Brightness-based homing model at four altitude layers in the environment (0.02 m, 0.15 m, 0.32 m, and 0.45 m) for the area around the artificial meadow (dense environment). The rows show different parameters for the memorised snapshots (eight positions taken either outside or inside the dense environment and either above the dense environment, bird’s eye view, or close to the ground, ground views). A&B: Examples of panoramic snapshots in A from the bird’s eye view outside the dense environment and in B ground views inside the dense environment. The axes of the panoramic images refer to the azimuthal directions (x-axis) and to the elevational directions from the simulated bee’s point of view (y-axis, dorsal meaning upwards, ventral downwards, equatorial towards the horizon). C: Rendered layers of the environment for a comparison of the current view of the simulated bee. The layers are at 0.02 m(orange), 0.15 m (blue), 0.32 m(green) and 0.45 m (red) heights. D&E: The first column shows were the snapshots were taken in relation to the nest position (nest position in black, objects in red and snapshot positions indicated by coloured arrows). The other two columns show the comparison of memorised snapshot for two layers of the environment (0.02 m and 0.45 m as shown in C). The heatmaps show the image similarity between the current view at the position in the arena and the memorised snapshots taken around the nest (blue = very similar, white = very different). Additionally, white lines and arrows present the vector field from which the homing potential is derived. Red circles indicate the positions of the objects and the white dot indicates the nest position. The background colour of each column indicates the height of the current views that the snapshots are compared to. D: Memorised bird’s eye view snapshots taken outside (distance to the nest = 0.55 m) and above the dense environment (height = 0.45 m) can guide the model at the highest altitude (red background) to the nest but fails to do so at the three lower altitudes. E: Memorised ground view snapshots taken outside (distance to the nest = 0.55 m) the dense environment and close to the floor (height = 0.02 m) can only guide the model towards the center.

A: We trained two groups of bees in a cylindrical flight arena with cylindrical densely distributed objects (‘artificial meadow’) around the nest entrance. The first group, B+G+, was trained with a ceiling height of the arena twice the height of the objects providing space to fly above the objects. They might have memorised both a ground view (G+) as well as a bird’s eye view (B+) when leaving the nest. The second group, B−G+, was trained with an arena height restricted to the height of the objects, allowing the bees to only use ground views B−G+. Both groups were tested to return home in three test conditions: HighCeiling (BG), Covered (B) and LowCeilng (G). In test BG the dense environment was shifted from the training position to another position in the arena to exclude the use of potential external cues; the bees could use both, a ground view and a bird’s eye view, during return. In test B a partial ceiling above and a transparent wall was placed around the objects preventing the bees from entering the artificial dense environment during return. In test G the ceiling was lowered to the top of the objects allowing the bees to use only ground views during return. B: 3D view of the setup with the hive and the foraging chamber.

Examples of return flights and bees’ search for their nest in a dense environment (N = 26). A&B:Exemplary flight trajectories in 3D (left column) and a top view in 2D (right column) from the group B+G+ in the BG condition (A), and from the group B−G+ in the B condition (B). The colour indicates the time, blue the start and red the end of the flight. The objects are depicted by red cylinders in the 3D plot and as red circles in the 2D plot. The black dots in the 2D plot shows the visual nest position within the dense environment. A: The bee searches for the nest within the dense environment at a low flight altitude. B: The bee is mainly trying to enter the covered dense environment from the side. C: Spatial search distribution represented by hexagonal binning of the percentage of visits of all bees (relative to each bee’s total flight time) in the BG condition from group B+G+. Orange circles indicate the true and the visual nest position. Black circles indicate the object positions of the dense environment. D: Percentage searching for the two groups B+G+ (filled boxes, N = 26) and B−G+ (hatched boxes, N = 26) in the tests BF, G and B relative to the total flight time. The search percentage at the true nest is given in blue and at the visual nest in green. For all tested conditions and both groups, the bees searched more at the visual nest within the dense environment than at the true nest location (refer to SI Table 1 for statistical tests).

Entry points of the bees of both groups (N = 52) in all three tests (total entry points = 149) to the dense environment, from the side (A, circular histogram in grey) and from the top (B, scatter plot in blue) of the dense environment. The direction of the direct path from the arena entrance to the nest is given by the green triangle. The kernel density estimation (KDE) of the entries from the side of the dense environment is shown as a black, dashed line in A. The radial axes represents the normalized magnitude of the KDE.

Probability density distribution of the flight altitude and the search distribution for the B condition of the groups B−G+ (A&B) and B+G+ C&D). A flight altitude of 0 is at the floor, of 300mm is at the height of the objects and 600mm at the ceiling. A: The group B−G+ constrained to a low ceiling during training shows two peaks for a low altitude and for a high altitude. C: The group B+G+ shows a broader distribution, with three peaks either half the height of the objects, just above the height of the objects, or close below the ceiling. B&D: The search distributions reveal that the bees tried to enter the dense environment between the objects.

Schematic of a hypothetical homing mechanisms based on multiple navigational strategies. A bee entering the arena (grey circle) could have memorised a home vector (black arrow) pointing towards the true nest location at the training position in the dense environment (black dot within the light red circle). However, the visual scene changed drastically in the test. Hence, a vector memory might point coarsely to the dense environment (light green arrow) triggered by the prominent visual cue of the dense environment shifted to the test position (dark red circle). While some bees might use this vector providing the shortest path to the nest, other bees could rely on visual memories for entering the clutter. They will search at the border of the dense environment (curved, yellow arrow) for a previously experienced entry position to the dense environment (visual memory, framed in yellow). This position could reload a refined dense environment vector pointing to the more precise nest position within the dense environment (blue arrow).

Examples of the memorised snapshots based on brightness values for inside and outside the dense environment as well as from the bird’s and ground view perspective. The axes of the panoramic images refer to the azimuthal directions (x-axis) and to the elevational directions from the simulated bee’s point of view (y-axis, dorsal meaning upwards, ventral downwards, equatorial towards the horizon).

Examples of the memorised snapshots based on contrast-weighted nearness for inside and outside the dense environment as well as from the bird’s and ground view perspective. The axes of the panoramic images refer to the azimuthal directions (x-axis) and to the elevational directions from the simulated bee’s point of view (y-axis, dorsal meaning upwards, ventral downwards, equatorial towards the horizon).

Brightness-based homing model at four altitudes (0.02 m, 0.15 m, 0.32 m, and 0.45 m) with bird’s eye view snapshots taken outside the dense environment (distance = 0.55 m, height = 0.45 m). A: We applied the model to a list of images, these images are examples of the eight memorised snapshots which are aligned in the nest direction and taken around the nest. For the rotational image difference function, we used memory 0 as a reference image, and compared the seven others by rotating them against memory 0. We observe that the image difference function is minimum for the memorised image at a null rotation, as expected. If the other images are not two far from the nest, we may see other local minima for each of these images, where the local minima are shifted according the nest bearing. B-C: Heatmaps of full environment (B) and only the dense area (C, as shown in D) of the image similarity. The colour indicates the image difference between the view at the position in the arena and the snapshots taken around the nest. The model leads the simulated bees with bird’s eye view snapshots outside the dense environment to the nest position when the images are compared to images at an altitude of 0.45 m.

Brightness-based homing model at four altitudes (0.02 m, 0.15 m, 0.32 m, and 0.45 m) with bird’s eye view snapshots taken inside the dense environment (distance = 0.1 m, height = 0.45 m). The colour indicates the image difference between the view at the position in the arena and the snapshots taken around the nest. A: We applied the model to a list of images, these images are examples of the eight memorised snapshots which are aligned in the nest direction and taken around the nest. For the rotational image difference function, we used memory 0 as a reference image, and compared the seven others by rotating them against memory 0. We observe that the image difference function is minimum for the memorised image at a null rotation, as expected. If the other images are not two far from the nest, we may see other local minima for each of these images, where the local minima are shifted according the nest bearing. B: Heatmaps of full environment (B) and only the dense area (C, as shown in D) of the image similarity. The colour indicates the image difference between the view at the position in the arena and the snapshots taken around the nest. The model leads the simulated bees, with bird’s eye view snapshots inside the dense environment, only coarsely to the dense environment but not to the nest when the images are compared to images at an altitude of 0.45 m.

Brightness-based homing model at four altitudes (0.02 m, 0.15 m, 0.32 m, and 0.45 m) with ground view snapshots taken inside the dense environment (distance = 0.1 m, height = 0.02 m). The colour indicates the image difference between the view at the position in the arena and the snapshots taken around the nest. A: We applied the model to a list of images, these images are examples of the eight memorised snapshots which are aligned in the nest direction and taken around the nest. For the rotational image difference function, we used memory 0 as a reference image, and compared the seven others by rotating them against memory 0. We observe that the image difference function is minimum for the memorised image at a null rotation, as expected. If the other images are not two far from the nest, we may see other local minima for each of these images, where the local minima are shifted according the nest bearing. B: Heatmaps of full environment (B) and only the dense area (C, as shown in D) of the image similarity. The colour indicates the image difference between the view at the position in the arena and the snapshots taken around the nest. The model leads the simulated bees, with ground view snapshots inside the dense environment, only to the center of the dense environment (altitude of 0.32 m) or shifted away from the nest (altitude of 0.45 m) but not to the nest.

Brightness-based homing model at four altitudes (0.02 m, 0.15 m, 0.32 m, and 0.45 m) with ground view snapshots taken outside the dense environment (distance = 0.55 m, height = 0.02 m). The colour indicates the image difference between the view at the position in the arena and the snapshots taken around the nest. A: We applied the model to a list of images, these images are examples of the eight memorised snapshots which are aligned in the nest direction and taken around the nest. For the rotational image difference function, we used memory 0 as a reference image, and compared the seven others by rotating them against memory 0. We observe that the image difference function is minimum for the memorised image at a null rotation, as expected. If the other images are not two far from the nest, we may see other local minima for each of these image, where the local minima are shifted according the nest bearing. B: Heatmaps of full environment (B) and only the dense area (C, as shown in D) of the image similarity. The colour indicates the image difference between the view at the position in the arena and the snapshots taken around the nest. The model leads the simulated bees, with ground view snapshots outside the dense environment, only to the center of the dense environment (altitude of 0.32 m) but not to the nest.

Contrast-weighted nearness based homing model at four altitudes (0.02 m, 0.15 m, 0.32 m, and 0.45 m) with bird’s eye snapshots taken outside the dense environment (distance = 0.55 m, height = 0.45 m). A: We applied the model to a list of images, these images are examples of the eight memorised snapshots which are aligned in the nest direction and taken around the nest. For the rotational image difference function, we used memory 0 as a reference image, and compared the seven others by rotating them against memory 0. We observe that the image similarity as based on [14] is the maximum for the memorised image at a null rotation, as expected. If the other images are not two far from the nest, we may see other local maxima for each of these image, where the local maxima are shifted according the nest bearing. B: Heatmaps of full environment (B) and only the dense area (C, as shown in D) of the image similarity. The colour indicates the image similarity between the view at the position in the arena and the snapshots taken around the nest. The model leads the simulated bees, with bird’s eye view snapshots outside the dense environment, only to the center of the dense environment (altitude of 0.32 m) or shifted away from the nest (altitude of 0.45 m) but not to the nest.

Contrast-weighted nearness based homing model at four altitudes (0.02 m, 0.15 m, 0.32 m, and 0.45 m) with bird’s eye view snapshots taken inside the dense environment (distance = 0.1 m, height = 0.45 m). A: We applied the model to a list of images, these images are examples of the eight memorised snapshots which are aligned in the nest direction and taken around the nest. For the rotational image difference function, we used memory 0 as a reference image, and compared the seven others by rotating them against memory 0. We observe that the image similarity as based on [14] is the maximum for the memorised image at a null rotation, as expected. If the other images are not two far from the nest, we may see other local maxima for each of these image, where the local maxima are shifted according the nest bearing. B-D: Heatmaps of full environment (B) and only the dense area (C, as shown in D) of the image similarity. The colour indicates the image similarity between the view at the position in the arena and the snapshots taken around the nest. The model leads the simulated bees with bird’s eye view snapshots inside the dense environment only to the center of the dense environment (altitude of 0.45 m) but not to the nest.

Contrast-weighted nearness based homing model at four altitudes (0.02 m, 0.15 m, 0.32 m, and 0.45 m) with ground view snapshots taken inside the dense environment (distance = 0.1 m, height = 0.02 m). The colour indicates the image difference between the view at the position in the arena and the snapshots taken around the nest. A: We applied the model to a list of images, these images are examples of the eight memorised snapshots which are aligned in the nest direction and taken around the nest. For the rotational image difference function, we used memory 0 as a reference image, and compared the seven others by rotating them against memory 0. We observe that the image similarity as based on [14] is the maximum for the memorised image at a null rotation, as expected. If the other images are not two far from the nest, we may see other local maxima for each of these images, where the local maxima are shifted according the nest bearing. B-D: Heatmaps of full environment (B) and only the dense area (C, as shown in D) of the image similarity. The colour indicates the image similarity between the view at the position in the arena and the snapshots taken around the nest. The model leads the simulated bees with ground view snapshots inside the dense environment only to the center of the dense environment (altitude of 0.45 m) but not to the nest.

Contrast-weighted nearness based homing model at four altitudes (0.02 m, 0.15 m, 0.32 m, and 0.45 m) with ground view snapshots taken outside the dense environment (distance = 0.55 m, height = 0.02 m). The colour indicates the image difference between the view at the position in the arena and the snapshots taken around the nest. A: We applied the model to a list of images, these images are examples of the eight memorised snapshots which are aligned in the nest direction and taken around the nest. For the rotational image difference function, we used memory 0 as a reference image, and compared the seven others by rotating them against memory 0. We observe that the image similarity as based on [14] is the maximum for the memorised image at a null rotation, as expected. If the other images are not two far from the nest, we may see other local maxima for each of these images, where the local maxima are shifted according the nest bearing. B-D: Heatmaps of full environment (B) and only the dense area (C, as shown in D) of the image similarity. The colour indicates the image similarity between the view at the position in the arena and the snapshots taken around the nest. The model leads the simulated bees with ground view snapshots outside the dense environment only to the center of the dense environment (altitude of 0.32 m) or slightly shifted away from center (altitude of 0.45 m) but not to the nest.

Brightness based homing model with the simulated wall of the cylinder at four altitudes (0.02 m, 0.15 m, 0.32 m, and 0.45 m) with bird’s eye view (D&E) and ground view (F&G) snapshots taken outside (D&F) and inside (E&G) the dense environment. A&B: Examples of panoramic snapshots in A from the bird’s eye view outside the dense environment and in B ground views inside the dense environment. The axes of the panoramic images refer to the azimuthal directions (x-axis) and to the elevational directions from the simulated bee’s point of view (y-axis, dorsal meaning upwards, ventral downwards, equatorial towards the horizon). C: Rendered layers of the environment for a comparison of the current view of the simulated bee. The layers are at 0.02 m(orange), 0.15 m (blue), 0.32 m(green) and 0.45 m (red) heights. D-G: The first column shows were the snapshots were taken in relation to the nest position (nest position in black, objects in red and snapshot positions indicated by coloured arrows). The other four columns show the comparison of memorised snapshot the four layers of the environment (as shown in C). The heatmaps show the image similarity between the current view at the position in the arena and the memorised snapshots taken around the nest (blue = very similar, white = very different). Additionally, white lines and arrows present the vector field from which the homing potential is derived. Red circles indicate the positions of the objects and the white dot indicates the nest position. The background colour of each column indicates the height of the current views that the snapshots are compared to.

Brightness-based homing model with the simulated wall of the cylinder at four altitudes (0.02 m, 0.15 m, 0.32 m, and 0.45 m) with bird’s eye view snapshots taken outside the dense environment (distance = 0.55 m, height = 0.45 m). A: We applied the model to a list of images, these images are examples of the eight memorised snapshots which are aligned in the nest direction and taken around the nest. For the rotational image difference function, we used memory 0 as a reference image, and compared the seven others by rotating them against memory 0. We observe that the image difference function is minimum for the memorised image at a null rotation, as expected. If the other images are not two far from the nest, we may see other local minima for each of these images, where the local minima are shifted according the nest bearing. B-C: Heatmaps of the dense area (B, as shown in C) of the image similarity. The colour indicates the image difference between the view at the position in the arena and the snapshots taken around the nest.

Brightness-based homing model with the simulated wall of the cylinder at four altitudes (0.02 m, 0.15 m, 0.32 m, and 0.45 m) with bird’s eye view snapshots taken inside the dense environment (distance = 0.1 m, height = 0.45 m). The colour indicates the image difference between the view at the position in the arena and the snapshots taken around the nest. A: We applied the model to a list of images, these images are examples of the eight memorised snapshots which are aligned in the nest direction and taken around the nest. For the rotational image difference function, we used memory 0 as a reference image, and compared the seven others by rotating them against memory 0. We observe that the image difference function is minimum for the memorised image at a null rotation, as expected. If the other images are not two far from the nest, we may see other local minima for each of these images, where the local minima are shifted according the nest bearing. B-C: Heatmaps of the dense area (B, as shown in C) of the image similarity. The colour indicates the image difference between the view at the position in the arena and the snapshots taken around the nest.

Brightness-based homing model with the simulated wall of the cylinder at four altitudes (0.02 m, 0.15 m, 0.32 m, and 0.45 m) with ground view snapshots taken inside the dense environment (distance = 0.1 m, height = 0.02 m). The colour indicates the image difference between the view at the position in the arena and the snapshots taken around the nest. A: We applied the model to a list of images, these images are examples of the eight memorised snapshots which are aligned in the nest direction and taken around the nest. For the rotational image difference function, we used memory 0 as a reference image, and compared the seven others by rotating them against memory 0. We observe that the image difference function is minimum for the memorised image at a null rotation, as expected. If the other images are not two far from the nest, we may see other local minima for each of these images, where the local minima are shifted according the nest bearing. B-C: Heatmaps of the dense area (B, as shown in C) of the image similarity. The colour indicates the image difference between the view at the position in the arena and the snapshots taken around the nest.

Brightness-based homing model with the simulated wall of the cylinder at four altitudes (0.02 m, 0.15 m, 0.32 m, and 0.45 m) with ground view snapshots taken outside the dense environment (distance = 0.55 m, height = 0.02 m). The colour indicates the image difference between the view at the position in the arena and the snapshots taken around the nest. A: We applied the model to a list of images, these images are examples of the eight memorised snapshots which are aligned in the nest direction and taken around the nest. For the rotational image difference function, we used memory 0 as a reference image, and compared the seven others by rotating them against memory 0. We observe that the image difference function is minimum for the memorised image at a null rotation, as expected. If the other images are not two far from the nest, we may see other local minima for each of these image, where the local minima are shifted according the nest bearing. B-C: Heatmaps of the dense area (B, as shown in C) of the image similarity. The colour indicates the image difference between the view at the position in the arena and the snapshots taken around the nest.

Four exemplary flight trajectories of the first outbound flight of bees in 3D (left subplot) and a top view in 2D (right subplot). The colour indicates the time, blue the start of the and red the end of the flight. The objects are depicted by red cylinders in the 3D plot and as red circles in the 2D plot. The black dots in the 2D plot shows the nest position within the dense environment.

Search distributions for the group B+G+ (left column) in the condition G (condition BG is shown in the main results in Fig.2D) and for group B−G+ (right column) in the tests BG and G (N = 26 for each plot). The bees of group B+G+ in the condition G searched for the nest inside the dense environment and spent more time at the visual nest (in the dense environment) than at the true nest (as during training). The bees of group B−G+ in the condition G and BG searched for the nest within the dense environment and spent more time at the visual nest than at the true nest.

Flight altitude distributions for the tests BG and G for the groups B+G+ and B−G+ (N = 26 for each plot).

Exemplary flight trajectories in 3D (left column) and a top view in 2D (right column) from the group B+G+ in the B test. The colour indicates the time, blue the start of the and red the end of the flight. The objects are depicted by red cylinders in the 3D plot and as red circles in the 2D plot. The black dots in the 2D plot shows the nest position within the dense environment. The bee is trying to enter the covered dense environment from the side but, eventually, it is increasing its altitude and it flies above the dense environment. However, the bee is not searching for the visual nest above the covered dense environment.

Statistical results of t-tests.