Landmark use by pigeons in a touch-screen spatial search task

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1 Animl Lerning &: Behvior 1992, 20 (3), Lndmrk use by pigeons in touch-screen sptil serch tsk MARCIA L. SPECH University ofalbert, Edmonton, Albert, Cnd KEN CHENG University of oronto, oronto, Ontrio, Cnd nd MICHAEL V. MONDLOCH University ofalbert, Edmonton, Albert, Cnd Pigeons obtined food by pecking t n unmrked trget loction on video screen equipped ith touch-sensitive frme. he trget re s locted ner the top edge of the screen in Experiment 1 nd ner the left edge of the screen in Experiment 2. On bseline trils, grphic lndmrk s locted belo nd left ofthe trget (Experiment 1) or belo nd right ofthe trget (Experiment 2). In both experiments, bseline serch distributions shoed single pek nd ere roughly symmetricl bout the trget re in both horizontl nd verticl dimensions. On occsionl test trils, the lndmrk s shifted horizontlly, verticlly, or digonlly by 1.5 em or 3 em. In both experiments, lndmrk shifts in the dimension prllel to the nerest edge produced systemtic shifts in the pek plce ofserch. Lndmrk shifts in the dimension perpendiculr to the nerest edge produced inconsistent (Experiment 1) or reltively smll (Experiment 2) shifts in pek plce. he mgnitude of the behviorl shift s lys less thn the mgnitude of the lndmrk shift nd s not consistently greter hen the lndmrk s shifted by 3 em thn hen it s shifted by 1.5 em. hese results demonstrted tht pigeons cn ccurtely locte n unmrked trget re in to-dimensionl verticl ren nd tht their use of lndmrks for sptil locliztion is similr in sever! respects to tht found in open-field sptil serch tsks. Mny orgnisms pilot their y bck to desired loctions by the use of visul lndmrks. Some spects of the sptil reltionships beteen the gol nd the surfces nd objects tht surround it re encoded nd lter used to seek the gol. Lndmrks re used both to get to the vicinity of the gol over long distnces nd to pinpoint the gol once the niml is in its vicinity. Gllistel (1990, ch. 5) gives numerous exmples ofsuch piloting. he most convincing experimentl strtegy for demonstrting tht n niml uses lndmrks in sptil serch is to systemticlly shift lndmrks surrounding gol. If the niml then systemticlly shifts its serching behvior in spce, this indictes tht it is relying on the shifted lndmrks. Vrints ofthis method hve been used to sho tht lndmrks re used by rts (Cheng, 1986; Suzuki, Augerinos, & Blck, 1980), gerbils (Collett, Crtright, & Smith, 1986), hmsters (Etienne, eroni, Humi, & Portenier, 1990), nutcrckers (Vnder ll, 1982), pigeons (Cheng, his reserch s supported by NSERC operting grnts to the first nd second uthors. e ish to thnk Sie n, Stefne Mdison, nd Lonn Cunninghm for ssistnce ith vrious spects ofthis reserch. Requests for reprints should be ddressed to Mrci Spetch, Deprtment of Psychology, University of Albert, Edmonton, AL Cnd OO 2E9 (e-mil: mrci@ultmts). 1988, 1989, 1990; Spetch & Edrds, 1988), octopuses (Mther, 1991), nts (ehner & Reber, 1979), bees (Crtright & Cotlett, 1982, 1983; Dyer & Gould, 1983; von Frisch, 1977), nd digger sps (inbergen, 1972). In series of recent studies on sptil locliztion (Cheng, 1988, 1989, 1990; Cheng & Sherry, in press), pigeons ere trined to find food buried belo the surfce of 1.2- or 1.6-m-squre ren. he gol s locted t constnt loction ner n edge ofthe ren, nd single rrngement of lndmrks surrounding the gol s used. Objects plced in the ren or stripe on the ll served s lndmrks. he birds in this tsk pecked t the ground in serch ofthe hidden food. Occsionlly, test tril s given in hich the food s bsent. Videotpe records shoed tht the serch distribution (of hed positions over spce) s symmetricl bout single pek, long dimensions both prllel nd perpendiculr to the ll. he spred of the distribution (rtio of idth to height) s constnt proportion of the distnce to the nerest lndmrk (Cheng, 1990). On tests here lndmrks ere shifted, the birds systemticlly chnged their positions ofserch. Specificlly, if lndmrk s shifted by x cm in directions prllel or perpendiculr to the edge nerest the gol, the bird shifted the pek position of serching by 0 to x cm in the direction oflndmrk shift, 281 Copyright 1992 Psychonomic Society, Inc.

2 282 SPECH, CHENG, AND MONDLOCH but it did not shift in the orthogonl direction. Hoever, shifts of lndmrk in digonl direction y from the edge nerest the gol did not cuse the birds to shift their plce of pek serching in the direction of the lndmrk shift (Cheng, 1990; Cheng & Sherry, in press). Insted, they shifted frther in the direction prllel to the nerest edge thn in the perpendiculr direction. In these studies, the fct tht the pek plce of serching shifted systemticlly hen the lndmrk s shifted indicted tht the birds used the lndmrks for locliztion. Hoever, the fct tht serch behvior often did not shift the full extent of the lndmrk suggested tht behvior s lso controlled by unshifted lndmrks (Cheng, 1988). he ork presented here represents first ttempt to trin pigeons in n nlogous tsk on different surfcenmely, the verticlly plced surfce of video monitor. he video screen provided to-dimensionl (2-D) sptil ren, nd specific re ner the edge of the screen served s the trget. Computer-generted grphic stimuli displyed t vrious loctions on the screen served s lndmrks. Pigeons ere rerded ith food for pecking t the trget. he loction of pecks s registered by touch frme tht emitted grid of infrred bems: henever one or more bems s interrupted, signl s sent to the computer to indicte the coordintes of the interruption. he touch-screen tsk provided differently oriented serch spce (verticl vs. horizontl), different kinds of lndmrks (computer-generted ptterns vs. objects), nd different sptil scle from tht provided in open-field tsks. e nted to determine hether pigeons cn lern to use grphic lndmrks to locte position nd to exmine the nture of the serch distribution obtined. he experiments lso tested hether control by lndmrks ithin this sptil ren ould be similr to control by lndmrks in the open-field setting (Cheng, 1988, 1989, 1990). In our experiments, the trget re s ner horizontl edge of the video screen in Experiment 1 nd verticl edge in Experiment 2. A rectngulr grphic stimulus locted ner the trget served s lndmrk. In both experiments, the trget s nerer to the edge of the screen thn s the lndmrk. On occsionl unrerded tests, the lndmrk s shifted by smll extent verticlly (up or don), horizontlly (left or right), or digonlly (combintions of equl verticl nd horizontl shifts). hese tests re nlogous to those tht hve been conducted in the open-field tsk. EXPERIMEN 1 Method Subjects he subjects ere 3 experimentlly nive hite Crneux pigeons from 1-2 yers old. Ech bird s mintined t 80% to 85% of its free-feeding eight by 45-mg Noyes pigeon pellets obtined during experimentl sessions nd by supplements of mixed grin in the home cge. he birds ere housed individully in lrge cges in colony mintined on 12:12-h light:drk cycle. ter nd grit ere freely vilble in the home cges. Apprtus he pprtus consisted of stndrd rectngulr pigeon chmber (BRS/LVE) ith lrge opening cut into one end ll. A color monitor (Zenith 1490) ith n ttched touch frme (Crroll ouch 1490 Smrt Frme) s plced ginst the opening. A thin sheet of Plexigls covered the video screen so tht the pigeons could not directly touch the screen, nd spcer of pproximtely 1.6 cm s used to seprte the touch frme from the monitor surfce. A food cup s centered on the ll belo the screen, nd smll lmp locted bove the food cup s turned on during food presenttions. A Colbourn pellet dispenser, ttched to the top of the chmber, dispensed 45-mg pellets through n ttched tube into the food cup. o prevent the birds from ttempting to perch on the tube, food cup, or touch frme, metl pnel s inserted 3.5 cm from the end ll to ct s brrier. A rectngulr hole 8 cm ide nd 6 cm high provided ccess to the food cup. Above this, lrge opening 27.5 cm ide nd 15 cm high provided ccess to ll except the bottom 5 cm of the video screen. A microcomputer locted in n djcent room s used to control the experimentl contingencies nd record the peck coordintes in units of pproximtely 1.5 cm. Progrms ere developed ith urbo Pscl (Borlnd, Inc.) nd used routines provided by Crroll ouch nd tchistoscopic disply procedure developed by Finley (1989). Generl Procedures Sessions ere run 5 or 6 dys per eek t pproximtely the sme time. Sessions lsted either until ll trils ere completed or for mximum of 1 h. he monitor screen s kept clen by iping it ith indo clener t the beginning of ech running dy nd beteen sessions s needed. rining Mgzine trining. Ech pigeon s given Noyes pellets in its home cge until the pellets ere redily consumed. hen, ech bird received to or three sessions of mgzine trining in the chmber. During these sessions, the screen s illuminted ith light gry bckground, hich provided dim chmber illumintion. Initilly, the food cup s filled ith mixed grin, nd the lmp bove it s turned on until the bird te ll the food. Next, the bird received severl trils in hich 10 food pellets ere dispensed nd the lmp s turned on until the bird te them. Subsequently, the bird received severl trils, seprted by 6O-sec intervls, in hich to pellets ere dispensed nd the food cup s illuminted for 4 sec. hese trils ere continued until the birds relibly consumed the pellets ithin these 4-sec periods. Initil peck trining. Ech pigeon next received number of sessions in hich food presenttions ere preceded by the presenttion of grphic trget mrker ( filled yello circle 2.0 cm in dimeter) on the center of the screen ginst the light gry bckground. If the bird pecked t 2.0-cm-squre re contining the trget mrker ithin 8 sec, or if 8 sec elpsed ithout peck, the trget mrker s removed (the gry bckground remined) nd food s presented. After 6O-sec intertril intervl (II), the trget mrker s presented gin. After bird mde severl pecks t the trget mrker, response requirement ( single peck in the trget re) s initited, nd the II s reduced to 5 sec. Over the next to sessions, the loction ofthe trget mrker s moved uprd nd to the right until it s in the plce on the screen tht ould serve s the trget re (see Figure 1). rget peck trining. During this phse, the lndmrk stimulus, blue br pproximtely 1.2 cm ide nd 2.4 cm high, s introduced in the loction shon in Figure 1. In ddition, frme round the sptil ren s introduced by dring drk gry grphic border pproximtely 1.2 cm ide round the perimeter of the screen (see Figure 1). A fding procedure s used to estblish pecking to the trget loction in the bsence of the trget mrker but in the presence ofthe lndmrk. Over number of ses-

3 OUCH-SCREEN SPAIAL SEARCH 283 Grphic Frme 2 em i----j L j I Lndmrk rget Figure 1. Digrm ofthe video disply presented during bseline nd control trils of Experiment 1. he trget is not visible to the birds. he grphic frme s drk gry border drn round the perimeter of the disply screen. sions, the trget mrker nd the trget re ere decresed to bout 1.5 cm x 1.5 cm (I unit idth x I unit height). hen, the trget mrker s fded by chnging the grphics fill pttern nd s further reduced in size until it s eventully eliminted. he rte t hich the birds proceeded through these steps s determined by their behvior: Correct pecks incremented counter by 5 counts, heres incorrect pecks decremented the counter by 1 count. hen the counter incresed by 50 counts, the bird s moved to the next step; if the counter decresed by 25 counts, the bird s moved bck to previous step. ypiclly, the birds pecked t the lndmrk during their first exposures to the fded trget mrker, nd consequently they moved bck nd forth beteen the vrious steps severl times before finlly proceeding to the condition in hich the trget mrker s bsent. hey remined in this condition until they ere ble to complete n entire session of 100 trils ithout the counter decrementing enough to require return to n erlier condition. rils ere seprted by 5-sec II, during hich the screen s drkened. he birds received beteen 12 nd 18 sessions of trining during this phse. Bseline trining. his phse s identicl to the lst condition of the preceding phse, except tht the bird s required to mke to, three, or four consecutive pecks to the trget loction to obtin food; the peck requirement s rndomly selected on ech tril. his requirement s instituted to prevent the birds from producing food by simply seeping their bek cross the generl re of the trget, behvior observed during the previous trining phse (see lso Morrison & Bron, 1990), nd to ccustom the birds to mking severl pecks to obtin food in preprtion for the subsequent test phse. o dpt the birds further to conditions used during testing, the lst fe bseline sessions included 10 control trils rndomly intermixed ith the 90 stndrd bseline trils. On control trils, the stimulus conditions ere identicl to the bseline trils, but pecks t the trget loction did not produce food. he tril ended 10 sec fter the first peck 110 mtter ho the bird behved. Birds 2367, 2774, nd 8935 received 20, 9, nd 19 bseline sessions, respectively. Lndmrk ests Folloing bseline trining, ech bird s given severl test phses, ech seprted by return to bseline trining conditions for fe sessions. Birds 2367 nd 2774 ere exposed, in order, to ll of the test phses described belo. Bird 8935 begn the ex- periment t lter time nd s not exposed to est Phse 1, but proceeded through the remining test phses in the sme order s the other birds. During ech test phse, control nd lndmrk-shift test trils ere rndomly interspersed mong reinforced bseline trils ithin ech session. On ll control nd lndmrk-shift trils, food s never presented, nd the tril s terminted 10 sec fter the first peck no mtter ho the bird behved. est Phse 1: Lndmrk shifts. his phse consisted of 18 sessions, ech contining 6 control trils nd 12 trils ith lndmrk shifts, interspersed mong 82 bseline trils. On control trils, the lndmrk s in its norml loction. On shift trils, the lndmrk s shifted by one or to 1.5-cm units left, right, up, don, left nd don, or right nd don. est Phse 2: Lndmrk shifts. During this test phse, ech session contined I control tril nd 8 trils ith lndmrk shifts, interspersed mong 91 bseline trils. Ech shift tril contined different direction of lndmrk shift: up, don, left, right, up nd right, don nd right, up nd left, or don nd left. During the first 14 sessions of this test phse, ll shifts ere by 2 units. During the next 7 sessions, ll shifts ere by I unit. est Phse 3: Lndmrk removl nd top-border mnipultioils. Ech ofthe eight sessions during this phse contined 2 control trils, 2 trils in hich the lndmrk s bsent, 2 trils in hich the top grphic border s bsent, nd 2 trils on hich the top border s doubled in idth (so tht it extended pproximtely I.2 cm frther into the serch ren). hese test trils ere rndomly mixed ithin 92 reinforced bseline trils nd ere designed to determine hether the lndmrk s necessry for ccurte serching nd hether serch loction s controlled by the locl edge provided by the grphic border t the top of the ren. est Phse 4: Lndmrk shifts. his phse replicted est Phse 2, ith the only difference being tht sessions during hich the lndmrks ere shifted by I unit ere lternted ith sessions during hich they ereshifted by 2 units. Ech bird received five sessions ith I-unit shift tests nd five sessions ith 2-unit shift tests. Dt Anlysis Pek plces in both the horizontl nd verticl dimensions ere clculted in ll phses by using forml procedure tht determines the middle ofthe highest region in distribution. First, the medin of the distribution s clculted. o ensure tht this medin represented the middle point of the highest region in the distribution, the medin clcultion s iterted by clculting it over the region in hich the previous medin s centered. hus, if the first medin s clculted over the rnge of 1-17 units nd gve medin unit of5, the next clcultion ould be over the rnge of 1-9 units. his process s repeted until to consecutive iterted medins differed by less thn 0.05 of unit. he lst vlue ofthe medin s tken to be the pek plce of the distribution. Justifiction for such procedure is given in Cheng (1989) nd in Roberts (1981). A mesure ofthe spred of the distribution bout the pek s provided by clculting the interqurtile rnge. his s defined s the distnce from the pek plce, minus 25% of the totl pecks in the distribution tht remined fter the lst itertion, to the pek plce plus 25% of the totl pecks in this distribution. Results nd Discussion Performnce on the lndmrk-shift tests s qulittively similr cross est Phses I, 2, nd 4. Becuse Bird 8935 did not prticipte in Phse 1, only results from the second to lndmrk-shift phses re presented. An nlysis of vrince (ANDYA) on pek plces from Phses 2 nd 4 reveled no significnt effect of test phse, nd therefore the peck distributions from these to phses ere combined for ll subsequent nlyses. Figure 2

4 2 SPECH,CHENG,ANDMONDLOCH (f) 80 u J «40 l.l Z 20 U 0::: Z f= «u ---.J OP o HORIZONAL VERICAL 20 BIRO 2367 v BIRD BIRD DIMENSION t:!:tl=...l.l...l-.i..-..jtl::1. LEF PECK LOCAION u 0... DIMENSION BOOM L...l -----" "- ----'-- ---' 60 PERCEN OF OAL PECKS RIGH Figure 2. Serch distributions long the horizontl nd verticl dimensions for ech bird on bseline trils in Phses 2 nd 4 of Experiment 1. represents the center of the trget loction in ech dimension. 80 shos the distribution of pecks in the horizontl nd verticl dimensions for individul birds, pooled cross ll bseline trils from Phses 2 nd 4. In both dimensions, the birds consistently pecked most in the vicinity of the trget, nd their serch distributions ere roughly symmetricl, similr to the distributions found in open-field tsks (Cheng, 1988, 1989). Figure 3 provides 2-D plot of serch distributions for ech bird. Serch density in ech 1.5-cm-squre sptil loction is shon ith respect to the percentge of mximum pecks, ith drker squres representing more dense serch. Serch behvior is centered round the trget loction nd is someht more loclized in the verticl dimension thn in the horizontl dimension. Figure 4 provides 2-D plot of the men pek plces of the 3 birds on test trils for the I-unit (top grph) nd the 2-unit (bottom grph) shift test sessions. he rros ttched to the dt points indicte the direction in hich the lndmrk s shifted. he in the centerof ech figure indictes the center point of the trget re on control (nd bseline) trils. he eight surrounding loctions correspond to the eight types of lndmrk shifts nd indicte the loction t hich the center ofthe trget ould be if the shifted lndmrk provided the only cue. Donrd or leftrd shifts re indicted by negtive numbers, nd uprd or rightrd shifts re indicted by positive numbers. Severl fetures of these dt should be noted. First, ith one exception (the condition in hich the lndmrk s shifted 2 units up nd 2 units left), leftrd shifts in the lndmrk produced leftrd shifts in pek loction, nd rightrd shifts in the lndmrk produced rightrd shifts in pek loction, reltive to control trils. he I-unit shifts in prticulr sho three cler clusters ofdt points tht differ in the horizontl but not in the verticl dimension. Second, the mgnitude of the shifts in pek loction s never s gret s the mgnitude of the lndmrk shift. hird, horizontl shifts ere D N U. < II rill <. '.. CL. CD Figure 3. o-dimensionl serch distributions for ech bird on bseline trils in Phses 2 nd 4 ofexperiment 1. he density ofserch in ech 1.5 cm squre loction is shon ith respect to the percentge of mximum pecks.

5 OUCH-SCREEN SPAIAL SEARCH 285. (/) Q) L 0-- (J -+oj L <V > Reltive rget Loction Men Pek Peck Loction -1-2 ' ' Horizontl (Perpendiculr) Shift Figure 4. Pek plce of serch in to dimensions on lndmrk shift nd control tests of Phses 2 nd 4 of Experiment 1. he connected to ech point shos the center ofthe trget loction reltive to the shifted lndmrk. not consistently lrger in response to 2-unit shifts thn to I-unit shifts. Fourth, systemtic shifts in pek plce ere not evident in the verticl dimension. For the I-unit shifts, serch plce chnged very little s function of verticl lndmrk shift, heres 2-unit shifts ofthe lndmrk tended to result in donrd shifts of pek plce regrdless of hether the lndmrk s shifted up or don. Finlly, digonl shifts of the lndmrk generlly produced less systemtic chnge in serch peks thn did horizontl shifts. he dt on pek plce in the horizontl nd verticl dimensions ere nlyzed ith seprte ANOVAs ith the three fctors being horizontl loction ofthe lndmrk (left, bseline, right), verticl loction of lndmrk (up, bseline, don), nd mgnitude of lndmrk shift (1 or 2 units). In the horizontl dimension, min effect ofthe horizontl loction ofthe lndmrk s found [F(2,4) = , p <.01], but min effect of the verticlloction of the lndmrk s not found [F(2,4) = 0.31]. hus, serch behvior shifted in the direction in hich the lndmrk s shifted, but not in the orthogonl direction. here s lso significnt interction beteen verticl nd horizontl plcement of the lndmrks [F(4,8) = 4.02, p <.05], reflecting the smller response to digonl lndmrk shifts thn to horizontl lndmrk shifts lone. he min effect of mgnitude of lndmrk shift (lor 2 units) s not significnt, nor did mgnitude oflndmrk shift interct significntly ith either the verticl or horizontl position of the lndmrk (ps >.1). hus, 2-unit shifts did not produce lrger shift of pek plce thn did I-unit lndmrk shifts. he three-y interction beteen mgnitude, horizontl plcement, nd verticl plcement pproched significnce [F(4,8) = 3.42, p =.065], becuse the to-y interction beteen verticl nd horizontl plcement s greter for the 2-unit shifts of the lndmrk. In the verticl dimension, the only significnt effect reveled by the ANOVA on pek plces s to-y interction beteen the mgnitude ofthe shift nd the verticl plcement ofthe lndmrk [F(2,4) = 8.17,p <.05]. his reflects the fct tht the 2-unit shifts ofthe lndmrk produced donrd shift in pek plce, heres I-unit shifts did not. In generl, these results prllel those found in the openfield serch tsk. ht is, shifts of the lndmrk in the direction prllel to locl edge (i.e., the horizontl dimension) produced systemtic shifts in serch behvior, heres shifts in the dimension perpendiculr to the nerest locl edge did not led to orderly shifts in serch behvior. he one nomlous result observed s the tendency ofthe birds to sho donrd shifts in pek plce hen the lndmrk s shifted uprd by 2 units. One possibility is tht shifting the lndmrk up to this extent my hve induced the birds to disregrd the lndmrk s n indictor of here to serch. On tests in hich the lndmrk s shifted digonlly, serch behvior ppered to shift more in the horizontl dimension thn in the verticl dimension (see the top pnel of Figure 4). o detennine hether the difference beteen the to dimensions s significnt, e clculted for the four digonl shift tests the extent to hich the horizontl nd verticl.pek plces shifted in the direction ofthe lndmrk shift, reltive to pek plces on control trils (shifts in the opposite direction ofthe lndmrk shift received negtive scores). hese scores ere then divided by the mgnitude of the lndmrk shift so tht they represented the extent of behviorl shift s proportion of the lndmrk shift. hese dt ere then nlyzed ith repeted mesures ANOVA ith shift mgnitude (1 or 2 units), shift direction (up nd left, up nd right, don nd left, don nd right), nd dimension (horizontl nd verticl) s fctors. he nlysis reveled significnt min effect of mgnitude of shift [F(1,2) = 24.66, p <.05], reflecting the fct tht behvior shifted proportionlly more in the direction ofthe lndmrk shifts for the I-unit tests thn for the 2-unit tests. here s

6 286 SPECH, CHENG, AND MONDLOCH <:J Z <! ::: -! i= ::: <! :::J ::: f Z -! <! f Z o N ::: o :r: ' <:J z <! ::: -! i= ::: <! :::J 1.5 ::: z -! <! VERICAL SHIF +1 o v HORIZONAL LM HORIZONAL SHIF o v o u 0.5 ::: > 0.0 SHIF VERICAL LM SHIF FIgUre 5. Interqurtile rnge ofthe distributions on lndmrk shift nd control tests of Phses 2 nd 4 of Experiment 1. lso significnt interction beteen mgnitude of shift nd direction of shift [F(3,6) = 9.52, p <.02], hich presumbly reflects the fct tht serch behvior shifted y from the lndmrk shift for 2-unit uprd digonl shifts. Hoever, the min effect of dimension filed to rech significnce [F(l,2) = 9.52, p >.05], nd dimension did not interct significntly ith ny other fctor (ll ps >.2). Figure 5 shos the men interqurtile rnge, the mesure ofspred bout the pek, under ech lndmrk shift o 2 condition. In generl, interqurtile rnge tended to increse hen the lndmrk s shifted, nd in prticulr hen the lndmrk s shifted by 2 units. An ANOVA on the horizontl interqurtile rnge reveled significnt interction beteen verticl lndmrk plcement nd mgnitude of the shift [F(2,4) = , P <.05]. No other effects reched the.05 level of significnce. In the verticl dimension, interqurtile rnge s significntly ffected by verticl plcement ofthe lndmrk [F(2,4) = 7.062, p <.05] nd by horizontl plcement of the lndmrk [F(2,4) = 7.415, P <.05]. In ddition, there s significnt three-y interction beteen verticl plcement, horizontl plcement, nd shift mgnitude [F(4,8) = 6.223, P <.02]. ble 1 shos the results from est Phse 3, in hich the lndmrk s removed or in hich the top border s removed or extended frther into the ren. On tests in hich the lndmrk s removed, the men pek plce of serching s belo nd to the right of control trils; this difference pproched significnce in both the horizontl dimension [t(2) = 3.61, p =.076] nd the verticl dimension [t(2) = 3.80, p =.070]. he tendency to peck loer thn norml hen the lndmrk s removed is consistent ith our specultion tht the loer pek plces in response to 2-unit uprd shifts ofthe lndmrk my hve reflected tendency to disregrd the lndmrk. Mnipultion of the top border hd no consistent effects on pek plces of serch in either dimension, suggesting tht this grphic borders notn importnt stimulus despite the fct tht it s the closest edge to the trget. his is surprising, becuse in the open-field serch tsk, nerer lndmrks re given more eight (Cheng, 1989). One possibility is tht 2-D grphic edge is not s slient s the 3-D frme surrounding the monitor itself. EXPERIMEN 2 he results of Experiment I indicted tht pigeons cn lern to ccurtely serch for n unmrked loction on video screen nd tht serch could be guided in prt by grphic lndmrk. hese results re similr to those obtined in open-field tsks in hich serch for unmrked loctions s guided by nerby lndmrks (Cheng, 1988, 1989). Also similr to results obtined in open-field tsks (Cheng, 1990; Cheng & Sherry, in press) s the finding tht the lndmrk exerted greter control hen shifted long the dimension prllel to the nerest edgethn hen shifted long the dimension perpendiculr to tht edge. Hoever, in Experiment 1, the verticl dimension nd the perpendiculrdimension ith respect to the edge ere ble 1 op-border Mnipultion nd Lndmrk-Removl ests in Experiment 1 Control No lndmrk op border removed op border extended Pek Plce Horizontl Verticl Interqurtile Interqurtile Rnge Pek Plce Rnge l

7 OUCH-SCREEN SPAIAL SEARCH 287 cl dimension. Lmps locted ithin ech feeder ere used to illuminte feeder presenttions. he control equipment s the sme s tht described in Experiment 1. rget !..J -Lndmrk 2 em Figure 6. Digrm ofthe video disply presented during bseline nd control trils of Experiment 2. he trget is not visible to the birds. No grphic border s provided in this experiment. confounded. hus, the lck ofcler control by lndmrk shifts long the perpendiculr dimension could be due to the vilbility ofother slient cues, such s proprioceptive cues, tht my guide serch in the verticl dimension. Although the tendency observed in Experiment 1 to peck loer in response to removl or 2-unit verticl shifts of the lndmrk rgues ginst exclusive control by proprioceptive cues, there remins lck ofevidence tht serch behvior in the verticl dimension cn be systemticlly guided by grphic lndmrk. Experiment 2 s designed to provide such evidence by using n rrngement in hich the nerest edge to the trget s long the verticl dimension (see Figure 6). Iflndmrk shifts long the dimension prllel to the edge cuse the gretest shifts in serch behvior, then ith this rrngement verticl lndmrk shifts should control serch behvior more effectively thn horizontl lndmrk shifts. Method Subjects he subjects ere Birds 2367 nd 2774 from Experiment 1, to Silver King pigeons tht hd previously served in timing experiment conducted in stndrd opernt chmbers (Birds 241 nd 242), nd one experimentlly nive Silver King pigeon (Bird 243). All birds ere housed nd mintined s described in Experiment I. Apprtus For this experiment, e used custom built touch-screen chmber tht s 44 cm high, 32 cm deep, nd 74 cm ide (inside dimensions). A Zenith 1492 color monitor ith ttched infrred touch frme (Crroll ouch, 1492 Smrt Frme) s plced ginst n opening centered in the bck ll of the chmber. his opening s 10 cm from the rised grid floor ofthe chmber nd provided ccess to the entire surfce of the monitor. Spcers ere used to recess the touch frme by pproximtely 3 cm from the opening nd to seprte the frme from the monitor by pproximtely 1.6 cm. o Gerbrnds pigeon grin feeders ere mounted on the bck ll, one on ech side of the monitor. he feeder openings begn 8.5 cm from the sides of the monitor opening in the horizontl dimension nd ere centered ith the monitor opening in the verti- rining Mgzine nd initil peck trining. All pigeons ere first given severl sessions ofmgzine trining until they relibly nd rpidly te from either feeder. Ech bird then received severl sessions of utoshping in hich trget mrker ( 3-cm-dim yello circle) s presented on the center ofthe screen ginst drk gry bckground nd folloed by 6-sec ccess to food. For this nd ll subsequent phses, the left or right food hopper s rndomly selected for ech food presenttion. If the bird pecked in the 3-cm-squre re contining the trget mrker, the trget mrker s extinguished nd food s presented immeditely. Otherise, the trget mrker s extinguished nd food s presented 8 sec fter stimulus onset. Once bird begn to peck t the trget mrker, number of chnges ere instituted over the course of severl sessions. First, the loction of the trget nd mrker s moved in three steps to the intended trget loction (see Figure 6). Second, the temporl prmeters ere grdully chnged until the II s only 5 sec, nd the trget mrker remined on until peck occurred. Ech bird remined in this phse until it relibly completed ll scheduled trils in session. rget locliztion trining. In this phse, the lndmrk s introduced nd the trget mrker s grdully eliminted. he lndmrk s green rectngle, pproximtely 1.2 cm high x 2.4 cm ide, locted belo nd to the right of the trget (see Figure 6). Over successive sessions, the trget mrker nd trget re ere grdully reduced in size until the trget re s pproximtely 2.3 cm squre; then, the trget mrker s further reduced in size nd fded, nd finlly completely eliminted. hese chnges ere instituted in steps, s described in Experiment 1, ith trnsitions beteen steps determined by ech bird's behvior. Bseline trining. In this phse, the trget mrker s never presented. rils begn ith presenttion ofthe lndmrk on the drk gry bckground nd lsted until ech bird hd mde criterion number of consecutive pecks on the unmrked trget re of the screen. he criterion number vried cross trils in rndomly determined order. During the first fe sessions, the criterion s 1, 2, or 3 consecutive pecks. Once performnce stbilized, the criterion s chnged to 2, 3, or 4 consecutive pecks. hen the peck criterion s reched, the screen s blckened nd one ofthe hoppers s rised for 6 sec. After 5-sec II, the screen s illuminted ith the drk gry bckground, nd the lndmrk s presented to initite nother tril. Bseline trining continued until performnce s stble nd ccurte. Lndmrk ests Lndmrk-shift tests. During this phse, to types of test sessions ere presented in lterntion until ech hd occurred 10 times. he to types of test sessions differed only in the mgnitude of lndmrk shifts: During I-unit shift tests, the lndmrk s shifted pproximtely 1.5 cm, heres during 2-unit shift tests, the lndmrk s shifted pproximtely 3.0 cm. During both types oftests, 91 of the 100 trils in ech session ere reinforced bseline trils tht ere identicl to those presented t the end of bseline trining. One tril in ech session s n unreinforced control tril ith the lndmrk in the usul bseline loction. he remining 8 trils ere test trils in hich the lndmrk s shifted horizontlly (left or right), verticlly (up or don), or in one of the four resulting digonl combintions of verticl nd horizontl shift. On both control nd lndmrk-shift test trils, the tril terminted ithout reinforcement 8 sec fter the first peck. Lndmrk-removl tests. Folloing the lndmrk-shift test phse, ech bird s given fe sessions on the bseline procedure nd then given 10 test sessions in hich the lndmrk s removed on occsionl test trils. During these sessions, 96 trils

8 288 SPECH, CHENG, AND MONDLOCH ere reinforced bseline trils, 2 trils ere control trils ith the lndmrk in the bseline loction, nd 2 ere test trils ith the lndmrk removed. DUring control nd test trils, the tril terminted ithout reinforcement 8 sec fter the first peck. (fj Y: U Q --.J «f l.l f z u ct: Q z f «U --.J Y: U CL OP 0 ll.l,-l--1:::efet::!::!t!.. LEF RIGH PECK LOCAION 20 r; BIRD BIRD 2774 BIRD 241 BIRD _ BIRD 24 Results nd Discussion Figure 7 shos the distribution of pecks in the horizontl nd verticl dimensions during the bseline trils, collpsed cross ll test sessions. As in Experiment I, the pek ofthe distribution for ech bird fell in the trget re, nd the distributions ere roughly symmetricl in the to dimensions. Figure 8 is 2-D plot of bseline peck distributions for ech bird nd shos tht serch is centered in the vicinity of the trget. Figure 9 shos the men pek plces clculted for control nd shift-test trils, ith the rros indicting the direction in hich the lndmrk s shifted. he loctions mrked ith indicte the center points of the hypotheticl trget loctions bsed on the shifted lndmrk. Severl fetures ofthese dt should be noted. First, HORIZONAL VERICAL 40 DIMENSION DIMENSION BOOM L..I ---'-- ---' 60 PERCEN OF OAL PECKS Figure 7. Serch distributions long the horizontl nd verticl dimensions for ech bird on bseline trils of Experiment 2. represents the center of the trget loction in ech dimension. I 80 verticl shifts produced systemtic shifts of pek plce in the verticl dimension only, s cn be seen for the three clusters ofdt points corresponding to uprd, control, or donrd shifts of the lndmrk. Second, behvior shifted pproximtely hlf of the distnce of the I-unit lndmrk shifts, indicting joint control by the shifted lndmrk nd other cues. hird, 2-unit lndmrk shifts did not produce consistently lrger shift of pek plce thn did I-unit shifts. Finlly, horizontl shifts ofthe lndmrk tended to shift pek plce in the horizontl dimension but not in the verticl dimension. Hoever, these shifts in pek plce produced by horizontl lndmrk shifts ere neither s lrge nor s systemtic s ere the verticl shifts in pek plce produced by verticl lndmrk shifts. he dt on pek plce ere nlyzed ith seprte ithin-subject ANOVAs for the horizontl nd verticl dimensions, s described in Experiment 1. In the horizontl dimension, only the min effect of horizontl loction of the lndmrk reched significnce [F(2,8) = 6.71, p <.02]; in the verticl dimension, only the min effect ofverticl loction ofthe lndmrk s significnt. [F(2,8) = 93.34, p <.0001]. hus, behvior shifted in the horizontl dimension only hen the lndmrk s shifted horizontlly, nd in the verticl dimension only hen the lndmrk s shifted verticlly. On tests in hich the lndmrk s shifted digonlly, serch behvior ppered to shift more in the verticl dimension thn in the horizontl dimension. o determine hether the difference beteen the to dimensions s significnt, e clculted nd nlyzed the proportionl extent of the shift in behvior produced by ech of the four digonl shift tests s described in Experiment 1. he ANOVA on these mesures reveled significnt min effect of dimension of shift [F(l,4) = 43.02, p <.01], indicting greter shift in the verticl thn in the horizontl dimension. No other effects ere significnt (ll ps >.1). Figure 10 shos the men interqurtile rnge under ech lndmrk-shift condition. In the horizontl dimension, the rnge s ffected only by horizontl plcement ofthe lndmrk [F(2,8) = 5.084,p <.05]. heanova on interqurtile rnge in the verticl dimension reveled no significnt effects. Removl ofthe lndmrk hd little systemtic effect on pek plces; t tests compring pek plces oncontrol nd lndmrk-removl test trils filed to revel ny significnt difference in either the horizontl dimension [control tests, M = -0.01; lndmrk-removl tests, M = -0.07; t(4) = , p >.50] or in the verticl dimension [control tests, M = -0.07; lndmrk-removl tests, M = -0.02; t(4) = 0.300, p >.50]. he interqurtile rnge of the serch distribution s generlly lrger in the bsence ofthe lndmrk, but this difference lso filed to rech significnce in either the horizontl dimension [control tests, M = 0.91; lndmrk-removl tests, M = 1.25; t(4) = 1.22, p >.25] or the verticl dimension [control tests, M = 0.78; lndmrk-removl

9 DO II II < OUCH-SCREEN SPAIAL SEARCH 289 Ell±].,.,.,.,.,.: Figure 8. o-dimensionl serch distributions for ech bird on bseline trils of Experiment 2. he density ofsercb in ecb I.S cm squre loction is shon ith respect to the percentge of mximum pecks. tests, M = 1.14; t(4) = 1.92, P >.10]. hus, despite the significnt effect of shifting the lndmrk, the birds locted the trget re ith resonble ccurcy in the bsence of the lndmrk. In open-field studies, Cheng (1990) found tht the spred ofpigeons' serch distributions in given dimension is constnt proportion ofthe perpendiculr distnce from the nerest lndmrk or edge to the gol (i.e., tht eber's l holds). he eber frction clculted for to different experiments s.817 nd.367 (Cheng, 1990). oprovide rough comprison, eclcultedech bird's spred ofserching in the horizontl dimension for the control trils from the three test series of this experiment (i.e., from the I-unit shift, the 2-unit shift, nd the no-lndmrk test series), using the procedure described in Cheng. eber frctions ere computed by dividing the spred by the distnce from the center of the trget re to the nerest edge. he eber frctions clculted for individul birds rnged from.573 to.973, nd the men frctions from the three test series ere.761,.668, nd.783. hus, the reltive spred of the serch distribution ppers similr to tht obtined in open-field tsks. Further reserch ith vried trget-to-lndmrk distnces is needed to determine hether eber's l holds in the touch-screen tsk. GENERAL DISCUSSION he present results demonstrted tht pigeons cn lern to ccurtely loclize n unmrked trget re on video screen. Serch distributions on bseline trils ere chrcterized by single pek in the vicinity ofthe trget nd ere roughly symmetricl bout the pek. In both experiments, the grphic lndmrk exerted good control of serching behvior ithin one dimension, s indicted by the systemtic shifts in pek plce ofserching produced hen the lndmrk s shifted long tht dimension. Serching shifted in the direction of the lndmrk shift nd not in the orthogonl dimension. Although comprisons cross the to experiments must be mde ith cution becuse of differences in procedurl nd pprtus detils, it is orth noting tht in both cses the dimension tht exerted good control s the one prllel to the nerest edge (horizontl in Experiment 1 nd verticl in Experiment 2). he lndmrk exerted less control in the dimension perpendiculr to the nerest edge, s indicted by the smller (Experiment 2) or inconsistent (Experiment 1) shifts in pek plce tht resulted hen the lndmrk s shifted in the perpendiculr dimension. Similr results ere obtined ith digonl shifts of the lndmrk; serching generlly shifted more in the dimen-

10 2 SPECH, CHENG, AND MONDLOCH..c (f) Q) o L- o 0- '-.../ o (.) +J L- Q) > 2 ",-V , ,?. -2 Reltive rget Loction Men Pek Peck Loction ,! Horizontl (Perpendiculr) Shift Figure 9. Pek plce of serch in to dimensions on lndmrk shift nd control tests of Experiment 2. he connected to ech point shos the center of the trget loction reltive to the shifted lndmrk. sion prllel to the nerest edge thn in the dimension perpendiculr to the nerest edge. In ll cses, the shift in pek plce s ofsmller mgnitude thn the shift of the lndmrk, nd 3.0-cm shifts did not produce consistently lrger shifts in pek plce of serching thn did 1.5-cm shifts. hese results indicte joint control by the shifted lndmrk nd the unshifted cues. he use of unshifted cues lso seems pprent from the resonbly ccurte serch behvior obtined hen the lndmrk s completely removed, prticulrly in Experiment 2. It is not cler hich unshifted cues the birds might hve used, but severl possibilities exist. For exmple, lthough the pigeons did not pper to use the grphic border provided in Experiment I, the frme provided by the opening in the chmber surrounding the monitor surfce could provide slient cues. Proprioceptive cues might lso be quite slient in this tsk. It is lso pos- 2 sible tht the birds creted their on lndmrks by leving mrks on the screen from their pecks. Although e cnnot completely rule out this ltter possibility, e-think it s n unlikely source of control for severl resons. First, lthough the screen s sometimes dusty fter sessions, e did not detect ny specific mrks tht could provide cues bout the loction of the trget re. Second, the screen s frequently iped clen just before session. herefore, ifthere ere peck-generted lndmrks tht ere not detectble to humn observer, they could only be vilble to guide behvior on lter trils of the session nd ould only be creted if the bird pecked ccurtely in their bsence. hey lso could not hve provided n exclusive source ofcontrol, becusethen the relible effects of lndmrk shifts ould not be expected. Finlly, e hve recently begun study in hich the trget re vries from tril to tril nd is determined solely 2.5 C) VERICAL SHIF Z +1 o +2 <{., +0 '< J f= «1.5 ::J z J <{ z N 0 I C) Z <{ ẉ...j f= 1.5 <{ ::J 1.0 z...j <{ u 0.5 f= > 0.0 v HORIZONAL LM SHIF HORIZONAL SHIF , +0 '< t - ""Z?><::i VERICAL LM SHIF Figure 10. Interqurtile rnge of the distributions on lndmrk shift nd control tests of Experiment 2.

11 OUCH-SCREEN SPAIAL SEARCH 291 on the bsis ofgrphic lndmrks tht move cross trils. his rrngement precludes control by proprioceptive cues or peck-generted lndmrks. Our preliminry results indicte tht trget locliztion in this sitution is lso very ccurte. In severl respects, the results obtined in the present study re quite similr to those obtined in the open-field serch tsk (Cheng, 1988, 1989, 1990). In the open-field tsk, serch distributions re lso symmetricl bout single pek, nd the rtio of the spred of pek serching to the distnce from the trget to the nerest lndmrk is similr to tht found here. Shifts of nerby lndmrk in dimensions prllel or perpendiculr to the nerest edge produce shifts in plce of serching in the direction of the lndmrk shift but not in the orthogonl direction (Cheng, 1988, 1989). Pek plce of serching generlly shifts only prt y tord the trget ssocited ith the shifted lndmrk, indicting control by unshifted lndmrks. hese chrcteristics of lndmrk use provided support for the vector sum model (Cheng, 1988, 1989). According to this model, gol is loclized by eighted verge of vectors from vrious lndmrks to the gol. hen one ofthese lndmrks is shifted, serching should shift in the direction in hich the lndmrk is shifted but not in orthogonl directions. Moreover, serching ill generlly shift only prt of the distnce of the lndmrk shift becuse of verging ith unshifted lndmrks. Certin fetures of the present findings re consistent ith other recent results from the open-field serch tsk. For exmple, shifts of lndmrk in the direction prllel to the nerest edge generlly produce lrger or more systemtic shifts in open-field serch behvior thn do shifts in the direction perpendiculr to the edge (Cheng & Sherry, in press). Digonl lndmrk shifts do not consistently produce shifts in serching tht re long the line in hich the lndmrk is shifted (Cheng, 1990; Cheng & Sherry, in press). hese ltter results cnnot be ccommodted by the vector sum model becuse ccording to tht model, plce of pek serching must shift long the line connecting the trgetof the shifted lndmrk nd the trget of the unshifted lndmrk-thus, in the direction of the lndmrk shift. Cheng nd Sherry suggested tht in ddition to, or perhps insted of, vector summtion, the perpendiculrdistnce ofthe trget from nerby edge is used in clculting here to serch. Some hints tht pigeons in the touch-screen tsk might lso be using the perpendiculr distnce to n edge is found in the top pnel of Figure 4. Here, it is shon tht the birds shifted systemticlly prllel to the edge (horizontlly) but mintined pproximtely the sme perpendiculr distnce to the edge (serched t the sme verticl position) under ll lndmrk shifts. It is interesting tht the results obtined in the present study provide the sme pttern of support nd disconfirmtion of the vector sum model found in the open-field serch tsks. Our touch-screen video tsk differs in numberofpotentilly importnt ys from the open-field tsk. In our tsk, the ren is considerbly smller thn tht provided by the typicl open-field ren nd is oriented verticlly rther thn horizontlly. In the open-field tsk, the subject moves through spce to loclize nd pproch the gol, heres our tsk provides top vie of the entire ren, nd very little movement of the body is required to move through the spce. Our lndmrk s 2-D rther thn 3-D, nd in our tsk food s delivered from loctions other thn the trget t hich the birds pecked. Serch behvior in the present tsk (pecks on the screen) produced no detectble chnge in stimulus conditions, heres serch behvior in the open-field tsk displces bedding tht could provide stimulus support for lter serch. Although further experiments my yet revel some differences, the findings tht bseline ptterns of serch behvior re similr nd tht lndmrk use shos similr chrcteristics ithin these to very different tsks suggest tht the processes governing sptil serch nd lndmrk use my hve considerble generlity. ouch-screen systems like those used in the present reserch offer the dvntges inherent in the use of utomted equipment, yet re more flexible thn stndrd opernt chmbers (Morrison & Bron, 1990; Piscret & Rilling, 1987). Mny stimuli, including dynmic ones, my be presented, nd time nd loction of responses over the entire video screen cn be recorded. he use of touchscreen systems hve lloed or fcilitted investigtions of texture discrimintions (Cook, 1992), visul serch (Blough, 1989), nd concept lerning (right, Cook, River, Snds, & Delius, 1988). he present results suggest tht they my lso provide vluble complementry tool for the study of sptil serch. REFERENCES BUGH, D. S. (1989). Contrst s seen in visul serch rection times. Journl ofthe Experimentl Anlysis of Behvior, 52, CARRIGH, B. A., It COLLE,. S. (1982). Ho honeybees use lndmrks to guide their return to food source. Nture, 295, CARRIGH, B. A., It COLLE,. S. (1983). Lndmrk lerning in bees. Journl of Comprtive Physiology A, 151, CHENG, K. (1986). A purely geometric module in the rt's sptil representtion. Cognition, 23, CHENG, K. (1988). Some psychophysics of the pigeon's use of lndmrks. Journl of Comprtive Physiology A, 162, CHENG, K. (1989). he vector sum model of lndmrk use. Journl ofexperimentl Psychlogy: Animl Behvior Processes, IS, CHENG, K. (1990). More psychophysics of the pigeon's use of lndmrks. Journl of Comprtive Physiology A, 166, CHENG, K., It SHERRY, D. (in press). Lndmrk-bsed sptil memory in birds: he use of edges nd distnces to represent sptil positions. Journl of Comprtive Psychology. COLLE,. S., CARRIGH, B. S., It SMIH, B. A. (1986). Lndmrk lerning nd visuo-sptil memories in gerbils. Journlo/Comprtive Physiology A, 158, COOK, R. G. (1992). he visul perception nd processing of textures by pigeons. In. K. Honig & J. G. Fettermn (Eds.), CognitiVt! specls 0/ stimulus control (pp ). Hillsdle, NJ: Erlbum. DYER, F. C., It GoULD, J. L. (1983). Honeybee nvigtion. Americn Scientist, 71, EIENNE, A., ERONI, E., HURNI, C., It PORENIER, V. (1990). he effect of single light cue on homing behviour of the golden hmster. Animl Behviour, 39, FINLEY, G. P. (1989). chistoscopic softre for the Hercules dis-

12 292 SPECH, CHENG, AND MONDLOCH ply controller. Behvior Reserch Methods, Instruments, & Computers, 21, GALLISEL, C. R. (1990). he orgniztion oflerning. Cmbridge, MA: MI Press. MAHER, J. A. (1991). Nvigtion by sptil memory nd use of visul lndmrks in octopuses. Journl ofcomprtive Physiology A, 168, MORRISON, S. K., & BRON, M. F. (1990). he touch screen system in the pigeon lbortory: An initil evlution of its utility. Behvior Reserch Methods, Instruments, & Computers, 22, I'ISACREA, R., & RILLING, M. (1987). Infrred touch technology s response detector in niml reserch. Behvior Reserch Methods, Instruments, & Computers, 19, ROBERS, S. (1981). Isoltion ofn internl clock. Journl ofexperimentl Psychology: Animl Behvior Processes, 7, SPECH, M. L., & EDARDS, C. A. (1988). Pigeons' (Columb Livi) use of globl nd locl cues for sptil memory. Animl Behviour, 36, SUZUKI, S., AUGERINOS, G., & BLACK, A. (1980). Stimulus control of sptil behvior on the eight-rm rdil mze in rts. Lerning & Motivtion, 11, INBERGEN, N. (1972). he niml nd its orld. Cmbridge, MA: Hrvrd University Press. VANDER ALL, S. B. (1982). An experimentl nlysis ofcche recovery in Clrk's nutcrcker. Animl Behviour, 30, VON FRISCH, K. (1977). Aus dem leben der bienen. Berlin: Springer. EHNER, R., & RAEBER, F. (1979). Visul sptil memories ofdesert nts, genus Ctglyphis. Journl ofcomprtive Physiology A, 142, RIGH, A. A., COOK, R. G., RIVERA, J. J., SANDS, S. F., & DELIUS, J. D. (1988). Concept lerning by pigeons: Mtching-to-smple ith tril-unique video picture stimuli. Animl Lerning & Behvior, 16, (Mnuscript received August 7, 1991; revision ccepted for publiction Mrch 6, 1992.)

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