The Appalachian Trail is a 2,184-mile-long footpath through the mountains of the eastern United States. Each year, approximately 2,000 “thru-hikers” attempt to backpack the trail's entire length, from Georgia to Maine, or vice versa. There are maps for each section of the trail, and hikers quickly learn that the most salient feature of these is the elevation profile. Miles are secondary to elevation change. When carrying a backpack, the amount of elevation gain is of paramount interest in planning the day's progress. Elevation has also been formalised in William Naismith's rule-of-thumb for estimating pedestrian distance: On flat ground, walkers usually cover 3 miles per hour, with an additional half hour added for each 1,000-foot elevation gain.
The consideration of three-dimensional spatial mapping by Jeffery et al. rightly brings attention to what thru-hikers and hill-walkers know firsthand – that elevation matters. But are distance and elevation represented in the same way, or in different ways? Jeffery et al., based on a review of behavioural and neurophysiological data, argue that three-dimensional space is represented in a bicoded (anistropic) internal map. Distances are represented metrically – likely by grid cells – whereas elevation is represented qualitatively, perhaps as a contextual cue. As an animal moves up, down, and across a complex environment, it may represent each surface as a map fragment, and these are linked in some way.
There is, however, a difficulty with map fragmentation, and it is not just in identifying how maps of different planes are linked. Rather, it is with the representations of space provided by grid, place, and to a lesser extent perhaps, head direction cells themselves. Put simply, while in an open space grid cells may encode distances, in more complex environments with similar, repeated geometric features, grid and place cells exhibit a fragmented encoding of space. Hence, the metric representation of space itself appears to be piecemeal. As we consider below, this may explain why demonstrations of novel spatial inference in the rat are a challenge.
For hippocampal place cells, accumulating evidence suggests that place fields are controlled by the local features of the environment. For example, Skaggs and McNaughton (Reference Skaggs and McNaughton1998) found that some place cells showed similar fields in each of two identical boxes. This result was replicated by Fuhs et al. (Reference Fuhs, VanRhoads, Casale, McNaughton and Touretzky2005) in their same box orientation condition, and repeated fields have been found in up to four adjacent boxes (Spiers et al. Reference Spiers, Jovalekic and Jeffery2009). These findings, and the demonstration that some place fields duplicate when a barrier is inserted into a square environment (Barry et al. Reference Barry, Lever, Hayman, Hartley, Burton, O'Keefe, Jeffery and Burgess2006), provide clear support for the hypothesis that place fields are driven by the boundaries of the immediate environment (Hartley et al. Reference Hartley, Burgess, Lever, Cacucci and O'Keefe2000; O'Keefe & Burgess Reference O'Keefe and Burgess1996). Thus, an animal traversing an environment with repeated geometric features may experience a repeated, fragmented place cell representation. Indeed, the repeated place cell firing in the spiral maze observed by Hayman et al. (Reference Hayman, Verriotis, Jovalekic, Fenton and Jeffery2011) may reflect this in the third dimension.
Fragmentary firing also occurs in medial entorhinal cortex grid cells. In an elegant experiment, Derdikman et al. (Reference Derdikman, Whitlock, Tsao, Fyhn, Hafting, Moser and Moser2009) showed that grid fields fragmented in a hairpin maze in which the animals ran in alternate directions through a series of alleyways. The firing of these cells appeared anchored to the start of each turn in a given direction for much of the distance in an alleyway, although firing near the end of the alley was anchored to the upcoming turn. In this same study, hippocampal place cells likewise exhibited repeated fields in different alleyways when the rat was running in the same direction. Thus, both grid cells and place cells exhibited a local, not global, representation of the environment. Presumably, this occurred even though the animal treated the environment as a whole.
What then of head direction cells? Here the situation is different. In the same hairpin maze, head direction cells were unchanged (i.e., they tended to fire in the same direction) compared to recording sessions in an open field (Whitlock & Derdikman Reference Whitlock and Derdikman2012). Remarkably, in cells that showed grid fields and directional tuning (conjunctive cells), grid fields fragmented in the hairpin maze, while directional firing was unaffected. The consistency of directional firing across maze compartments is in agreement with previous demonstrations that the preferred firing of head direction cells is maintained, with some error, across environments when the animal walks between them (Dudchenko & Zinyuk Reference Dudchenko and Zinyuk2005; Stackman et al. Reference Stackman, Golob, Bassett and Taube2003; Taube & Burton Reference Taube and Burton1995).
On the face of the existing place and grid cell evidence, it is unclear how rodents solve distance problems in environments with repeated boundaries. This raises two possibilities. First, the distance map may become more global with repeated experience, though there is not strong evidence for this yet (Barry et al. Reference Barry, Lever, Hayman, Hartley, Burton, O'Keefe, Jeffery and Burgess2006; Spiers et al. Reference Spiers, Jovalekic and Jeffery2009). Second, it may be that rodents are not all that good at navigating multiple enclosure environments. For example, we have found that rats are surprisingly limited in their ability to take a novel shortcut between familiar environments (Grieves & Dudchenko Reference Grieves and Dudchenko2013). In short, their representations of the world may be local, and only incidentally global.
To return to Jeffery et al.'s main argument: The firing of grid and place cells in three-dimensional mazes is certainly consistent with a bicoded representation of space. Challenges that emerge from this view, and from the findings reviewed above, include identifying how global distance is represented when there is a change in elevation, and how it is represented when the environment contains repeated geometric features.
The Appalachian Trail is a 2,184-mile-long footpath through the mountains of the eastern United States. Each year, approximately 2,000 “thru-hikers” attempt to backpack the trail's entire length, from Georgia to Maine, or vice versa. There are maps for each section of the trail, and hikers quickly learn that the most salient feature of these is the elevation profile. Miles are secondary to elevation change. When carrying a backpack, the amount of elevation gain is of paramount interest in planning the day's progress. Elevation has also been formalised in William Naismith's rule-of-thumb for estimating pedestrian distance: On flat ground, walkers usually cover 3 miles per hour, with an additional half hour added for each 1,000-foot elevation gain.
The consideration of three-dimensional spatial mapping by Jeffery et al. rightly brings attention to what thru-hikers and hill-walkers know firsthand – that elevation matters. But are distance and elevation represented in the same way, or in different ways? Jeffery et al., based on a review of behavioural and neurophysiological data, argue that three-dimensional space is represented in a bicoded (anistropic) internal map. Distances are represented metrically – likely by grid cells – whereas elevation is represented qualitatively, perhaps as a contextual cue. As an animal moves up, down, and across a complex environment, it may represent each surface as a map fragment, and these are linked in some way.
There is, however, a difficulty with map fragmentation, and it is not just in identifying how maps of different planes are linked. Rather, it is with the representations of space provided by grid, place, and to a lesser extent perhaps, head direction cells themselves. Put simply, while in an open space grid cells may encode distances, in more complex environments with similar, repeated geometric features, grid and place cells exhibit a fragmented encoding of space. Hence, the metric representation of space itself appears to be piecemeal. As we consider below, this may explain why demonstrations of novel spatial inference in the rat are a challenge.
For hippocampal place cells, accumulating evidence suggests that place fields are controlled by the local features of the environment. For example, Skaggs and McNaughton (Reference Skaggs and McNaughton1998) found that some place cells showed similar fields in each of two identical boxes. This result was replicated by Fuhs et al. (Reference Fuhs, VanRhoads, Casale, McNaughton and Touretzky2005) in their same box orientation condition, and repeated fields have been found in up to four adjacent boxes (Spiers et al. Reference Spiers, Jovalekic and Jeffery2009). These findings, and the demonstration that some place fields duplicate when a barrier is inserted into a square environment (Barry et al. Reference Barry, Lever, Hayman, Hartley, Burton, O'Keefe, Jeffery and Burgess2006), provide clear support for the hypothesis that place fields are driven by the boundaries of the immediate environment (Hartley et al. Reference Hartley, Burgess, Lever, Cacucci and O'Keefe2000; O'Keefe & Burgess Reference O'Keefe and Burgess1996). Thus, an animal traversing an environment with repeated geometric features may experience a repeated, fragmented place cell representation. Indeed, the repeated place cell firing in the spiral maze observed by Hayman et al. (Reference Hayman, Verriotis, Jovalekic, Fenton and Jeffery2011) may reflect this in the third dimension.
Fragmentary firing also occurs in medial entorhinal cortex grid cells. In an elegant experiment, Derdikman et al. (Reference Derdikman, Whitlock, Tsao, Fyhn, Hafting, Moser and Moser2009) showed that grid fields fragmented in a hairpin maze in which the animals ran in alternate directions through a series of alleyways. The firing of these cells appeared anchored to the start of each turn in a given direction for much of the distance in an alleyway, although firing near the end of the alley was anchored to the upcoming turn. In this same study, hippocampal place cells likewise exhibited repeated fields in different alleyways when the rat was running in the same direction. Thus, both grid cells and place cells exhibited a local, not global, representation of the environment. Presumably, this occurred even though the animal treated the environment as a whole.
What then of head direction cells? Here the situation is different. In the same hairpin maze, head direction cells were unchanged (i.e., they tended to fire in the same direction) compared to recording sessions in an open field (Whitlock & Derdikman Reference Whitlock and Derdikman2012). Remarkably, in cells that showed grid fields and directional tuning (conjunctive cells), grid fields fragmented in the hairpin maze, while directional firing was unaffected. The consistency of directional firing across maze compartments is in agreement with previous demonstrations that the preferred firing of head direction cells is maintained, with some error, across environments when the animal walks between them (Dudchenko & Zinyuk Reference Dudchenko and Zinyuk2005; Stackman et al. Reference Stackman, Golob, Bassett and Taube2003; Taube & Burton Reference Taube and Burton1995).
On the face of the existing place and grid cell evidence, it is unclear how rodents solve distance problems in environments with repeated boundaries. This raises two possibilities. First, the distance map may become more global with repeated experience, though there is not strong evidence for this yet (Barry et al. Reference Barry, Lever, Hayman, Hartley, Burton, O'Keefe, Jeffery and Burgess2006; Spiers et al. Reference Spiers, Jovalekic and Jeffery2009). Second, it may be that rodents are not all that good at navigating multiple enclosure environments. For example, we have found that rats are surprisingly limited in their ability to take a novel shortcut between familiar environments (Grieves & Dudchenko Reference Grieves and Dudchenko2013). In short, their representations of the world may be local, and only incidentally global.
To return to Jeffery et al.'s main argument: The firing of grid and place cells in three-dimensional mazes is certainly consistent with a bicoded representation of space. Challenges that emerge from this view, and from the findings reviewed above, include identifying how global distance is represented when there is a change in elevation, and how it is represented when the environment contains repeated geometric features.