Horizontal biases in rats' use of three-dimensional space

Tactile cues compensate for unbalanced vestibular cues during progression on inclined surfaces

A previous study demonstrated that rodents on an inclined square platform traveled straight vertically or horizontally and avoided diagonal travel. Through behavior they aligned their head with the horizontal plane, acquiring similar bilateral vestibular cues - a basic requirement for spatial orientation and a salient feature of animals in motion. This behavior had previously been shown to be conspicuous in Tristram's jirds. Here, therefore jirds were challenged by testing their travel behavior on a circular arena inclined at 0°-75°. Our hypothesis was that if, as typical to rodents, the jirds would follow the curved arena wall, they would need to display a compensating mechanism to enable traveling in such a path shape, which involves a tilted frontal head axis and unbalanced bilateral vestibular cues. We found that with the increase in inclination, the jirds remained more in the lower section of the arena (geotaxis). When tested on the steep inclinations, however, their travel away from the arena wall was strictly straight up or down, in contrast to the curved paths that followed the circular arena wall. We suggest that traveling along a circular path while maintaining contact with the wall (thigmotaxis), provided tactile information that compensated for the unbalanced bilateral vestibular cues present when traveling along such curved inclined paths. In the latter case, the frontal plane of the head was in a diagonal posture in relation to gravity, a posture that was avoided when traveling away from the wall.

An allocentric human odometer for perceiving distances on the ground plane

We reliably judge locations of static objects when we walk despite the retinal images of these objects moving with every step we take. Here, we showed our brains solve this optical illusion by adopting an allocentric spatial reference frame. We measured perceived target location after the observer walked a short distance from the home base. Supporting the allocentric coding scheme, we found the intrinsic bias 1, 2 , which acts as a spatial reference frame for perceiving location of a dimly lit target in the dark, remained grounded at the home base rather than traveled along with the observer. The path-integration mechanism responsible for this can utilize both active and passive (vestibular) translational motion signals, but only along the horizontal direction. This anisotropic path-integration finding in human visual space perception is reminiscent of the anisotropic spatial memory finding in desert ants 3 , pointing to nature's wondrous and logically simple design for terrestrial creatures.

Dissociating two aspects of human 3D spatial perception by studying fighter pilots

Human perception of 3D space has been investigated extensively, but there are conflicting reports regarding its distortions. A possible solution to these discrepancies is that 3D perception is in fact comprised of two different processes-perception of traveled space, and perception of surrounding space. Here we tested these two aspects on the same subjects, for the first time. To differentiate these two aspects and investigate whether they emerge from different processes, we asked whether these two aspects are affected differently by the individual's experience of 3D locomotion. Using an immersive high-grade flight-simulator with realistic virtual-reality, we compared these two aspects of 3D perception in fighter pilots-individuals highly experienced in 3D locomotion-and in control subjects. We found that the two aspects of 3D perception were affected differently by 3D locomotion experience: the perception of 3D traveled space was plastic and experience-dependent, differing dramatically between pilots and controls, while the perception of surrounding space was rigid and unaffected by experience. This dissociation suggests that these two aspects of 3D spatial perception emerge from two distinct processes.

A small step for rats alters spatial behavior: rats on a bi-level arena explore each level separately

We tested rats on a 'bi-level open-field' whose two halves were separated vertically by an 8-cm step that the rats could easily ascend/descend. We sought to determine what might be the factors that shape traveling in three-dimensional environments; what makes an environment perceived as multileveled; and how are multileveled environments explored compared to two-dimensional environments? We found that rats on the bi-level open-field traveled a greater distance on the lower level compared to the upper one. They also spent a long time at the foot of the step before ascending to the upper level. They established a home-base on one level and a local base on the other one, and explored each level separately. We could not find a particular factor that accounted for the preference for the lower level. We suggest that the momentary egocentric sensation of moving vertically, together with an overall area large enough for exploration, result in perceiving an environment as multilevel. Exploration of such environments is fragmented, and each level is explored relatively independently, as has also been shown in other studies. Regarding the unanswered question of earlier studies concerning what integrates fragmented representations, this is the first study that suggests that in rats, and perhaps also in other rodent species, such integration is achieved by means of home-base behavior, resulting in the establishment of a single comprehensive representation of the multilevel environment.

Symmetries and asymmetries in the neural encoding of 3D space

The neural coding of space centres on three foundational cell types: place cells, head direction cells and grid cells. One notable characteristic of these neurons is the symmetry properties of their spatial firing patterns. In symmetric environments, firing patterns are often also symmetric: for example, place cells show translational symmetry in aligned sub-compartments of a multi-compartment environment. A single head direction cell has a mirror-symmetric firing pattern, while a sub-class of head direction cells can show multi-fold rotational symmetries in multi-compartment environments, matching the symmetry of the recently experienced environment. The entorhinal grid cells are notable for the symmetry of their firing patterns in both rotational and translational domains. However, these symmetries are broken in a variety of situations. These symmetry-making and -breaking observations shed light on the underlying computations that generate these firing patterns, and also invite speculation as to whether they may have a functional role. This article outlines these findings and speculates on the consequences of the resultant firing symmetries and asymmetries for spatial coding and cognition. This article is part of a discussion meeting issue 'New approaches to 3D vision'.

Can rats and ants exchange information between the horizontal and vertical domains?

Since traveling in nature involves encountering various vertical structures, integration of horizontal and vertical spatial information is required. One form of such integration is to use information acquired in one plane for spatial navigation in another plane. Here we tested whether rats and ants that learned a reward location in a horizontal maze could utilize this information when the maze was rotated to a vertical orientation and vice versa. Rats that were trained in a horizontal Y-maze required more time to reach the reward when the maze was vertically rotated, but they were more accurate in choosing the correct arm. In contrast, rats tested in a horizontal maze after being trained in a vertical maze were less accurate but reached the reward faster. Changes after maze rotation were moderate and non-significant in ants, perhaps since the number of ants arriving at the reward increased over trials, diminishing the effect of maze rotation in ants compared to rats. According to the notion that horizontal spatial information is encoded in more detail than vertical information, the slow performance of rats in the vertical domain could be due to a more physically demanding task whereas their accuracy was due to a preceding detailed horizontal encoding. In contrast, rats in the vertical maze could gather less detailed information and therefore were less accurate in subsequent horizontal trials, where the lower energy cost enabled them to swiftly correct wrong choices. Altogether, the present results provide an indication for transferring spatial information between horizontal and vertical dimensions.

Rodents Prefer Going Downhill All the Way (Gravitaxis) Instead of Taking an Uphill Task

We directly tested whether, when given the choice to ascend or descend, rodents would favor traveling downwards or upwards. The test incorporated different rodent species that dwell in different habitats and display different life and motor styles. Testing was performed in a three-dimensional Y-maze in which the basis was horizontal and, by rotating it, one arm of the maze could be pointing upwards at a certain angle and the other arm pointed downwards at the same angle. All the tested species displayed a general preference for descent, with rodents from complex habitats being less affected by inclination compared with rodents from flatlands. Unlike laboratory rats, wild species traveled greater distances along the lower compared to the upper maze arm. All the rodents initially tended to travel the entire length of the inclined maze arms, but such complete trips decreased with the increase in inclination. When introduced into the maze from top or bottom, flatland dwellers traveled mainly in the entry arm. Overall, when given the choice to ascend or descend, all the tested species displayed a preference to descend, perhaps as attraction to the ground, where they usually have their burrows.

Keep a level head to know the way ahead: How rodents travel on inclined surfaces?

Animals traveling on a horizontal surface stabilize their head in relation to the substrate in order to gather spatial information and orient. What, however, do they do when traveling on an incline? We examined how three rodent species differing in motor abilities and habitats explore a platform tilted at 0–90°, hypothesizing that they would attempt to maintain bilateral vestibular cues. We found that traveling up or down was mainly straight vertically rather than diagonally, which results in identical bilateral vestibular cues. This was also achieved when traveling horizontally through rotating the head to parallel the horizontal plane. Traveling diagonally up or down was avoided, perhaps due to different bilateral vestibular cues that could hinder orientation. Accordingly, we suggest that maintaining identical bilateral cues is an orientational necessity that overrides differences in motor abilities and habitats, and that this necessity is a general characteristic of animals in motion.

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Three rodent species were tested on a platform inclined at 0°–90°

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Increased inclination results in traveling straight vertically or horizontally

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Both these shapes of trajectories feature a horizontal leveled head

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We suggest that such posture is required for spatial orientation when in motion

Irregular distribution of grid cell firing fields in rats exploring a 3D volumetric space

We investigated how entorhinal grid cells encode volumetric space. On a horizontal surface, grid cells usually produce multiple, spatially focal, approximately circular firing fields that are evenly sized and spaced to form a regular, close-packed, hexagonal array. This spatial regularity has been suggested to underlie navigational computations. In three dimensions, theoretically the equivalent firing pattern would be a regular, hexagonal close packing of evenly sized spherical fields. In the present study, we report that, in rats foraging in a cubic lattice, grid cells maintained normal temporal firing characteristics and produced spatially stable firing fields. However, although most grid fields were ellipsoid, they were sparser, larger, more variably sized and irregularly arranged, even when only fields abutting the lower surface (equivalent to the floor) were considered. Thus, grid self-organization is shaped by the environment's structure and/or movement affordances, and grids may not need to be regular to support spatial computations.

EthoLoop: automated closed-loop neuroethology in naturalistic environments

Accurate tracking and analysis of animal behavior is crucial for modern systems neuroscience. However, following freely moving animals in naturalistic, three-dimensional (3D) or nocturnal environments remains a major challenge. Here, we present EthoLoop, a framework for studying the neuroethology of freely roaming animals. Combining real-time optical tracking and behavioral analysis with remote-controlled stimulus-reward boxes, this system allows direct interactions with animals in their habitat. EthoLoop continuously provides close-up views of the tracked individuals and thus allows high-resolution behavioral analysis using deep-learning methods. The behaviors detected on the fly can be automatically reinforced either by classical conditioning or by optogenetic stimulation via wirelessly controlled portable devices. Finally, by combining 3D tracking with wireless neurophysiology we demonstrate the existence of place-cell-like activity in the hippocampus of freely moving primates. Taken together, we show that the EthoLoop framework enables interactive, well-controlled and reproducible neuroethological studies in large-field naturalistic settings.

Volumetric spatial behaviour in rats reveals the anisotropic organisation of navigation

We investigated how access to the vertical dimension influences the natural exploratory and foraging behaviour of rats. Using high-accuracy three-dimensional tracking of position in two- and three-dimensional environments, we sought to determine (i) how rats navigated through the environments with respect to gravity, (ii) where rats chose to form their home bases in volumetric space, and (iii) how they navigated to and from these home bases. To evaluate how horizontal biases may affect these behaviours, we compared a 3D maze where animals preferred to move horizontally to a different 3D configuration where all axes were equally energetically costly to traverse. Additionally, we compared home base formation in two-dimensional arenas with and without walls to the three-dimensional climbing mazes. We report that many behaviours exhibited by rats in horizontal spaces naturally extend to fully volumetric ones, such as home base formation and foraging excursions. We also provide further evidence for the strong differentiation of the horizontal and vertical axes: rats showed a horizontal movement bias, they formed home bases mainly in the bottom layers of both mazes and they generally solved the vertical component of return trajectories before and faster than the horizontal component. We explain the bias towards horizontal movements in terms of energy conservation, while the locations of home bases are explained from an information gathering view as a method for correcting self-localisation.

On the absence or presence of 3D tuned head direction cells in rats: a review and rebuttal

A major question in the field of spatial cognition is how animals represent three-dimensional (3D) space. Different results have been obtained across various species and may depend on whether the species inhabits a 3D environment or is terrestrial (land dwelling). The head direction (HD) cell system is an attractive candidate to study in terms of 3D representations. HD cells fire as a function of the animal's directional heading in the horizontal plane, independent of the animal's location and on-going behavior. Another issue concerns whether HD cells are tuned in 3D space or tuned to the 2D horizontal plane. Shinder and Taube (Shinder ME, Taube JS. J Neurophysiol 121: 4-37, 2019) addressed this issue by manipulating a rat's orientation in 3D space while monitoring responses from classic HD cells in the rat anterodorsal thalamus. They reported that HD cells did not display conjunctive firing with pitch or roll orientations. Direction-specific firing was primarily derived from horizontal semicircular canal information and that the gravity vector played an important role in influencing the cell's firing rate and its preferred firing direction. Laurens and Angelaki (Laurens J, Angelaki DE. J Neurophysiol 122: 1274-1287, 2019) challenged this view by performing a mathematical analysis on the Shinder and Taube data and concluded that they would not have seen 3D tuning based on their experimental approach. We provide a historical review of these issues followed by a summary of the experiments, which includes additional analyses. We then define what it means for a HD cell to be tuned in 3D and finish by rebutting the reanalyses performed by Laurens and Angelaki.

The place-cell representation of volumetric space in rats

Place cells are spatially modulated neurons found in the hippocampus that underlie spatial memory and navigation: how these neurons represent 3D space is crucial for a full understanding of spatial cognition. We wirelessly recorded place cells in rats as they explored a cubic lattice climbing frame which could be aligned or tilted with respect to gravity. Place cells represented the entire volume of the mazes: their activity tended to be aligned with the maze axes, and when it was more difficult for the animals to move vertically the cells represented space less accurately and less stably. These results demonstrate that even surface-dwelling animals represent 3D space and suggests there is a fundamental relationship between environment structure, gravity, movement and spatial memory.

"It's all in their head": hierarchical exploration of a three-dimensional layered pyramid in rats

Wayfinding in a three-dimensional (3D) environment is intricate, and surface-bounded animals may overcome this complexity by breaking it down into horizontal layers along with the vertical location of each layer. Here, we examined how rats explored a layered pyramid placed in a large open field. We found that exploration presented a hierarchical (or fractal) shape of three types of roundtrips: (1) from the primary home-base to the open-field floor; (2) from the floor up and down the pyramid levels; and (3) from local home-base on each pyramid level. Ascent was slow and interrupted, whereas descent was fast. This difference was a result of level altitude, remaining after data were normalized proportionally to level area. In contrast, the time spent and the distance traveled on each level were dependent on level area, not on level altitude. This structure of spatial behavior accords with multilevel exploration, presenting a relatively independent exploration of each level. The vertical dimension in this experiment thus did not alter the typical spatiotemporal behavior, and the 3D environment was explored by application of the same spatiotemporal approach as that of a horizontal open field. We suggest that this lack of alteration is due to the horizontal posture of the animal's head and trunk during progression on the pyramid. This behavior also seems to fit the bicoding hypothesis, in which the vertical information is virtually contextual (non-metric), and so, when the rat progresses to a new level, it explores it as a newly accessed horizontal floor area.

Distorted mental spatial representation of multi-level buildings - Humans are biased towards equilateral shapes of height and width

A distorted model of a familiar multi-level building with a systematic overestimation of the height was demonstrated earlier in psychophysical and real world navigational tasks. In the current study we further investigated this phenomenon with a tablet-based application. Participants were asked to adjust height and width of the presented buildings to best match their memory of the dimensional ratio. The estimation errors between adjusted and true height-width ratios were analyzed. Additionally, familiarity with respect to in- and outside of the building as well as demographic data were acquired. A total of 142 subjects aged 21 to 90 years from the cities of Bern and Munich were tested. Major results were: (1) a median overestimation of the height of the multi-level buildings of 11%; (2) estimation errors were significantly less if the particular building was unknown to participants; (3) in contrast, the height of tower-like buildings was underestimated; (4) the height of long, flat shaped buildings was overestimated. (5) Further features, such as the architectonical complexity were critical. Overall, our internal models of large multi-level buildings are distorted due to multiple factors including geometric features and memory effects demonstrating that such individual models are not rigid but plastic with consequences for spatial orientation and navigation.

Hippocampus, Retrosplenial and Parahippocampal Cortices Encode Multicompartment 3D Space in a Hierarchical Manner

Humans commonly operate within 3D environments such as multifloor buildings and yet there is a surprising dearth of studies that have examined how these spaces are represented in the brain. Here, we had participants learn the locations of paintings within a virtual multilevel gallery building and then used behavioral tests and fMRI repetition suppression analyses to investigate how this 3D multicompartment space was represented, and whether there was a bias in encoding vertical and horizontal information. We found faster response times for within-room egocentric spatial judgments and behavioral priming effects of visiting the same room, providing evidence for a compartmentalized representation of space. At the neural level, we observed a hierarchical encoding of 3D spatial information, with left anterior hippocampus representing local information within a room, while retrosplenial cortex, parahippocampal cortex, and posterior hippocampus represented room information within the wider building. Of note, both our behavioral and neural findings showed that vertical and horizontal location information was similarly encoded, suggesting an isotropic representation of 3D space even in the context of a multicompartment environment. These findings provide much-needed information about how the human brain supports spatial memory and navigation in buildings with numerous levels and rooms.

Anisotropy of Human Horizontal and Vertical Navigation in Real Space: Behavioral and PET Correlates

Spatial orientation was tested during a horizontal and vertical real navigation task in humans. Video tracking of eye movements was used to analyse the behavioral strategy and combined with simultaneous measurements of brain activation and metabolism ([18F]-FDG-PET). Spatial navigation performance was significantly better during horizontal navigation. Horizontal navigation was predominantly visually and landmark-guided. PET measurements indicated that glucose metabolism increased in the right hippocampus, bilateral retrosplenial cortex, and pontine tegmentum during horizontal navigation. In contrast, vertical navigation was less reliant on visual and landmark information. In PET, vertical navigation activated the bilateral hippocampus and insula. Direct comparison revealed a relative activation in the pontine tegmentum and visual cortical areas during horizontal navigation and in the flocculus, insula, and anterior cingulate cortex during vertical navigation. In conclusion, these data indicate a functional anisotropy of human 3D-navigation in favor of the horizontal plane. There are common brain areas for both forms of navigation (hippocampus) as well as unique areas such as the retrosplenial cortex, visual cortex (horizontal navigation), flocculus, and vestibular multisensory cortex (vertical navigation). Visually guided landmark recognition seems to be more important for horizontal navigation, while distance estimation based on vestibular input might be more relevant for vertical navigation.

3-D Maps and Compasses in the Brain

The world has a complex, three-dimensional (3-D) spatial structure, but until recently the neural representation of space was studied primarily in planar horizontal environments. Here we review the emerging literature on allocentric spatial representations in 3-D and discuss the relations between 3-D spatial perception and the underlying neural codes. We suggest that the statistics of movements through space determine the topology and the dimensionality of the neural representation, across species and different behavioral modes. We argue that hippocampal place-cell maps are metric in all three dimensions, and might be composed of 2-D and 3-D fragments that are stitched together into a global 3-D metric representation via the 3-D head-direction cells. Finally, we propose that the hippocampal formation might implement a neural analogue of a Kalman filter, a standard engineering algorithm used for 3-D navigation.

Predictive representations can link model-based reinforcement learning to model-free mechanisms

Humans and animals are capable of evaluating actions by considering their long-run future rewards through a process described using model-based reinforcement learning (RL) algorithms. The mechanisms by which neural circuits perform the computations prescribed by model-based RL remain largely unknown; however, multiple lines of evidence suggest that neural circuits supporting model-based behavior are structurally homologous to and overlapping with those thought to carry out model-free temporal difference (TD) learning. Here, we lay out a family of approaches by which model-based computation may be built upon a core of TD learning. The foundation of this framework is the successor representation, a predictive state representation that, when combined with TD learning of value predictions, can produce a subset of the behaviors associated with model-based learning, while requiring less decision-time computation than dynamic programming. Using simulations, we delineate the precise behavioral capabilities enabled by evaluating actions using this approach, and compare them to those demonstrated by biological organisms. We then introduce two new algorithms that build upon the successor representation while progressively mitigating its limitations. Because this framework can account for the full range of observed putatively model-based behaviors while still utilizing a core TD framework, we suggest that it represents a neurally plausible family of mechanisms for model-based evaluation.

Going Up or Sideways? Perception of Space and Obstacles Negotiating by Cuttlefish

While octopuses are mostly benthic animals, and squid prefer the open waters, cuttlefish present a special intermediate stage. Although their body structure resembles that of a squid, in many cases their behavior is mostly benthic. To test cuttlefish's preference in the use of space, we trained juvenile Sepia gibba and Sepia officinalis cuttlefish to reach a shelter at the opposite side of a tank. Afterwards, rock barriers were placed between the starting point and the shelter. In one experiment, direct paths were available both through the sand and over the rocks. In a second experiment the direct path was blocked by small rocks requiring a short detour to by-pass. In the third experiment instead, the only direct path available was over the rocks; or else to reach the goal via an exclusively horizontal path a longer detour would have to be selected. We showed that cuttlefish prefer to move horizontally when a direct route or a short detour path is available close to the ground; however when faced with significant obstacles they can and would preferentially choose a more direct path requiring a vertical movement over a longer exclusively horizontal path. Therefore, cuttlefish appear to be predominantly benthic dwellers that prefer to stay near the bottom. Nonetheless, they do view and utilize the vertical space in their daily movements where it plays a role in night foraging, obstacles negotiation and movement in their home-range.

Spatial learning in the cuttlefish Sepia officinalis: preference for vertical over horizontal information

The world is three-dimensional; hence, even surface-bound animals need to learn vertical spatial information. Separate encoding of vertical and horizontal spatial information seems to be the common strategy regardless of the locomotory style of animals. However, a difference seems to exist in the way freely moving species, such as fish, learn and integrate spatial information as opposed to surface-bound species, which prioritize the horizontal dimension and encode it with a higher resolution. Thus, the locomotory style of an animal may shape how spatial information is learned and prioritized. An alternative hypothesis relates the preference for vertical information to the ability to sense hydrostatic pressure, a prominent cue unique to this dimension. Cuttlefish are mostly benthic animals, but they can move freely in a volume. Therefore, they present an optimal model to examine these hypotheses. We tested whether cuttlefish could separately recall the vertical and horizontal components of a learned two-dimensional target, and whether they have a preference for vertical or horizontal information. Sepia officinalis cuttlefish were trained to select one of two visual cues set along a 45 deg diagonal. The animals were then tested with the two visual cues arranged in a horizontal, vertical or opposite 45 deg configuration. We found that cuttlefish use vertical and horizontal spatial cues separately, and that they prefer vertical information to horizontal information. We propose that, as in fish, the availability of hydrostatic pressure, combined with the ecological value of vertical movements, determines the importance of vertical information.

Detour Behavior of Mice Trained with Transparent, Semitransparent and Opaque Barriers

Detour tasks are commonly used to study problem solving skills and inhibitory control in canids and primates. However, there is no comparable detour test designed for rodents despite its significance for studying the development of executive skills. Furthermore, mice offer research opportunities that are not currently possible to achieve when primates are used. Therefore, the aim of the study was to translate the classic detour task to mice and to compare obtained data with key findings obtained previously in other mammals. The experiment was performed with V-shaped barriers and was based on the water escape paradigm. The study showed that an apparently simple task requiring mice to move around a small barrier constituted in fact a challenge that was strongly affected by the visibility of the target. The most difficult task involved a completely transparent barrier, which forced the mice to resolve a conflict between vision and tactile perception. The performance depended both on the inhibitory skills and on previous experiences. Additionally, all mice displayed a preference for one side of the barrier and most of them relied on the egocentric strategy. Obtained results show for the first time that the behavior of mice subjected to the detour task is comparable to the behavior of other mammals tested previously with free-standing barriers. This detailed characterization of the detour behavior of mice constitutes the first step toward the substitution of rodents for primates in laboratory experiments employing the detour task.

The Representation of Three-Dimensional Space in Fish

In mammals, the so-called “seat of the cognitive map” is located in place cells within the hippocampus. Recent work suggests that the shape of place cell fields might be defined by the animals’ natural movement; in rats the fields appear to be laterally compressed (meaning that the spatial map of the animal is more highly resolved in the horizontal dimensions than in the vertical), whereas the place cell fields of bats are statistically spherical (which should result in a spatial map that is equally resolved in all three dimensions). It follows that navigational error should be equal in the horizontal and vertical dimensions in animals that travel freely through volumes, whereas in surface-bound animals would demonstrate greater vertical error. Here, we describe behavioral experiments on pelagic fish in which we investigated the way that fish encode three-dimensional space and we make inferences about the underlying processing. Our work suggests that fish, like mammals, have a higher order representation of space that assembles incoming sensory information into a neural unit that can be used to determine position and heading in three-dimensions. Further, our results are consistent with this representation being encoded isotropically, as would be expected for animals that move freely through volumes. Definitive evidence for spherical place fields in fish will not only reveal the neural correlates of space to be a deep seated vertebrate trait, but will also help address the questions of the degree to which environment spatial ecology has shaped cognitive processes and their underlying neural mechanisms.

"Taller and Shorter": Human 3-D Spatial Memory Distorts Familiar Multilevel Buildings

Animal experiments report contradictory findings on the presence of a behavioural and neuronal anisotropy exhibited in vertical and horizontal capabilities of spatial orientation and navigation. We performed a pointing experiment in humans on the imagined 3-D direction of the location of various invisible goals that were distributed horizontally and vertically in a familiar multilevel hospital building. The 21 participants were employees who had worked for years in this building. The hypothesis was that comparison of the experimentally determined directions and the true directions would reveal systematic inaccuracy or dimensional anisotropy of the localizations. The study provides first evidence that the internal representation of a familiar multilevel building was distorted compared to the dimensions of the true building: vertically 215% taller and horizontally 51% shorter. This was not only demonstrated in the mathematical reconstruction of the mental model based on the analysis of the pointing experiments but also by the participants’ drawings of the front view and the ground plan of the building. Thus, in the mental model both planes were altered in different directions: compressed for the horizontal floor plane and stretched for the vertical column plane. This could be related to human anisotropic behavioural performance of horizontal and vertical navigation in such buildings.

Spatial learning by mice in three dimensions

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Mouse spatial memory was tested on a novel 3D radial arm maze.

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Mice exhibited learning on working and reference memory tasks on the 3D maze.

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Working memory was not impaired on the 3D maze when compared with a 2D analogue.

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Reference memory was impaired on the 3D maze when compared with the 2D maze.

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This may be explained by a differential encoding of vertical and horizontal space.

We tested whether mice can represent locations distributed throughout three-dimensional space, by developing a novel three-dimensional radial arm maze. The three-dimensional radial maze, or “radiolarian” maze, consists of a central spherical core from which arms project in all directions. Mice learn to retrieve food from the ends of the arms without omitting any arms or re-visiting depleted ones. We show here that mice can learn both a standard working memory task, in which all arms are initially baited, and also a reference memory version in which only a subset are ever baited. Comparison with a two-dimensional analogue of the radiolarian maze, the hexagon maze, revealed equally good working-memory performance in both mazes if all the arms were initially baited, but reduced working and reference memory in the partially baited radiolarian maze. This suggests intact three-dimensional spatial representation in mice over short timescales but impairment of the formation and/or use of long-term spatial memory of the maze. We discuss potential mechanisms for how mice solve the three-dimensional task, and reasons for the impairment relative to its two-dimensional counterpart, concluding with some speculations about how mammals may represent three-dimensional space.

Solving the detour problem in navigation: a model of prefrontal and hippocampal interactions

Adapting behavior to accommodate changes in the environment is an important function of the nervous system. A universal problem for motile animals is the discovery that a learned route is blocked and a detour is required. Given the substantial neuroscience research on spatial navigation and decision-making it is surprising that so little is known about how the brain solves the detour problem. Here we review the limited number of relevant functional neuroimaging, single unit recording and lesion studies. We find that while the prefrontal cortex (PFC) consistently responds to detours, the hippocampus does not. Recent evidence suggests the hippocampus tracks information about the future path distance to the goal. Based on this evidence we postulate a conceptual model in which: Lateral PFC provides a prediction error signal about the change in the path, frontopolar and superior PFC support the re-formulation of the route plan as a novel subgoal and the hippocampus simulates the new path. More data will be required to validate this model and understand (1) how the system processes the different options; and (2) deals with situations where a new path becomes available (i.e., shortcuts).

Navigating in a three-dimensional world

The study of spatial cognition has provided considerable insight into how animals (including humans) navigate on the horizontal plane. However, the real world is three-dimensional, having a complex topography including both horizontal and vertical features, which presents additional challenges for representation and navigation. The present article reviews the emerging behavioral and neurobiological literature on spatial cognition in non-horizontal environments. We suggest that three-dimensional spaces are represented in a quasi-planar fashion, with space in the plane of locomotion being computed separately and represented differently from space in the orthogonal axis - a representational structure we have termed "bicoded." We argue that the mammalian spatial representation in surface-travelling animals comprises a mosaic of these locally planar fragments, rather than a fully integrated volumetric map. More generally, this may be true even for species that can move freely in all three dimensions, such as birds and fish. We outline the evidence supporting this view, together with the adaptive advantages of such a scheme.

Navigating in a volumetric world: metric encoding in the vertical axis of space

Animals navigate through three-dimensional environments, but we argue that the way they encode three-dimensional spatial information is shaped by how they use the vertical component of space. We agree with Jeffery et al. that the representation of three-dimensional space in vertebrates is probably bicoded (with separation of the plane of locomotion and its orthogonal axis), but we believe that their suggestion that the vertical axis is stored "contextually" (that is, not containing distance or direction metrics usable for novel computations) is unlikely, and as yet unsupported. We describe potential experimental protocols that could clarify these differences in opinion empirically.

Three-dimensional spatial cognition in a benthic fish, Corydoras aeneus

The way animals move through space is likely to affect the way they learn and remember spatial information. For example, a pelagic fish, Astyanax fasciatus, moves freely in vertical and horizontal space and encodes information from both dimensions with similar accuracy. Benthic fish can also move with six degrees of freedom, but spend much of their time travelling over the substrate; hence they might be expected to prioritise the horizontal dimension. To understand how benthic fish encode and deploy three-dimensional spatial information we used a fully rotational Y-maze to test whether Corydoras aeneus (i) encode space as an integrated three-dimensional unit or as separate elements, by testing whether they can decompose a three-dimensional trajectory into its vertical and horizontal components, and (ii) whether they prioritise vertical or horizontal information when the two conflict. In contradiction to the expectation generated by our hypothesis, our results suggest that C. aeneus are better at extracting vertical information than horizontal information from a three-dimensional trajectory, suggesting that the vertical axis is learned and remembered robustly. Our results also showed that C. aeneus prioritise vertical information when it conflicts with horizontal information. From these results, we infer that benthic fish attend preferentially to a cue unique to the vertical axis, and we suggest that this cue is hydrostatic pressure.

Reorienting with terrain slope and landmarks

Orientation (or reorientation) is the first step in navigation, because establishing a spatial frame of reference is essential for a sense of location and heading direction. Recent research on nonhuman animals has revealed that the vertical component of an environment provides an important source of spatial information, in both terrestrial and aquatic settings. Nonetheless, humans show large individual and sex differences in the ability to use terrain slope for reorientation. To understand why some participants--mainly women--exhibit a difficulty with slope, we tested reorientation in a richer environment than had been used previously, including both a tilted floor and a set of distinct objects that could be used as landmarks. This environment allowed for the use of two different strategies for solving the task, one based on directional cues (slope gradient) and one based on positional cues (landmarks). Overall, rather than using both cues, participants tended to focus on just one. Although men and women did not differ significantly in their encoding of or reliance on the two strategies, men showed greater confidence in solving the reorientation task. These facts suggest that one possible cause of the female difficulty with slope might be a generally lower spatial confidence during reorientation.

Three-dimensional space: locomotory style explains memory differences in rats and hummingbirds

While most animals live in a three-dimensional world, they move through it to different extents depending on their mode of locomotion: terrestrial animals move vertically less than do swimming and flying animals. As nearly everything we know about how animals learn and remember locations in space comes from two-dimensional experiments in the horizontal plane, here we determined whether the use of three-dimensional space by a terrestrial and a flying animal was correlated with memory for a rewarded location. In the cubic mazes in which we trained and tested rats and hummingbirds, rats moved more vertically than horizontally, whereas hummingbirds moved equally in the three dimensions. Consistent with their movement preferences, rats were more accurate in relocating the horizontal component of a rewarded location than they were in the vertical component. Hummingbirds, however, were more accurate in the vertical dimension than they were in the horizontal, a result that cannot be explained by their use of space. Either as a result of evolution or ontogeny, it appears that birds and rats prioritize horizontal versus vertical components differently when they remember three-dimensional space.

Making a stronger case for comparative research to investigate the behavioral and neurological bases of three-dimensional navigation

The rich diversity of avian natural history provides exciting possibilities for comparative research aimed at understanding three-dimensional navigation. We propose some hypotheses relating differences in natural history to potential behavioral and neurological adaptations possessed by contrasting bird species. This comparative approach may offer unique insights into some of the important questions raised by Jeffery et al.

What counts as the evidence for three-dimensional and four-dimensional spatial representations?

The dimension of spatial representations can be assessed by above-chance performance in novel shortcut or spatial reasoning tasks independent of accuracy levels, systematic biases, mosaic/segmentation across space, separate coding of individual dimensions, and reference frames. Based on this criterion, humans and some other animals exhibited sufficient evidence for the existence of three-dimensional and/or four-dimensional spatial representations.

Does terrain slope really dominate goal searching?

If you can locate a target by using one reliable source of information, why would you use an unreliable one? A similar question has been faced in a recent study on homing pigeons, in which, despite the presence of better predictors of the goal location, the slope of the floor in an arena dominated the searching process. This piece of evidence seems to contradict straightforward accounts of associative learning, according to which behavior should be controlled by the stimulus that best predicts the reward, and has fueled interest toward one question that, to date, has received scarce attention in the field of spatial cognition: how are vertical spaces represented? The purpose of this communication is to briefly review the studies on this issue, trying to determine whether slope is a special cue--driving behavior irrespective of other cues--or simply a very salient one.

Three-dimensional spatial representation in freely swimming fish

Research on spatial cognition has focused on how animals encode the horizontal component of space. However, most animals travel vertically within their environments, particularly those that fly or swim. Pelagic fish move with six degrees of freedom and must integrate these components to navigate accurately--how do they do this? Using an assay based on associative learning of the vertical and horizontal components of space within a rotating Y-maze, we found that fish (Astyanax fasciatus) learned and remembered information from both horizontal and vertical axes when they were presented either separately or as an integrated three-dimensional unit. When information from the two components conflicted, the fish used the previously learned vertical information in preference to the horizontal. This not only demonstrates that the horizontal and vertical components are stored separately in the fishes' representation of space (simplifying the problem of 3D navigation), but also suggests that the vertical axis contains particularly salient spatial cues--presumably including hydrostatic pressure. To explore this latter possibility, we developed a physical theoretical model that shows how fish could determine their absolute depth using pressure. We next considered full volumetric spatial cognition. Astyanax were trained to swim towards a reward in a Y-maze that could be rotated, before the arms were removed during probe trials. The subjects were tracked in three dimensions as they swam freely through the surrounding cubic tank. The results revealed that fish are able to accurately encode metric information in a volume, and that the error accrued in the horizontal and vertical axes whilst swimming in probe trials was similar. Together, these experiments demonstrate that unlike in surface-bound rats, the vertical component of the representation of space is vitally important to fishes. We hypothesise that the representation of space in the brain of vertebrates could ultimately be shaped by the number of the degrees of freedom of movement that binds the navigating animal.