Route ﬁnding by rats in an open arena and Reid 2005.pdfBehavioural Processes 68 (2005) 51–67 Route ﬁnding by rats in an open arena Rebecca A. Reida, Alliston K. Reidb,∗ a South

Behavioural Processes 68 (2005) 51–67

Route finding by rats in an open arena

Rebecca A. Reida, Alliston K. Reidb,∗

a South Carolina Governor’s School for Science and Mathematics and Wofford College, USAb Department of Psychology, Wofford College, 429 N. Church Street, Spartanburg, SC 29303, USA

Received 11 August 2004; accepted 6 November 2004

Abstract

Rats were repeatedly exposed to an open arena containing two depletable food sources in a discrete-trials procedure. Theirmovement patterns were recorded and compared to adaptive foraging tactics such as minimizing distance or energy expenditure,thigmotaxis, and trail following. They were also compared to the predictions of the associative route-finder model of Reid andStaddon [Reid, A.K., Staddon, J.E.R., 1998. A dynamic route finder for the cognitive map. Psychol. Rev. 105 (3), 585–601]. Wemanipulated the presence/absence of food, goal cups, and a wooden runway to determine the influence of local and distal stimuli(visual, olfactory, and tactile) on movement patterns. Increased experience in the arena produced decreases in travel distanceand time to the food sources. Local and distal stimuli influenced movement patterns in ways compatible with visual beacons andtrail following. The route-finder model accurately predicted movement patterns except those that were influenced by local anddistal stimuli. These results show how certain stimuli influence movement and provide a guide for the incorporation of local anddistal stimuli in a future version of the dynamic route-finder model.©

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eywords:Cognitive map; Computer simulation; Foraging; Generalization; Route; Spatial navigation

. Introduction

In the last few decades, spatial navigation hastimulated substantial research, especially following’Keefe and Nadel (1978)classic work proposing theippocampus as a cognitive map.Biegler (2003)identi-es three current approaches to the study of spatial nav-

gation that have different assumptions and goals: (a)

∗ Corresponding author. Tel.: +1 864 597 4642;ax: +1 864 597 4649.

E-mail address:[email protected] (A.K. Reid).

The ethological or adaptationist approach tends tocentrate on species-specific adaptations, wherea(b) cognitive approach and the (c) associative appraim to discover general principles underlying behior. Biegler argues that the cognitive approach assuthat different species may perform qualitativelyferent types of computation during spatial navigatwhereas the associative approach generally assthat the computations are only quantitatively differacross species and task domains. The main goalcurrent study was to contrast explanations of spforaging patterns based on species-specific adapta

376-6357/$ – see front matter © 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.beproc.2004.11.004

52 R.A. Reid, A.K. Reid / Behavioural Processes 68 (2005) 51–67

with the predictions of theReid and Staddon (1998)as-sociative route-finder model.

Reid and Staddon (1998)point out that spatial ori-entation has two logical parts, knowledge and action.Their route-finder model was designed to explain ac-tion — it was not intended to explain how the organismacquired spatial knowledge, or how the animal knowswhere it is. Nevertheless, most recent research in spatialnavigation has centered on the mechanisms that per-mit the acquisition of spatial knowledge. Such knowl-edge includes learning the location of a goal in relationto landmarks or beacons (e.g.,Benhamou and Poucet,1998; Mackintosh, 2002; Poucet, 1993; Roberts andPearce, 1998), computation of position based onpath integration (e.g.,Etienne, 2003; Gallistel, 1990;Wallace et al., 2003; Wehner and Srinivasan, 2003)or the geometric properties of the environment (e.g.,Cheng, 1986), the creation of a cognitive map (e.g.,O’Keefe and Nadel, 1978), and various other processes.The current debate about the existence of a cognitivemap is centered on the knowledge that enables spa-tial orientation. For the interested reader, the variouschapters inJeffrey (2003), Healy (1998)andWang andSpelke (2002)provide comprehensive overviews of theacquisition of spatial knowledge and discussions of thevarious systems or modules (including species-specificadaptations) involved in acquiring spatial knowledge.

The Reid and Staddon (1998)route-finder focuseson action — the means by which spatial knowledge isused to produce movement patterns, such as when an-i t. Its cesss ying“ en-t allya ap”R oca-t willh pacew odes.T de-t delw n-r stepm

osedf ;G lke,

2002, 2003), modules have also been proposed foraction. The most well-known approach, representedextensively in the ethology and adaptationist literature,is the assumption that different movement patternsrepresent different adaptive behavioral modules, orsearch tactics, that may combine to produce elaboratemovement patterns. Examples of these tactics inrats are thigmotaxis, distance minimization, trailfollowing, detour avoidance, central-place foraging,area-restricted (focal) search, and other win-shift orwin-stay strategies compatible with the maximizationof net rate of energy gain (e.g.,Hoffman et al., 1999;Krebs and McCleery, 1984; Olton and Samuelson,1976; Rodrigo, 2002; Stephens and Krebs, 1986;Timberlake et al., 1999). This conceptual approach hasconsiderable appeal because these behavioral tacticsare normally assumed to be independent of each other,yet they may be simultaneously expressed in many en-vironments. It is easy to imagine evolutionary selectionpressures that would favor or suppress each of theseforaging strategies in a known environment, eventuallyresulting in highly adaptive foraging patterns. Thisconceptual approach implies that: (a) the separatebehavioral modules may have evolved independentlyof one another; (b) they may represent the interactionsof multiple motivational systems (such as foraging andpredator avoidance); and (c) they may be influencedby different characteristics of the environment (suchas distance, walls, trails, sounds, and odors).

Surprisingly, theReid and Staddon (1998)route-fi cticsi well-k ad-d ostp ove-m vari-e h asa hort-c l fitss dy-n n inw and-s hill-c easo 8;St thed des

mals forage for food in a well-learned environmenimply assumes the existence of an orientation proufficient to locate the animal in space. The underlmap” could be quite detailed, or it could be rudimary and incomplete, and it could change dynamics the animal forages or encounters barriers. By “meid and Staddon mean only that for every spatial l

ion, there must be one and only one node (whichave a defined state) and adjacent locations in sould be represented by a connection between nhis model promises, “If you can provide certain

ails of the animal’s knowledge of space, the moill show how the animal’s history of reward and no

eward in that space will produce dynamic step-by-ovement patterns as the animal forages.”Just as systems and modules have been prop

or acquiring spatial knowledge (e.g.,Cheng, 1986allistel, 1990; Rodrigo, 2002; Wang and Spe

nder model produces most of these behavioral tan a single one-parameter model, based on thenown process of diffusion, without the need ofitional modules. Their goal was to identify the marsimonious mechanism that would generate ment patterns consistent with those observed in aty of species in the open field and in mazes, sucrea-restricted search, avoiding barriers, finding suts, and radial maze behavior. Thus, their modequarely within the associative approach. Theiramic model is based on stimulus generalizatiohich an elementary diffusion process produces a lcape of reward expectancy, and the simplestlimbing algorithm produces movement toward arf higher expected reward (seeReid and Staddon, 199taddon, 2001; Staddon and Reid, 1990for addi-

ional details). Thus, the model has only two parts:iffusion of reward expectancy along adjacent no

R.A. Reid, A.K. Reid / Behavioural Processes 68 (2005) 51–67 53

(with only one parameter representing the rate of diffu-sion) and the simplest local movement rule. This unre-alistically simple model successfully generates move-ment compatible with each of the behavioral tacticsdescribed above, even though none of the tactics areexplicitly built into the model (seeBiegler, 2000; Reidand Staddon, 1998; Staddon, 2001for demonstrationsof movement patterns produced by the model). Thatis, the model produces behavior commonly classifiedas thigmotaxis, distance minimization, area-restrictedsearch, win-shift and win-stay strategies, spatial “in-sight”, short cuts, and detours even though only theunitary process of diffusion of reward expectancy cre-ates the model’s landscape and produces movement.

As Reid and Staddon’s goal was to create themost parsimonious model possible, diffusion acts onlyas a local process on adjacent locations. They pur-posely limited the model to local connections betweennodes (representing adjacent locations), and reward ex-pectancy diffuses only along these connections. There-fore, the model does not include the visual detectionof beacons or any distal stimuli other than the unspeci-fied stimuli that allow the organism to know where it isin space.Reid and Staddon (1998)demonstrated thatno detection of distal stimuli, “insight”, or overviewof the situation as a whole is required to reproducethe foraging tactics listed above. They explicitly com-pared the predicted step-by-step movement patterns oftheir simulated organism with the actual movementpatterns of rats, badgers, dogs, insect larvae, and antsi s oft par-iii be ac wl-e t bea el ofs ,2 orep calm

wes tac-t les tob gi-c leo-l m of

behavior that is produced by a simpler mechanism,potentially denying the validity of these categories asseparate behavioral modules? Should we expect evo-lutionary selection pressures to act on each of thesebehavioral tactics independently, or to act on a singleprocess (such as a diffusion process) that produces eachof these descriptive categories of behavior?

What type of evidence would allow us to answerthese questions? It is not clear that these two conceptualapproaches can be reconciled experimentally in spatialnavigation studies. But we can test the adequacy of theReid and Staddon (1998)route-finder model in forag-ing situations that normally produce the behavioral tac-tics described above. Thus, one goal of the current studywas to identify the behavioral tactics observed duringforaging in a well-learned environment that cannot beaccounted for by the route-finder model.

In this experiment, we exposed rats to an open rect-angular arena in which food was located at two fixedpositions in each trial. We measured the step-by-stepmovement patterns of rats in a well-known environ-ment and compared them to the predictions of the route-finder model. We also examined how these movementpatterns changed across trials as subjects became morefamiliar with the task. The local-process route finderdoes not contain a learning rule or the ability to de-tect goal stimuli from a distance. It contains no distalstimuli at all, other than unspecified landmarks used bythe organism to orient itself in space. Therefore, twoadditional goals of this experiment were to identify thec trialsi anda isualb nt byd tionw

ouru edb e-m azel thefl pos-s wasm armt asedtfi ande ces

n published studies that provided detailed figurehese movements. Subsequently, additional comsons have been carried out byStaddon (2001)involv-ng vervet monkeys andRobles (2003)with humansn a virtual maze. The model was not intended toomplete model of action (much less a model of knodge acquisition), but they concluded that it mighn essential ingredient in any comprehensive modpatial orientation in animals. Recently,Biegler (2000003)has extended this route-finder model into a mowerful, biologically compatible neurophysiologiodel of action.The theoretical issue of concern is whether

hould conceptualize each of these behavioralics as independent species-specific action modue employed in a given environment (the etholoal/adaptationist approach). Or, might they be teogical categories imposed on an observed strea

hanges in movement patterns: (a) in successiven the same environment, and (b) in the presencebsence of distal food cups, which could serve as veacons, while keeping the olfactory cues constaelivering the same amount of food at the same locahether the cups were present or not.A final goal of this experiment was to increase

nderstanding of the “trail-following” tactic describy Timberlake et al. (1999). They measured the movent patterns of rats exposed to a radial arm m

ocated on the floor (rather than elevated aboveoor) — thus, shortcuts across arms were quiteible. They demonstrated that spatial navigationore strongly influenced by the edge of a maze

han by its surface, and clipping the whiskers decrehis foraging tactic. TheReid and Staddon (1998)routender does not include stimuli such as surfacesdges of arms. If these stimuli are important influen


on foraging patterns, then we need to determine whichpart of spatial navigation they affect: knowledge or ac-tion. Therefore, in some trials we added a board (witha wooden surface and prominent edges) to see if thestrength of the “trail-following” tactic was sufficient toalter the direction of movement in the arena.

2. Materials and methods

2.1. Subjects

Five adult female Long Evans rats (Rattus norvegi-cus), approximately nine months old at the beginning ofthe study (mean weight 302 g), were used as subjects.Although the rats were maze-naıve, they had previousexperience in a laboratory project (rat basketball, e.g.,http://www.wofford.edu/psychology/ratBasketball.asp)for approximately 3 months, which involved dailyhandling by various students, exposure to relativelyopen areas in a noisy environment, and reinforcementwith the same 45 mg Noyes pellets used in thisstudy. The rats were housed individually in standardpolycarbonate cages in a room with relatively constanttemperature and humidity with a 12:12 light/dark

cycle. Water was continuously available in the homecages. After completing the daily session, the ratswere provided with unlimited access to food for 1 h(Teklad Rodent Diet) in their home cages to maintaina 23 h deprivation level for each daily experimentalsession.

2.2. Apparatus

The open-area arena (seeFig. 1) was constructed byplacing 38 cm high polystyrene walls (Owens CorningExtruded Polystyrene Insulation Foamular 150) arounda table (96 cm× 183 cm). The tabletop was coveredwith plastic sheeting and covered with 32 kg of cleansand (Bonsal Play Sand) spread to a uniform thicknessof approximately 2 cm. The locations of the startingposition and goals can be most easily identified by de-scribing the arena in Cartesian coordinates with 1 in.units (2.54 cm). Thus, the bottom left corner would berepresented as position (0, 0), and the upper right cornerwould be (72, 38). An 8 in. (20.3 cm) circular block cutfrom 1/2 in. (1.3 cm) plywood was used as the startingposition, centered and placed on top of the sand againstthe short wall on the left side of the arena, centered atposition (4, 19). Two 3.7 cm× 1.5 cm aluminum bottle

nd spa
Fig. 1. The dimensions a tial layout of the open arena.
http://www.wofford.edu/psychology/ratbasketball.asp


tops served as the two goal cups to hold the food pel-lets. The two goals were placed at unequal fixed dis-tances from the starting position. The near goal was10 in. (25.4 cm) from the lower long wall at position(36, 10), and the far goal was located 10 in. (25.4 cm)from the opposite wall at position (54, 28). Thus, thedistance between the middle of the starting position andthe near goal was 33.2 in. (84.3 cm), and the distanceto the far goal was 53.1 in. (134.9 cm). In some trials,a 158 cm× 6.6 cm× 2 cm poplar board, cut to abut thecircular starting platform, was present in a fixed loca-tion shown inFig. 1. The board was partially buried inthe sand to ensure that its surface was the same heightabove the sand as the starting platform (1.3 cm). Thesand was carefully smoothed around the board aftereach trial to ensure that its vertical edges would pro-vide a consistent stimulus to the rats’ whiskers.

Three 1 in. PVC pipes were used to create a tripod,which supported a Pro Video CVC-770PH color minia-ture camera with a conical pinhole lens. The cameralooked down through a 5 cm washer placed inside themetal shell of a Hubbell Twist-Lock 20 Amp connectortaped to the tripod, which supported the camera 2.44 mabove the arena. This arrangement allowed the camerato be rotated manually inside the stationary connector,and three screws on the connector adjusted the positionof the washer to provide fine-grain adjustments of thecamera’s viewing angle. The camera fed into a SonyDual-Deck VHS Recorder and a 24 in. Metravox tele-vision so the images from the camera would appearo d ber

ingt ium,2 or-m ns.T Wb tedl ona ulds ent,w sev-e wallo ra-t dowo beu bot-t top

wall. An air conditioner (turned off) was visible on thewall nearest the bottom left corner of the arena. Duringevery trial, one experimenter stood motionless approx-imately 3 ft from one end of the arena in a positionvisible from most locations in the tabletop arena. Fi-nally, the geometry of the rectangular arena and fixedposition of the starting platform and goal cups couldserve as within-maze orientation cues.

The viewing angle of the TV camera was adjustedeach day to ensure that the rectangular arena was dis-played the same size and in the same fixed position onthe television screen for every trial. This made digi-tizing the movement patterns easier and reliable fromtrial to trial. During all trials and subsequent videodigitizing, a large transparent grid with 1/2 in. squareswas taped over the entire television screen to providea constant reference for the coordinate system. The38 in.× 72 in. arena was always displayed on the televi-sion as a 21-unit by 40-unit rectangle (10.5 in.× 20 in.),so the scale transformation from actual arena to tele-vision image was 3.6–1 along both thex- andy-axes.Following the experiment, the same experimenter dig-itized every videotaped trial by manually tracing thelocomotion of the subject onto the transparent grid onthe television, and then typing the grid coordinates foreach 1/2 in. square into a personal computer using Mi-crosoft Excel. To prevent experimenter bias, this exper-imenter was blind to the predictions of the route-findermodel whose predicted movement pattern for each trialwould later be compared to the rats’ actual movementp sed.

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t thee omea fora cedo loref ughn ng.T sentd toodm thee andp

n the television screen during each trial and coulecorded onto RCA standard grade VHS tapes.

The maze was in a fixed position in the room durhe study. The room was an empty circular planetar1.5 ft in diameter, with a white spherical ceiling nally used for projecting images of star constellatiohe room was dimly illuminated with a single 60ulb in a clamp-on aluminum reflector that direc

ight in a forward direction. This room configuratillowed tight control of extra-maze stimuli that coerve as landmarks for orientation. For this experime provided abundant extra-maze visual stimuli ofral types. The light source was stationary on onef the room, and it illuminated the tripod and appa

us in such a way to produce a large distinctive shan the wall and ceiling. The tripod itself could alsosed for orientation since two legs were over the

om wall of the arena and only one was over the

atterns. No inter-rater reliability measures were u

.3. Procedure

.3.1. Habituation trainingWhen the rats were 48 h food deprived,

ransported all five rats in their home cages toxperimental room where we allowed them to becdjusted to the dim lighting and odors of the roombout 30 min. The rats were then individually plan the starting platform and were allowed to exp

or 10 min. Both goal cups were present, althoo food was provided during habituation trainihe board serving as a runway was not preuring habituation training. Three experimenters sotionless in the room and remained silent. Atnd of habituation we stopped the video recordinglaced each subject back in its respective cage.


2.3.2. Experimental procedureThe same general procedure was used for each trial.

Differences between trial conditions are presentedbelow. Subjects were 23 h food deprived and trialsbegan at approximately the same time each day.All subjects were weighed and transported in theirhome cages (without food or water bottles) to theexperimental room, where they became adjusted to thedim lighting and odors of the room for about 30 min.Subjects were run in the same order for every trial.We began recording each trial before the subject wasplaced into the open arena. Two experimenters wereinvolved in all trials: one operated the VCR, placed thesubject in the same position on the starting platform foreach trial, and removed the subject when the trial wasover. The other experimenter displayed a clipboardto the camera with the identifying details of the trial,then stood motionless one meter from the right side ofthe arena to observe the subject and time the subjectwith a stopwatch. Timing began with the subjectbeing released on the starting platform and endedwhen all pellets had been consumed in both goals.Reinforcement at each goal consisted of three 45 mgNoyes pellets (Formula A/I). The trial ended when thesubject appeared to stop looking for food, usually afterreturning to the vicinity of the starting location, atwhich point the video recording was stopped and thesubject was returned to its home cage in the same room.

The conditions of each trial were manipulated inthe following way. The board (runway) was present inthe arena only for Trials 11–15. Both goal cups werepresent in the arena in all trials except Trials 16–19.

Trial 1. Both goal cups were present, but food (threefood pellets) was available only in one of them. Foodwas available in the near goal for Rats 1 and 2, and inthe far goal for Rats 3–5.

Trials 2–10. Three food pellets were provided inboth goal cups for all subjects.

Trials 11–15. The board (runway) was present in thearena in the position shown inFig. 1. After the subjectsfound the food in Trial 11, they were allowed to remainin the arena for several minutes to explore the board andhabituate to the modified environment.

Trial 16. We removed the board and the goal cupsfor Trial 16. Three pellets were buried in the same twolocations as the goal cups had been located previously.

Trial 17. For both goals, we buried three pellets andplaced three additional pellets above them on the sur-

face of the sand in the same location (for a total of sixpellets at each goal location).

Trials 18–19. These trials were extinction trials inwhich no food, goal cups, or board were present.

2.3.3. Simulation detailsThe observed movement patterns of the rats were

compared to the predictions of theReid and Staddon(1998) dynamic route-finder model. The simulationwas carried out on a 20× 40 grid of units represent-ing an eight-neighbor lattice. Thus, every grid location(except along the walls) was assumed to be adjacent tothe eight surrounding locations represented by the eightstandard directions on a compass (i.e., N, NE, E, SE,S, etc.). Movement and diffusion of reward expectationoccurred only via these local connections. The diffu-sion rate parameter (α) was set to 0.08 in all simula-tions. At the beginning of the simulation of habituationto the arena, all nodes were initialized with the samelow reward expectation, producing a uniform field ofreward expectancy across the arena. Each movement(each “step”) by the hill-climbing algorithm producedone iteration of the discrete diffusion equation, actingon every node represented in the arena. Each time thesimulated organism stepped in a location (thus, with re-ward expectation >0) where no reward was present, thereward expectation for that location was set to zero forthe next iteration. When reward was found at a location,the reward expectation at that location was incrementedby 1.0 for the next iteration. Each iteration producedc h un-r duet arde re-w atea ter-a d att dingfl c-t cedm sma om-p p asa ov-e ereti rthere

hanges in the reward expectancy landscape, witewarded steps leaving tracks that slowly filled ino diffusion flow from adjacent locations where rewxpectation had been higher. The effect of findingard at a single location (during Trial 1) was to cren impulse at that location, which (with repeated itions) formed a hill of reward expectancy centere

hat location. Repeated iterations produced a spreaow from the center of the hill outward in each direion. Finding reward at additional locations produultiple hills. Movement by the simulated organicted on this dynamic landscape to produce a clex landscape changing dynamically at each stefunction of diffusion, additional reward, and discred non-reward. All details of our simulations w

he same as those inReid and Staddon (1998), so thenterested reader may examine this reference for fuxplanation and quantitative details.


3. Results and discussion

This procedure provided multiple opportunities tocompare the movement patterns of rats in an open arenato that predicted by theReid and Staddon (1998)route-finder model. The main purpose of this comparison wasto identify behavioral processes involved in movementpatterns that are not included in their parsimoniousmodel. It also allowed us to compare the movementpatterns to the foraging patterns observed byHoffmanet al. (1999)andTimberlake et al. (1999)using a radialarm maze placed on the floor of the experimental room.

3.1. Initial encounter with food

In Trial 1, food was provided in only one goal cup— in the near goal cup for some subjects and in the fargoal for the other subjects. We wanted to know whatrole distal beacons have in the movement patterns offoraging rats, and how much experience is necessaryfor beacons to become predictive of food. Would find-ing food in one goal cup produce directed orientationtoward the other (empty) food cup in the same trial,given that the cups were identical in appearance? Al-

ternatively, the rats might orient naturally toward bothgoal cups as beacons in the otherwise uniform arena,independent of the presence of food, just as wood antsdo (Graham et al., 2003). Finally, how would obtainingfood at a single goal location affect movement patternsin subsequent trials? For example, would each subjectreturn directly to that same goal location in the nexttrial before beginning a more general search?

Fig. 2 depicts the movement patterns of each sub-ject during Trial 1, along with a computer simulation oftheReid and Staddon (1998)route-finder model. Thetrial lasted until each subject had visited both cups. Thesolid lines represent the movement patterns until bothcups were visited, and the dotted lines show movementafter both cups were visited, as they generally returnedto the starting platform. A major question concernedthe potential influence of olfaction (i.e., smelling thefood pellets) in the movement patterns of these hungryrats. If the pellets could be detected from a distance,one would expect directed orientation to the cup thatactually contained the food. We observed that whenfood was provided only in the near cup, one rat (Rat 2)visited this goal first, but the other rat (Rat 1) visitedthe far cup first. When food was provided only in the

F ubject resent them food h t traveled tob lationR them odel d

ig. 2. Solid lines represent the movement patterns of each sovement patterns after both goal cups were visited. Althoughoth cups as though they served as visual beacons. The simuovement patterns predicted during habituation because the m

in Trial 1, following habituation training. The dashed lines repad been placed only in one cup for each subject, each subjec

of theeid and Staddon (1998)route-finder model generally repeatedoes not provide for stimuli such as beacons.


far cup, only one rat (Rat 3) visited this cup first, andtwo rats (Rats 4 and 5) visited the (empty) near cupfirst. Therefore, the order of visiting the two cups didnot appear to be correlated with the location of food.Movement was clearly not random, however. All sub-jects oriented toward both goal cups as beacons in theotherwise uniform arena, independent of the presenceof food, replicating the patterns observed with woodants and other species (Graham et al., 2003).

The computer simulation of Trial 1 is depicted in thebottom right panel ofFig. 2. Recall that subjects hadbeen previously exposed to the open arena for a 10 minhabituation session, and at the beginning of Trial 1,no food had been obtained in the arena. Therefore, thesimulation needed to begin with a habituation session,followed by the depicted simulation of Trial 1. Thesimulated movement patterns of Trial 1 could dependupon the prior experience of habituation, so we brieflydescribe the habituation simulation first.

Simulation of the habituation session (not depicted)began by initializing all units with the same low valueof reward expectancy (0.001) and placing the sim-ulated organism at the coordinates representing thestarting platform. Movement was oriented exclusivelyalong the walls (thigmotaxis) until the entire arena hadbeen circumnavigated, accurately replicating the thig-motaxis observed in the actual subjects during the ha-bituation session. Only then did the simulated organismtraverse the open areas of the arena. The movement pat-tern representing the simulated 10 min habituation ses-s oughn

ion.T thec or-g qua-t edi ts inR r-a ormfi ntingt bit-u entpl tion.U ismd ringi n

(1998) route-finder model does not provide the abil-ity to detect visual stimuli such as the food cups, andeven after 440 steps, the locations representing the foodcups had not been visited. The food cups acted as vi-sual beacons for the actual subjects, but the route-findermodel could not replicate this influence on movementpatterns.

3.2. Subsequent encounter with food

We wanted to know how obtaining food at a singlegoal location would affect movement patterns in thearena in subsequent trials. For example, would eachsubject return immediately to that same goal locationbefore beginning a more general search?Fig. 3depictsthe movement patterns of each subject during Trial2, along with two computer simulations (explainedbelow) of theReid and Staddon (1998)route-findermodel. Recall that Trial 2 provided food in both goallocations. As expected, both rats that had previously re-ceived food only in the near goal (Rats 1 and 2) traveledfirst to the near goal, but (unexpectedly) then immedi-ately traveled to the far goal, even though they had notfound food there previously. The other three subjects(Rats 3–5), who had previously found food only in thefar goal, also visited the near goal before the far goaleven though they had never obtained food there. Thus,all subjects visited the near goal cup before the far goal,independent of where they received food previously.

Potentially, there are three ways of explaining thism thats ectt vi-s jectt ternsw t ad arlyd n,l ellt t. InT outt rieda findt . oft

oodp t toa lity.

ion appeared complex and unpredictable (even tho random process was involved).

Trial 1 occurred 24 h after the habituation sessherefore, in order to represent this time period inomputer simulation, we “removed” the simulatedanism from the arena and iterated the diffusion e

ion for 300 steps. (Note: This same procedure was usn the simulations of European badger movemeneid and Staddon, 1998.) Because diffusion is an aveging process, this procedure produced a fairly unifeld of reward expectancy across the units represehe arena, similar to the original conditions of the haation simulation. As a result, the predicted movematterns of Trial 1 (depicted inFig. 2) were highly simi-

ar to those observed during the habituation simulanlike the actual rats in Trial 1, the simulated organisplayed considerable thigmotaxis before ventu

nto the open areas of the arena. TheReid and Staddo

ovement pattern. One potential explanation isubjects’ olfactory abilities were sufficient to dethe food from several feet away, so olfaction (notion) determined the direction of movement. We rehis explanation because the rats’ movement patere clearly not greatly influenced by olfaction (aistance) in other trials. For example, olfaction cleid not direct orientation during Trial 1. In additio

ater trials led us to believe that their ability to smhe pellets was limited to several inches, not feerials 16 and 17 food pellets were presented with

he goal cups, either buried in the sand or both bund on the surface. Yet the subjects often did not

he pellets even though they traveled within 2–3 inhe food while foraging.

A second potential explanation is that one goal-fairing from Trial 1 was sufficient for each subjecssociate both goal cups with high food probabi


Fig. 3. Lines represent the movement patterns of each subject in Trial 2 until food was depleted in both goal cups. Two separate computersimulations of theReid and Staddon (1998)route-finder model demonstrate area-restricted search around the single location in which food hadbeen found in the previous trial.

This argument, based on stimulus generalization of aconditioned stimulus, assumes that subjects would gen-eralize from the food cup where they had found foodto the other food cup located at a different position inthe arena. The design of this study did not allow us totest the validity of this explanation.

The third potential explanation is that foraging ratsnaturally orient toward visual beacons, and this ten-dency is enhanced when the beacon has been previouslypaired with food. In Trial 1, we observed that each sub-ject did orient movement toward both food cups, eventhough they did not travel directly to the nearest cup.In Trial 2, they did travel more directly to the nearercup, and this improvement in travel efficiency may havebeen due to associating both goal cups with high foodprobability. While we cannot test this explanation di-rectly in the current study, we conclude that travel tothe near goal on Trial 2 was guided more by the visualbeacons than by olfaction.

The conclusion that visual beacons guide movementpatterns is important because it points out a limitation oftheReid and Staddon (1998)route-finder model. Thismodel was designed to be the most parsimonious expla-nation of how knowledge of space (i.e., some minimalcognitive map) and reinforcement history can produce

ostensibly goal-directed spatial behavior without pro-viding a global overview of the arena. Thus, it providesonly local connections between locations, and move-ment is based on a local hill-climbing rule acting ona landscape representing changing reinforcement ex-pectations. There are no “stimuli” in the model such asgoal cups (other than the unspecified landmarks pre-sumably used by the organism to orient itself in space).Therefore, the model does not allow the organism to“see” goal cups from a distance, much less generalizefrom one to the other. Thus, if the organism is rein-forced in one location, the diffusion process creates apeak on the reinforcement expectation landscape, andthe hill-climbing algorithm moves the organism towardthat peak, leaving transient footprints in its path. Twoindependent examples of this predicted movement pat-tern are provided in the two simulations in the bottomright panel ofFig. 3: if food has been obtained in the farlocation (the top movement pattern), movement occursin that direction in the next trial. Once food has beendepleted, movement around the goal occurs in a widen-ing area-restricted search. A similar movement patternis predicted if food is obtained only in the near goal,depicted by the lower pattern. After retrieving food, themodel predicts area-restricted search that widens over


time, but it does not include direct travel to the sec-ond goal location (assuming food had been found onlyat the first goal). The model predicts direct travel be-tween goals (shortcuts) only when multiple goals haveprovided food. (Note: Figs. 4 and 7demonstrate themodel’s accurate predictions of shortcuts when foodhad been found at both locations.)

In Trial 2 all subjects traveled to a goal locationwhere they had never received reinforcement, insteadof traveling exclusively in the direction of higher ob-tained reinforcement probability. Movement patternswere influenced by the visual detection of distant goalcups, and subjects may have generalized from one goalto the other. Neither feature is provided by the currentversion of theReid and Staddon (1998)route-findermodel, but they seem to be general across animals (ob-served in all five subjects). A more comprehensive ver-sion of the model will need to incorporate both features.

3.3. Increased travel efficiency during foraging

Trials 3–10 provided food at both goals and pro-duced similar foraging patterns across subjects.Fig. 4depicts the movement patterns of each subject during

Trial 3, as well as the predictions of the route-findermodel. The solid line shows the path taken to visit bothgoals, and the dotted line shows the movement patternobserved after consuming all the pellets. We expectedthe dotted line to meander more than the solid line be-cause all of the food in the arena had already beenconsumed.Fig. 5 depicts the movement patterns ob-served during Trial 10, showing how travel to the goalsbecame more direct (less meandering) with repeatedexposure to the same conditions. Rats 1 and 4 showedconsiderable thigmotaxis on the way to the goals inTrial 3, but it was eliminated by Trial 10.

In 42 of the 45 trials, subjects visited the near goalbefore the far goal. After depleting the food in the fargoal, subjects usually revisited the near goal (e.g., thedashed line for Rat 5 inFig. 3). In nearly all trials, toour surprise, each subject returned to the starting lo-cation after depleting the food, even though there wasno requirement to return and food was never presentednear that location. Returns to the starting location re-sulted in termination of the trial and returning the sub-ject to its empty home cage, without food or a waterbottle. Returns to the starting location were observedas early as Trial 3 for all subjects (seeFig. 4). Re-

F ject in es representt n repre l.T t to the by a returnt ition ob

ig. 4. Solid lines represent the movement patterns of each subhe movement patterns after all food was gone. The simulatiohe model accurately predicted direct goal-oriented movemen

o the near goal. It did not predict the return to the starting pos

Trial 3 until food was depleted in both goal cups. The dashed linsents the predictions of theReid and Staddon (1998)route-finder modenear goal, and subsequent movement to the far goal, followedserved in all subjects.


Fig. 5. Solid lines represent the movement patterns of each subject in Trial 10 until food was depleted in both goal cups. The dashed linesrepresent the movement patterns after all food was gone.

call that the entire arena was covered with fine sandexcept for the starting position, which was a circularpiece of plywood (8 in. diameter, 0.5 in. thick) placedon top of the sand. At first we assumed that the rats pre-ferred to stand on wood. However, after returning to thestarting position, subjects would meander in the sandin the general vicinity of the starting position. Thus,they were not avoiding the sand. Recently,Wallaceet al. (2003)have provided careful documentation ofrats returning to the starting location. They argue thatexploring rats set up “virtual home bases” where theyrear and groom, even in impoverished environments.They argue that the outward and homeward portionsof exploratory trips are distinct behaviors governed bydifferent orientation mechanisms and serving differentfunctions.

Fig. 4 also shows the predictions of theReid andStaddon (1998)route-finder model. The reinforcementhistory at the beginning of this simulation was pro-vided by Trial 2, in which food was obtained at bothgoals. The simulated organism began at the startingposition and proceeded to the near goal, followed bya fairly direct route to the far goal — a clear demon-stration of the model’s ability to take shortcuts. Af-ter food was depleted, the organism displayed a small

amount of area-restricted search in the vicinity of thefar goal, before returning to the near goal and begin-ning more area-restricted search. Thus far, the move-ment pattern predicted by the model closely matchesthat observed in most subjects. However, the rats thenreturned to the starting position, whereas the simula-tion did not. Instead, the simulation produced a patternof ever-widening general search (not depicted) ratherthan returning to the starting position (a location ofpresumably low reinforcement probability).

The model makes identical predictions for Trials 3and 10 (cf.Figs. 4 and 5). The model does not includea learning rule, so it yields identical predictions whenthe initial starting conditions are the same.

Learning did occur between Trials 2 and 15.Fig. 6shows the mean distance traveled across subjects fromthe starting location until all food had been foundand consumed in both goals. The average distancedecreased significantly over trials,F(4, 13) = 24.538,P< 0.01. The mean time required to deplete all food de-creased significantly as well,F(4, 13) = 2.519,P< 0.01,also depicted inFig. 6. Even though foraging behavioris likely to represent some optimal allocation of the or-ganism’s energy budget while simultaneously avoidingpredation, there has been considerable disagreement


Fig. 6. Travel distance (filled circles) and travel time (open circles) decreased across trials with additional exposure to the consistent foodlocations in the arena.

as to whether foraging animals minimize travel dis-tance, travel time, energy expenditure, or none of these(e.g.,Krebs and McCleery, 1984; Shettleworth, 1998;Staddon, 1983; Stephens and Krebs, 1986). Travel tothe goals clearly became more efficient across trials(cf. Fig. 6). Distance traveled and duration of travelboth decreased from Trial 2 through Trial 15 as sub-jects left the starting platform and consumed all theavailable food in the two goal cups. Distance traveled(or time spent traveling) also strongly influenced thechoice of which goal cup to visit first, as all subjectstraveled first to the near goal before traveling to the fargoal (in 42 of 45 trials). Movement patterns were notusually represented by straight lines (cf.Fig. 5) repre-senting minimal distances between points, but travel tothe goals generally became shorter with experience.

3.4. Evaluating trail following

Timberlake et al. (1999)presented compelling evi-dence that travel along the arms of a radial arm maze lo-cated on the floor (rather than elevated above the floor)and along the walls (thigmotaxis) was based on a trail-following tactic in rats. The tendency to follow the ra-dial arms was curious because the rats could easily havetaken shortcuts across arms to minimize distance to thefood. Yet, they were more likely to continue along theradial arms, maintaining contact with their whiskerswith the arm surface or sides of the arms. Whisker con-tact appeared important: trail following was reduced

when the whiskers were cut. The movement patternsin their study were interesting because the procedurepitted the tendency to follow trails against the tendencyto reduce travel distance. Trail following won.

In a similar vein, in the current study we pitted trailfollowing against the tendency to reduce travel dis-tance by providing a board (with a surface and edgessimilar, but not identical, to those used byTimberlakeet al., 1999) between the starting platform and the fargoal. Without the board, subjects first traveled to thenear goal before traveling to the far goal. Then after de-pleting the food in the far goal, they typically returnedto the near goal (which they had already depleted) be-fore returning to the starting location. We wanted toknow if the strength of the trail-following tendency wassufficiently strong: (a) to produce a change in prefer-ence — would they visit the far goal first (adjacentto the board) rather than the near goal, (b) to producea change after food was depleted — would they con-tinue to revisit the near goal or return directly to thestarting position? This manipulation provided a roughindication of the strength of the trail-following tactic.Changes in the route taken to the first goal would implymore strength (a more powerful tendency) than changesin the route taken after all food was depleted.

Fig. 7 shows the movement patterns during Trial12, just after the subjects first experienced and were al-lowed to habituate to the board in Trial 11. In Trial 12every subject walked either on or adjacent to the board,but only after retrieving the food from both goals. The


Fig. 7. Solid lines represent the movement patterns of each subject in Trial 12, just after the wooden runway was introduced, until food wasdepleted in both goal cups. The dashed lines represent the movement patterns after all food was gone. All subjects traveled on the runway,generally returning to the starting position, but only after all food had been depleted. The predictions of the route-finder model ofReid andStaddon (1998)were not influenced by the presence of the runway because the model does not incorporate such stimuli.

presence of the board did not reverse the order of visit-ing the goals. Instead, the rats generally traveled alongthe board as they returned to the starting location. Al-though the board did encourage movement in its vicin-ity, the “trail-following tendency” was not as strong asthe tendency to reduce travel distance to the goals.

Travel along the board decreased with additionalexposure to the board in Trials 12–15.Fig. 8shows themovement patterns of Trial 15. Although every subjectused the board in Trial 12, by Trial 15 all rats generallyreverted to the movement pattern observed in Trial 10(cf. Fig. 5): they revisited the near goal on return to thestarting position rather than returning via the board. Atthis point, the board seemed to have minimal influenceon movement patterns (except, perhaps, for Rat 3).

In general, the board produced a change in theroute taken only after all food was depleted, and thischange was transient, lasting no more than two or threeconsecutive trials with the board present. Thus, whilewe did observe evidence for a trail-following tactic,it appeared weak and transient. Clearly, differentdimensions in height or width of the board could haveproduced different effects.

The simulation depicted inFig. 7is the same as thatshown inFig. 4 because the route-finder model doesnot include stimuli such as the texture of the sand andrunway or global views such as the direction of the run-way. The model does not predict travel along the boardto the starting position, just as it did not predict the re-turn to the starting position observed inFigs. 4 and 5without the board.

3.5. Removing the beacons

Trial 16 degraded visual and olfactory cues by elim-inating the goal cups and by burying the food pelletsunder 2 cm of sand in the same locations as before.All subjects traveled to within 5 cm of the goal loca-tions, even though they failed to find the food in fiveout of 10 instances. The movement patterns on the wayto both goals were similar to those observed in Trial10 (Fig. 5), but subjects generally meandered after vis-iting the second goal rather than returning directly tothe starting position. The frequent failure to find thethree buried pellets at each goal, even though stand-ing within 5 cm of the location, leads us to believe that


Fig. 8. Solid lines represent the movement patterns of each subject in Trial 15, several trials after the wooden runway was introduced, untilfood was depleted in both goal cups. The dashed lines represent the movement patterns after all food was gone. Subjects generally ignored therunway, and returned to the movement pattern observed in Trial 10 before the runway was introduced. All subjects returned to the near goal afterdepleting the food in the far goal. The route-finder model ofReid and Staddon (1998)replicated this movement pattern, just as inFig. 4.

the rats probably could not smell the pellets from dis-tances greater than several inches. The fact that eachgoal location was visited within 5 cm in the absenceof the goal cups (often without detecting the presenceof the food) is evidence that each subject had learnedto locate these positions in the arena based on othercues, such as the geometry of the arena and distal land-marks.

Trial 17 confirmed our conclusion that movementpatterns were not greatly influenced by olfaction. InTrial 17, three pellets of food were buried and three ad-ditional pellets were placed on the surface of the sand inthe same locations as the previous positions of the goalcups. Subjects would travel directly to the near goal,but they would often fail to find and consume some ofthe pellets (even those on the surface) before travelingto the far goal. Only one of the five subjects found andconsumed all 12 pellets before returning to the start-ing position. Most subjects left pellets on the surfaceof the sand, as well as those hidden below the sand,even though uneaten pellets were within one or 2 in. ofthe subjects’ noses. If olfaction had been an importantdeterminant of movement patterns in this study, one

would have expected the hungry rats to locate all thepellets since they were placed in well-known locationsthat the rats did visit accurately.

3.6. Extinction

Trials 18 and 19 were extinction trials in whichno food, goal cups, or board were present. Movementpatterns were highly variable across subjects.Fig. 9,representing Trial 19, shows that rats traveled con-siderably in the open area of the arena as well asoccasionally along the walls. The general pattern re-flected travel back and forth between the starting po-sition and the two goal locations, rather than fromone goal location to the other. This general patternstands in contrast to the pattern predicted by theReidand Staddon (1998)route-finder model. The simula-tion produced a back and forth movement pattern be-tween the two goals in an ever-widening general searchpattern. The model did not predict movement back tothe starting position, which had been a prominent fea-ture demonstrated by each subject (e.g.,Wallace et al.,2003).


Fig. 9. Lines represent the movement patterns of each subject in Trial 19, the second extinction trial. Subjects generally moved back and forthbetween the starting position and the goal cups. However, the route-finder model produced alternation between the two goal cups, failing toreturn to the starting position.

4. Successes and limitations of theReid andStaddon (1998)route-finder model

These results identify variables that influence move-ment patterns during foraging and point out successesand limitations of theReid and Staddon (1998)route-finder model. How well did the route-finder modelaccount for the movement patterns? The model per-formed surprising well for the situations in which itwas designed to make predictions (i.e., those with-out the effects of stimuli other than food). The modelsuccessfully predicted the meandering and subsequentarea-restricted search in Trial 1 when subjects foundfood at one goal location. It successfully predictedthe shortcuts taken in Trials 3–10 and 12–15 (e.g.Figs. 4, 5 and 8) as subjects traveled directly to thenear goal, from the near goal to the far goal, and backagain to the near goal.

However, our results point out three limitations ofthe route-finder model. Some of these limitations wereanticipated byReid and Staddon (1998), and some werenot. First, we observed that travel efficiency improvedwith practice.Reid and Staddon (1998)pointed outthat their intentionally simplistic model did not con-

tain a learning rule, so it would not be able to produceimprovements that relied on learning. This limitationwas also pointed out byBiegler (2000), who proposedone way of incorporating learning into the route-findermodel.

A second limitation was that each of the subjectstraveled toward areas of low reinforcement probabil-ity in two situations: (a) they returned to the start-ing location after depleting the food, and (b) travel inTrial 1 was oriented toward a beacon (an empty goalcup). The route-finder model explicitly assumes thatall movement is directed toward areas of higher re-inforcement probability. It assumes that movement iscontrolled by a single behavioral system (Timberlakeand Lucas, 1989) — that of foraging for food. It doesnot include influences of other motivational systemssuch as avoiding predation, grooming, or reproduc-tion. Wallace et al. (2003)argue that the outwardand homeward portions of foraging trips serve dif-ferent functions. It is likely that the outward por-tion is governed by the feeding system, whereas thehomeward portion is governed by a different sys-tem. Biegler (2003)has recently proposed ways ofaltering the route-finder model to include multiple


behavioral systems representing different types ofgoals.

Finally, the route-finder model was not successful atpredicting any movement that was influenced by distalstimuli such as the beacons mentioned above. Becausethe local-process model does not include distal stim-uli, it could not account for the routes taken in Trials1 and 2, in which subjects traveled directly to previ-ously unreinforced goal cups — locations in whichthe model predicted reinforcement probability wouldbe low. Nor could the model account for the observedchanges, albeit transient, in the routes taken when theboard was first introduced. According to the model, theboard would not influence movement patterns becausethe model does not include a mechanism of allowingenvironmental stimuli to influence behavior (other thanblockades and the presence or absence of food). Eventhough the authors were well aware of this limitation,the current data provide clear evidence of the need toincorporate the influence of environmental stimuli intomodels that predict foraging patterns.

How should this be done? Recall thatReid andStaddon (1998)argued that spatial orientation has twological parts, knowledge and action. Their route-findermodel was designed to explain action — it is a read-out process that converts spatial knowledge to action.Where do environmental stimuli exert their influence,on spatial knowledge or on action? If their influencewere on spatial knowledge, then one would expectchanges to the underlying representation of space (thec acto itself.D atialkc ther im-i

ersw fol-l seoS ofs urs( n-i entedm ep-r thec pted

location (the adjacent node). The diffusion rule andthe hill-climbing rule were not affected directly, but bybreaking the link between normally adjacent neighbors,neither diffusion nor movement could occur directlybetween the two neighbors. Thus, the underlying rep-resentation of space (spatial knowledge) would changedynamically as the simulated organism foraged.

This dynamic mechanism could be extended to trailfollowing with slight modification. The local stimulithat are encountered while following the edges of arunway probably provide improved spatial knowledge(increased spatial resolution) of the current location.This improved resolution could be incorporated into theroute-finder model by increasing the density of nodesrepresenting the vicinity. That area of the open arenawould have a denser representation in the rudimentarycognitive map than would other areas. This change maybe temporary, lasting as long as the organism is in thearea, as when whisker contact helps identify the edgesof the runway. Or, it could be permanent, representingthe enduring effects of landmarks on spatial resolu-tion. Thus, one way of incorporating stimuli into theroute-finder model is to have stimuli affect the under-lying representation of space (knowledge) rather thandirectly affecting the mechanism that produces action(the diffusion and hill-climbing rules). An increaseddensity of nodes may require temporary changes in thediffusion rate parameter and/or the speed of iterations,but it should not require changes in the route-findingprocess itself. Additional simulations will be necessaryt

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ognitive map) that the diffusion and action rulesn, rather than changes to the readout mechanismistal stimuli such as beacons do seem to affect spnowledge (seeJeffrey, 2003for a recent review). Alear example of this effect is the observation thatesolution of spatial knowledge increases with proxty to landmarks and beacons (Cheng, 1988, 1989).

Local stimuli — those that the animal encounthile moving, such as whisker contact during trail

owing — appear more difficult to classify becauf their dynamic influence on movement.Reid andtaddon (1998)provided a way of including one typetimulus into their model in their simulations of detothe umwegproblem). When their simulated orgasm encountered an unexpected obstacle that prev

ovement in a direction, it altered the underlying resentation of space by breaking the link betweenurrent location (the active node) and the attem

o test the adequacy of this model.

eferences

iegler, R., 2000. Possible uses of path integration in animalgation. Anim. Learning Behav. 28 (3), 257–277.

iegler, R., 2003. Reading cognitive and other maps: how to agetting buried in thought. In: Jeffery, K.J. (Ed.), The Neurobogy of Spatial Behaviour. Oxford University Press, New Yopp. 259–273.

enhamou, S., Poucet, B., 1998. Landmark use by navigatingcontrasting geometric and featural information. J. Comp.chol. 112, 317–322.

heng, K., 1986. A purely geometric module in the rat’s sprepresentation. Cognition 23, 149–178.

heng, K., 1988. Some psychophysics of the pigeon’s use ofmarks. J. Comp. Physiol. 162, 815–826.

heng, K., 1989. The vector sum model of pigeon landmark uExp. Psychol.: Anim. Behav. Process. 15, 366–375.


Etienne, A., 2003. How does path integration interact with olfaction,vision, and the representation of space? In: Jeffery, K.J. (Ed.),The Neurobiology of Spatial Behaviour. Oxford University Press,New York, pp. 48–66.

Gallistel, C.R., 1990. The Organization of Learning. MIT Press,Cambridge, MA.

Graham, P., Fauria, K., Collett, T.S., 2003. The influence of beacon-aiming on the routes of wood ants. J. Exp. Biol. 206, 535–541.

Healy, S. (Ed.), 1998. Spatial Representation in Animals. OxfordUniversity Press, Oxford.

Hoffman, C.M., Timberlake, W., Leffel, J., Grant, R., 1999. Howis radial arm maze behavior in rats related to locomotor searchtactics? Anim. Learning Behav. 27 (4), 426–444.

Jeffrey, K.J. (Ed.), 2003. The Neurobiology of Spatial Behaviour.Oxford University Press, New York.

Krebs, J.R., McCleery, R.H., 1984. Optimization in behavioral ecol-ogy. In: Krebs, J.R., Davies, N.B. (Eds.), Behavioural Ecology,2nd ed. Sinauer, Sunderland, MA, pp. 91–121.

Mackintosh, N.J., 2002. Do not ask whether they have a cognitivemap, but how they find their way about. Psicologica 23, 165–185.

O’Keefe, J., Nadel, L., 1978. The Hippocampus as a Cognitive Map.Clarendon Press, Oxford.

Olton, D., Samuelson, R.J., 1976. Remembrance of places passed:spatial memory in rats. J. Exp. Psychol.: Anim. Behav. Process.2, 97–116.

Poucet, B., 1993. Spatial cognitive maps in animals: new hypotheseson their structure and neural mechanisms. Psychol. Rev. 100,163–182.

Reid, A.K., Staddon, J.E.R., 1998. A dynamic route finder for thecognitive map. Psychol. Rev. 105 (3), 585–601.

Roberts, A.D.L., Pearce, J.M., 1998. Control of spatial behavior byan unstable landmark. J. Exp. Psychol.: Anim. Behav. Process.25, 225–235.

Robles, J.R., 2003. Spatial search behavior of humans in an artificialenvironment. In: Proceedings of the Poster Session Presented at

the Annual Conference of the Association for Behavior Analysis,San Francisco, CA.

Rodrigo, T., 2002. Navigational strategies and models. Psicologica23, 3–32.

Shettleworth, S.J., 1998. Cognition, Evolution, and Behavior. OxfordUniversity Press, New York.

Staddon, J.E.R., 1983. Adaptive Behavior and Learning. CambridgeUniversity Press, Cambridge, MA.

Staddon, J.E.R., 2001. Adaptive Dynamics: The Theoretical Analysisof Behavior. MIT Press, Cambridge, MA.

Staddon, J.E.R., Reid, A.K., 1990. On the dynamics of generaliza-tion. Psychol. Rev. 97, 576–578.

Stephens, D.W., Krebs, J.R., 1986. Foraging Theory. Princeton Uni-versity Press, Princeton, NJ.

Timberlake, W., Leffel, J., Hoffman, C.M., 1999. Stimulus controland function of arm and wall travel by rats on a radial arm floormaze. Anim. Learning Behav. 27 (4), 445–460.

Timberlake, W., Lucas, G.A., 1989. Behavior systems and learn-ing: from misbehavior to general principles. In: Klein, S.B.,Mowrer, R.R. (Eds.), Contemporary Learning Theories: Instru-mental Conditioning and the Impact of Biological Constraints onLearning. Erlbaum, Hillsdale, N. J, pp. 237–275.

Wallace, D., Hines, D., Gorny, J., Whishaw, I., 2003. A role forthe hippocampus in dead reckoning: an ethological analysis us-ing natural exploratory and food-carrying tasks. In: Jeffery, K.J.(Ed.), The Neurobiology of Spatial Behaviour. Oxford UniversityPress, New York, pp. 31–47.

Wang, R.F., Spelke, E.S., 2002. Human spatial representation: in-sights from animals. Trends Cogn. Sci. 6 (9), 376–382.

Wang, R.F., Spelke, E., 2003. Comparative approaches to humannavigation. In: Jeffery, K.J. (Ed.), The Neurobiology of SpatialBehaviour. Oxford University Press, New York, pp. 119–143.

Wehner, R., Srinivasan, M.V., 2003. Path integration in insects. In:Jeffery, K.J. (Ed.), The Neurobiology of Spatial Behaviour. Ox-ford University Press, New York, pp. 9–30.

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Route ﬁnding by rats in an open arena and Reid 2005.pdfBehavioural Processes 68 (2005) 51–67 Route ﬁnding by rats in an open arena Rebecca A. Reida, Alliston K. Reidb,∗ a South