The efforts of Jeffery et al. to synthesize and provide an overarching theoretical interpretation for the literature on two-dimensional and three-dimensional spatial representation will undoubtedly prove useful to the field. Their focus on 3D space also highlights the importance of investigating navigation performance in more complex, ecologically valid task environments. Despite these strengths, the authors fall prey to a common confusion involving the central egocentric/allocentric distinction.
At the outset, the authors flag this familiar distinction to emphasize how the “focus of the present article is on the allocentric encoding of the space that is being moved through” (target article, sect. 2, para. 1). Although a discrete distinction is widely assumed in the literature, and the authors imply it is incidental to the main goals of the article and hence can be glossed over, taking it at face value is problematic for two reasons. First, much of the neural and behavioral evidence the authors survey undermines a clean division. Second, and more strikingly, their positive proposal – the bicoded map hypothesis, in which different encoding schemes are employed for horizontal versus vertical space, yet both are referenced to the organism's plane of locomotion – clearly reflects a more complex interplay between egocentric and allocentric spatial representation than the authors explicitly acknowledge.
Egocentric and allocentric representations are primarily distinguished by the different reference frames they employ. Reference frames specify locations in terms of distances along two (or three) perpendicular axes spanning out from an intersection point at the origin. Egocentric representations specify locations relative to a reference frame centered on a body axis, such as the midline, or on a body part of the organism (e.g., “20 cm to the right of my right hand”). Allocentric representations encode locations relative to a reference frame centered on some environmental feature or object (or set of these), and independently of the organism's own orientation or possibly even position (e.g., “33°S 151°E”). Framed in this way, the key difference underlying the egocentric/allocentric distinction concerns the origin or center of the reference frame for the spatial representation, a point which is clearly reflected etymologically in the terms “egocentric” and “allocentric.” Nevertheless, characterizing a spatial reference frame involves more than just specifying the origin. Axis orientation and a metric for assessing distances along these axes must also be determined. This gives rise to another facet of the egocentric/allocentric distinction that has been largely ignored in the literature (for an exception, see Grush Reference Grush2007).
There are at least two senses in which a spatial representation may be egocentric (or allocentric). As canvassed above, a representation can be egocentric if the origin of the reference frame is anchored to the observer's location. But a spatial representation can also be egocentric if the alignment or orientation of the reference frame axes is itself dependent on properties of the organism (independently of whether the origin is fixed to the organism or not). Consider how bodily features such as the dorsal/ventral axis of the head might serve to determine the up/down axis for certain egocentric spatial representations used in early vision (Pouget et al. Reference Pouget, Fisher and Sejnowski1993), or how the body midline might serve to orient the left/right axis for spatial representations employed in reach planning (Pouget & Sejnowski Reference Pouget and Sejnowski1997). These representations are plausible candidates for being egocentric in both senses. Although these two kinds of egocentricity can go hand in hand, this is not necessary. Importantly, allocentric spatial representations are subject to an equivalent analysis, such that a representation may be allocentric with respect to its origin, axes, or both.
A more nuanced egocentric/allocentric distinction facilitates the identification of a richer representational taxonomy including hybrid cases incorporating both egocentric and allocentric elements as building blocks. For example, consider a hybrid representation in which locations are specified relative to an egocentric origin, but where the horizontal and vertical axes are aligned with respect to some environmental feature such as the Earth's magnetic field. The axes defined by the cardinal directions are allocentric, as they bear no direct relationship to any egocentrically defined axes and are invariant across changes in orientation and position of the subject.
This is important because the authors' bicoded map hypothesis posits a hybrid spatial representation, incorporating an allocentrically defined origin and egocentrically defined axes. According to the hypothesis, different encoding schemes (metric vs. non-metric) are used for the representation of horizontal and vertical space in the hippocampus and medial entorhinal cortex (MEC). Importantly, these schemes are not referenced to horizontal and vertical per se (i.e., gravitationally defined earth-horizontal and earth-vertical) as might be expected based on previous navigation studies employing two-dimensional arenas. Instead, studies conducted by the authors using three-dimensional environments (Hayman et al. Reference Hayman, Verriotis, Jovalekic, Fenton and Jeffery2011) and by other groups using microgravity conditions (Knierim et al. Reference Knierim, McNaughton and Poe2000), in which egocentric and allocentric axes can be explicitly dissociated, indicate that the “horizontal” axis is defined by the organism's canonical orientation during normal locomotor behavior and the axis orthogonal to this defines “vertical.” If correct, this organism-dependent axial alignment makes the spatial representation under consideration egocentric in the second sense outlined above. Nevertheless, the metrically coded (horizontal) portion of this map, implemented by assemblies of hippocampal place cells and entorhinal grid cells, also possesses characteristic features of an allocentric representation, as its reference frame is anchored to the external environment and does not depend on the organism's own location. The bicoded map is a hybrid spatial representation.
When the bicoded map hypothesis is interpreted as has been suggested here, its link to recent work in the field of embodied cognition becomes evident. Embodied cognition researchers have long sought to reveal how physical embodiment and motor behavioral capacities shape and constrain our ability to represent space. Until now, findings in support of this link were restricted to how organisms represent their local workspace. If Jeffery et al. are right, evidence is emerging for how an organism's motor behavioral repertoire may also influence its representation of large-scale, navigable space.
The efforts of Jeffery et al. to synthesize and provide an overarching theoretical interpretation for the literature on two-dimensional and three-dimensional spatial representation will undoubtedly prove useful to the field. Their focus on 3D space also highlights the importance of investigating navigation performance in more complex, ecologically valid task environments. Despite these strengths, the authors fall prey to a common confusion involving the central egocentric/allocentric distinction.
At the outset, the authors flag this familiar distinction to emphasize how the “focus of the present article is on the allocentric encoding of the space that is being moved through” (target article, sect. 2, para. 1). Although a discrete distinction is widely assumed in the literature, and the authors imply it is incidental to the main goals of the article and hence can be glossed over, taking it at face value is problematic for two reasons. First, much of the neural and behavioral evidence the authors survey undermines a clean division. Second, and more strikingly, their positive proposal – the bicoded map hypothesis, in which different encoding schemes are employed for horizontal versus vertical space, yet both are referenced to the organism's plane of locomotion – clearly reflects a more complex interplay between egocentric and allocentric spatial representation than the authors explicitly acknowledge.
Egocentric and allocentric representations are primarily distinguished by the different reference frames they employ. Reference frames specify locations in terms of distances along two (or three) perpendicular axes spanning out from an intersection point at the origin. Egocentric representations specify locations relative to a reference frame centered on a body axis, such as the midline, or on a body part of the organism (e.g., “20 cm to the right of my right hand”). Allocentric representations encode locations relative to a reference frame centered on some environmental feature or object (or set of these), and independently of the organism's own orientation or possibly even position (e.g., “33°S 151°E”). Framed in this way, the key difference underlying the egocentric/allocentric distinction concerns the origin or center of the reference frame for the spatial representation, a point which is clearly reflected etymologically in the terms “egocentric” and “allocentric.” Nevertheless, characterizing a spatial reference frame involves more than just specifying the origin. Axis orientation and a metric for assessing distances along these axes must also be determined. This gives rise to another facet of the egocentric/allocentric distinction that has been largely ignored in the literature (for an exception, see Grush Reference Grush2007).
There are at least two senses in which a spatial representation may be egocentric (or allocentric). As canvassed above, a representation can be egocentric if the origin of the reference frame is anchored to the observer's location. But a spatial representation can also be egocentric if the alignment or orientation of the reference frame axes is itself dependent on properties of the organism (independently of whether the origin is fixed to the organism or not). Consider how bodily features such as the dorsal/ventral axis of the head might serve to determine the up/down axis for certain egocentric spatial representations used in early vision (Pouget et al. Reference Pouget, Fisher and Sejnowski1993), or how the body midline might serve to orient the left/right axis for spatial representations employed in reach planning (Pouget & Sejnowski Reference Pouget and Sejnowski1997). These representations are plausible candidates for being egocentric in both senses. Although these two kinds of egocentricity can go hand in hand, this is not necessary. Importantly, allocentric spatial representations are subject to an equivalent analysis, such that a representation may be allocentric with respect to its origin, axes, or both.
A more nuanced egocentric/allocentric distinction facilitates the identification of a richer representational taxonomy including hybrid cases incorporating both egocentric and allocentric elements as building blocks. For example, consider a hybrid representation in which locations are specified relative to an egocentric origin, but where the horizontal and vertical axes are aligned with respect to some environmental feature such as the Earth's magnetic field. The axes defined by the cardinal directions are allocentric, as they bear no direct relationship to any egocentrically defined axes and are invariant across changes in orientation and position of the subject.
This is important because the authors' bicoded map hypothesis posits a hybrid spatial representation, incorporating an allocentrically defined origin and egocentrically defined axes. According to the hypothesis, different encoding schemes (metric vs. non-metric) are used for the representation of horizontal and vertical space in the hippocampus and medial entorhinal cortex (MEC). Importantly, these schemes are not referenced to horizontal and vertical per se (i.e., gravitationally defined earth-horizontal and earth-vertical) as might be expected based on previous navigation studies employing two-dimensional arenas. Instead, studies conducted by the authors using three-dimensional environments (Hayman et al. Reference Hayman, Verriotis, Jovalekic, Fenton and Jeffery2011) and by other groups using microgravity conditions (Knierim et al. Reference Knierim, McNaughton and Poe2000), in which egocentric and allocentric axes can be explicitly dissociated, indicate that the “horizontal” axis is defined by the organism's canonical orientation during normal locomotor behavior and the axis orthogonal to this defines “vertical.” If correct, this organism-dependent axial alignment makes the spatial representation under consideration egocentric in the second sense outlined above. Nevertheless, the metrically coded (horizontal) portion of this map, implemented by assemblies of hippocampal place cells and entorhinal grid cells, also possesses characteristic features of an allocentric representation, as its reference frame is anchored to the external environment and does not depend on the organism's own location. The bicoded map is a hybrid spatial representation.
When the bicoded map hypothesis is interpreted as has been suggested here, its link to recent work in the field of embodied cognition becomes evident. Embodied cognition researchers have long sought to reveal how physical embodiment and motor behavioral capacities shape and constrain our ability to represent space. Until now, findings in support of this link were restricted to how organisms represent their local workspace. If Jeffery et al. are right, evidence is emerging for how an organism's motor behavioral repertoire may also influence its representation of large-scale, navigable space.