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Navigating in a Three-Dimensional World BEHAVIORAL AND BRAIN SCIENCES (2013) 36, 523–587 doi:10.1017/S0140525X12002476 Navigating in a three-dimensional world Kathryn J. Jeffery Department of Cognitive, Perceptual and Brain Sciences, Division of Psychology & Language Sciences, University College London, London WC1H 0AP, United Kingdom [email protected] www.ucl.ac.uk/jefferylab/ Aleksandar Jovalekic1 Institute of Neuroinformatics, University of Zurich, CH-8057 Zurich, Switzerland [email protected] Madeleine Verriotis1 Department of Neuroscience, Physiology and Pharmacology, University College London, London WC1E 6BT, United Kingdom [email protected] Robin Hayman Institute of Cognitive Neuroscience, Alexandra House, London WC1N 3AR, United Kingdom [email protected] Abstract: 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. Keywords: ethology; grid cells; head direction cells; hippocampus; navigation; neural encoding; place cells; spatial cognition; three- dimensional 1. Introduction volumetric space is computationally complicated, because of the increased size of the representation needed, and Behavioural and neurobiological studies of spatial cognition because rotations in three dimensions interact. It remains have provided considerable insight into how animals an open question how the brain has solved these problems, (including humans) navigate through the world, establish- and whether the same principles of spatial encoding ing that a variety of strategies, subserved by different operate in all three dimensions or whether the vertical neural systems, can be used in order to plan and execute dimension is treated differently. trajectories through large-scale, navigable space. This Studies of how animals and humans navigate in environ- work, which has mostly been done in simplified, labora- ments with a vertical component are slowly proliferating, tory-based environments, has defined a number of sub-pro- and it is timely to review the gathering evidence and cesses such as landmark recognition, heading offer a theoretical interpretation of the findings to date. determination, odometry (distance-measuring), and In the first part of the article, we review the current context recognition, all of which interact in the construction literature on animal and human orientation and locomotion and use of spatial representations. The neural circuitry in three-dimensional spaces, highlighting key factors that underlying these processes has in many cases been ident- contribute to and influence navigation in such spaces. ified, and it now appears that the basics of navigation are The second part summarizes neurobiological studies of reasonably well understood. the encoding of three-dimensional space. The third and The real world, however, is neither simple nor two- final part integrates the experimental evidence to put dimensional, and the addition of vertical space to the two forward a hypothesis concerning three-dimensional horizontal dimensions adds a number of new problems spatial encoding – the bicoded model – in which we for a navigator to solve. For one thing, moving against propose that in encoding 3D spaces, the mammalian gravity imposes additional energy costs. Also, moving in a brain constructs mosaics of connected surface-referenced © Cambridge University Press 2013 0140-525X/13 $40.00 523 Jeffery et al.: Navigating in a three-dimensional world maps. The advantages and limitations of such a quasi-planar therefore, concerns what the reference frame might be encoding scheme are explored. and how the coordinate system encodes distances and directions within the frame. 2. Theoretical considerations The majority of studies of navigation, at least within neu- robiology, have up until now taken place in laboratory set- Before reviewing the behavioural and neurobiological aspects tings, using restricted environments such as mazes, which of three-dimensional navigation it is useful to establish a are characterized both by being planar (i.e., two-dimen- theoretical framework for the discussion, which will be devel- sional) and by being horizontal. The real world differs in – oped in more detail in the last part of this article. The study of both of these respects. First, it is often not planar air and navigation needs to be distinguished from the study of spatial water, for example, allow movement in any direction and perception per se, in which a subject may or may not be so are volumetric. In this article, therefore, we will divide moving through the space. Additionally, it is also important three-dimensional environments into those that are locally to distinguish between space that is encoded egocentrically planar surfaces, which allow movement only in a direction (i.e., relative to the subject) versus space that is encoded allo- tangential to the surface, and those that are volumetric centrically (independently of the subject – i.e., relative to the spaces (air, water, space, and virtual reality), in which move- world). The focus of the present article is on the allocentric ment (or virtual movement) in any direction is uncon- encoding of the space that is being moved through, which strained. Second, even if real environments might be probably relies on different (albeit interconnected) neural (locally) planar, the planes may not necessarily be horizontal. systems from the encoding of egocentric space. These factors are important in thinking about how subjects An animal that is trying to navigate in 3D space needs to encode and navigate through complex spaces. know three things – how it is positioned, how it is oriented, What does the vertical dimension add to the problem of fi and in what direction it is moving. Further, all these things navigation? At rst glance, not much: The vertical dimen- require a reference frame: a world-anchored space-defin- sion provides a set of directions one can move in, like any ing framework with respect to which position, orientation, other dimension, and it could be that the principles that and movement can be specified. There also needs to be have been elucidated for navigation in two dimensions some kind of metric coordinate system – that is, a signal extend straightforwardly to three. In fact, however, the ver- that specifies distances and directions with respect to this tical dimension makes the problem of navigation consider- reference frame. The core question for animal navigation, ably more complex, for a number of reasons. First, the space to be represented is much larger, since a volume is larger than a plane by a power of 3/2. Second, the direc- tional information to be encoded is more complex, because there are three planes of orientation instead of just one. Furthermore, rotations in orthogonal planes KATHRYN (KATE)JEFFERY is Professor of Behavioural interact such that sequences of rotations have different out- Neuroscience at University College London (UCL), comes depending on the order in which they are executed United Kingdom. After graduating in 1985 in medicine (i.e., they are non-commutative), which adds to processing from the University of Otago, New Zealand, she complexity. Third, the vertical dimension is characterized embarked on a research career to study neural rep- by gravity, and by consequences of gravity such as hydro- resentation, training with Cliff Abraham (University of static or atmospheric pressure, which add both information Otago), Richard Morris (University of Edinburgh), and and effort to the computations involved. And finally, there John O’Keefe (UCL). In 1999 she joined the Psychology Department (now Division of Psychology & Language are navigationally relevant cues available for the horizontal plane that are absent in the vertical: for example, the pos- Sciences) at UCL, where she continues research into fi the neural basis of spatial cognition. ition of the sun and stars, or the geomagnetic eld. The internal spatial representation that the brain con- ALEKSANDAR JOVALEKIC currently is a Postdoctoral structs for use in large-scale navigation is often referred Fellow at the Institute of Neuroinformatics in Zurich. to as a “cognitive map” (O’Keefe & Nadel 1978). The cog- He obtained his PhD at University College London in nitive map is a supramodal representation that arises from 2012, where his doctoral work focused on how rodents the collective activity of neurons in a network of brain areas navigate in three-dimensional environments. that process incoming sensory information and abstract higher-order spatial characteristics
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