Introduction

Is spatial learning distinct from other forms of learning? According to associative learning theories, when we encounter new information, whether temporal or spatial, that information is processed according to the same associative mechanisms ([1], see also [2–5]). In contrast, according to cognitive mapping theory [6, 7], when we explore a new environment we automatically construct a representation of that environment in which all distinctive landmarks, together with the geometric relationships between those landmarks, are stored. A mental representation of the environment in this structure can be employed to solve novel spatial problems. As the geometric relationships in a cognitive map are vectorial they do not conform to the accepted description of Humean associations, which comprise links between ideas or sensations [8]. Therefore, when vectorial knowledge is assumed to underpin navigation, the mechanisms that underpin spatial and associative learning are presumed to differ.

There are many ways to reach a goal. In their classic discussion of spatial learning and navigation O’Keefe and Nadel (1978) [7] distinguished between taxon and locale systems. They suggest that the taxon system incorporates ‘orientation’ and ‘guidance’ mechanisms, which essentially refer to stimulus and response associative learning. The locale system, by contrast, processes true spatial knowledge which forms the basis of an allocentric cognitive map. While navigation might rely on either system depending on the cues that are available, cognitive mapping and associative learning theories make a number of different predictions about the way in which humans and other animals process spatial information. For example, associative learning theories predict cue-interaction effects, such as the competition between spatial cues found in a blocking design [9–11]. In this experimental arrangement, stimuli which have already been established as good predictors of a goal location, can restrict what interrelationships are learned about newly introduced stimuli and that goal [12, 13]. In contrast, cognitive mapping theory maintains that an internal representation of spatial interrelationships is only useful if it is automatically updated when changes occur in the environment. Therefore, under circumstances in which cognitive mapping forms the basis of navigation, phenomena such as blocking should not occur.

One important prediction which differs between associative learning theories and cognitive mapping theory is that only cognitive mapping predicts that we can compute a short-cut based on geometric interrelationships. For example, to learn a route by exploring one path from landmark a to landmark b, and another from landmark a to landmark c, and then be able to select a new short-cut from landmark b directly to landmark c.

Early evidence in support of the prediction of short-cutting from cognitive mapping theory is provided by the seminal study by Tolman, Ritchie, and Kalish (1946) [14] (henceforth referred to as Tolman et al.), who gave rats repeated experience of navigating a fixed route through a maze comprising several turns, before presenting them with an altered version of the environment in which multiple alternative routes were available (see also [15]). The training phase consisted of a straight path into a circular chamber, leading directly ahead to an entrance corridor, followed by 90° turns to the left, then right, then right again, to proceed down a longer path than the others to a food goal (see Fig 1A); this route was repeated over several days. The testing phase involved a single trial in an altered version of the environment in which the original path to the food was blocked, and 18 alternative pathways (at 10° increments) were made available (see Fig 1B). Tolman et al. reasoned that in this scenario a cognitive map would lead the animals to enter the corridor that faces directly toward the location in which the reward was experienced during the training phase (toward the East of the starting location, assuming that the first direction of travel during training is considered North, i.e. upward on Fig 1A and 1B). Alternatively, associative learning theory would predict that animals would have originally learned to find the goal by approaching the entrance corridor, then moving forward, making turns as required to reach the food. This latter strategy does not involve knowledge which can be used to deduce a short-cut to the goal. In the test phase, predictions from this account include selecting a pathway immediately adjacent to the originally trained corridor due to generalisation [16, 17]. Conceivably, selecting a pathway to the West is a plausible alternative if generalizing from the first turn, to the left, during each training trial was sufficient to elicit a positive association with the food [5] (see also [18]).

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Fig 1. A replication of the experiment of Tolman, Ritchie, and Kalish (1946) in a virtual environment.

A Plan view of the layout of the environment in the training phase. Participants begin at the Southernmost point and negotiate a sequence of turns through narrow corridors to a goal located in a square chamber to the North-East. A distinctive light source (for groups Light-light and Light-Shifted) is located above and adjacent to the goal. B Plan view of the testing environment, in which the original route to the North is blocked and eighteen additional routes are made available. C First-person view from the center of the circular chamber in the training environment in the Light-light condition. D First-person view from the center of the testing environment in the Light-light condition. E-F First-person views from equivalent locations in the training and testing phases in the Ambient condition. G-H First-person views from equivalent locations in the training and testing phases in the Light-Shifted condition. Note that panels C and G are identical.

https://doi.org/10.1371/journal.pone.0208794.g001

In the test phase of the original study, the rats overwhelmingly chose to explore a route pointing directly to where the reward had previously been experienced (to the overall East of the orientation of the blocked corridor). This result has been cited as evidence for the ability of animals to compute short-cuts, and thus as evidence in support of cognitive mapping theory. However, the original experiment has a well known potential flaw in its design [4, 19]. In the original study a lightbulb was present above and adjacent to the goal, and was present in both the training and the testing environments. Therefore, it is possible that choosing the path that led to the goal in the testing phase did not reflect the construction of a cognitive map of the route by integrating spatial information about the distances and angles between spatial features in the training phase.

At least two alternative accounts of the original results of Tolman et al. are plausible. The most parsimonious explanation is that in the absence of any learning during the training phase, the animals may have navigated toward the light as the most distinctive feature of the test environment. Alternatively, the animals may have learned during the training phase to associate the approach to the light with the subsequent delivery of a food reward. This latter account is consistent with a somewhat weaker interpretation of the original data offered by Tolman et al.; “…we believe that it is not correct to say that our rats were merely running towards the light. Rather we should say that they were running to the position of the former goal, and that this location was indicated by the position of the light” [14].

Indeed, a number of reviewers have argued that there are no unequivocal demonstrations of successful short-cutting in the absence of the opportunity for guidance by landmarks proximal to the goal [2, 3]. For example, studies with a range of species suggest that when a distinctive landmark consistently appears at a short distance from a rewarded location, the landmark may come to serve as a ‘beacon’, and as such elicit a behavioural strategy in which the animal first approaches the beacon and then searches locally for the goal, either with respect to additional directional information [20, 21] or by randomly searching outwards from the beacon. Before assuming a more complex process, such as the integration of spatial information to form a route between start location and goal, we need to know more about the role of local cues in short-cutting. As Mackintosh [3] notes: to the extent that there are many ways by which animals can find their way directly to their goal, they may have little need to develop an integrated map of an entire environment. While there is evidence that animals can successfully take a short-cut based on path integration or dead reckoning [22], we know of no unequivocal demonstrations of short-cutting that are necessarily based on the integration of cognitively based route knowledge. The absence of evidence for successful short-cutting is not the same as evidence for an inability to take short-cuts, hence by appropriately modifying the original experimental design of Tolman et al., we will here seek evidence for short-cutting.

Despite the potential shortcoming in Tolman et al.’s experiment, the basic methodology can readily be extended to provide a sound test of the hypothesis that an integrated cognitive spatial structure underpins short-cutting. The present study was designed to investigate short-cutting in people exploring a virtual environment in a design which replicated the essential features of the original experiment of Tolman, Ritchie, and Kalish (1946) [14] with rats (see Fig 1 for an overview of the design). To address the potential criticism related to the light in the original experiment, one group of participants, group ‘Ambient’, was trained and tested in the simulated environment under conditions of unlocalised ambient lighting. The question of interest for this group was whether, in the absence of the light-beacon, they would make similar choices to those of Tolman et al.’s rats and select test-paths that were oriented in the direction of the goal. This outcome would be entirely consistent with cognitive mapping theory, at least in the human case. Or, whether they would choose paths adjacent to the path that was available during the training phase as a ‘generalization’ account might predict. A second group, group ‘Light-Light’, replicated Tolman et al.’s procedure in having a light above and adjacent to the goal in both the training and test phases. The question of interest for this group was whether more participants would select a path that was oriented toward the light than in group Ambient. Should significantly more people choose a path directed toward the light than in group Ambient, this would reinforce the conclusion that the light acts as a beacon that indicates the goal location. To the extent that short-cutting is based on a cognitive map, a significant difference between groups Ambient and Light-Light would not be expected. Finally, group ‘Light-Shifted’ replicated Tolman et al.’s procedure in having a light above and adjacent to the goal in the training phase, but differed in that during the test the light was moved to a different location within the environment. Should path selection in the test be based purely on the beacon properties of the light, participants should select the path that leads toward the relocated light. Should a conjunction of the light and the spatial features of the environment guide the choice of path, selection would be more varied. Given that the light location in the test differs from that during training, in the test the light cannot support approach to the original light location in this group. Therefore, in group Light-Shifted fewer arm choices consistent with the learning phase would be anticipated due to generalization decrement.

Methods

Participants

Participants were thirty males and thirty females distributed equally across three conditions (ten males and ten females in each condition), with a mean age of 20.33±0.97 years (mean ± standard deviation). The study received ethical approval from the ethics committee of the Department of Psychology at the University of Sheffield. Participants provided informed consent to participate in ‘a study on spatial learning in virtual environments’, were informed about the procedure, and were fully debriefed about the scientific aims of the experiment following data collection.

Results

To analyse the distribution of path choices, the 18 possible paths that participants could choose in the test phase were labeled in terms of the anti-clockwise ordering of the angles at which they projected from the center of the large circular chamber, starting from path 1 at 0° (East) and incrementing to path 18 at 180°. As the original path to the North was blocked and some paths were not selected, while some were selected by relatively few participants, non-parametric analyses were employed to compare the median numbers of the paths chosen between groups. The median angle of the paths chosen by participants in the Ambient and Light-Shifted conditions was 80° (path 9). The median angle of the paths chosen by participants in the Light-Light condition was 55° (between paths 6 and 7). A Kruskal-Wallis test on the path choices revealed a significant difference between the median scores; H = 7.89, p = 0.02. To explore the significant difference between groups, Mann-Whitney U pairwise tests were carried out for the three pairs of conditions using a Bonferroni correction. The median path chosen in the Light-Light condition was significantly different from the median path chosen in the Ambient condition (U = 106, p = 0.01, two-tailed test). The difference between the median path chosen in the Light-Light condition and in the Light-Shifted condition approached but did not meet the corrected significance level (U = 116.5, p = 0.023, two-tailed test) (Bonferroni correction, p = 0.017). No difference was found between the median path choices in the Ambient versus Light-Shifted conditions (p > 0.05). Histograms of the chosen paths are presented in Fig 2.

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Fig 2. Histograms showing the distribution of paths chosen in the testing phase of the three groups.

A Path choices in the Light-Light condition. B Path choices in the Ambient condition. C Path choices in the Light-Shifted condition. Paths are labelled in reverse order, such that paths in Westerly directions appear towards the left and paths in the Easterly directions appear towards the right. The path between choices 9 and 10 was blocked in the testing phase. Path 6 corresponds to the path leading directly to the location at which the target was located in the training phase. Blue vertical lines indicate the median for each distribution.

https://doi.org/10.1371/journal.pone.0208794.g002

These analyses suggest that participants in group Ambient tended to choose paths adjacent to the path that was available during the training phase, as a ‘generalization’ account might predict. They did not make similar choices to those of Tolman et al.’s rats, and did not conform to Tolman’s expectation based on a cognitive representation of the route. In the Light-Light condition, a replication of the condition tested by Tolman, Ritchie, and Kalish (1946) [14], participants were more likely to select a path oriented toward the goal/light location than in the Ambient condition in which no distinctive landmark provided spatial information about the location of the target. This outcome conforms to the expectations of Tolman et al. based on short-cutting, and reinforces the conclusion that the light can act as a beacon that indicates the goal location in this procedure. In group Light-Shifted, path selection was not purely based on the beacon properties of the light. If it had been, in the test participants should have principally selected the path leading toward the new location of the light. In this group the (weak) tendency was to approach the paths adjacent to the originally trained path, suggesting that movement of the light location from that during the training phase disrupted learning that the goal was in a North-Easterly direction: a generalization decrement. Nonetheless, the difference in path choices between groups Light-Light and Light-Shifted reinforces the importance of the light as a landmark.

Pointing accuracy was defined as the absolute difference, in degrees, between the actual direction to the goal location and the participant’s estimate of that direction. Groups did not differ significantly in accuracy, with mean absolute errors for groups Ambient = 32.4°, Light-Light = 33.4°, and Light-Shifted = 26.3°, (p > 0.05). Fig 3 shows the direction in which each participant pointed for each condition. Absolute pointing errors were subject to a between-participant ANOVA analysis with group and gender as factors; this analysis revealed no main effects and no interaction between main effects (ps > 0.05).

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Fig 3. Movement patterns in the testing phase and participant estimates of the direction toward the goal in the goal orientation test.

A-C Movement patterns for each of the 20 participants in each condition are shown overlaid as black traces. The light grey image shows the layout of the environments in the testing phase. A black square indicates the position of the goal, and a black circle indicates the position of the light. D-F Pointing directions for each of the 20 participants in each condition are shown as overlaid black lines, originating from the location of the handheld controller at the time of pointing, and extending in the direction at which the controller was oriented.

https://doi.org/10.1371/journal.pone.0208794.g003

Inspection of the individual trajectories (see Fig 3A–3C) revealed that approximately half of the participants across the groups explored the blocked path prior to making their recorded path choice (50% in condition Light-Light, 65% in condition Ambient and 50% in condition Light-Shifted), and that the vast majority of these approached the center of the circular chamber before directly approaching and exploring only the path that was subsequently recorded.

The plan views of the training environment, drawn after completion of the test procedure, were blind-rated according to an ordinal 5-point scale from ‘1. Inaccurate plan which is not reminiscent of the actual space’ to ‘5. Accurate plan view with 4 paths leading from the centre, in the correct arrangement. Angle from centre of circle to the ‘goal’ within 10° either way’. An example drawing for each of the five ratings is shown in Fig 4. The median rating for all three groups was 4 (‘Accurate plan view with 4 paths leading from the centre, in the correct arrangement. Angle from centre of circle to the ‘end’ greater than 10° either way, but less than 90°’). The majority of drawings were rated 4 (62%) with the remainder receiving ratings of 5 (10%), 3 (12%), 2 (14%) and 1 (2%). No significant difference was found between group medians, Kruskal-Wallis p = 0.13. Most participants drew fairly accurate plan views with the most common deviation, for those receiving scores of 4, a tendency to make the final path to the goal of similar length to the other paths leading from the central circular chamber. This tendency resulted in plots of the goal location that were shifted toward the West of the actual location, conforming to the majority of path choices across groups. While this finding is suggestive that map-like representations might have guided path choices, more detailed individual comparisons do not conform to this view: Correlations between map ratings and path choices were near zero for participants collectively across groups, Spearman’s rho ρ = −0.14, p > 0.05, and for each group individually, Spearman’s rho ρ < 0.1, ps > 0.05. Similarly when accuracy of pointing toward the goal (in degrees) was compared with map ratings (ordinal scale 1-5), correlations were near zero for participants collectively across groups, Spearman’s rho ρ = −0.14, ps > 0.05, and for each group individually, Spearman’s rho ρ < 0.1, ps > 0.05. Thus, map drawing quality and wayfinding measures were unrelated, which would not be expected if path-choice and goal-pointing relied on the same knowledge as that used to draw the maps.

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Fig 4. Examples of drawings of the layout of the virtual environment in the training phase.

Drawings are arranged from left to right to reflect increasingly good scores assigned by a blind rater. A Drawing by a female participant assigned to group Light-Light, scoring 1/5. B Drawing by a male participant assigned to group Ambient, scoring 2/5. C Drawing by a female participant assigned to group Light-Shifted, scoring 3/5. D Drawing by a male participant assigned to group Ambient, scoring 4/5. E Drawing by a male participant assigned to group Light-Light, scoring 5/5.

https://doi.org/10.1371/journal.pone.0208794.g004

While there was no gender effect for any individual group (ps > 0.05), there was an overall (all groups combined) difference in map ratings with mean map ratings of 3.9 for men (range 2-5) being higher than the mean map ratings of 3.6 for women (range 1-5), Mann-Whitney U, p = 0.04. Separate analyses of path choice and pointing error data for those participants whose map drawings were rated 4 or 5 (group Light-Light n = 12 participants, group Ambient n = 12, group Light-Shifted n = 18) presented a very similar statistical picture to analyses of all participants’ data as reported above.

Discussion

This study replicated with human participants the essential features of the seminal short-cutting experiment by Tolman, Ritchie, and Kalish (1946) [14] with rats. In Tolman et al.’s study a distinctive light above the location of a food reward was present when the animals were trained and tested. As Tolman et al. noted (but rejected by argument), this cue could have acted as a beacon that guided path choice in the test. Therefore, we included groups to evaluate the influence of the light in addition to a group, group Ambient, which assessed short-cutting free from the influence of this potential confound.

Replication of the original experimental design in the Light-Light condition using humans in virtual environments rather than rats as subjects, yielded similar short-cutting behaviour in humans, with the median and modal path choice in the testing phase both pointing in the direction that was rewarded during training. This pattern is consistent with similar spatial strategies in rats and humans.

In the absence of the beacon, participants in group Ambient tended to make path choices in the test that were adjacent to the location of the path that led away from the central chamber during the training phase. This pattern does not conform to that anticipated by Tolman et al., which assumes path choices in the test that were based on the shortest route to the goal location experienced during training. However, in group Light-Light, a close replication of the arrangement in the study of Tolman et al., path choices tended toward the paths leading to the goal/light. This pattern is what would be expected if, contrary to their arguments, the light acted as a beacon indicating proximity to the goal. That participants chose paths in the direction of the goal (path 6) more often than paths in the direction of the light (path 5) suggests that the availability of the light as a cue for learning during the training phase allowed it to be used to localize the goal during testing, and suggests that participants were not simply approaching the light in the test phase. In group Light-Shifted, path choices were centred around path 9, as they were in group Ambient, rather than tending toward path 14 as would be expected purely on the basis of the light’s properties as a beacon. This pattern suggests that path choices were determined by more than the beacon properties of the light. Moving the light location and reversing its facing direction, with concomitant changes to the direction of the shadows, appears to have engendered a generalization decrement in the goal-location information within the spatial array as a whole. Overall, these findings are consistent with those obtained using related experimental designs with humans in virtual environments, demonstrating a lack of accurate short-cutting behaviour in the absence of salient landmarks, an improvement in short-cutting when stable landmarks are present, and a disruption of short-cutting when landmarks are shifted between training and testing phases [24, 25].

In the present study we tested participants in virtual environments for their obvious practical advantages, and because there is good evidence that findings from exploration translate and transfer between VE and real-world scenarios [26, 27]. Of course, a VE can never capture every aspect of the original Tolman et al. study. It is conceivable that path choices in rats were influenced by additional spatial cues that were presented in a consistent relationship with the reward location in both training and testing phases, e.g., extra-maze visual landmarks (doors, ceiling corners, equipment etc.), smells or sounds. However, the present data collected in the Light-Light condition by exploration of precisely controlled VEs confirm that in combination with the geometry of the training and test arenas, the presence of a single consistent distinctive landmark alone is sufficient to guide path choices to a previously rewarded location.

Unlike the rats of Tolman et al., our participants were able to supply direct evidence of map-like knowledge when asked to draw the layout or plan view of the training environment. In the median-rated case for each group, these plan views were generally reflective of the space explored during training, in that the general arrangements of spatial features was quite accurate. A frequently observed limitation on accuracy was a tendency to draw the final path to the goal as shorter than its actual relative length; rather, this path was depicted as of a similar length to the other paths (see Fig 4D). It is possible that the shortening of the final drawn path reflects a mismatch in the available proprioceptive feedback, which in our setup (with a head tracking volume comprising a few cubic meters) was informative about rotations of the head and body, but less informative about distance.

The generally high accuracy of participants’ drawings is nonetheless consistent with the possibility that path selection was based on an internal representation with map-like qualities. However there are several reasons for questioning this assumption. First, the accuracy of the plan-view drawings was very similar for all groups; therefore, had map-like knowledge formed the basis of path selection, we would not expect a difference in median path choices between groups. That there was a difference between median choices suggests a different selection mechanism between groups. Second, the accuracy of the plan-views seems at odds with the relatively disparate path choices within each group (see Fig 2). Indeed, the rats of Tolman et al. presented a more consistent pattern of path choices than our participants, with 36% of rats choosing path 6, compared with only 20% of human participants in group Light-Light. Surely there would be greater consistency in path choices if these were guided by maps of similar structure. With respect to the apparently low consistency of human choices compared with rats, note that the rats in Tolman, Ritchie, and Kalish (1946) were reportedly ‘maze-wise’, having concluded 18 days of maze training immediately before the experiment (see also [16, 28]). Such training should facilitate the short-cut task by habituating the rats to the general maze-learning environment and procedure.

Perhaps the most important reason to question a plan-view basis for short-cut performance is the essentially zero correlation between map accuracy ratings and the accuracy of pointing toward the goal, and a similar lack of correlation between map accuracy ratings and path choices. That is, the significant differences that we found between groups were manifest at the time at which any such map should first have been invoked to guide navigation behaviour. Given these observations, we suggest that plan views were likely deduced when requested, subsequent to the operation of mechanisms which actually determined pointing accuracy and path choice. The main mechanism leading to a short-cut choice in this procedure appears to be using the light as a beacon to locate the goal (cf. [3]).

A wealth of important data is accumulating related to patterns of neural activity during spatial exploration (see [6, 29] for reviews), with many researchers concentrating on the hippocampal formation as the underlying substrate for the construction and maintenance of cognitive maps. However, there remains a surprising lack of behavioural evidence to support the idea that humans or other animals routinely maintain veridical representations of spatial interrelationships which can be used to solve problems such as short-cutting. Our current data broadly reinforce this conclusion, with the only evidence for successful short-cut performance found in a group who were given the opportunity to use information which does not reflect truly spatial knowledge: approach to a beacon. Therefore, we await more conclusive evidence to implicate truly spatial knowledge in spatial problem solving. Meanwhile we maintain conservative assumptions about the ability of people to derive novel routes from stored representations of spatial interrelationships.

Supporting information

Acknowledgments

The authors are grateful to the undergraduate student experimenters who contributed to data collection as part of dissertation projects undertaken in the Department of Psychology at the University of Sheffield in 2016 and 2017. This work was supported by the European Commission, Horizon 2020 Research and Innovation Programme, Human Brain Project SGA1, programme 720270 (HBP SGA1).