Humans' spatial representations enable navigation and reaching to targets above the ground plane, even without direct perceptual support. Such abilities are inconsistent with an impoverished representation of the third dimension. Features that differentiate humans from most terrestrial animals, including raised eye height and arms dedicated to manipulation rather than locomotion, have led to robust metric representations of volumetric space.

The target article does not consider neural data on primate spatial representations, which we suggest provide grounds for believing that navigational space may be three-dimensional rather than quasi–two-dimensional. Furthermore, we question the authors' interpretation of rat neurophysiological data as indicating that the vertical dimension may be encoded in a neural structure separate from the two horizontal dimensions.

Jeffery et al. accurately identify the importance of developing an understanding of spatial reference frames in a three-dimensional world. We examine human spatial cognition via a unique paradigm that investigates the role of saliency and adjusting reference frames. This includes work with adults, typically developing children, and children who develop non-typically (e.g., those with autism).

I propose that it is premature to assert that a fully three-dimensional map has never evolved in any species, as data are lacking to show that space coding in all animals is the same. Instead, I hypothesize that three-dimensional representation is tied to an animal's mode of locomotion through space. Testing this hypothesis requires a large body of comparative data.

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.

Single-cell studies of monkey posterior parietal cortex (PPC) have revealed the extensive neuronal representations of three-dimensional subject motion and three-dimensional layout of the environment. I propose that navigational planning integrates this PPC information, including gravity signals, with horizontal-plane based information provided by the hippocampal formation, modified in primates by expansion of the ventral stream.

Jeffery et al. suggest that three-dimensional environments are not represented according to their volumetric properties, but in a quasi-planar fashion. Here we take into consideration the role of visual experience and the use of technology for spatial learning to better understand the nature of the preference of horizontal over vertical spatial representation.

We describe an augmented topological map as an alternative for the proposed bicoded map. Inverting causality, the special nature of the vertical dimension is then no longer fixed a priori and the cause of specific navigation behavior, but a consequence of the combination of the specific geometry of the experimental environment and the motor capabilities of the experimental animals.

Evidence from egocentric space is cited to support bicoding of navigation in three-dimensional space. Horizontal distances and space are processed differently from the vertical. Indeed, effector systems are compatible in horizontal space, but potentially incompatible (or chaotic) during transitions to vertical motion. Navigation involves changes in coordinates, and animal models of navigation indicate that time has an important role.

Does the psychological and neurological evidence concerning three-dimensional localization and navigation fly in the face of optimality? This commentary brings a computational and robotic engineering perspective to the question of “optimality” and argues that a multicoding manifold model is more efficient in several senses, and is also likely to extend to “volume-travelling” animals, including birds or fish.

Perceived slope varies with the viewing distance, and is consistent with the effects of foreshortening. Distant viewing makes uphill slopes appear steeper and downhill slopes flatter than does near viewing. These effects are obvious to skiers and climbers in mountainous country. They have also been measured in outdoor experiments with controlled viewing distances. There are many other sources of slope illusions.

In a surface-dwelling animal like the rat, experimental strategies for investigating the hippocampal correlates of three-dimensional space appear inevitably complicated by the interplay of global versus local reference frames. We discuss the impact of the resulting confounds on present and future empirical analysis of the “bicoded map” hypothesis by Jeffery and colleagues.

Although the bicoded map constitutes an interesting candidate representation, proposing it as the predominant representation for three-dimensional space is too restrictive. We present and argue for scalable spatial representation structures as a more comprehensive alternative account that includes the bicoded map as a special case.

An animal confronts numerous challenges when constructing an optimal navigational route. Spatial representations used for path optimization are likely constrained by critical environmental factors that dictate which neural systems control navigation. Multiple coding schemes depend upon their ecological relevance for a particular species, particularly when dealing with the third, or vertical, dimension of space.

We show that, given extensive exploration of a three-dimensional volume, grid units can form with the approximate periodicity of a face-centered cubic crystal, as the spontaneous product of a self-organizing process at the single unit level, driven solely by firing rate adaptation.

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.

The vertical component of space occurs in two distinct fashions in natural environments. One kind of verticality is orthogonal-to-horizontal (as in climbing trees, operating in volumetric spaces such as water or air, or taking elevators in multilevel buildings). Another kind of verticality, which might be functionally distinct, comes from navigating on sloped terrain (as in traversing hills or ramps).

The suggestion that three-dimensional space is represented by a mosaic of neural map fragments, each covering a small area of space in the plane of locomotion, receives support from studies in complex two-dimensional environments. How map fragments are linked, which brain circuits are involved, and whether metric is preserved across fragments are questions that remain to be determined.

The presumption that navigation requires a cognitive map leads to its conception as an abstract computational problem. Instead of loading the question in favor of an inquiry into the metric structure and evolutionary origin of cognitive maps, the task should first be to establish that a map-like representation actually is operative in real animals navigating real environments.

We have argued that the neurocognitive representation of large-scale, navigable three-dimensional space is anisotropic, having different properties in vertical versus horizontal dimensions. Three broad categories organize the experimental and theoretical issues raised by the commentators: (1) frames of reference, (2) comparative cognition, and (3) the role of experience. These categories contain the core of a research program to show how three-dimensional space is represented and used by humans and other animals.