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.     

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.     

Goldfish (Carassius auratus) matching geometric and featural cues: a reinterpretation of some of the data of Vargas, López, Salas, and Thinus-Blanc (2004)

Vargas, López, Salas, and Thinus-Blanc showed that goldfish (Carassius auratus) can use both geometric and featural cues in relocating a target corner in a rectangular enclosure. When featural cues (arrangement of striped walls) were put in conflict with geometric cues, results differed according to target location during training. Vargas, López, et al. explained the results of their cue conflict in terms of 2 different strategies: mapping and cue guidance. I provide an alternative, more parsimonious interpretation in which the same strategy of attempting to match as many cues as possible applies to both cases.     

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.     

Spatial reorientation: the effects of space size on the encoding of landmark and geometry information

The effects of the size of the environment on animals’ spatial reorientation was investigated. Domestic chicks were trained to find food in a corner of either a small or a large rectangular enclosure. A distinctive panel was located at each of the four corners of the enclosures. After removal of the panels, chicks tested in the small enclosure showed better retention of geometrical information than chicks tested in the large enclosure. In contrast, after changing the enclosure from a rectangular-shaped to a square-shaped one, chicks tested in the large enclosure showed better retention of landmark (panels) information than chicks tested in the small enclosure. No differences in the encoding of the overall arrangement of landmarks were apparent when chicks were tested for generalisation in an enclosure differing from that of training in size together with a transformation (affine transformation) that altered the geometric relations between the target and the shape of the environment. These findings suggest that primacy of geometric or landmark information in reorientation tasks depends on the size of the experimental space, likely reflecting a preferential use of the most reliable source of information available during visual exploration of the environment.     

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.     

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.     

Searching in the center: pigeons (Columba livid) encode relative distance from walls of an enclosure

Pigeons (Columba livia) searched for food hidden in the center of a square enclosure. On occasional tests without food, the enclosure was (a) unchanged from training (control tests), (b) moved to different corners of the testing room (corner tests), or (c) doubled in size (expansion tests). The birds showed localized search in the center of the enclosure on control and corner tests. On expansion tests, some birds searched near the center of the enclosure, suggesting relative-distance encoding. Other birds searched at locations that maintained the training distance from walls, suggesting absolute-distance encoding. These results are consistent with previous studies on chicks (Gallus gallus) in similar enclosures and contrast with previous results on pigeons' responses to expansions of discrete landmark arrays.     

Reorientation in a two-dimensional environment: II. Do pigeons (Columba livia) encode the featural and geometric properties of a two-dimensional schematic of a room?

Pigeons (Columba livia) searched for a hidden target area in images showing a schematic rectangular environment. The absolute position of the goal varied across trials but was constant relative to distinctive featural cues and geometric properties of the environment. Pigeons learned to use both of these properties to locate the goal. Transformation tests showed that pigeons could use either the color or shape of the features, but performance was better with color cues present. Pigeons could also use a single featural cue at an incorrect corner to distinguish between the correct corner and the geometrically equivalent corner; this indicates that they did not simply use the feature at the correct corner as a beacon. Interestingly, pigeons that were trained with features spontaneously encoded geometry. The encoded geometric information withstood vertical translations but not orientation transformations.     

Animals' use of landmarks and metric information to reorient: effects of the size of the experimental space

Disoriented children could use geometric information in combination with landmark information to reorient themselves in large but not in small experimental spaces. We tested fish in the same task and found that they were able to conjoin geometric and non-geometric (landmark) information to reorient themselves in both the large and the small space used. Moreover, fish proved able to reorient immediately when dislocated from a large to a small experimental space and vice versa, suggesting that they encoded the relative rather than the absolute metrics of the environment. However, fish tended to make relatively more errors based on geometric information when transfer occurred from a small to a large space, and to make relatively more errors based on landmark information when transfer occurred from a large to a small space. The hypothesis is discussed that organisms are prepared to use only distant featural information as landmarks.     

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.     

Reorientation by geometric and landmark information in environments of different size

It has been found that disoriented children could use geometric information in combination with landmark information to reorient themselves in large but not in small experimental spaces. We tested domestic chicks in the same task and found that they were able to conjoin geometric and nongeometric (landmark) information to reorient themselves in both the large and the small space used. Moreover, chicks reoriented immediately when displaced from a large to a small experimental space and vice versa, suggesting that they used the relative metrics of the environment. However, when tested with a transformation (affine transformation) that alters the geometric relations between the target and the shape of the environment, chicks tended to make more errors based on geometric information when tested in the small than in the large space. These findings suggest that the reliance of the use of geometric information on the spatial scale of the environment is not restricted to the human species.     

Penetrating the geometric module: catalyzing children's use of landmarks

We used a reference memory paradigm to examine whether 4- and 5-year-old children could be trained to use landmark features to relocate targets after disorientation. In Experiment 1, half of the children were pretrained in a small equilateral triangle-shaped room. Each of the three walls was a different color, and the target was always in the middle of the yellow wall. These children and a control group were tested in a small rectangular room with three white walls and one yellow wall; the target was placed in one of the corners. Children with pretraining responded more frequently to the correct corner than to the diagonally congruent corner on their first set of four trials in the rectangular room, whereas the children in the control group used geometric cues exclusively. Three additional groups of children (Experiment 2) showed that the use of landmark features--both salient and subtle--can be learned in as few as four practice trials in a small rectangular room. The data support the view that both geometry and landmark features are adaptively combined in the same representation.     

Environment size and the use of feature and geometric cues for reorientation

We tested associative-based accounts of orientation by investigating the influence of environment size on the use of feature and geometric cues for reorientation. Two groups of participants were trained in dynamic three-dimensional virtual rectangular environments that differed in size to find a distinctly colored bin located at one of the four corners. Subsequently, we probed the reliance on feature and geometric cues for reorientation during test trials by presenting six trial types: Small Geometry Only, Large Geometry Only, Small Cue Conflict, Large Cue Conflict, Small Distal, and Large Distal. During Geometry Only test trials, all bins were black; thus, all distinctive featural information was removed leaving only geometric cues. For Cue Conflict test trials, all colored bins were shifted counter-clockwise one corner; thus, the geometric cues from the trained corner and the trained color were in direct conflict. During Distal test trials, the bin in the geometrically incorrect corner farthest from the trained corner was colored the same as during training; the remaining three bins were black. Thus, only this distant feature cue could be used to determine the location of the goal bin. Results suggested that geometric cues were used across changes in environment size, featural cues exerted greater influence when in conflict with geometric cues, and the far featural cue was used to disambiguate the correct from the rotationally equivalent location. In short, both feature and geometric cues were used for reorientation, and environment size influenced the relative use of feature and geometric cues. Collectively, our results provide evidence against associative-based accounts of orientation.     

几何模块论的局限性——来自梯形实验的证据

以往研究表明幼儿主要依赖几何信息进行再定向,但这些研究大多使用矩形空间。在本研究中,幼儿所处的空间为几何信息更丰富,目标物体所在位置确定的梯形。结果发现,幼儿并不会利用新增的几何信息确定目标物体,仍然去正确位置的对角寻找,表现出的寻找模式与矩形空间一样,这说明幼儿在空间再定向任务中对几何信息的利用很有限。此外,录像分析的结果发现,幼儿在面向梯形两底边时会更多地且径直地走向正确位置或对角,这种寻找过程上的特点表明他们可能基于空间轴朝向结合左右方位感表征物体位置     

Rhesus monkeys use geometric and nongeometric information during a reorientation task

Rhesus monkeys (Macaca mulata) were subjected to a place finding task in a rectangular room perfectly homogeneous and without distinctive featural information. Results of Experiment 1 show that monkeys rely on the large-scale geometry of the room to retrieve a food reward. Experiments 2 and 3 indicate that subjects use also nongeometric information (colored wall) to reorient. Data of Experiments 4 and 5 suggest that monkeys do not use small angular cues but that they are sensitive to the size of the cues (Experiments 6, 7, and 8). Our findings strengthen the idea that a mechanism based on the geometry of the environment is at work in several mammalian species. In addition, the present data offer new perspectives on spatial cognition in animals that are phylogenetically close to humans. Specifically, the joint use of both geometric and landmark-based cues by rhesus monkeys tends to demonstrate that spatial processing became more flexible with evolution.     

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.     

Growing in circles: rearing environment alters spatial navigation in fish

ABSTRACT— Animals of many species use the geometric shape of an enclosed rectangular environment to reorient, even in the presence of a more informative featural cue. Manipulating the rearing environment affects performance on spatial tasks, but its effect on the use of geometric versus featural navigational cues is unknown. Our study varied the geometric information available in the rearing environment (circular vs. rectangular rearing tanks) of convict cichlids ( Archocentrus nigrofasciatus ) and tested their use of navigational cues. All the fish used geometric information to navigate when no features were present. When features were present, the fish used geometric and featural information separately. If cues were in conflict, fish raised in a circular tank showed significantly less use of geometric information than fish raised in a rectangular tank. Thus, the ability to use geometry to navigate does not require exposure to angular geometric cues during rearing, though rearing environment affects the dominance of featural and geometric cues.     

Finding the best angle: pigeons (<Emphasis Type="Italic">Columba livia</Emphasis>) weight angular information more heavily than relative wall length in an open-field geometry task

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.     

Sex differences and the effect of instruction on reorientation abilities by humans

This study examined whether differences in the amount of information provided to men and women, in the form of verbal instruction, influenced their encoding during a reorientation task. When a navigator needs to orient, featural (e.g., colour or texture) and geometry (e.g., metric information) are used to determine which direction to begin traveling. The current study used a spatial reorientation task to examine how men and women use featural and geometric cues and whether the content of the task’s instructions influenced how these cues were used. Participants were trained to find a target location in a rectangular room with distinctive objects situated at each corner. Once the participants were accurately locating the target, various tests manipulating the spatial information were conducted. We found both men and women encoded the featural cues, and even though the features provided reliable information, participants generally showed an encoding of geometry. However, when participants were not provided with any information about the spatial aspects of the task in the instructions, they failed to encode geometry. We also found that women used distant featural cues as landmarks when the featural cue closest to the target was removed, whereas men did not. Yet, when the two types of cues were placed in conflict, both sexes weighed featural cues more heavily than geometric cues. The content of the task instructions also influenced how cues were relied upon in this conflict situation. Our results have important implications for our understanding of how spatial cues are used for reorientation.