Revisions to cyberchapter by Cheng and Newcombe

Front page
The intro or basic phenomenon is found in the rat section. So that should be section A. Maybe the section can be titled Rats: Basic phenomena, so that readers know where the basic ideas are.

Suggested revisions to the front page:

Abstract

With much pictorial support, we review research on how vertebrate animals orient in enclosed rectilinear spaces. The phenomenon of the rotational error is introduced, along with the distinction between geometric and featural information. The circumstances under which a number of species use geometric and featural information for relocating a target place are reviewed. Other sections examine cue competition (actually lack thereof) between geometric information and landmark cues, artificial intelligence, and the neurophysiological bases underlying the coding of geometric information, and. We then examine two theoretical issues: 1) how geometry is encoded and used, 2) the modularity of mind.

Orientation to the cyberchapter

We recently reviewed this literature in print (Cheng & Newcombe, 2005). Here we present an updated and far more pictorial review. To take full advantage of the web format, results and theory are discussed briefly in words, in ‘nugget form’. Each section is illustrated by appropriate pictures and other visual presentations. The basic phenomenon (Rat section) and the distinction between geometric and featural information are crucial for understanding the entire literature. We suggest that you read this section first. Otherwise, the following sections on data can be read in any order as you wish. We suggest, however, that you read at least a few of them before proceeding to the theoretical sections.

Sections

Rats: Basic phenomena
Chicks
Pigeons
Fish
Monkeys
Humans
Cue competition
Artificial intelligence
Neurophysiological bases

Theory of geometric encoding
Modularity
Conclusions

Section B (rats)
In Fig. B-7, C. The arena …. Returned to the arena. [Change “box” to “arena”, as the box was referring to the food box.]

Throughout, the font sizes vary. Maybe a good standard is to have the smaller font inside the figures, and to have the bigger font outside of figures. For me personally, I prefer the bigger font; I don’t like looking at small letters.

Section C (pigeons)
This section should follow, not precede, the section on chicks.

Figure C-4. Kelly & Spetch (2001) apparatus.

Figure C-5. Pigeons went with the shape. In this example, they preferred to search at a corner with a shorter wall to the right and a longer wall to the left, even though in the test space, the absolute lengths of walls did not match those in the training space.

Figure C-8. Removing the color (add “the”)

These manipulations led to … : delete this sentence

Revised description for Table C-1
Some manipulations led to the appearance of systematic rotational errors (Table C-1). When color information was removed by making all symbols the same color (shape only), when the feature at the target location and its diagonal opposite were removed (distant features), or when only a single feature at an adjacent corner was provided on a test (single feature), the percent of correct choices decreased compared with control tests. The errors, however, tended to be rotational errors. If the errors were distributed evenly, only one third of the errors should have been rotational errors, but the rotational errors in Table C-1 exceed this chance value.

Section D. (chicks)
This section should go before pigeons. Other than font sizes, the section is ok.

Section E (fish)
New figures for E-11, E-12, (E-13, E-14, same as 11 and 12, respectively) to be supplied.

  … alternative explanation (Cheng, 2005) [add a reference in press]

E-11 and E-13: Results (percentages) and alternative explanation of Experiment 3 of Vargas et al. (2004).
E-13. As an alternative explanation (Cheng, 2005), we tallied up the likely properties that the goldfish might attempt to match on a test (left), and assumed that the fish would try to match as many as possible. Geometry (long wall to the left, short wall to the right) was one property. A local feature to match consisted of having stripy wall on the right and plain wall on the left. (Panels were left out of consideration because they are the same in every corner.) A property of being near a wall of particular length and decoration pattern (stripy or plain), irrespective of which end of the wall was nearest to the corner, was also considered a property to match. The right panel shows that these properties are distributed across the four corners on the test in Experiment 3. One reasonable prediction is that the fish would search about equally at all four corners, a prediction confirmed by the data.

E-12 and E-14: Results (percentages) and alternative explanation of Experiment 4 of Vargas et al. (2004).

E-14. In Experiment 4, however, when the same set of properties tallied on the left panel are distributed among the different corners on the test, we see that the corner with the correct local feature has the most properties, the two geometrically correct corners have the next most properties, while the corner at the bottom left has nothing to recommend it for matching. The results reflect this ordering.

In this fashion, a single representational scheme explains both experiments, with no need to invoke different strategies in different situations. Whether an explanation along these lines proves better than Vargas et al.’s two-strategies interpretation remains to be tested.

Section F (monkeys)
Small features
With small features, monkeys used …

Large features
With large features, monkeys used …

Section G: Humans

1. The following text should appear first in this section, before any figures, and should also have the bolded changes below:
Hermer and Spelke (1994, 1996) tested children of 18-24 months in a reference memory paradigm, albeit one with only 4 trials. In all the experiments, the hidden toy remained in one corner throughout training. The children were disoriented between trials, so that they had to use cues within the arena to orient. 
They found that the children used geometric properties readily but did not use featural properties. In later work, this lab found that featural cues began to be used at 6 years of age and were virtually always used by adults. 
Figure G1 shows a schematic drawing of their 4 by 6 foot rectangular room. Figure G2 shows a photo of a room this size used by the Newcombe lab. Figure G3 shows representative results from one of the Hermer-Spelke experiments with children, followed by a representative result with adults in Figure G4. 
2. The following text should appear above Figure G5, and should say: Using geometric information is easier when an organism is inside a space than outside a space (Huttenlocher & Vasilyeva, 2003). As shown in Figure G5, one likely reason is that the distinctiveness of the space is greater when inside.
Also, that text is in a larger font than the rest of the text and this should be changed.
Furthermore, the text that does appear currently before Figure G5 needs adjustment; please delete the phrase in parentheses, add the bolded sentence, and then add the “Using….” sentence: 
Taking geometric sensitivity first, Huttenlocher and Vasilyeva (2003) found that children could use geometry to find a hidden object in enclosures of different shapes, triangles as well as rectangles, both when inside and when outside the space (see next slide). However, they did better when inside the space. 
Children rarely surveyed the various locations before going to the corner where they believed the object was hidden, suggesting that they represent the entire space so that, no matter where they face after disorientation, they know their relation to the hiding corner. 
3. This text should appear before (not after) Fig G6 with the noted change:
Learmonth, Newcombe, & Huttenlocher (2001) found that toddlers CAN use features to reorient, as shown by the data in Figure G6. Searches were much more likely in the correct corner than in the rotational equivalent.

Some new material with two new figures:

One new way to think about the roles of geometric and featural information is that the usage of each kind of information may vary with the situation and with the learning history of the organism (or other variables that determine individual differences). Consider a recent experiment by Hartley, Trinkler and Burgess (2004). Using virtual reality, people were placed in arenas in which they searched for targets. There were landmarks such as cliffs located in the far distance. The figure below gives a sense of the situation. 

On some trials, the shape of the arena was changed as shown in the next figure. People’s searches, as also shown in the figure, were guided by a variety of kinds of spatial information, including fixed distance to walls, a ratio of distances, and angles to corners of the arenas. The relative reliance on these types of information varied, with absolute distances more heavily weighted when distances were shorter, and thus likely to be estimated with less uncertainty. In addition, when the shape of the arena was altered, some people seemed to try to continue to use geometry to find the target while others seemed to rely on external features (such as the cliffs) for orientation. How different kinds of information are utilized and combined will likely be understood better in the near future as we analyze these kinds of situational and individual information more closely.

Section H: AI

Figure H-3 (3 missing)

Section I: Cue competition

Figure I-1:
The panel in white could be made a bit bigger. It is not very clear, and contains conceptual material for explaining cue competition. The panel on the right, a beacon, can be made much smaller, so that it does not look so degraded. Both the beacons are just examples without important conceptual consequences. That is, you do not need to see them in any detail to understand the story.

Caption: left top, … situations
Left bottom and right, … beacons

Lines to add below Figure I-1:
Tommasi and Vallortigara (2000, top left panel, top part) trained chicks to search in the middle of a square. They either had a prominent beacon at the center or not. The beacon was a potential cue competitor with geometric cues. When tested with the geometric cues alone (without the beacon), however, both groups performed similarly, giving no evidence of the overshadowing of geometric cues by a beacon.

Pearce et al. (2001) and Hayward et al. (2003) trained rats to find a corner of a swimming pool, where a hidden platform was located for escaping the water. An example is shown in the top left panel, bottom part. They found that having a prominent beacon right at the target corner neither overshadowed nor blocked the learning of geometric cues. The rats in these situations with cue competition still managed to find the target without the beacon present, as well as animals that learned geometric cues without a beacon. A beacon failed to be a cue competitor of geometric cues.

Figure I-2. Paper is published. Will supply a new figure with Wall et al. (2004) in title. The text should also have Wall et al. (2004).

Section J: Neuro

J-1: delete “In the photo”

J-2. add some lines at the end:
Hippocampal place cells (O’Keefe & Nadel, 1978) are typically found in the hippocampus proper. They fire preferentially when a rat is at a particular place in space.

Add an additional figure as J-9 (renumber all following figures)

J-9: adapted from Golob et al. (2001), Figures 1 and 2

Other cells, so called …
Delete entire paragraph and replace with the following expanded version:

Other cells in the hippocampal complex, called head direction cells, are sensitive to the direction that the rat’s head is facing, irrespective of the place that the rat is currently at (review: Dudchenko, 2003). These cells are typically found outside the hippocampus proper, in diverse areas ranging from the lateral dorsal thalamus to the dorsal tegmental nucleus. As these cells appear to encode direction, we may wonder whether their performance has something to do with encoding geometry and with rotational errors.

Golob, Stackman, Wong, and Taube (2001) probed this question. Head direction cells were recorded while a thirsty rat was in a square arena (Figure J-9A). The rat was not disoriented, but circular curtains surrounded the arena. Its home cage might change locations on different trials, as illustrated in Figure J-9A. A cue card on one wall provided directional cues. The rat had the behavioral task of finding one constant corner at which water was available; this was thus a reference memory task. The performance of a head direction cell was generally consistent, but on occasional trials, its preferred direction might shift by some multiple of 90o, as the dashed curve in Figure J-9B shows.

The question that arises is whether these shifts in the performance of head direction cells predict behavioral errors on the part of the rats. Across a number of experiments, the answer was a clear no. Golob et al. found no significant relations between the preferred direction of head direction cells and behavior.

J-13. Vargas et al. (2004) in caption and in text (paper appeared in print).

Section A: Modularity

This is not section A. It should go in the theoretical parts at the end, probably best after the theory section (K).

Title: Modularity (delete “Introduction:”)

The following figure  Figures A-1 to A-3 (or whatever letter the section will have).

channels: delete quotes; don’t really need them

Figure A-1

run in parallel (add “in”)

A-3
completely integrated view (Newcombe, 2002, 2005) [add a 2005 ref]

after A-3, add a new figure, A-4, and the following:

One of us (Cheng, 2005) has recently put forth another view of modularity that takes on elements of all the views in Figures A-1 to A-3 (Figure A-4). In this view, all spatial information, geometric and featural, is stored together in one representation, in this respect resembling Figure A-3 and Newcombe’s (2002, 2005) views. But at least one process that operates on the stored information is modular, the heading-by-axes process. This is a global direction-determining process that uses global shape parameters derived solely from geometric properties based on the entire shape of the space. This process is consistent with Wang and Spelke’s (2002) views. Other processes are not modular in this fashion. In particular, the process of determining an exact location of a target is based on both featural and geometric information. This process, however, weights preferentially cues near the target location. Such a view is foreshadowed in Cheng (1986, p. 172).

Figure A-4 becomes A-5

Figure A-5 becomes A-6

put in conflict (right panel): insert “(right panel)”

A-6 becomes A-7

Section K: Theory of Geometric Encoding

Figure K-1:

different nonuniform ‘subjective density’

K-2:
Figure K-2 This figure

Cheng and Gallistel, 2005 in press

K-5
Figure above K-5

K-8:
The Figure above K-8

K-9:
Cheng & Gallistel, 2005 in press. In this Figure K-9

Now, these figures …
Delete entire paragraph. Replace with the following:

A new added figure: K-10. An M-shape, with some axes of symmetry drawn through it in red by free hand.

Cheng (2005) suggests that principal axes may not be the best scheme for capturing global shape information. The trouble is that a principal axis is always a straight line, no matter what the shape; it really does not tell us anything about the shape. The M-shape in Figure K-10 has a roughly horizontal straight line as a principal axis, just as a horizontally oriented rectangle would.

In Figure K-10, we have also drawn in red, by free hand and approximately, a set of axes of symmetry. These bend with the curvature of the shape and capture regional symmetries, roughly bisecting the nearest walls. A glance at the red axes shows that they capture the M of the shape. Such axes of symmetry, a variety of them, can be formally defined (see Leyton, 1992, ch. 6).

Another shape-capturing scheme is the medial axis scheme (Fritsch, Pizer, Morse, Eberly, & Liu, 1994; Pizer, Fritsch, Yushkevich, Johnson, & Chaney, 1999), designed for the purpose of medical imaging. In brief this kind of scheme draws a stick-figure trunk and branch structure to capture the gist of the shape. The trunk goes through the middle of the space, and the branches indicate distances to the boundary. Substructures, such as the middle finger of the M in Figure K-10 would have their own skeletons, and be linked to the ‘parent’ shape. The scheme thus also captures something of the structure of the shape.

K-10 becomes Figure K-11.

Concluding words [a new final segment]

In sum, the burgeoning geometry literature arose from the rotational error that rats in Cheng’s (1986) study made. The rats confused geometrically equivalent locations (e.g., diagonally opposite corners) that are associated with different featural cues such as brightnesses of walls or patterns on panels in the corners. Mammalian species reviewed make rotational errors systematically under some circumstances. That is, in some situations, rotational errors are found significantly more than other kinds of errors. With intact, undegraded featural cues, either a wall of a distinctive color or objects in the corners, birds and fish have not been found to make systematic rotational errors. When featural cues are degraded on tests (for example, by making all features the same color), pigeons sometimes make systematic rotational errors. Under at least some conditions, however, all species also learn to use featural cues, choosing a correct location more often statistically than a rotational error.

Currently, debate concerning 1) the nature of geometric cues encoded, and 2) the modularity of geometric encoding form current topics of research. The work reviewed all use domesticated species or at least animals living most of their lives in rectilinear indoor spaces. This applies to the humans, monkeys, rats, pigeons, chicks (although they had few days of life before being tested), and even the fish in aquaria. Cheng and Newcombe (2005) wondered what this experience with rectilinear spaces in development might contribute to the encoding of geometric and featural cues. Recent research has also spread to wild-caught birds who have had at least substantial experience outdoors in natural settings. Some interesting differences have already been found (Gray et al., in press), and perhaps more will be found (e.g., Kelly’s program of testing Clark’s nutcrackers in ‘geometry’ paradigms).

References

Benhamou, S., & Poucet, B. (1998). Landmark use by navigating rats (Rattus norvegicus): Contrasting geometric and featural information. Journal of Comparative Psychology, 112, 317-322.
Burgess, N., Jackson, A., Hartley, T., & O’Keefe, J. (2000). Predictions derived from modelling the hippocampal role in navigation.  Biological Cybernetics, 83, 301-312.
Burgess, N. & O’Keefe, J. (2003). Neural representations in human spatial memory. Trends in Cognitive Science, 7, 517-519.
Chamizo, V.D. (2003). Acquisition of knowledge about spatial location: Assessing the generality of the mechanism of learning. Quarterly Journal of Experimental Psychology, 56B, 102-113.
Cheng, K. (1986). A purely geometric module in the rat’s spatial representation. Cognition, 23, 149-178.
Cheng, K. (2005a). Reflections on geometry and navigation. Connection Science, in press.
Cheng, K. (2005b). Goldfish matching geometric and featural cues: A re-interpretation of some of the data of Vargas et al. (2004). Journal of Comparative Psychology, in press.
Cheng, K., & Gallistel, C.R. (1984). Testing the geometric power of a spatial representation. In H.L. Roitblat, H.S. Terrace, & T.G. Bever (Eds.) Animal cognition (pp. 409-423). Hillsdale, NJ: Erlbaum.
Cheng, K., & Gallistel, C.R. (2005). Shape parameters explain data from spatial transformations: Comment on Pearce et al. (2004) and Tommasi and Polli (2004).  Journal of Experimental Psychology: Animal Behavior Processes, 31, 254-259.
Cheng K., & Newcombe, N.S. (2005). Is there a geometric module for spatial orientation? Squaring theory and evidence.  Psychonomic Bulletin & Review, 12, 1-23.
Dudchenko, P. (2003). The head direction system and navigation. In K.J. Jeffery (Ed.), The neurobiology of spatial behaviour (pp. 173-186). Oxford: Oxford University Press.
Egerton, S., Callaghan, V., & Chernett, P. (2000). A biologically inspired mapping model for autonomous mobile robots. In M. Mohammadin (Ed.), New frontiers in computational intelligence and its applications (pp. 20-29). Amsterdam: IOS Press.
Ekstrom, A.D., Kahana, M.J., Caplan, J.B., Fields, T.A., Isham, E.A., Newman, E.L., et al. (2003). Cellular networks underlying human spatial navigation. Nature, 425, 184-187.
Epstein, R., DeYoe, E.A., Press, D.Z., Rosen, A.C., & Kanwisher, N. (2001). Neuropsychological evidence for a topographical learning mechanism in parahippocampal cortex. Cognitive Neuropsychology, 18, 481-508.
Epstein, R., Graham, K.S., & Downing, P.E. (2003). Viewpoint-specific scene representations in human parahippocampal cortex. Neuron, 37, 865-876.
Epstein, R., Harris, A., Stanley, D., & Kanwisher, N. (1999). The parahippocampal place area: Recognition, navigation, or encoding? Neuron, 23, 115-125.
Epstein, R., & Kanwisher, N. (1998). A cortical representation of the local visual environment. Nature, 392, 598-601.
Fodor, J.A. (1983). The modularity of mind. Cambridge, MA: MIT Press.
Fritsch, D.S., Pizer, S.M., Morse, B.S., Eberly, D.H., & Liu, A. (1994). The multiscale medial axis and its applications in image registration.  Pattern Recognition Letters, 15, 445-452.
Gallistel, C.R., (1990). The organization of learning. Cambridge, MA: MIT Press.
Golob, E.J., Stackman, R.W., Wong, A.C., & Taube, J.S. (2001). On the behavioral significance of head direction cells: Neural and behavioral dynamics during spatial memory tasks. Behavioral Neuroscience, 115, 285-304.
Gouteux, S., Thinus-Blanc, C., & Vauclair, J. (2001). Rhesus monkeys use geometric and nongeometric information during a reorientation task. Journal of Experimental Psychology: General, 130, 505-519.
Hartley, T., Burgess, N., Lever, C., Cacucci, F., & O’Keefe, J. (2000). Modeling place fields in terms of the cortical inputs to the hippocampus.  Hippocampus, 10, 369-379.
Hartley, T., Maguire, E.A., Spiers, H.J., & Burgess, N. (2003). The well-worn route and the path less travelled: Distinct neural bases of route following and way finding in humans. Neuron, 37, 877-888.
Hartley, T., Trinkler, I., & Burgess, N. (2004). Geometric determinants of human spatial memory. Cognition, 94, 39-75.
Hayward, A., McGregor, A., Good, M.A., & Pearce, J.M. (2003). Absence of overshadowing and blocking between landmarks and geometric cues provided by the shape of a test arena. Quarterly Journal of Experimental Psychology, 56B, 114-126.
Hermer, L., & Spelke, E. (1994). A geometric process for spatial representation in young children. Nature, 370, 57-59.
Hermer, L., &  Spelke, E. (1996). Modularity and development: The case of spatial reorientation. Cognition, 61, 195-232.
Hermer-Vazquez, L., Spelke, E., & Katsnelson, A. (1999). Source of flexibility in human cognition: Dual task studies of space and language. Cognitive Psychology, 39, 3-36.
Huttenlocher, J., & Vasilyeva, M. (2003). How toddlers represent enclosed spaces. Cognitive Science, 27, 749-766.
Jacobs, L.F., & Schenk, F. (2003). Unpacking the cognitive map: The parallel map theory of hippocampal function. Psychological Review, 110, 285-315.
Jeffery, K.J. (Ed.) (2003). The neurobiology of spatial behaviour. Oxford: Oxford University Press.
Kelly, D., & Spetch, M.L. (2001). Pigeons encode relative geometry. Journal of Experimental Psychology: Animal Behavior Processes, 27, 417-422.
Kelly, D., & Spetch, M.L. (2004a). Reorientation in a two-dimensional environment I: Do adults encode the featural and geometric properties of a two-dimensional schematic of a room? Journal of Comparative Psychology, 118, 82-94.
Kelly, D., & Spetch, M.L. (2004b). 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?  Journal of Comparative Psychology, 118, 384-395.
Kelly, D., Spetch, M.L., & Heth, C.D. (1998). Pigeon’s encoding of geometric and featural properties of a spatial environment. Journal of Comparative Psychology, 112, 259-269.
Learmonth, A.E., Nadel, L., & Newcombe, N.S. (2002). Children’s use of landmarks: Implications for modularity theory. Psychological Science, 13, 337-341.
Learmonth, A.E., Newcombe, N.S., & Huttenlocher, J. (2001). Toddlers’ use of metric information and landmarks to reorient. Journal of Experimental Child Psychology, 80, 225-244.
Lever, C., Wills, T., Caccucci, F., Burgess, N., & O’Keefe, J. (2002). Long term plasticity in hippocampal place-cell representation of environmental geometry. Nature, 416, 90-94.
Leyton, M. (1992). Symmetry, Causality, Mind. Cambridge, MA: MIT Press.
Maguire, E.A., Burgess, N., Donnett, J.G., Frackowiak, R.S.J., Frith, C.D., & O’Keefe, J. (1998). Knowing where and getting there: A human navigation network. Science, 280, 921-924.
Maguire, E.A., Burgess, N., & O’Keefe, J. (1999). Human spatial navigation: cognitive maps, sexual dimorphism, and neural substrates. Current Opinion in Neurobiology, 9, 171-177.
Maguire, E.A., Frith, C.D., Burgess, N., Donnett, J.G., & O’Keefe, J. (1998). Knowing where things are: Parahippocampal involvement in encoding object locations in virtual large-scale space. Journal of Cognitive Neuroscience, 10, 61-76.
Margules, J., & Gallistel, C.R. (1988). Heading in the rat: Determination by environmental shape. Animal Learning & Behavior, 16, 404-410.
Marr, D. (1982). Vision. Cambridge, MA: MIT Press.
Newcombe, N.S. (2002). The nativist-empiricist controversy in the context of recent research on spatial and quantitative development. Psychological Science, 13, 395-401.
Nolfi, S. (2002). Power and limits of reactive agents. Robotics and Autonomous Systems, 42, 119-145.
O’Keefe, J., & Burgess, N. (1996). Geometric determinants of the place fields of hippocampal neurons. Nature, 381, 425-428.
O’Keefe, J., Burgess, N., Donnett, J.G., Jeffery, K.J., & Maguire, E.A. (1999). Place cells, navigational accuracy, and the human hippocampus. In G.W. Humphreys, J. Duncan, & A. Treisman (Eds.), Attention, space, and action: Studies in cognitive neuroscience (pp. 153-164). Oxford: Oxford University Press.
O’Keefe, J., & Nadel, L. (1978). The hippocampus as a cognitive map. Oxford: Clarendon Press.
Pearce, J.M., Good, M.A., Jones, P.M., & McGregor, A. (2004). Transfer of spatial behavior between different environments: Implications for theories of spatial learning and for the role of the hippocampus in spatial learning.  Journal of Experimental Psychology: Animal Behavior Processes, 30, 135-147.
Pearce, J.M., Ward-Robinson, J., Good, M., Fussell, C., & Aydin, A. (2001). Influence of a beacon on spatial learning based on the shape of the test environment. Journal of Experimental Psychology: Animal Behavior Processes, 27, 329-344.
Pizer, S.M., Fritsch, D.S., Yushkevich, P.A., Johnson, V.E., & Chaney, E.L. (1999). Segmentation, registration, and measurement of shape variation via image object shape.  IEEE Transactions on Medical Imaging, 18, 851-865.
Poucet, B., Lenck-Santini, P.-P., & Save, E. (2003). Drawing parallels between the behavioural and neural properties of navigation. In K.J. Jeffery (Ed.), The neurobiology of spatial behaviour (pp. 187-198). Oxford: Oxford University Press.
Sovrano, V.A., Bisazza, A., & Vallortigara, G. (2002). Modularity and spatial reorientation in a simple mind: encoding of geometric and nongeometric properties of a spatial environment by fish. Cognition, 85, B51-B59.
Sovrano, V.A., Bisazza, A., & Vallortigara, G. (2003). Modularity as a fish (Xenotoca eiseni) views it: Conjoining geometric and nongeometric information for spatial reorientation. Journal of Experimental Psychology: Animal Behavior Processes, 29, 199-210.
Tommasi, L., Gagliardo, A., Andrew, R.J., & Vallortigara, G. (2003). Separate processing mechanisms for encoding geometric and landmark information in the avian brain. European Journal of Neuroscience, 17, 1695-1702.
Tommasi, L., & Polli, C. (2004). Representation of two geometric features of the environment in the domestic chick (Gallus gallus). Animal Cognition, 7, 53-59.
Tommasi, L., & Vallortigara, G. (2000). Searching for the center: Spatial cognition in the domestic chick (Gallus gallus). Journal of Experimental Psychology: Animal Behavior Processes, 26, 477-486.
Tommasi, L., Vallortigara, G., & Zanforlin, M. (1997). Young chicks learn to localize the center of a spatial environment. Journal of Comparative Physiology A, 180, 567-572.
Vallortigara, G., Pagni, P., & Sovrano, V.A. (2004). Separate geometric and non-geometric modules for spatial reorientation: Evidence from a lopsided animal brain. Journal of Cognitive Neuroscience, 16, 390-400.
Vallortigara, G., Zanforlin, M., & Pasti, G. (1990). Geometric modules in animals’ spatial representations: A test with chicks (Gallus gallus domesticus). Journal of Comparative Psychology, 104, 248-254.
Vargas, J.P., López, J.C., Salas, C., & Thinus-Blanc, C. (2004). Encoding of geometric and featural information by goldfish (Carassius auratus).  Journal of Comparative Psychology, 118, 206-216.
Vargas, J.P., Petruso, E.J., & Bingman, V.P. (2004). Hippocampal formation and geometric navigation in pigeons. European Journal of Neuroscience, 20, 1937-1944.
Wall, P.L., Botly, L.C.P., Black, C.K., & Shettleworth, S.J. (2004). The geometric module in the rat: independence of shape and feature learning in a food finding task. Learning & Behavior, 32, 289-298.
Wang, R.F., & Spelke, E.S. (2002). Human spatial representation: Insights from animals. Trends in Cognitive Sciences, 6, 376-382.
Wang, R.F., & Spelke, E.S. (2003). Comparative approaches to human navigation. In K.J. Jeffery (Ed.), The neurobiology of spatial behaviour (pp. 119-143). Oxford: Oxford University Press.
Webb, B. (2000). What does robotics offer animal behaviour? Animal Behaviour, 60, 545-558.
Yeap, W.K., & Jefferies, M.E. (1999). Computing representations of the local environment. Artificial Intelligence, 107, 265-301.

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