiting, with few scans, but in random directions.

RotIDF depth and minima

RotIDF minima are visible in every treatment except for the Negative Control Condtion, which had no useful visual information (Fig. 1i–l). While there are apparent differences between the two nests, the overall pattern is similar, with the Terrestrial and Upper Conditions having small rotIDF depths (2.37–7.24 r.m.s pd; Fig. 1k–l) and higher rotIDF means (92.43–103.58 r.m.s pd; Fig. 1i–j), whereas the Front, Back, and Lower Conditions have greater rotIDFdepths (11.85–50.68 r.m.s pd; Fig. 1k–l), and similar means (76.31–87.83 r.m.s pd; Fig. 1i–j) [Supplimentary Table 1]. The biggest difference between the two nests is in the Front and Back Conditions, which have similar rotIDF means (81.73–87.84 r.m.s pd; Fig. 1i–j) across both nests, but whose rotIDF depths diverge more at Nest A (front: 32.48, back: 11.85 r.m.s pd; Fig. 1k–l) than at Nest B (front: 26.43, back: 18.97 r.m.s pd; Fig. 1k–l) [Supplimentary Table 1]. Overall, from the rotIDFs, we would expect navigators to be able to find a heading in most treatments, except for the Terrestrial and Upper Conditions, where finding a minimum may prove difficult. Unsurprisingly, in the Negative Control Condition, with all useful visual cues blocked, the analysis suggests that navigation should be impossible.

Initial homing direction

In each of our key comparisons, where we blocked opposing portions of the panorama, foragers showed differences in their ability to find a nest-directed heading (Table 1; Table 2; Figs. 2 and 3). With none of the panorama blocked (Positive Control), foragers were non-uniformly distributed, with a mean heading not distinguishable from the nest direction at 50 cm (Rayleigh test, p < 0.0001; V test, p < 0.0001). In contrast, blocking the whole panorama (Negative Control) prevented the ants from finding the home direction; they instead headed in random orientations, forming a uniform distribution of initial headings with a mean significantly different to the nest orientation (Rayleigh test, p = 0.053; V test, p = 0.719). While foragers in one nest in the Back treatment formed non-uniform, nest-directed distributions (Rayleigh test, p < 0.0001; V test, p = 0.031; Table 1), when the Front was blocked, foragers at both nests showed no directedness, forming a uniform distribution of headings (Rayleigh test, p = 0.119; V test, p = 0.328; Table 1). In the Front treatment, ants showed a tendency towards a bimodal distribution (D = 0.059659, p = 0.08079) where some ants aimed towards the edge of barrier at 90°, but others headed towards the other edge of the barrier at 270° (Supplementary Fig. 2). Foragers also failed to find home-directed headings when the Lower panorama was blocked, showing uniform, non-nest-directed orientations (Rayleigh test, p = 0.075, V-test, p = 0.737; Table 1), but ants were nest-directed and non-uniform when the Upper panorama was blocked (Rayleigh test, p = 0.0081, V test, p = 0.0073; Table 1). Blocking the celestial or canopy panorama had no discernible adverse effect on homing orientation (Rayleigh test, p < 0.0001; V test, p < 0.0001; Table 1), whereas blocking the terrestrial panorama left foragers unable to find the nest-ward heading (Rayleigh test, p = 0.157; V test, p = 0.856; Table 1).

Table 1 Inferential statistics of all test conditions for both nests combined Fig. 2

Circular histograms of initial headings of individual foragers of M. midas at 50 cm in the different conditions of their familiar routes. The histograms show orientation data in 15° bins, and the nest direction is indicated at 0°. The arrows in each histogram represent the length and the direction of the mean vector of foragers (see Table 2). The olive arrow indicates the combined mean vector of both nests whereas the black and sky colours denote Nest-A and Nest-B, respectively

Fig. 3

The paths of foragers in different experimental conditions on the goniometer. Ant path samples are selected randomly from all paths collected. The olive arrow indicates the nest direction, and the circle indicates the goniometer area (50 cm radius). In the Positive Control Condition (Fig. 3a), foragers were tested without any changes around the goniometer centre. The paths were randomly selected samples among all paths collected. The surrounding panoramic view and cues around the goniometer centre were changed in different ways (see details in Methods) in other conditions (Fig. 3b–h). Below each circle, the mean scans, durations, and Path Straightness (PS) with standard deviations are reported

Scanning

Foragers performed 1–2 scans in the first 50 cm of their return to the nest under normal (Positive Control) conditions, but most other treatments prompted an increase in the amount of initial scanning. These differences in scans across treatments were significant (Welch’s ANOVA: F7, 78.56 = 10.428, p < 0.001). Pairwise comparison to the Positive Control showed significant increases in total scans in the Front, Back, Lower, Upper and Visual Conditions (Tukey posts hoc tests p < 0.05; Fig. 4a), but no significant difference from the Positive Control in the Terrestrial and Celestial treatments (Terrestrial p = 0.716, Celestial: p = 0.855; Fig. 4a).

Fig. 4

a The number of scans on the goniometer (50 cm radius) in different experimental conditions. A ‘*’ indicates significant differences in number of scans compared to the Positive Control Condition. The box plot indicates medians (solid black line), box margins (25th and 75th percentiles) and whiskers (5th and 95th percentiles). b The mean number of scans as a function of location on the goniometer in different view-blocking conditions. Same conventions for box plots

Table 2 Statistical outcomes of different conditions in Nest-A, Nest-B, and the two nests combined

The patterns of scanning in the Start stage of travel and on the rest of the Route on the goniometer differed (Fig. 4b). At both stages of travel, variation among treatments was statistically significant (Start Welch’s ANOVA F7, 78.14 = 10.54, p < 0.001; Route: Welch’s ANOVA F7,78.14 = 8.621, p < 0.001; Fig. 4b), but the pattern of post hoc comparisons differed between the Start and Route segments. At the Start, the number of initial scans was significantly higher than the Positive Control in all the treatments (Tukey post hoc: p < 0.05) except the terrestrial condition, which bordered on significance (Tukey post hoc p = 0.058; Fig. 4b). Compared to the Positive Control, the number of Route scans were significantly higher in the Front, Back, Lower, Upper and Negative Control (Tukey post hoc p < 0.05; Fig. 4b), but not in the Terrestrial (Tukey post hoc p = 0.238) or Celestial treatments (Tukey post hoc p = 0.445) [Fig. 4b].

Duration on platform

Except for Celestial and Terrestrial treatments, foragers spent significantly more time on the platform after emerging from the goniometer hole than they did when the whole panorama was visible (Positive Control) (Welch’s ANOVA F7, 79.89 = 8.621, p < 0.001). In the Positive Control, foragers left the platform quickly (M = 9.86 s), and in the Negative Control they took more than three times as long (M = 28.23s, Tukey post hoc p < 0.05; Fig. 5). Further Tukey post hoc tests revealed that compared to the Positive Control, the durations were significantly longer in the Front, Back, Lower, and Upper Conditions (p < 0.05), but not in the Terrestrial, and Celestial Conditions (p > 0.1; Fig. 5).

Fig. 5

The duration of time that foragers took to pass 50 cm from the releasing point. Same conventions as in Fig. 4a

Path straightness

We found a large variation between treatments in the straightness of the plotted paths (Welch’s ANOVA, F7,78.14 = 23.812, p < 0.001; Figs. 3 and 6). Path Straightness of the Front, Back, Lower, Upper and Negative Control, were significantly different (Tukey, p < 0.05) from the Positive Control in the conditions, but Terrestrial, and Celestial were not significantly different from that control (Tukey, p > 0.1; Fig. 6).

Fig. 6

The Path Straightness of foragers in different experimental conditions. Maximum Path Straightness (a straight line) is 1. Same conventions as Fig. 4a