Geometric orientation by humans: angles weigh in

Human participants were trained to navigate to two geometrically equivalent corners of a parallelogram-shaped 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.     

Reorientation in diamond-shaped environments: encoding of features and angles in enclosures versus arrays by adult humans and pigeons (Columbia livia)

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.     

Representation of two geometric features of the environment in the domestic chick (<Emphasis Type="Italic">Gallus gallus</Emphasis>)

We report experiments based on a novel test in domestic chicks (Gallus gallus), designed to examine the encoding of two different geometric features of an enclosed environment: relative lengths of the walls and amplitude of the corners. Chicks were trained to search for a food reward located in one corner of a parallelogram-shaped enclosure. Between trials, chicks were passively disoriented and the enclosure was rotated, making reorientation possible only on the basis of the internal spatial structure of the enclosure. In order to reorient, chicks could rely on two sources of information: the relative lengths of the walls of the enclosure (associated to their left-right sense order) and the angles subtended by walls at corners. Chicks learned the task choosing equally often the reinforced corner and its rotational equivalent. Results of tests carried out in novel enclosures, the shapes of which were chosen ad hoc (1) to induce reorientation based only on the ratio of walls lengths plus sense (rectangular enclosure), or (2) to induce reorientation based only on corner angles (rhombus-shaped enclosure), suggested that chicks encoded both features of the environment. In a third test, in which chicks faced a conflict between these geometric features (mirror parallelogram-shaped enclosure), reorientation seemed to depend on the salience of corner angles. These results shed light on the elements of the environmental geometry which control spatial reorientation, and broaden the knowledge on the geometric representation of space in animals.     

Pigeons encode relative geometry.

Pigeons were trained to search for hidden food in a rectangular environment designed to eliminate any external cues. Following training, the authors administered unreinforced test trials in which the geometric properties of the apparatus were manipulated. During tests that preserved the relative geometry but altered the absolute geometry of the environment, the pigeons continued to choose the geometrically correct corners, indicating that they encoded the relative geometry of the enclosure. When tested in a square enclosure, which distorted both the absolute and relative geometry, the pigeons randomly chose among the 4 corners, indicating that their choices were not based on cues external to the apparatus. This study provides new insight into how metric properties of an environment are encoded by pigeons.     

How fish do geometry in large and in small spaces

It has been shown that children and non-human animals seem to integrate geometric and featural information to different extents in order to reorient themselves in environments of different spatial scales. We trained fish (redtail splitfins, Xenotoca eiseni) to reorient to find a corner in a rectangular tank with a distinctive featural cue (a blue wall). Then we tested fish after displacement of the feature on another adjacent wall. In the large enclosure, fish chose the two corners with the feature, and also tended to choose among them the one that maintained the correct arrangement of the featural cue with respect to geometric sense (i.e. left-right position). In contrast, in the small enclosure, fish chose both the two corners with the features and the corner, without any feature, that maintained the correct metric arrangement of the walls with respect to geometric sense. Possible reasons for species differences in the use of geometric and non-geometric information are discussed.     

Is there an innate geometric module? Effects of experience with angular geometric cues on spatial re-orientation based on the shape of the environment

Non-human animals and human children can make use of the geometric shape of an environment for spatial reorientation and in some circumstances reliance on purely geometric information (metric properties of surfaces and sense) can overcome the use of local featural cues. Little is known as to whether the use of geometric information is in some way reliant on past experience or, as would likely be argued by advocates of the notion of a geometric module, it is innate. We tested the navigational abilities of newborn domestic chicks reared in either rectangular or circular cages. Chicks were trained in a rectangular-shaped enclosure with panels placed at the corners to provide salient featural cues. Rectangular-reared and circular-reared chicks proved equally able to learn the task. When tested after removal of the featural cues, both rectangular- and circular-reared chicks showed evidence that they had spontaneously encoded geometric information. Moreover, when trained in a rectangular-shaped enclosure without any featural cues, chicks reared in rectangular-, circular-, or c-shaped cages proved to be equally able to learn and perform the task using geometric information. These results suggest that effective use of geometric information for spatial reorientation does not require experience in environments with right angles and metrically distinct surfaces, thus supporting the hypothesis of a predisposed geometric module in the animal brain.     

Experience and geometry: controlled-rearing studies with chicks

Animals can reorient making use of the geometric shape of an environment, i.e., using sense and metric properties of surfaces. Animals reared soon after birth either in circular or in rectangular enclosures (and thus affording different experiences with metric properties of the spatial layout) showed similar abilities when tested for spatial reorientation in a rectangular enclosure. Thus, early experience in environments with different geometric characteristics does not seem to affect animals’ ability to reorient using sense and metric information. However, some results seem to suggest that when geometric and non-geometric information are set in conflict, rearing experience could affect the relative dominance of featural (landmark) and geometric information. In three separate experiments, newborn chicks reared either in circular- or in rectangular-shaped home-cages were tested for spatial reorientation in a rectangular enclosure, with featural information provided either by panels at the corners or by a blue-coloured wall. At test, when faced with affine transformations in the arrangement of featural information that contrasted with the geometric information, chicks showed no evidence of any effect of early experience on their relative use of geometric and featural information for spatial reorientation. These findings suggest that, at least for this highly precocial species, the ability to deal with geometry seems to depend more on predisposed mechanisms than on learning and experience after hatching.     

Multiple cue use and integration in pigeons (<Emphasis Type="Italic">Columba livia</Emphasis>)

Encoding multiple cues can improve the accuracy and reliability of navigation and goal localization. Problems may arise, however, if one cue is displaced and provides information which conflicts with other cues. Here we investigated how pigeons cope with cue conflict by training them to locate a goal relative to two landmarks and then varying the amount of conflict between the landmarks. When the amount of conflict was small, pigeons tended to integrate both cues in their search patterns. When the amount of conflict was large, however, pigeons used information from both cues independently. This context-dependent strategy for resolving spatial cue conflict agrees with Bayes optimal calculations for using information from multiple sources.     

Hippocampus lesions impair landmark array spatial learning in homing pigeons: a laboratory study

Hippocampal (HF)-lesioned pigeons display impaired homing ability when flying over familiar terrain, where they are presumably relying on a map-like representation of familiar landmarks to navigate. However, research carried out in the field precludes a direct test of whether hippocampal lesions compromise the ability of homing pigeons to navigate by familiar landmarks. To examine more thoroughly the relationship between hippocampus and landmark spatial learning, control, neostriatum-lesioned, and HF-lesioned homing pigeons were trained on two open field, laboratory, conditional discrimination tasks. One was a visual landmark array task, and the other was a room color discrimination task. For the tasks, the correct of three differently colored food bowls was determined by the spatial relationship among a group of five landmarks and room color, respectively. Intact control birds successfully learned both tasks, while neostriatum-lesioned birds successfully learned the landmark array task-the only task on which they were trained. By contrast, HF-lesioned birds successfully learned the room color task but were unable to learn the landmark array task. The data support the hypothesis that homing performance deficits observed in the field following hippocampal lesions are in part a consequence of an impairment in the ability of lesioned pigeons to use familiar visual landmarks for navigation.     

Dissecting the geometric module: a sense linkage for metric and landmark information in animals' spatial reorientation

Disoriented children can use geometric information in combination with featural information to reorient themselves in large but not in small spaces; somewhat similar effects have been found in nonhuman animals. These results call for an explanation. We trained young chicks to reorient to find food in a corner of a small or a large rectangular room with a distinctive featural cue (a blue wall) -- a task similar to that used with children. Then we tested the chicks after displacement of the feature to an adjacent wall. In the large enclosure, chicks chose the corner that maintained the correct arrangement of the featural cue with respect to sense, whereas in the small enclosure, they chose the corner that maintained the correct metrical arrangement of the walls with respect to sense. On the basis of these findings, we propose a simple model that can explain the effects of room size on spatial reorientation.     

Enclosure size and the use of local and global geometric cues for reorientation

Multiple spatial cues are utilized to orient with respect to the environment, but it remains unclear why feature (i.e., objects in the environment) and geometric (i.e., shape of the environment) cues are differentially influenced by enclosure size, and the extent to which local (i.e., wall lengths and corner angles) and global (i.e., principal axis of space) geometric cues are influenced by enclosure size. In the present study, we investigated the extent to which environmental size influenced the use of corner angle (i.e., a local geometric cue) and the principal axis of space (i.e., a global geometric cue) for reorientation. We developed an orientation task that allowed the manipulation of enclosure size during training and the isolation of the use of the principal axis of space during testing. Participants were trained to respond to a location in either a small or a large trapezoid-shaped enclosure uniquely specified by both local (i.e., wall lengths and corner angles) and global (i.e., principal axis of space) geometric cues. During testing, we presented both groups with a small and large rectangle (to assess the use of principal axis of space) and a small and large parallelogram (to asses relative use of corner angles and the principal axis of space when in conflict). Enclosure size influenced the relative use of corner angles but not of the principal axis of space. Results suggest that corner angles function like features and that changes in the use of feature cues are the source of the relative reliance on feature and geometric cues during changes of enclosure size.     

Peck tracking: a method for localizing critical features within complex pictures for pigeons

The pigeon is a standard animal in comparative psychology and is frequently used to investigate visuocognitive functions. Nonetheless, the strategies that pigeons use to discriminate complex visual stimuli remain a difficult area of study. In search of a reliable method to identify features that control the discrimination behaviour, pecking location was tracked using touch screen technology in a people-absent/people-present discrimination task. The correct stimuli contained human figures anywhere on the picture, but the birds were not required to peck on that part. However, the stimuli were designed in a way that only the human figures contained distinguishing information. All pigeons focused their pecks on a subarea of the distinctive human figures, namely the heads. Removal of the heads significantly impaired performance, while removal of other distinctive parts did not. Thus, peck tracking reveals the location within a complex visual stimulus that controls discrimination behaviour, and might be a valuable tool to reveal the strategies pigeons apply in visual discrimination tasks.     

Wild hummingbirds rely on landmarks not geometry when learning an array of flowers

Rats, birds or fish trained to find a reward in one corner of a small enclosure tend to learn the location of the reward using both nearby visual features and the geometric relationships of corners and walls. Because these studies are conducted under laboratory and thereby unnatural conditions, we sought to determine whether wild, free-living rufous hummingbirds (Selasphorus rufus) learning a single reward location within a rectangular array of flowers would similarly employ both nearby visual landmarks and the geometric relationships of the array. Once subjects had learned the location of the reward, we used test probes in which one or two experimental landmarks were moved or removed in order to reveal how the birds remembered the reward location. The hummingbirds showed no evidence that they used the geometry of the rectangular array of flowers to remember the reward. Rather, they used our experimental landmarks, and possibly nearby, natural landmarks, to orient and navigate to the reward. We believe this to be the first test of the use of rectangular geometry by wild animals, and we recommend further studies be conducted in ecologically relevant conditions in order to help determine how and when animals form complex geometric representations of their local environments.     

The impact of landmark properties in shaping exploration and navigation

This study was aimed at uncovering physical and geometric properties that make a particular landmark a target of exploration and navigation. Rats were tested in a square open-field arena with additional portable corners featuring the same properties as the arena corners. It was found that the routes of progression converged upon the added corners, whether located at the arena wall or the arena center. Route convergence upon the added corners involved numerous visits to these corners. However, time spent at the added corners was relatively short compared with the arena corners, including that from which rats were introduced into the arena. There was no differential effect of testing rats in light or dark, or with a low versus a high portable corner. It is suggested that the added corners were distinct against the background of the arena enclosure, whereas the four arena corners and walls were encoded by the rats as one geometric module. This distinctness, together with the greater accessibility of the added corners, made them salient landmarks and a target of exploration. Thus, the impact of a landmark extended beyond its specific self-geometry to include accessibility and distinctness, which are contextual properties. In addition to the contextual impact on locomotor behavior there was also a temporal effect, with security initially dominating the rats’ behavior but then declining along with an increased attraction to salient landmarks. These spatiotemporal patterns characterized behavior in both lit and dark arenas, indicating that distal cues were secondary to local proximal cues in shaping routes.     

Coding location in enclosed spaces: is geometry the principle?

Both animals and human toddlers can find an object in a rectangular enclosure after they have been disoriented. They use geometric cues (relative lengths of walls) to discriminate among different corners (e.g. long wall to the left, short to the right). It has been claimed that this ability is 'modular', i.e. exclusively geometric. The present study demonstrates that the ability toddlers exhibit is a more general one, namely, an ability to discriminate relative quantity. Using a square enclosure, we show that toddlers use the relative sizes of the figures on different walls to characterize different corners. We also show that they do not use simple non-relative features to distinguish different corners. Possible reasons for differences in the ability to use relative versus non-relative cues are discussed.     

Orientation in trapezoid-shaped enclosures: implications for theoretical accounts of geometry learning

Human participants learned to select 1 of 4 distinctively marked corners in a rectangular virtual enclosure. After training, control and test trials were interspersed with training trials. On control and test trials, all markers were equivalent in color, but only during test trials was the shape of the enclosure manipulated. Specifically, for each test trial, a single long wall or short wall of the enclosure increased twice as long as or decreased half as long as that present in the training enclosure. These manipulations produced 8 unique trapezoid-shaped enclosures. Participants were allowed to select 1 corner during control and test trials. Performance during control trials revealed that participants selected the correct and rotationally equivalent locations. Performance during test trials revealed that participants selected locations in trapezoid-shaped enclosures that were consistent with those predicted by global geometry (i.e., principal axis of space) but were inconsistent with those predicted by local geometry (i.e., proportion of rewarded training features present at a location). Results have implications for theoretical accounts of geometry learning.     

Influence of distal and proximal cues in encoding geometric information

Vertebrates use geometric and featural information for spatial navigation. When both geometric and featural cues are available, animals can use a variety of spatial strategies based on this information. To examine the nature of these strategies, we manipulated the spatial relationship between a conspicuous cue and the position of the goal when goldfish (Carassius auratus) were searching for the exit of a rectangular environment with one distinctive wall. Two groups of fish were used, one with the distinctive wall close to the goal and the other with the distinctive wall on the other end of the enclosure. Results showed that fish encoded featural and geometric information in both conditions but the spatial relationship between the goal and the distinctive wall influences the characteristics of the encoding of the spatial cues and the strategy used to locate the goal. These results suggest that fish in both procedures use the local featural cues associated with the goal instead of the whole set of spatial cues as previous studies propose.     

Use of cue configuration geometry for spatial orientation in human infants (Homo sapiens)

Research with both rats and human infants has found that after inertial disorientation, the geometry of an enclosed environment is used in preference over distinctive featural information during goal localization. Infants (Homo sapiens, 18-24 months) were presented with a toy search task involving inertial disorientation in 1 of 2 conditions. In the identical condition, 4 identical hiding boxes in a rectangular formation were set within a circular enclosure. In the distinctive condition, 4 distinctive hiding boxes were used. Infants searched the goal box and its rotational equivalent significantly more than would be expected by chance in the identical condition, showing that they were sensitive to the geometric configuration of the array of boxes. Unlike the results of studies using a rectangular enclosure, however, in the distinctive condition, infants searched at the correct location significantly more than at other locations.     

Young children's use of features to reorient is more than just associative: further evidence against a modular view of spatial processing

Proponents of a geometric module have argued that instances of young children's use of features as well as geometry to reorient can be explained by a two-stage process. In this model, only the first stage is a true reorientation, accomplished by using geometric information alone; features are considered in a second stage using association ( Lee, Shusterman & Spelke, 2006 ). This account is contradicted by the data from two experiments. Experiment 1a sets the stage for Experiment 1b by showing that young children use geometric information to reorient in a complex geometric figure without a single principal axis of symmetry (an octagon). In such a figure, there are two sets of geometrically congruent corners, with four corners in each set. The addition of a colored wall leads to the existence of three geometrically congruent but, crucially, all unmarked corners; using the colored wall to distinguish among them could not be done associatively. In Experiment 1b, both 3- and 5-year-old children showed true non-associative reorientation using features by performing at above-chance levels on all-white trials. Experiment 2 used a paradigm without distinctive geometry, modeled on Lee et al. (2006) , involving an equilateral triangle of hiding places located within a circular enclosure, but with a large stable feature rather than a small moveable one. Four-year-olds (the age group studied by Lee et al.) used features at above-chance levels. Thus, features can be used to reorient, in a way not dependent on association, in contradiction to the two-stage version of the modular view.     

Egocentric search for disappearing objects in domestic dogs: evidence for a geometric hypothesis of direction

In several species, the ability to locate a disappearing object is an adaptive component of predatory and social behaviour. In domestic dogs, spatial memory for hidden objects is primarily based on an egocentric frame of reference. We investigated the geometric components of egocentric spatial information used by domestic dogs to locate an object they saw move and disappear. In experiment 1, the distance and the direction between the position of the animal and the hiding location were put in conflict. Results showed that the dogs primarily used the directional information between their own spatial coordinates and the target position. In experiment 2, the accuracy of the dogs in finding a hidden object by using directional information was estimated by manipulating the angular deviation between adjacent hiding locations and the position of the animal. Four angular deviations were tested: 5, 7.5, 10 and 15°. Results showed that the performance of the dogs decreased as a function of the angular deviations but it clearly remained well above chance, revealing that the representation of the dogs for direction is precise. In the discussion, we examine how and why domestic dogs determine the direction in which they saw an object disappear.