Landmark-Based Spatial Memory in the Pigeon

LANDMARK-BASED SPATIAL MEMORY IN THE PIGEON Ken Cheng

Finding the way back to a desired place is an oft-encountered problem in animal life. For many, survival and reproduction are based on it. The Clark’s nutcracker, for example, is a bird that stores thousands of caches of pine seeds. To survive a winter, it must retrieve an estimated 2200-3000 such caches (Vander Wall & Balda, 1981).For another example, the digger wasp is so called because the females dig nests in the ground in which they lay eggs. The wasp is then faced with the problem of finding the way back to her nests to provision the future larvae with a source of food. In general, many creatures need to get back to locations of food and home. It is little wonder, then, that a number of place-finding mechanisms are found across the animal kingdom. In this chapter, I will describe wayfinding mechanisms, and in particular, the use of landmark-based spatial memory as servomechanisms. I will then describe one model for landmark-based spatial memory in pigeons, the vector sum model, and then revise it on the basis of further data. At the end, the servomechanism (1) uses the metric properties of space (that is, distances and directions) in guiding search, and (2) computes directions and distances separately and independently. This system is compared to the honeybee’s landmark-based spatial memory, which also shares these two properties. These systems break down the problem into separate modules and average the dictates of different sources of information. Comments on this form of modular neurocognitive architecture will complete the chapter. THE PSYCHOLOGY OF LEARNING AND MOTIVATION. VOL. 33

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Copyright 8 1YYS by Academic Press. Inc. All rights of reproduction in any form reserved.

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I. Wayfinding as Servomechanisms A servomechanism, which Gallistel (1980) called a basic unit of action, attempts to maintain a particular level on one or more variables behaviorally or physiologically (or both). I call the level to maintain a standard. The standard can be of an internal physiological variable, such as blood pH level or temperature, or some aspect of the world, such as keeping a moving object on the fovea. The latter is typically maintained by behavior. Figure 1 illustrates the servomechanism. At its core, a comparator compares a reading of the environment, called a record, with the standard. The environment must be broadly defined to include the internal milieu of the body as well. The discrepancy or error drives the mechanism to initiate action to reduce the error, thus completing a negative feedback loop. Servomechanisms of orientation are generally called taxes (plural of tuxis) in the ethological literature (Fraenkel & Gum, 1940). Most taxes move the animal not to any particular place, but to a place with more “desired” characteristics. But in two cases explained below, the standard is a particular place, and the mechanism compares a specification of the current place with the standard and generates action to reduce this discrepancy. Tropotaxis (Fig. 2) serves as an example of taxic orientation (Gallistel, 1980). It moves the animal, for example, a moth, toward a source of light.

COMPARATOR STANDARD

RECORD

ACTION

t

I

Fig. 1. The servomechanism. In a servomechanism. a comparator compares a perceptual signal (R, record) to a standard (S). The difference (error) drives behavior to reduce the error.

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COMPARATOR

Fig. 2. The tropotaxis, an example of a servomechanism where the comparator compares light intensity levels on the two eyes. The mechanism turns the organism toward the side receiving more light.

The comparator compares the light intensities on the two eyes of the moth, which are placed toward the side of the head. If the source of light is to the right of the moth, the right eye receives more light than the left. The action generated turns the moth to the right, thus reducing the discrepancy between the direction of light and the direction of the moth’s flight. If the left eye receives more light, the moth turns to the left, which also veers the moth toward the light. A. PATHINTEGRATION

Path integration, also known as inertial navigation or dead reckoning (Gallistel, 1990, ch. 4), is a wayfinding servomechanism that returns the animal to the starting place of the journey, typically its home (Fig. 3). The creature does so by keeping track of the vector it has covered since the beginning of the journey, that is, the straight line distance and direction from the starting point. This vector then allows it to deduce the approximate distance and direction home. Somehow then, it must be continuously adding, in the fashion of vector addition, the path it covers as it meanders, thus giving rise to the term path integration, literally the summing of small steps along the journey. In this servomechanism, the standard is the 0 vector, and the record is the vector deduced en route. To put the mechanism

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COMPARATOR

ERROR

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SUN, POLARIZED LIGHT, MOVEMENT, VISUAL FLOW, ETC.

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MOVE IN DlRECTl$N -V FORIVI

Fig. 3. Path integration as an example of a servomechanism. The system keeps track of the vector (straight line distance and direction) from the starting place to where it ends up (V). The specification of the starting position (S) is the 0 vector. Comparison of S with the current position (R) gives the vector V. The organism thus must move according to the vector - V to reach home (starting position).

into operation, the animal reverses the deduced vector to derive the direction and distance home. Path integration is found in insects (Mueller & Wehner, 1988; Wehner & Srinivasan, 1981), birds (von St. Paul, 1982), and rodents (Etienne, 1987; Mittelstaedt & Mittelstaedt, 1980; Potegal, 1982, SCguinot, Maurer, & Etienne, 1993).

B. LANDMARK-BASED SPATIAL MEMORY Another common wayfinding servomechanism, and the main topic of this chapter, is landmark-based spatial memory (Gallistel, 1990, ch. 5). The ethological literature calls this rnnernofuxis(mnemo for memory), and modern practice also labels it piloting (Fig. 4). Some aspects of the spatial relationships between the goal and its surrounding landmarks are used to guide the way back. The standard here is some specification of the goal in terms of its relationship to landmarks, and the record is some specification of the current place. The mechanism works to reduce this discrepancy; I spell out more specific details below. Landmarks at different scales are undoubtedly used in zeroing in on a goal. The broad features of the terrain guide the subject to the region of the goal, and then nearer landmarks often must be used to pinpoint the

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MNEMOTAXIS PILOTING COMPARATOR %GOAL W.R.T. LANDMARKS

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RiCURRENT POSITION

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LANDMARKS

1k-

VECTORS BASED ON D(R,S), ETC. I

Fig. 4. Landmark-basedspatial memory as an example of a servomechanism.The organism compares a specification of its current location (R), in terms of its relationshipwith landmarks, to a standard specification (S) representing the location of the goal with respect to landmarks. It reduces the discrepancy between the two (D(R,S)) in finding its way to the goal.

goal itself, which is often hidden and has no obvious characteristics marking it out. The food caches of Clark’s nutcrackers and the nests of digger wasps are such beaconless examples. I will restrict discussion to the final stage of using landmarks to pinpoint a goal. One experimental strategy, the most convincing to me, for demonstrating that a set of landmarks is used in pinpointing a location is to displace systematically the landmarks and observe that the subject systematically follows the displacement. Tinbergen (1972) provided one early classic example of this strategy. He placed pine cones around the nests of digger wasps, and while the wasps were away foraging, he displaced the cones. The wasps’ searches were displaced just as the cones were, indicating that the insects were relying on the provided landmarks in their search for their nests. Since then, such a strategy has been used to show that landmarks are used by diverse creatures, including rodents (Cheng, 1986; Collett, Cartwright, & Smith, 1986; Etienne, Teroni, Hurni, & Portenier, 1990; Suzuki, Augerinos, & Black, 1980), birds (Cheng, 1988,1989,1990; Cheng & Sherry, 1992; Spetch & Edwards, 1988;Vander Wall, 1982), cephalopods (Mather, 1991), and insects (Cartwright & Collett, 1982, 1983; Dyer & Gould, 1983; von Frisch, 1953; Wehner & Rgiber, 1979).

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11. The Vector Sum Model

The first model I developed to account for landmark-based spatial memory in pigeons was inspired by the work on gerbils by Collett et al. (1986). They used cylindrical tubes as landmarks and suggested that the animal treats each tube as a landmark element, recording the distance and compass direction from the landmark to the goal. I call these landmark-goal vectors (Fig. 5), and they provide the basis for pointing the subject toward the goal. How the natural world, or even the laboratory world, is divided into landmark elements is unclear, but the model can nevertheless be tested. Artifical objects such as cylinders intuitively form landmark units, but intuitions provide little guidance for dividing up surfaces like walls, large objects like trees or tables, or clumps of objects like bushes. No theory takes the place of intuitions either. But the vector sum model makes a testable prediction no matter how landmarks are divided into elements, a prediction that was its glory and its downfall. The creature derives from every landmark-goal vector a vector directing itself to the goal. It does this by a bit of vector addition. For each landmark-goal vector, it adds the landmark from itself to the landmark in

B

A LEFT-RIGHT AXIS

Fig. 5. An illustration of the vector sum model. (A) The pigeon is trained to find hidden food at the goal, which stands in a constant location with respect to the landmark (LM) and the arena. Occasionally, it is tested with the goal and food absent. (B) When the landmark is shifted (to the right in this case) on a test, the navigation (self-goal) vectors associated with the shifted (s) landmark points to a location shifted in the direction and to the extent of the landmark shift. The rest of the navigation vectors, associated with unshifted (u) landmarks, point to the original goal location. The vector sum model predicts that the pigeon will search somewhere on the straight line connecting these two theoretical points (the dotted line).

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question. Self-to-landmark vector plus landmark-to-goal vector create selfto-goal vector. The bird then averages the dictates of all the self-to-goal vectors. This averaging process gives rise to an interesting prediction. A. LANDMARK-BASED SEARCH TASK To explain the prediction, I must first describe the task, using the example shown in Fig. 5. The pigeon searches for food hidden under wood chips in some search space. The space might be an arena, as in Fig. 5, or a tray, or the entire floor of a lab room. Conditions in the search space remain constant from trial to trial, and some landmarks near the target usually help the search. In the example, a block of wood is to the right of the goal. The goal, a hidden food cup or hole in the ground, stands in a constant spatial relationship to the landmarks from trial to trial. After the bird is trained, it is occasionally tested with the food and goal absent. On a test, landmarks are sometimes manipulated. In Fig. 5B for example, the landmark has been shifted to the right. Search behavior on tests make up the data. Most often, a single-peaked search distribution is found, and a place of peak searching is formally calculated from the distribution (e.g., Cheng, 1989,1994). The vector sum model makes an interesting prediction on tests in which a landmark has been translated from its usual location. When a landmark is moved, the landmark-goal vectors associated with it point to a goal that is moved in the same direction by the same extent (open dot in Fig. 5B). The rest of the unmanipulated landmarks of course point to the original goal location (filled dot in Fig. 5B). When the dictates of these vectors are averaged, the averaged position must lie on the line connecting the two theoretical goal locations (the dotted line in Fig. SB). This much follows from Euclidean vector geometry. What this means is that when a landmark has been shifted on a test, the place of peak searching might shift in the direction of the landmark shift, but not in the orthogonal direction. This prediction was first tested in rectangular arenas in which the goal was near one of the edges (Cheng, 1988,1989). Shifts of landmarks parallel or perpendicular to the edge produced results supporting the prediction (Fig. 6A,B). When the landmark shifted parallel to the edge, the birds shifted their search parallel but not perpendicular to the edge. When the landmark shifted perpendicular to the edge, the birds shifted their search perpendicular but not parallel to the edge. But shifts of landmarks in a diagonal direction produced results contradicting the prediction (Cheng, 1990; Cheng & Sherry, 1992; Spetch, Cheng, & Mondloch, 1992). According to the model, the birds should shift in the diagonal direction, or equal amounts parallel and perpendicular to the edge. The birds, however, shifted

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Fig. 6. Summary of results found with landmark shift experiments. The goal is near an edge, with a landmark (LM) near it. When the LM is shifted parallel to the edge (A), the birds shifted their searching parallel to the edge. When the LM is shifted perpendicular to the edge (B), the birds shifted their searching perpendicular to the edge. Both these patterns of results support the vector sum model. But when the LM is shifted diagonal to the edge (C), the birds shifted their searching more in the parallel direction than in the perpendicular direction, violating the predictions of the vector sum model.

far more in the parallel direction than in the perpendicular direction (Fig. 6C). We (Cheng & Sherry, 1992) suggested that the perpendicular distance of the goal from the edge also enters into the computation. A perpendicular distance, like a vector, has a distance and a direction, but it does not have a defined starting point; anywhere from the edge might be the starting point. The vectors we speak of have a defined starting point. This perpendicular distance enters into the averaging process and acts to hold the creature near the edge in the perpendicular dimension. Hence, searching shifts in the parallel direction but not much in the perpendicular direction. What is averaged with the perpendicular distance? It might be the landmark-goal vector in its entirety, or it might be only the perpendicular component of the landmark-goal vector. In the former case, the spirit of the vector sum model remains: vectors are averaged, but an additional component is thrown in. In the latter case, vector averaging does not take place; only elements of vectors are averaged. The spirit of the model is changed.

III. Are Vectors or Components of Vectors Averaged? I found no way to differentiate between the two cases with some variation of the paradigm, and hence used a new method to test whether entire vectors are averaged or components of vectors. The new method relied on

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directional conflict, and its experimental logic is illustrated in Fig. 7. On crucial tests, two sources of information pointed in different directions from a point that can be considered as the center of the search space. In all the experiments, the two landmark-goal vectors have the same distance, but pointed 90" apart. If conditions are set up right, the pigeon will average the dictates of the two sources and search somewhere in between the dictates of the two vectors. It has two ways of averaging: Entire vectors might be averaged, which I have called the vector-averaging model, or distances and directions, components of vectors, might be separately averaged, a scheme I call the direction-averaging model. The two models make different predictions about the radial distance of search, that is, the distance from the center of the search space to the place of peak searching. Suppose that the two entire vectors are averaged. That means that the resulting average must lie on the straight line connecting the endpoints of the vectors. The radial distance of search thus should be shorter than the radial distance of search on tests where no directional conflict is presented. The amount of shortening depends on the angle between the two vectors and the direction of search. It is indicated by the formula given in Fig. 7. On the other hand, suppose that distances and directions are averaged separately. In that case, the averaged radial distance should not differ from the radial distance of search on tests without direc-

1x1 =

IUI. cos(%)

cos(b: - 19)

Fig. 7. Predictions of the vector-averaging and direction-averagingmodels when two conflicting directions of search are present. The vector-averaging model predicts peak searching somewhere on the line segment connecting the endpoints of u and s, whereas the directionaveraging model predicts peak searching somewhere on the arc connecting the endpoints of u and s. (Reprinted from Cheng (1994) with permission of the Psychonomic Society Publications.)

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tional conflict because the radial distance of the two landmark-goal vectors are the same. Directions can be averaged, and the resulting place of peak searching should lie somewhere on an arc connecting the endpoints of the landmark-goal vectors. In the intermediate range of directions then, the two models make detectably different predictions. As an example of this paradigm (Cheng, 1994, Experiment l), pigeons were trained to find hidden food at a constant distance and direction from one cylindrical bottle. On the bottle, facing the goal, was taped a cardboard strip. On crucial tests, the bottle was rotated by No, the strip along with it. The strip thus pointed at a direction 90"apart from the rest of the landmarks. RESULTS FAVOR THE DIRECTION-AVERAGING MODEL The data from a series of experiments using the directional conflict paradigm are plotted against the predictions of the two models in Fig. 8. The dependent measure is the radial distance of search on experimental tests, tests in which a directional conflict was presented. The predicted measure for the direction-averaging model is the radial distance on the corresponding control test. For the vector-averaging model, the predicted measure is

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PREDICTED RADIAL DISTANCE (cm)

PREDICTED RADIAL DISTANCE (em)

Fig. 8. Observed radial distance of the place of peak searching on experimental tests plotted against the predicted radial distance for the vector-averaging model (A) and the direction-averagingmodel (B). The dotted lines represent perfect fit between data and model. The solid lines represent the best-fitting linear function through the origin by the least squares criterion. (Reprintedfrom Cheng (1994)with permission of the Psychonomic Society Publications.)

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calculated according to the formula in Fig. 7. Each point represents one bird in one experiment. The dotted line represents the exact predictions of each of the models, neither of which has any free parameters. The solid lines represent the straight line through (0,O) that best fits each set of data points. The data points are scattered unsystematically about the dotted line for the direction-averaging model, whereas they lie systematically above the dotted line for the vector-averaging model. This means that the data support the direction-averaging model but contradict the vector-averaging model, which systematically underpredicted the data. A number of statistical tests confirmed this impression (Cheng, 1994). We thus arrive at a different model that still retains the flavor of the vector sum model (Fig. 9). Whereas the vector sum model averages vectors in their entirety, the new model separately averages the distance and direction components of vectors. Different subsystems compute distances and directions, and their outputs are combined to determine where to search. In Fig. 9, I have listed some of the factors that affect the direction of search, although doubtlessly other factors are also used. Experimental

DIRECTIONAL DETERMINATION

LANDMARK ORIENTATION

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\

S U MM

LOCAL

DISTANCE DETERMINATION

COMPUTATIONAL SYSTEMS

I 1c ACTION

GEOMETRY

Fig. 9. Distances and directions are separately and independently calculated in the landmark-based spatial memory of the pigeon. The summator averages the dictates of various cues.

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evidence has been found for each of these factors. The experiment on landmark orientation, with the bottle with a stripe on it, has already been described. In the unpublished experiment on the direction of light, done in collaboration with Sylvain Fiset, two lights were placed high on the walls, 90" apart. A circular search tray served as the search space. During training, only one of the lights was lit. On crucial tests when the training light was turned off and the alternate light turned on, each of three birds shifted its location of peak searching. Thus the direction from which light emanates in part determines the direction of search. In the unpublished experiment on local geometry, the circular search space was placed asymmetrically in a larger square tray. The orientation of the larger tray thus gave a directional cue, a local geometric frame about the search tray. When the square tray was rotated about the center of the search space by 90",some birds followed the local geometry and rotated their place of peak searching. And finally, based on results with rats (Cheng, 1986; Gallistel, 1990, ch. 6; Margules & Gallistel, 1988), I assume that the global geometry defined by the shape of the room is also used in determining the direction of search. In those experiments, directionally disoriented rats searched for food in an enclosed rectangular arena. On the walls of the arena were found many distinguishing features, including black and white panels on different walls, and different smells, textures, and visual patterns in the corners. The rats in this task often confused the correct location with a geometrically equivalent location located at 180" rotation through the center from the correct location. In some conditions, they chose the geometric equivalent as often as the correct location. The two locations are indistinguishable based on the geometry of the shape of the enclosure alone. That is, without noting and remembering the features that stand on the shape carved out by the walls, the two locations cannot in principle be distinguished. That the rats make this geometric error suggests a module of the spatial representation system that encodes only the broad shape of the environment, a geometric module. Recent experiments with human infants have found the same pattern of errors (Hermer & Spelke, 1994). As for the distance component, manipulations of landmark size have no systematic effects on the distance of search (Cheng, 1988). The birds apparently do not rely much on the projected retinal size of landmarks (although gerbils do in part; see Goodale, Ellard, & Booth, 1990). Sources of information that deliver the three-dimensional distance from goal to landmarks are used, presumably a number of different sources.

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IV. Of Honeybees and Pigeons The piloting servomechanism of the pigeon shares many features with that of the honeybee. I present together here the honeybee’s system as well as the comparison. The experiments on honeybees ran in the same spirit as those on pigeons (Cartwright & Collett, 1982, 1983; Cheng, Collett, & Wehner, 1986; Cheng, Collett, Pickhard, & Wehner, 1987; Collett & Baron, 1994). Free-flying bees searched for a dish of sugar water in a test room. An array of landmarks marked the location of the goal, which stood in a constant spatial relationship with respect to the array. Occasionally, the bees were tested with the sugar water absent. Landmarks might be manipulated on these tests. In the model developed from the results, the honeybees, like the pigeons, divided the array into separate landmark elements, and made computations based on distances and directions separately and independently. A. ELEMENTALISTIC SYSTEMS Cartwright and Collett (1982, 1983) proposed that the honeybee encodes a panoramic retinal template of the way the surrounding landmarks look from the viewpoint of the goal. The bee compares the current retinal panorama to the template and moves so as to reduce the discrepancy, in the classic manner of a servomechanism. The pigeons too compare current perceptual input with an encoded record and act so as to reduce the discrepancy between the two. The term template, however, is misleading because it implies an entire, holistic picture or record to which comparisons are made. But the piloting servomechanisms in both honeybees and pigeons are elementalistic rather than holistic. The landmark array is analyzed into separate elements, and comparisons and computations are made on each element independently. We ought to think of the servomechanism as having multiple comparators, or else a comparator with multiple independent standards to which comparisons are made. Whether we speak of multiple comparators or multiple standards within a single comparator is purely a terminological difference at the moment, as I do not know how to distinguish the two cases empirically. An elementalistic system brings on the problem of how an array is divided into elements. The problem has two facets: (1) how the array is divided into elements, and (2) how each element in the percept is matched to its corresponding partner in the encoded representation, also called the matching problem. An artificial landmark array often presents us an intuitive way of dividing it into elements. For example, in the work on honeybees, where colored cylindrical tubes served as landmarks, each tube served

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as an element as well as each of the spaces between the tubes. But in a natural setting, intuition is far from clear. B. THEMATCHING PROBLEM The matching problem is an even graver problem. My guess is that the systems would work with a large variety of divisions into elements. Getting the systems to work depends far more crucially on matching elements correctly, or at least enough elements correctly. A mismatched element systematically misdirects the honeybee or pigeon, and enough of those will make the system dysfunctional. For the honeybee, Cartwright and Collett (1982,1983) proposed that an element on the template is matched to the spatially nearest element of the same type on the percept. Spatial nearness is defined in terms of compass direction and the type of element refers to whether the element represents a tube or the space in between tubes. Mismatches are produced with this scheme. But not enough of them are generated to sabotage the system. Of course, other characteristics, such as color (Cheng et al., 1986), can help solve the matching problem. For pigeons, I suggested (Cheng, 1992) another spatial scheme for identifying landmarks. Landmarks are identified by their particular (approximate) location in the global space rather than by any particular set of characteristics or features. In this scheme, the pigeons must have a higher level representation of the overall layout of space for locating particular landmarks to be used for piloting. One piece of evidence from unpublished data suggests that a landmark moved a substantial distance from its usual place is not identified as the same landmark. In this experiment, the birds’ task was to go to a food cup at the middle of one wall of a square arena in which food was hidden. Similar food cups were found at the other three walls. By the target food cup was a sizable block. When this block was moved to another wall on an unrewarded test, no pigeon followed it in its search. They all went to search at the usual place in the room where food was always found, even though the block was the only thing within the arena that distinguished the four walls. Apparently, the birds had used their inertial sense and landmarks outside the arena to locate at least the approximate place of reward. Another way of putting this is that a landmark moved too far from its usual place is not the same landmark anymore. Identification depends on spatial localization. Similar nonidentification of displaced landmarks or target objects have been noted in rodents. Mittelstaedt and Mittelstaedt (1980), studying homing by path integration in gerbils, displaced their home at the edge of the arena by some 20 cm and found that the returning gerbils went to the place

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where they thought the home should be, and not to the nearby place from which the sounds and smells of their young were emanating. Devenport and Devenport (1994) trained chipmunks and ground squirrels to come to a distinctive feeder for food. When they displaced the feeder, to a place within easy sight of the original location, all the creatures but one went first to the original location where the feeder was and looked for it there. (The exception did not go to the new feeder either, but to another marked location serving as a control location.) They did this despite having the beacon within easy sight. A displaced beacon is apparently not the same beacon anymore, and the animals needed to learn again to find food at the new location. C. COMPARISONS OF DISTANCES AND DIRECTIONS DRIVETHE SYSTEM SEPARATELY For honeybees as for pigeons, comparisons of distances and directions are separately done. The piloting system is modular not only in breaking down the landmark array into elements, but also in breaking each element into a distance and a directional component. For the pigeon, these components make up parts of the landmark-to-goal vectors that help specify the exact location to search. For the honeybee, these components independently direct the bee in the direction it should fly to get to the target. No exact specification of the target location is derived. Each element in the template is compared to its corresponding element on the percept for projected (retinal) size and compass direction. Mismatches in size move the bee closer or farther from the element in question: The bee moves toward (in a centrifugal direction) elements that look too small and away from (in a centripetal direction) elements that look too big. It turns left (tangent to the left) when the matching element on the percept is to the left, and right when the matching element is to the right. All these different directional vectors are averaged in a weighted fashion to determine the direction of flight for the next step. The model bee takes a quantum step and does the comparisons and computations over again. The real bee presumably does this continuously. At po point is the entire template or representation as a whole invoked in guiding movement. An interesting problem arises in the honeybee system; the directions specified in the template must be compass directions, or have an earthbased reference. As the precept is specified in retinal coordinates, it would seem that the two coordinate systems must somehow be matched. In other words, the template must be rotated to be in the correct alignment with respect to the world. It turns out that this problem never arises because the honeybees always face the same direction in flight when searching for

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a landmark-based goal (Collett & Baron, 1994). They first identify the nearby landmark (only one was used in the experiments in question) and fly toward it. When they are near the landmark, they then turn to fly in a particular direction and conduct the landmark-based search. The direction seems to be specified in geomagnetic coordinates. V. Averaging Independent Sources of Information

These piloting servomechanisms illustrate a neurocognitive architecture of dividing and averaging. They illustrate modular systems in a number of senses. They suggest certain neural and cognitive control mechanisms. They seem also to require some neurophysiological mechanisms for storing the values of dimensions of information that enter into averaging. I conclude this chapter with some thoughts along these lines. A. MODULARITY Landmark-based spatial memories in the pigeon and the honeybee work in a modular fashion in three senses. (1) I consider the systems as a whole modular. (2) They modularize the information input in breaking down a whole landmark array into elements. (3) They modularize computation over types of information in working separately and independently on the metric properties of distances and directions. These piloting systems take in and compare a particular, restricted set of information and generate behavior on the basis of that. Other kinds of information do not play a role in the systems. They are specialized systems or special learning devices designed particularly to perform one kind of task. They illustrate par excellence what Chomsky (1980) has called mental organs, of which they are examples, and what Fodor (1983) terms vertical modularity. They are each a candidate for a special memory system (Sherry & Schacter, 1987). As such, they throw doubt on the empiricist view that the organism is simply one general learning device. The systems work with the metric properties of space, distances and directions. These geometric properties, highest in the hierarchy of geometric properties (Cheng & Gallistel, 1984; Gallistel, 1990, ch. 6), are intuitively the most spatial to us. This further suggests specialized systems particularly geared to computing spatial information. Attempts to incorporate spatial knowledge in an associationist framework have posited the use of “lower” geometric properties, such as graph-theoretic properties (e.g., Lieblich & Arbib, 1982). These systems are inadequate in accounting for the use of metric information as they have no way of capturing metric information.

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The landmark-based spatial memories of honeybees and pigeons also modularize within the system. As I mentioned before, the landmark array is broken down into elements for analysis and computation. Each element is separately and independently analyzed, and the outputs are later integrated by way of the averaging process. Likewise, the two types of metric information, distances and directions, are treated in modular fashion. We can compare this to a perceptual system, in which incoming sensory information is separated and sent to different channels, to be reconstructed later into percepts. The different “channels” in the piloting servomechanisms are reconstructed not into percepts but to generate behavior bringing the animal nearer to its goal. We can call such systems internally modular. B. CONTROL BY WEIGHTING Internally modular systems provide many handles for control. Each of the boxes in Fig. 9, for example, can be emphasized or dampened. Factors external to the system can control which factors play a larger role in the averaging process that guides behavior, giving flexibility to the system. Control is exerted by adjusting the weighting parameters of each of the boxes. How this is done neurophysiologically is easy to imagine and understand. Presumably, the boxes give neural outputs that are represented neurally by synaptic connections to other parts of the systems. The strengths of the outputs can be modulated by other inputs that potentiate or depotentiate the connection (Gallistel, 1980). Potentiation and depotentiation are typical methods of hierarchical control of action. The flexibility of the control system means that we might find variation in behavior across organisms and situations. In the case of pigeons, this is reflected in the data: often when compromises are to be made, different animals show different weighting patterns. I should emphasize that this does not represent noise or imperfections in the data. Individual variation here shows where free parameters are found in the system. The data show constancy in other respects. For example, the data for particular individuals usually show astounding order (see, for example, Cheng, 1988). Or, when a landmark was moved parallel to the edge near the goal, pigeons did not shift their peak location of search in the perpendicular direction. The system works well enough with a large range of weighting schemes: All the animals find the food usually. It is a functional desideratum for a system to work with a range of parameter values, relieving the animal of the task of learning exact parameter values. Nevertheless, aside from idiosyncratic parametric variation, some general principles in weighting can be found. Both honeybees (Cheng et al., 1987)

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and pigeons (Cheng, 1989) put more weight on nearer landmarks, with the honeybees in this case gauging distance by motion parallax (Lehrer, Srinivasan, Zhang, & Homdge, 1988; Srinivasan, Lehrer, Zhang, & Horridge, 1989). Honeybees also put more weight on landmarks that project a larger retinal size. Functionally speaking, the two species do this presumably because nearer and larger landmarks guide more accurately. Control by modulating the weights in averaging also takes place with two wayfinding servomechanisms, namely piloting and path integration. Etienne et al. (1990) put piloting (landmark) cues and path integrational cues in conflict for hamsters by displacing a salient landmark. The hamsters wandered from their home at the edge of a circular arena to the middle of the arena to retrieve some food for hoarding. A salient landmark, a light usually positioned over their home, was displaced by 90"on one series of tests. Many subjects followed the landmark given this conflict, but some struck out homeward in a compromise direction in between the direction of the landmark and the inertial direction home. The path integration and piloting systems were averaged in these cases. I suspect that the weighted averaging of independent sources of information is a common feature in neurocognitive architecture. The modularity of information processing makes any problem more tractable. Weighted averaging allows ready control over the system and is readily realizable in the brain. C. NEUROPHYSIOLOGICAL INSTANTIATION The entire scheme of a weighted average of the values of different submodules of information suggests other points concerning the neurophysiological basis of memory and learning, although matters here become far more speculative. The averaging of values suggests that the brain must somehow store the values of dimensions stably. I conclude with some reflections on this point. The most straightforward suggestion of such a system is that to average values, one must have stored the values in the brain, and then retrieve them for averaging. Values must be stable to be useful. Values that decay or change unpredictably over time without further informational input will mislead the animal. To me, values are unlikely to be represented by firing rates. Firing rates can fluctuate depending on the state of the brain, such as the availability of neurotransmitters. Functionally, firing rates are also expensive as a storage device. The brain is energetically expensive compared to the body, a fact that makes it especially inefficient to store values, which are only used on occasion, with a process that constantly uses energy. It is like using lit light bulbs to represent a number rather than, say, pieces of stones, the former being far more expensive energetically.

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The alternative to using firing rate is some kind of stable structural representation, something stable rather than dynamic. This might be some “memory” substance the amount of which represents the value on a dimension. Gallistel (1990, ch. 15) provides more insights into this issue. Or it might be some structural change in the neuron that makes it fire at different rates when called upon. By “called upon,” I mean when it comes time to retrieve the value. The retrieval process might well be dynamic, represented by the firing of neurons. One scheme I can imagine is to have a retrieval neuron fire at a constant rate in accessing a value. The structure of a value neuron, which functions to store the value, then determines the rate at which it fires in response to the retrieval neuron, and the output of the value neuron can represent a value. Representing the outputting of values by firing rates has the advantage that it readily allows modulatory control by potentiators and depotentiators. That is, other processes can weight the value by affecting its connection to other units. It is not clear how the modulation can take place on the structurally stored values. To me, it seems unlikely that values to be averaged can be stored as associative connective strengths, including the modern version of this in the form of weights in a connectionist network. How do values about distances and directions from landmarks get stored in any such network? How do they get modulated in weighted averaging? I can only await concrete proposals in this regard, but I remain doubtful. Finally, by speculating on neurophysiology here, I mean far less to propose particular neurophysiological mechanisms of memory and far more to illustrate the point that to come up with the neurophysiological underpinnings, we must strive for a deep and theoretical understanding of the behavior that the physiology is supposed to underpin. We can identify many kinds of neurophysiological events in the brain, though there might be others that we have not yet identified. The kind of neurophysiological mechanisms that we seek must depend heavily on the models of behavior we devise. Perhaps the most central physiological function of the brain is to store and use information about the world gathered by the senses. Neuroscience’s grand failure is not having a definitive account of how the brain does this job. To overcome this central shortcoming, it would be best to pay far more attention to behavior. ACKNOWLEDGMENTS The author’s research reported in this chapter was supported by a research grant from the Natural Sciences and Engineering Research Council of Canada. The chapter was written while the author was at the Department of Psychology, University of Toronto.Correspondence

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about this chapter should be sent to Ken Cheng, School of Behavioural Sciences, Macquarie University, Sydney NSW 2109, Australia (electronic mail: KCHENG9bunyip.bhs.mq.edu.au).

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