25 years of research on the use of geometry in spatial reorientation: a current theoretical perspective

The purpose of this article is to review and evaluate the range of theories proposed to explain findings on the use of geometry in reorientation. We consider five key approaches and models associated with them and, in the course of reviewing each approach, five key issues. First, we take up modularity theory itself, as recently revised by Lee and Spelke (Cognitive Psychology, 61, 152–176, 2010a; Experimental Brain Research, 206, 179–188, 2010b). In this context, we discuss issues concerning the basic distinction between geometry and features. Second, we review the view-matching approach (Stürzl, Cheung, Cheng, & Zeil, Journal of Experimental Psychology: Animal Behavior Processes, 34, 1–14, 2008). In this context, we highlight the possibility of cross-species differences, as well as commonalities. Third, we review an associative theory (Miller & Shettleworth, Journal of Experimental Psychology: Animal Behavior Processes, 33, 191–212, 2007; Journal of Experimental Psychology: Animal Behavior Processes, 34, 419–422, 2008). In this context, we focus on phenomena of cue competition. Fourth, we take up adaptive combination theory (Newcombe & Huttenlocher, 2006). In this context, we focus on discussing development and the effects of experience. Fifth, we examine various neurally based approaches, including frameworks proposed by Doeller and Burgess (Proceedings of the National Academy of Sciences of the United States of America, 105, 5909–5914, 2008; Doeller, King, & Burgess, Proceedings of the National Academy of Sciences of the United States of America, 105, 5915–5920, 2008) and by Sheynikhovich, Chavarriaga, Strösslin, Arleo, and Gerstner (Psychological Review, 116, 540–566, 2009). In this context, we examine the issue of the neural substrates of spatial navigation. We conclude that none of these approaches can account for all of the known phenomena concerning the use of geometry in reorientation and clarify what the challenges are for each approach.

[1]  Michela Ponticorvo,et al.  Encoding geometric and non-geometric information: a study with evolved agents , 2009, Animal Cognition.

[2]  J. O’Keefe,et al.  Boundary Vector Cells in the Subiculum of the Hippocampal Formation , 2009, The Journal of Neuroscience.

[3]  Marcia L. Spetch,et al.  Comparing black-capped (Poecile atricapillus) and mountain chickadees (Poecile gambeli): use of geometric and featural information in a spatial orientation task , 2009, Animal Cognition.

[4]  Valeria Anna Sovrano,et al.  Separate Geometric and Non-Geometric Modules for Spatial Reorientation: Evidence from a Lopsided Animal Brain , 2004, Journal of Cognitive Neuroscience.

[5]  J. Rieser,et al.  Bayesian integration of spatial information. , 2007, Psychological bulletin.

[6]  Marcia L Spetch,et al.  Reorientation in a two-dimensional environment: II. Do pigeons (Columba livia) encode the featural and geometric properties of a two-dimensional schematic of a room? , 2004, Journal of comparative psychology.

[7]  Noam Miller,et al.  Modeling the effects of enclosure size on geometry learning , 2009, Behavioural Processes.

[8]  Valeria Anna Sovrano,et al.  Modularity as a fish (Xenotoca eiseni) views it: conjoining geometric and nongeometric information for spatial reorientation. , 2003, Journal of experimental psychology. Animal behavior processes.

[9]  J. Zeil,et al.  The properties of the visual system in the Australian desert ant Melophorus bagoti. , 2011, Arthropod structure & development.

[10]  A. Lew Looking beyond the boundaries: time to put landmarks back on the cognitive map? , 2011, Psychological bulletin.

[11]  E. Spelke,et al.  Modularity and development: the case of spatial reorientation , 1996, Cognition.

[12]  Juan Pedro Vargas,et al.  Encoding of geometric and featural spatial information by goldfish (Carassius auratus). , 2004, Journal of comparative psychology.

[13]  Valeria Anna Sovrano,et al.  How fish do geometry in large and in small spaces , 2006, Animal Cognition.

[14]  Thomas S. Collett,et al.  Memory use in insect visual navigation , 2002, Nature Reviews Neuroscience.

[15]  Kiralee M. Hayashi,et al.  Dynamic mapping of normal human hippocampal development , 2006, Hippocampus.

[16]  K. Cheng,et al.  The determination of direction in landmark-based spatial search in pigeons: A further test of the vector sum model , 1994 .

[17]  R. Wehner The architecture of the desert ant's navigational toolkit (Hymenoptera: Formicidae) , 2009 .

[18]  Allen Cheung,et al.  The information content of panoramic images I: The rotational errors and the similarity of views in rectangular experimental arenas. , 2008, Journal of experimental psychology. Animal behavior processes.

[19]  Giorgio Vallortigara,et al.  View-based strategy for reorientation by geometry , 2010, Journal of Experimental Biology.

[20]  C Thinus-Blanc,et al.  Rhesus monkeys use geometric and nongeometric information during a reorientation task. , 2001, Journal of experimental psychology. General.

[21]  K. Jeffery,et al.  Preserved performance in a hippocampal‐dependent spatial task despite complete place cell remapping , 2003, Hippocampus.

[22]  Ralph R. Miller,et al.  Biological Significance as a Determinant of Cue Competition , 1996 .

[23]  Russell A. Epstein Parahippocampal and retrosplenial contributions to human spatial navigation , 2008, Trends in Cognitive Sciences.

[24]  T. Hafting,et al.  Microstructure of a spatial map in the entorhinal cortex , 2005, Nature.

[25]  E. Spelke,et al.  Children's use of geometry and landmarks to reorient in an open space , 2001, Cognition.

[26]  Sean Duffy,et al.  It Is All Relative: How Young Children Encode Extent , 2005 .

[27]  Lynn Nadel,et al.  Children's Use of Landmarks: Implications for Modularity Theory , 2002, Psychological science.

[28]  Sara J Shettleworth,et al.  An associative model of geometry learning: a modified choice rule. , 2008, Journal of experimental psychology. Animal behavior processes.

[29]  M Zanforlin,et al.  Geometric modules in animals' spatial representations: a test with chicks (Gallus gallus domesticus). , 1990, Journal of comparative psychology.

[30]  P. Graham,et al.  Which portion of the natural panorama is used for view-based navigation in the Australian desert ant? , 2009, Journal of Comparative Physiology A.

[31]  Sean Duffy,et al.  Developing symbolic capacity one step at a time , 2008, Cognition.

[32]  J. Knierim,et al.  Hippocampal place cells: Parallel input streams, subregional processing, and implications for episodic memory , 2006, Hippocampus.

[33]  Nora S Newcombe,et al.  Reorienting When Cues Conflict , 2008, Psychological science.

[34]  Christian F. Doeller,et al.  Parallel striatal and hippocampal systems for landmarks and boundaries in spatial memory , 2008, Proceedings of the National Academy of Sciences.

[35]  L. Hedges,et al.  Categories and particulars: prototype effects in estimating spatial location. , 1991, Psychological review.

[36]  K. Cheng Distances and directions are computed separately by honeybees in landmark-based search , 1998 .

[37]  R. Wehner Desert ant navigation: how miniature brains solve complex tasks , 2003, Journal of Comparative Physiology A.

[38]  Stella F. Lourenco,et al.  Coding location in enclosed spaces: is geometry the principle? , 2007, Developmental science.

[39]  David Waller,et al.  Handbook of spatial cognition , 2013 .

[40]  Neil Burgess,et al.  Predictions derived from modelling the hippocampal role in navigation , 2000, Biological Cybernetics.

[41]  Giorgio Vallortigara,et al.  Is there an innate geometric module? Effects of experience with angular geometric cues on spatial re-orientation based on the shape of the environment , 2007, Animal Cognition.

[42]  Nora S Newcombe,et al.  Why size counts: children's spatial reorientation in large and small enclosures. , 2008, Developmental science.

[43]  Holk Cruse,et al.  No Need for a Cognitive Map: Decentralized Memory for Insect Navigation , 2011, PLoS Comput. Biol..

[44]  J. O’Keefe Place units in the hippocampus of the freely moving rat , 1976, Experimental Neurology.

[45]  Jochen Zeil,et al.  Catchment areas of panoramic snapshots in outdoor scenes. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[46]  Ian M. Lyons,et al.  The Influence of Cue Reliability and Cue Representation on Spatial Reorientation in Young Children , 2014 .

[47]  J. O'Keefe,et al.  The hippocampus as a spatial map. Preliminary evidence from unit activity in the freely-moving rat. , 1971, Brain research.

[48]  Giuseppe Iaria,et al.  Hippocampal function and spatial memory: evidence from functional neuroimaging in healthy participants and performance of patients with medial temporal lobe resections. , 2004, Neuropsychology.

[49]  Debbie M. Kelly,et al.  Pigeons' (Columba livia) encoding of geometric and featural properties of a spatial environment. , 1998 .

[50]  R. J. McDonald,et al.  Multiple Parallel Memory Systems in the Brain of the Rat , 2002, Neurobiology of Learning and Memory.

[51]  R. Muller,et al.  Failure of Centrally Placed Objects to Control the Firing Fields of Hippocampal Place Cells , 1997, The Journal of Neuroscience.

[52]  Neil Burgess,et al.  Distinct error-correcting and incidental learning of location relative to landmarks and boundaries , 2008, Proceedings of the National Academy of Sciences.

[53]  C R Cavonius,et al.  Human Visual Acuity Measured with Colored Test Objects , 1966, Science.

[54]  Alexandra D. Twyman,et al.  Of mice (Mus musculus) and toddlers (Homo sapiens): evidence for species-general spatial reorientation. , 2009, Journal of comparative psychology.

[55]  I. Whishaw,et al.  Variation in visual acuity within pigmented, and between pigmented and albino rat strains , 2002, Behavioural Brain Research.

[56]  J. Huttenlocher,et al.  Development of Spatial Cognition , 2007 .

[57]  T. Gurley,et al.  Orientation in trapezoid-shaped enclosures: implications for theoretical accounts of geometry learning. , 2011, Journal of experimental psychology. Animal behavior processes.

[58]  R U Muller,et al.  Head-direction cells recorded from the postsubiculum in freely moving rats. I. Description and quantitative analysis , 1990, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[59]  Peter L. Hurd,et al.  Growing in Circles , 2007 .

[60]  S. Shettleworth,et al.  Learning about Environmental Geometry: an Associative Model , 2022 .

[61]  T. S. Collett,et al.  Landmark learning in bees , 1983, Journal of comparative physiology.

[62]  Leslie G. Ungerleider,et al.  Object vision and spatial vision: two cortical pathways , 1983, Trends in Neurosciences.

[63]  M. Spetch,et al.  Averaging temporal duration and spatial position. , 1996, Journal of experimental psychology. Animal behavior processes.

[64]  R. Passingham The hippocampus as a cognitive map J. O'Keefe & L. Nadel, Oxford University Press, Oxford (1978). 570 pp., £25.00 , 1979, Neuroscience.

[65]  Giorgio Vallortigara,et al.  Reorienting strategies in a rectangular array of landmarks by domestic chicks (Gallus gallus). , 2010, Journal of comparative psychology.

[66]  N. Burgess,et al.  Geometric determinants of human spatial memory , 2004, Cognition.

[67]  D. Nardi,et al.  The world is not flat: can people reorient using slope? , 2011, Journal of experimental psychology. Learning, memory, and cognition.

[68]  J. D. McGaugh,et al.  Inactivation of Hippocampus or Caudate Nucleus with Lidocaine Differentially Affects Expression of Place and Response Learning , 1996, Neurobiology of Learning and Memory.

[69]  Arne D. Ekstrom,et al.  Cellular networks underlying human spatial navigation , 2003, Nature.

[70]  Almut Hupbach,et al.  Reorientation in a rhombic environment: No evidence for an encapsulated geometric module , 2005 .

[71]  Ken Cheng,et al.  Landmark use by Clark’s nutcrackers (Nucifraga columbiana): influence of disorientation and cue rotation on distance and direction estimates , 2009, Animal Cognition.

[72]  S. Becker,et al.  Remembering the past and imagining the future: a neural model of spatial memory and imagery. , 2007, Psychological review.

[73]  M. Goodale,et al.  Separate visual pathways for perception and action , 1992, Trends in Neurosciences.

[74]  K. Jeffery,et al.  The Boundary Vector Cell Model of Place Cell Firing and Spatial Memory , 2006, Reviews in the neurosciences.

[75]  Jennifer E. Sutton,et al.  What is geometric information and how do animals use it? , 2009, Behavioural Processes.

[76]  Caroline Murphy,et al.  Use of geometry for spatial reorientation in children applies only to symmetric spaces. , 2010, Developmental science.

[77]  Elizabeth M. Brannon,et al.  Space, time and number in the brain : searching for the foundations of mathematical thought , 2011 .

[78]  Katherine D. Kinzler,et al.  Core knowledge. , 2007, Developmental science.

[79]  Wolfgang Stürzl,et al.  Depth, contrast and view-based homing in outdoor scenes , 2007, Biological Cybernetics.

[80]  Valeria Anna Sovrano,et al.  Animals' use of landmarks and metric information to reorient: effects of the size of the experimental space , 2005, Cognition.

[81]  Stella F. Lourenco,et al.  Origins and Development of Generalized Magnitude Representation , 2011 .

[82]  R. Wehner,et al.  Traveling in clutter: Navigation in the Central Australian desert ant Melophorus bagoti , 2009, Behavioural Processes.

[83]  K. Jeffery,et al.  Dissociation of the geometric and contextual influences on place cells , 2003, Hippocampus.

[84]  Nora S. Newcombe,et al.  1 Explaining the Development of Spatial Reorientation : Modularity-Plus-Language Versus the Emergence of Adaptive Combination , 2007 .

[85]  N. Newcombe,et al.  Is there a geometric module for spatial orientation? squaring theory and evidence , 2005, Psychonomic bulletin & review.

[86]  E. Tolman Cognitive maps in rats and men. , 1948, Psychological review.

[87]  Giorgio Vallortigara,et al.  Animals as Natural Geometers , 2009 .

[88]  D. Nitz,et al.  Spatial‐specificity of single‐units in the hippocampal formation of freely moving homing pigeons , 2005, Hippocampus.

[89]  Alexandra D. Twyman,et al.  Geometry three ways: an fMRI investigation of geometric information processing during reorientation. , 2012, Journal of experimental psychology. Learning, memory, and cognition.

[90]  Sang Ah Lee,et al.  A modular geometric mechanism for reorientation in children , 2010, Cognitive Psychology.

[91]  J. Huttenlocher,et al.  Spatial Scaling in Young Children , 1999 .

[92]  Antoine Wystrach,et al.  Geometry, features, and panoramic views: ants in rectangular arenas. , 2011, Journal of experimental psychology. Animal behavior processes.

[93]  Giuseppe Iaria,et al.  Gray Matter Differences Correlate with Spontaneous Strategies in a Human Virtual Navigation Task , 2007, The Journal of Neuroscience.

[94]  Daniele Nardi,et al.  Slope-driven goal location behavior in pigeons. , 2010, Journal of experimental psychology. Animal behavior processes.

[95]  M. Moser,et al.  Representation of Geometric Borders in the Entorhinal Cortex , 2008, Science.

[96]  R. Muller,et al.  Head-direction cells recorded from the postsubiculum in freely moving rats. II. Effects of environmental manipulations , 1990, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[97]  Antoine Wystrach,et al.  Ants in rectangular arenas , 2009, Communicative & integrative biology.

[98]  J. Pearce,et al.  Spatial learning based on the shape of the environment is influenced by properties of the objects forming the shape. , 2006, Journal of experimental psychology. Animal behavior processes.

[99]  Sean Duffy,et al.  Infants and Toddlers Discriminate Amount: Are They Measuring? , 2002, Psychological science.

[100]  J. Spencer,et al.  The Emerging Spatial Mind , 2007 .

[101]  Andrew Philippides,et al.  How might ants use panoramic views for route navigation? , 2011, Journal of Experimental Biology.

[102]  Valeria Anna Sovrano,et al.  Dissecting the Geometric Module , 2006, Psychological science.

[103]  J. O’Keefe,et al.  Modeling place fields in terms of the cortical inputs to the hippocampus , 2000, Hippocampus.

[104]  SIMON BENHAMOU,et al.  No evidence for cognitive mapping in rats , 1996, Animal Behaviour.

[105]  Sang Ah Lee,et al.  Two systems of spatial representation underlying navigation , 2010, Experimental Brain Research.

[106]  N. Ulanovsky,et al.  Hippocampal cellular and network activity in freely moving echolocating bats , 2007, Nature Neuroscience.

[107]  Debbie M. Kelly,et al.  Geometry and landmark representation by pigeons: evidence for species‐differences in the hemispheric organization of spatial information processing? , 2009, The European journal of neuroscience.

[108]  Valeria Anna Sovrano,et al.  Modularity and spatial reorientation in a simple mind: encoding of geometric and nongeometric properties of a spatial environment by fish , 2002, Cognition.

[109]  M. Goodale,et al.  The visual brain in action , 1995 .

[110]  E. Save,et al.  Spatial Firing of Hippocampal Place Cells in Blind Rats , 1998, The Journal of Neuroscience.

[111]  J. Huttenlocher,et al.  Toddlers' use of metric information and landmarks to reorient. , 2001, Journal of experimental child psychology.

[112]  Antoine Wystrach,et al.  Landmarks or panoramas: what do navigating ants attend to for guidance? , 2011, Frontiers in Zoology.

[113]  Ken Cheng,et al.  Whither geometry? Troubles of the geometric module , 2008, Trends in Cognitive Sciences.

[114]  Marko Nardini,et al.  A viewpoint-independent process for spatial reorientation , 2009, Cognition.

[115]  J. Pearce Similarity and discrimination: a selective review and a connectionist model. , 1994, Psychological review.

[116]  Jeffrey Loewenstein,et al.  The Repetition-Break Plot Structure: A Cognitive Influence on Selection in the Marketplace of Ideas , 2009, Cogn. Sci..

[117]  J. Taube,et al.  On the behavioral significance of head direction cells: neural and behavioral dynamics during spatial memory tasks. , 2001, Behavioral neuroscience.

[118]  M. Petrides,et al.  Cognitive Strategies Dependent on the Hippocampus and Caudate Nucleus in Human Navigation: Variability and Change with Practice , 2003, The Journal of Neuroscience.

[119]  Michael R. W. Dawson,et al.  Using perceptrons to explore the reorientation task , 2010, Cognition.

[120]  Almut Hupbach,et al.  Factors moderating blocking in human place learning: The role of task instructions , 2009, Learning & behavior.

[121]  W. Gerstner,et al.  Is there a geometric module for spatial orientation? Insights from a rodent navigation model. , 2009, Psychological review.

[122]  J Ward-Robinson,et al.  Influence of a beacon on spatial learning based on the shape of the test environment. , 2001, Journal of experimental psychology. Animal behavior processes.

[123]  Ken Cheng,et al.  How to navigate without maps: The power of taxon-like navigation in ants , 2012 .

[124]  Michael R W Dawson,et al.  Learning about environmental geometry: a flaw in Miller and Shettleworth's (2007) operant model. , 2008, Journal of experimental psychology. Animal behavior processes.

[125]  Allen Cheung,et al.  The information content of panoramic images II: view-based navigation in nonrectangular experimental arenas. , 2008, Journal of experimental psychology. Animal behavior processes.

[126]  Nora S. Newcombe,et al.  Five Reasons to Doubt the Existence of a Geometric Module , 2010, Cogn. Sci..

[127]  Russell A. Epstein,et al.  Hippocampal size predicts rapid learning of a cognitive map in humans , 2013, Hippocampus.

[128]  Janellen Huttenlocher,et al.  How toddlers represent enclosed spaces , 2003, Cogn. Sci..

[129]  B. A. Cartwright,et al.  How honey bees use landmarks to guide their return to a food source , 1982, Nature.

[130]  Barbara Landau,et al.  Impaired geometric reorientation caused by genetic defect , 2010, Proceedings of the National Academy of Sciences.

[131]  Janellen Huttenlocher,et al.  Preexisting Knowledge Versus On-Line Learning , 2005, Psychological science.

[132]  Robin Hayman,et al.  Geometric Cues Influence Head Direction Cells Only Weakly in Nondisoriented Rats , 2011, The Journal of Neuroscience.

[133]  Alinda Friedman,et al.  Penetrating the geometric module: catalyzing children's use of landmarks. , 2007, Developmental psychology.

[134]  Stella F. Lourenco,et al.  General Magnitude Representation in Human Infants , 2010, Psychological science.

[135]  K. Jeffery,et al.  Please Scroll down for Article the Quarterly Journal of Experimental Psychology Theoretical Accounts of Spatial Learning: a Neurobiological View(commentary on Pearce, 2009) , 2022 .

[136]  Stella F. Lourenco,et al.  Location representation in enclosed spaces: what types of information afford young children an advantage? , 2009, Journal of experimental child psychology.

[137]  Sang Ah Lee,et al.  Young Children Reorient by Computing Layout Geometry, Not by Matching Images of the Environment , 2010 .

[138]  Sara J Shettleworth,et al.  The geometric module in the rat: independence of shape and feature learning in a food finding task , 2004, Learning & behavior.

[139]  Alexandra D. Twyman,et al.  Young children's use of features to reorient is more than just associative: further evidence against a modular view of spatial processing. , 2010, Developmental science.

[140]  Daniel L. Schacter,et al.  Spatial Representation in the Entorhinal Cortex , 2004 .

[141]  Sang Ah Lee,et al.  Navigation as a source of geometric knowledge: Young children’s use of length, angle, distance, and direction in a reorientation task , 2012, Cognition.

[142]  R. Rescorla A theory of pavlovian conditioning: The effectiveness of reinforcement and non-reinforcement , 1972 .

[143]  Jennifer E Sutton,et al.  Spinning in the scanner: neural correlates of virtual reorientation. , 2010, Journal of experimental psychology. Learning, memory, and cognition.

[144]  Veronique D. Bohbot,et al.  Maze training in mice induces MRI-detectable brain shape changes specific to the type of learning , 2011, NeuroImage.

[145]  K. Cheng A purely geometric module in the rat's spatial representation , 1986, Cognition.

[146]  Elizabeth S. Spelke,et al.  A geometric process for spatial reorientation in young children , 1994, Nature.

[147]  Nora S. Newcombe,et al.  The development of location coding: An adaptive combination account. , 2013 .

[148]  Sang Ah Lee,et al.  Beyond Core Knowledge: Natural Geometry , 2010, Cogn. Sci..

[149]  P. Graham,et al.  Ants use the panoramic skyline as a visual cue during navigation , 2009, Current Biology.

[150]  Neil Burgess,et al.  Children reorient using the left/right sense of coloured landmarks at 18–24 months , 2008, Cognition.

[151]  Daniele Nardi,et al.  Pigeon (Columba livia) encoding of a goal location: the relative importance of shape geometry and slope information. , 2009, Journal of comparative psychology.

[152]  Giorgio Vallortigara,et al.  Experience and geometry: controlled-rearing studies with chicks , 2010, Animal Cognition.

[153]  Vincent Walsh A theory of magnitude: common cortical metrics of time, space and quantity , 2003, Trends in Cognitive Sciences.

[154]  C. Gallistel The organization of learning , 1990 .

[155]  Nora S. Newcombe,et al.  Infants' coding of location in continuous space. , 1999 .

[156]  Laurie L Bloomfield,et al.  Spatial encoding in mountain chickadees: features overshadow geometry , 2005, Biology Letters.

[157]  N. Burgess,et al.  The hippocampus and memory: insights from spatial processing , 2008, Nature Reviews Neuroscience.

[158]  Andrew Philippides,et al.  A Model of Ant Route Navigation Driven by Scene Familiarity , 2012, PLoS Comput. Biol..

[159]  Antoine Wystrach,et al.  Ants Learn Geometry and Features , 2009, Current Biology.

[160]  Alexandra D. Twyman,et al.  Malleability in the development of spatial reorientation. , 2013, Developmental psychobiology.

[161]  J. Taube The head direction signal: origins and sensory-motor integration. , 2007, Annual review of neuroscience.