Human participants were trained to navigate to two geometrically equivalent corners of a parallelogramshaped virtual environment. The unique shape of the environment combined three distinct types of geometric information that could be used in combination or in isolation to orient and locate the goals: the angular amplitudes of the corners, the relative wall length relationships, and the principal axis of symmetry. In testing, participants were placed in manipulated versions of the training environment that tested which types of geometry they had encoded and how angular information weighed in against the other two geometric properties. The test environments were (a) a rectangular environment that removed the angular information, (b) a rhombic environment that removed wall length information and drastically reduced the principal axis, and (c) a reverse-parallelogram-shaped environment that placed angular information against both wall length and principal axis information. Participants chose accurately in the rectangular and rhombus environments, despite the removal of one of the cues. In the conflict test, participants preferred corners with the correct angular amplitudes over corners that were correct according to both wall length relationships and the principal axis. These results are comparable to recent findings with pigeons and suggest that angles are a salient orientation cue for humans.

Pigeons were trained to locate food in two geometrically equivalent corners of a parallelogram-shaped enclosure. Both the angular amplitude of the corners and the length of the walls alone were sufficient for successfully completing the task. Following training, birds were tested in three separate conditions that manipulated the geometric information available. During tests in both a rectangular-shaped enclosure that preserved the wall length information but not the angular amplitude, and a rhombus-shaped enclosure that did the opposite, pigeons located their goal corners with a high degree of accuracy, indicating an ability to use both types of geometric information in isolation. This result is consistent with prior research with domestic chicks. However, in a conflict test in a reverse parallelogram-shaped enclosure, in which the correct angular location was paired with an incorrect wall length location, birds showed a preference for the correct angular location. This suggests that pigeons weight angles more heavily than wall lengths in this type of navigation task, which differs from findings in a similar task conducted with the domestic chick. Results in the conflict test also suggest that pigeons did not use the principal axis as their main strategy of small-scale navigation.

Although geometric reorientation has been extensively studied in numerous species, most research has been conducted in enclosed environments and has focused on use of the geometric property of relative wall length. The current studies investigated how angular information is used by adult humans and pigeons to orient and find a goal in enclosures or arrays that did not provide relative wall length information. In enclosed conditions, the angles formed a diamond shape connected by walls, whereas in array conditions, free-standing angles defined the diamond shape. Adult humans and pigeons were trained to locate two geometrically equivalent corners, either the 60° or 120° angles. Blue feature panels were located in the goal corners so that participants could use either the features or the local angular information to orient. Subsequent tests in manipulated environments isolated the individual cues from training or placed them in conflict with one another. In both enclosed and array environments, humans and pigeons were able to orient when either the angles or the features from training were removed. On conflict tests, female, but not male, adult humans weighted features more heavily than angular geometry. For pigeons, angles were weighted more heavily than features for birds that were trained to go to acute corners, but no difference in weighting was seen for birds trained to go to obtuse corners. These conflict test results were not affected by environment type. A subsequent test with pigeons ruled out an interpretation based on exclusive use of a principal axis rather than angle. Overall, the results indicate that, for both adult humans and pigeons, angular amplitude is a salient orientation cue in both enclosures and arrays of free-standing angles.

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