The use of relative and absolute bearings by Clark's nutcrackers, Nucifraga columbiana

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1 University f Nebraska - Lincln DigitalCmmns@University f Nebraska - Lincln Papers in Behavir and Bilgical Sciences Papers in the Bilgical Sciences 2001 The use f relative and abslute bearings by Clark's nutcrackers, Nucifraga clumbiana Juli E. Jnes University f Massachusetts - Amherst Alan C. Kamil University f Nebraska - Lincln, akamil1@unl.edu Fllw this and additinal wrks at: Part f the Behavir and Ethlgy Cmmns Jnes, Juli E. and Kamil, Alan C., "The use f relative and abslute bearings by Clark's nutcrackers, Nucifraga clumbiana" (2001). Papers in Behavir and Bilgical Sciences This Article is brught t yu fr free and pen access by the Papers in the Bilgical Sciences at DigitalCmmns@University f Nebraska - Lincln. It has been accepted fr inclusin in Papers in Behavir and Bilgical Sciences by an authrized administratr f DigitalCmmns@University f Nebraska - Lincln.

2 Animal Learning & Behavir (2) The use f relative and abslute bearings by Clark's nutcrackers, Nucifraga clumbiana JUUE.JONES University f Massachusetts, Amherst, Massachusetts and ALAN C. KAMIL University f Nebraska, Lincln, Nebraska Tw grups f Clark's nutcrackers were trained t find buried seeds whse lcatin was defined by a cnstant angle frm tw landmarks whse interlandmark distance and psitin in the rm varied acrss trials. The first grup had a landmark array that was always placed in the same rientatin with respect t the walls, allwing the animals t use bth relative and abslute bearings. The secnd grup had a landmark array that rtated acrss trials s that nly relative bearings culd be used t lcate the seeds. The birds in each grup learned the task and transferred t new interlandmark distances bth within and beynd the range f training distances. Results frm these experiments indicate that nutcrackers can learn a gemetric relatinship that relies exclusively n relative bearings even thugh the use f abslute bearing yields mre efficient search. The hidden gal technique (Bssema & Pt, 1974) has been widely used t study hw animals use landmarks t find a lcatin (Bennett, 1993; Guld-Beierle & Kamil, I! 1996, 1998; Spetch, Cheng, & MacDnald, 1996; Spetch et al., 1997). Over many trials, fd is hidden in a lcatin i that bears a cnstant spatial relatinship t a set f land marks. The landmarks themselves are mved abut the experimental rm while maintaining a cnstant relatinship amng themselves and with respect t the crrect lcatin. Once the prblem has been learned, buried-seed trials in which the landmark array is manipulated are used t discern which aspect f the spatial relatinship between the landmarks and the gal lcatin cntrl search. In mst such experiments, the landmarks are presented at the same distance and directin frm the gal thrughut training (e.g., Bssema & Pt, 1974; Guld Beierle & Kamil, 1996; Spetch et al., 1996; Spetch et al., 1997). A disadvantage f this prcedure is that when experimenters alter landmark-landmark gemetry during prbe tests, gal-landmark gemetry is als changed. This led us (Kamil & Jnes, 1997) t develp a mdificatin f the hidden gal prcedure in which the gemetric relatinship between the gal and the landmarks was held cnstant during training. In this riginal experiment, the distance between tw landmarks varied thrughut training and the gal was always placed halfway between the landmarks. Thus, the gemetric relatinship f halfway was maintained, but distance between the landmarks and between the gal and the landmarks varied. The This research was supprted by Grant IBN frm the Natinal Science Fundatin. Crrespndence shuld be addressed t 1. E. Jnes, University f Massachusetts, Neurscience and Behavir Prgram, Amherst, MA ( jnes@cns.umass.edu). nutcrackers readily learned the task. When the landmarks were presented at nvel interlandmark distances within the range with which they had been trained, birds cntinued t search halfway between the landmarks, demnstrating they had prbably learned smething abut the gemetric relatinship between the gal and landmarks rather than memrizing the training cnfiguratins (but see Biegler, McGregr, & Healy, 1999, and the reply by Kamil & Jnes, 1999). We have subsequently extended these findings by training different grups f nutcrackers with different gemetric principles gverning the spatial relatinship between gal and landmarks (Kamil & Jnes, 2000). We fund that nutcrackers culd learn t find the pint nequarter f the way between tw landmarks as well as halfway between. We als fund that nutcrackers culd learn t find the third pint f a triangle, whse base was defined by the landmarks, when the gal was lcated at a cnstant directin (bearing r angle) frm the landmarks while distance varied. The birds als generalized all three f these gemetric rules t nvel interlandmark distances, bth within and utside the range f training distances. Thrughut the training stages f these experiments, the landmarks were always presented nrth and suth f each ther, parallel t tw f the walls f the rm and perpendicular t the ther tw. Therefre, the birds culd have used either (r bth) f tw different methds f judging directin, abslute r relative bearings. Abslute bearings refer t a cmpass reading (e.g., nrth f the suth landmark). Relative bearings refer t using the apparent angular distance between the landmarks and d nt require reference t a cmpass (althugh they can be determined by cmparing tw cmpass directins). Rtating the landmark array wuld place these tw types f bear- Cpyright 2001 Psychnmic Sciety, Inc. 120

3 RELATIVE AND ABSOLUTE BEARING APPLIED TO A GEOMETRIC PROBLEM 121 ings in cnflict. Fr example, suppse there are tw landmarks lcated nrth and suth f each ther and that a gal is lcated nrthwest f ne landmark and suthwest f the ther. If the landmark array is nw rtated s that the landmarks are east and west f each ther, the abslute bearings will nt intersect. But there will still be a set f pints at which the relative bearings are unchanged. We fund that when the landmark array was slightly rtated during prbe tests, search ccurred at lcatins that suggested the birds cmprmised between searching at the lcatin predicted by relative bearings and the lcatin predicted by the abslute bearings. Hwever, when the landmark array was rtated 90 s that the landmarks were placed east and west f each ther, the birds ignred relative bearings and searched at the lcatin predicted by use f an abslute bearing frm ne landmark (Kamil & Jnes, 1997, 2000). These results raise the questin f whether r nt Clark's nutcrackers can learn a gemetric task that requires the use f relative bearings. The purpse f the present experiment was t cmpare the perfrmance f a grup f nutcrackers required t use relative bearings with that f a grup that culd use abslute bearings as well as relative bearings. We apprached this prblem by cmparing the perfrmance f a grup trained with landmarks whse rientatin rtated during training with that f a cntrl grup fr whm the rientatin f the landmarks was cnstant during training. EXPERIMENT 1 Methd Subjects. Ten experimentally naive Clark's nutcrackers, randmly divided int tw grups, served as subjects fr all experiments. One bird died within the first 3 weeks f the initial training. The birds were individually hused at the University f Nebraska Schl f Bilgical Sciences in a clny rm kept at 22 Celsius n a 14: 10-h light:dark cycle. Thrughut the curse f the experiment the birds were kept at apprximately 90% f their free-feeding weights by cntrlled daily feedings f turkey starter, sunflwer seeds, parrt pellets, mealwrms, pine seeds, and vitamin supplements. The birds had unlimited access t water and grit in their hme cages. Apparatus The experiment was cnducted in a 4.4 by 2.7 m bservatin rm. The birds entered the rm thrugh a prthle n the east wall just belw a smked glass bservatin windw with a drawn curtain. The bserver entrance dr was nrth f the prthle n the east wall. Behind the prthle, utside the bservatin rm, was a hlding cage in which the birds were kept between trials. A Panasnic vide camera (Mdel WV-BL200) was munted abve the ceiling and cnnected t a vide mnitr and VCR (Mdel JVC BR- 3200U). Subjects were bserved thrugh the bservatin windw and n the vide mnitr. A 7 -cm raised flr began 90 cm frm the east wall, which was brdered by a 15-cm high edge. The wden flr extended the width f the rm t the west wall and was cvered with a 2-cm layer f cellulse substrate. Fur centrally lcated flurescent lights illuminated the rm. There were tw 40-cm high landmarks (blue and red PVC pipe 2.5 cm in diameter). The distance between the landmarks varied (in increments f 24 cm) frm 36 t 108 cm during training and frm 24 t 120 cm during transfer tests. The ttal area ver which the landmark array was presented, measured frm the center f the rm, was ± 60 cm in the east-west directin and ± 40 cm in the nrth-suth directin. Within this area there were 116 lcatins where the landmark array culd be placed. The rm was divided int fur equal quadrants, and the array was placed in each quadrant nce per day (Figure 1). Each day the placement f the apparatus within each quadrant was randmly assigned, as was the trial rder f the quadrants. Sampling f psitins was dne randmly withut replacement, ensuring that n bird received the same target psitin twice within a blck f 116 trials (29 days). Habituatin Habituatin testing was cnducted fr tw trials per day fr 5 days. On each trial f the 1 st day, tw unshelled pine seeds were placed n the surface f the substrate n a 3.5-cm diameter plastic lid in the center f the rm. Each bird entered the rm thrugh the prthle and the sessin cntinued until the seeds had been fund. The fllwing days, the substrate was placed in the lid cmpletely cvering the seeds. This prcedure insured that the birds used the lid as a cue t seed lcatin. Fr each trial fllwing the 1 st day, the lid was mved t varius lcatins within the rm. Training Fr each grup the arbitrary line that cnnected the landmarks defined the base fa triangle. The third pint f the triangle was the gal lcatin. The gal was always placed at equal 45 angles frm the base f the triangle and each landmark, thus creating a right triangle. The difference between the grups was in the rientatin f the landmark array with respect t the rm. Fr the unrtated grup, the landmark rientatin was always nrth-suth s that the line cnnecting the landmarks was always parallel t the walls n the east and west sides f the rm and perpendicular t the walls n the nrth and suth. Fr the rtated grup, five different landmark rientatins were used: 0 (nrth-suth, identical t the unrtated grup) and rtated 30 and 60 clckwise and cunterclckwise (Figure 1). The presentatin f the rtated psitins acrss training trials was rganized int a cmpletely randmized blck design. The birds were brught individually frm their hme cage t the hlding cage utside the bservatin rm. Initially, the lights in the hlding rm were ff and the lights in the bservatin rm were n. The sliding dr in the prthle was pened, and a bird was allwed t enter the rm. When the bird reached criterin fr cmpleting the trial, the bservatin rm lights were turned ff, the sliding dr was pened, the hlding rm lights were turned n, and the bird flew back t the hlding cage. Trials cntinued until the gal was lcated, 40 prbes were made, r the bird had been in the rm fr 10 min. The definitin fa prbe was when the bird's beak came int cntact with the substrate. If the bird was remved frm the rm prir t finding the seeds, it was nt allwed anther attempt at that psitin. After the cmpletin ffur trials. the bird was taken back t its hme cage. Fur different interlandmark distances were used in training: , 84, and 108 cm. Each interlandmark distance was presented in randm rder nce a day, with the exceptin that each interlandmark distance must have been a buried-seed trial nce ut f every fur buried-seed trials in a randm rder. Fr the first 30 days f training each bird had three training trials preceding ne buriedseed trial. During the training trials, a part f the lid was expsed. During a buried-seed trial, the seeds and lid were buried, and the sessin was videtaped and analyzed t prvide acquisitin data. The buried-seed trials were rganized int a cmpletely randmized blck design, and the interlandmark distances nt in the buried-seed trial each day were randmly assigned t the training trials. After

4 122 JONES AND KAMIL A.-N B Figure 1. Diagrammatic representatin f the psitin f the landmark array and gal psitin fr three trials fr each grup. (A) The cnditins fr the unrtated grup: Interlandmark distance varied; psitin in rm varied but the landmark array always stayed in the same rientatin with respect t the walls. (B) The cnditins fr the rtated grup: Interlandmark distance varied; psitin in rm varied and the rientatin f the landmark array was rtated. Black circle: blue landmark. Gray circle: red landmark. Crss: lcatin fthe buried seed. Black line: relative bearing frm the blue landmark. Gray line: relative bearing frm the red landmark. Dashed line: hypthetical line that cnnects the landmarks. 30 days, tw buried-seed trials per day n Trials 3 and 4 were presented fr an additinal 30 days. Finally, fr 10 additinal days all trials presented were buried-seed trials. Beginning n Day 71 f training, we intrduced ne "n-seed" trial (prbe trial) each day. Fr a prbe trial, neither the lid nr the seeds were placed in the rm, and the bird was remved frm the rm after five digs. This n-seed prbe trial was randmly assigned t the secnd, third, r furth trial each day. The intrductin f the prbe trial phase lasted fr 8 days, during which each bird received tw prbe trials at each training interlandmark distance. A prbe trial at each interlandmark distance was experi.enced prir t receiving a secnd prbe trial at an interlandmark distance. Determining Psitin f Prbes and Data Analyses T determine the psitin f the prbes, each sessin was analyzed thrugh a review f the videtaped trial n a Panasnic VCR (Mdel AG-1730) that allwed frame-by-frame playback and was attached t a TARGA videgraph system. First the landmark and gal psitins were recrded, and then each prbe lcatin was recrded using a digitizing pad. The bird's first 10 digs were recrded n buried-seed trials, and all 5 digs were recrded n prbe trials. Each marked lcatin was assigned an X and Y crdinate by the TARGA videgraph system. Fr analysis, the crdinates fr each f the first 5 digs were subtracted frm thse f the gal lcatin and cnverted t centimeters. The abslute value f each errr dis-

5 RELATIVE AND ABSOLUTE BEARING APPLIED TO A GEOMETRIC PROBLEM 123 tance was then averaged. The X errr was related t the errr in the east-west axis, and the Yerrr was related t the errr in the nrthsuth axis (discussed belw). Frm the average X and Yerrr fr each day, ttal errr distance was calculated by using the Pythagrean therem. Data analysis was carried ut by analyses f variance (ANOVAs); subsequent Fisher's LSD tests were carried ut nly after significant verall F ratis (with alpha.05). Results The training data were divided int 13 blcks f 10 buried-seed trials each and analyzed with a grup X blck repeated measures ANOVA. As the experiment prceeded, perfrmance imprved, resulting in a statistically significant effect f blck [F(12,84) = 44.79,p <.05; Figure 2]. The unrtated grup cnsistently perfrmed with a higher level f accuracy than the rtated grup, but this difference was nt statistically significant [F( 1,7) = 5.10, p >.05], nr was there any significant grup X blck interactin [F(12,84) < 1]. A subsequent Fisher's LSD revealed that there was n significant difference amng Blcks Next we cmpared perfrmance n n-seed trials with perfrmance n trials with a seed buried at the gal. In this cmparisn, nly the first tw prbes frm each trial were included, because the birds usually fund the seed within tw t three prbes n seed trials, and using mre prbes wuld intrduce a bias. In rder t determine whether the absence f a seed affected perfrmance, ttal errr distance data cllected during the intrductin f n-seed trials perid was subjected t an ANOVA in which seed/n seed and grups were the factrs. Perfrmance did nt differ n buried-seed trials and prbe trials [F(1,7) < 1]. Bth grups perfrmed at the same level f accuracy [F(1,7) = 1.78,p>.05], and there was n grup X cnditin interactin [F(1, 7) = 4.64, p <.05]. Since there was n difference between prbe trials and buried-seed trials, we cmbined the data frm all 32 trials during which the prbe prcedure was intrduced fr the fllwing analyses. An ANOVA was perfrmed using the cmbined data n the effect f interlandmark distance and grup n ttal errr distance. As the interlandmark distance increased, ttal errr distance als increased [F(3,21) = 10.14, p <.05]. The unrtated grup perfrmed with higher accuracy thrughut the intrductin f the prbe trials phase, but this difference was nt significant [F(1,7) = 4.46,p>.05]. Althugh increasing the interlandmark distance appeared t affect the perfrmance f the rtated grup mre than that f the unrtated grup, the grup X interlandmark distance interactin was nt significant [F(3,21) = 2.04, p>.05]. Next, errr distance was brken dwn int tw axis cmpnents. The first axis was parallel t the hypthetical line cnnecting the landmarks, and the secnd axis was perpendicular t that line. Fr the rtated grup, the rientatin fthese lines changed, in glbal terms, as the rientatin f the landmark array was rtated Rtated... Unrtated 60 - E 50 e U -- :l.- :I.- :I.- 40 W «S 30 e Trial Blcks Figure 2. Mean distance ±SE between the lcatin f the first five digs and the gal lcatin n buried-seed trials thrughut training. Each blck cntains 10 buried-seed trials.

6 124 JONES AND KAMIL A 25 B Unrtated -.- Rtated.... Unrtated -.- Rtated E W ",' - 15 E - e 10 W 5... f Interlandmark Distance Interlandmark Distance Figure 3. (A) Mean errr distance ±SE between the lcatin f the first tw digs and the gal lcatin in the parallel axis. (8) Mean errr distance ±SE between the lcatin f the first tw digs and the gal lcatin in the perpendicular axis. Separate ANOVAs were perfrmed n errr distance in each axis, with grup and interlandmark distance as factrs. In the parallel axis, as interlandmark distance increased, errr distance als increased [F(3,21) = 8.32, p <.05]. Bth grups perfrmed at apprximately the same level f accuracy [F(l,7) < 1], and there was n grup X interlandmark distance interactin [F(3,21) = 1.41, p >.05]. In the perpendicular axis, the unrtated grup perfrmed with higher accuracy than the rtated grup [F(l,7) = 6.80,p <.05]. Again, as interlandmark distance increased, errr distance als increased [F(3,21) = 5.17,p <.05], and there was n grup X interlandmark distance interactin [F(3,21) = 1.34,p>.05; Figure 3]. Cnsidering that the rtated grup was tested at five different rtated psitins, rientatin f the landmark array culd have affected search accuracy. The rtated grup's ttal errr distance was analyzed with a rtated psitin by interlandmark distance ANOVA. The rientatin f the landmark array had n effect n accuracy [F( 4,16) < 1]. As interlandmark distance increased, errr distance increased [F(3,12) = 5.76, p <.05], and there was n interlandmark distance X rtated psitin interactin [F(l6,60) < 1]. Discussin These results have fur implicatins. First, the accuracy f the rtated grup demnstrates that hutcrackers can use relative bearings t find a hidden gal. Fr this grup, the directinal relatinships fthe gal-landmark array varied in abslute terms thrughut acquisitin, yet the nutcrackers appeared t learn as rapidly as the unrtated grup. In fact, the results leave sme dubt abut whether r nt learning relative bearings is mre difficult than learning abslute bearings. Althugh the evidence is equivcal, we suspect that there is a small quantitative difference. Several statistical tests apprached significance, and the unrtated grup did perfrm significantly better than the rtated grup in the perpendicular axis. Hwever, this issue is nt as imprtant as the mre basic finding that the birds were able t learn this prblem abut as readily as the birds that learned the prblem when abslute bearings culd be used. Secnd, the fact that the rtated grup perfrmed wrse than the unrtated grup in the perpendicular but nt the parallel axis suggests a particular hypthesis abut hw the grups may have differed. Suppse that the birds in bth grups used tw lines t lcate the gal, ne line alng which all pints were equidistant frm the landmarks and the ther line a bearing frm ne r bth landmarks. The equidistant line is perpendicular t the line cnnecting the landmarks and can be fund withut the use f bearings. Fr example, apparent distance t the landmarks culd be used. Hwever, the ther line must invlve the use f bearings. This bearing culd have been an abslute cmpass bearing fr the unrtated grup, but nt the rtated grup. Therefre, the finding that the grup difference was limited t the perpendicular axis suggests either that relative bearings are less accurate than abs-

7 RELATIVE AND ABSOLUTE BEARING APPLIED TO A GEOMETRIC PROBLEM 125 lute bearings r that tw surces f infrmatin are mre accurate than ne. Third, as interlandmark distance increased, errr distance increased. This result is similar t findings frm ur tw previus hidden gal studies (Kamil & Jnes, 1997, 2000). The increasing errr distance is prbably due t increased difficulty judging distance and directin as distance frm an bject increases. While the increase in distance estimatin errr may be an instance f Weber's law (Cheng, 1989), the increase in errr in directinal estimatin may nt be. If the directinal errr is cnstant in angular terms (measured in degrees), this wuld lead t increased errr when measured in centimeters. Finally, the prbe trial data indicate that the birds did nt rely n lfactry cues t lcate the buried seeds, replicating earlier cache recvery (Balda, 1980; Kamil, Balda, Olsn, & Gd, 1993) and hidden gal studies (Guld Beierle & Kamil, 1996; Kamil & Jnes, 1997,2000). This allwed us t use prbe trials withut seeds t investigate effects f manipulatins f the landmark array n search. The use f prbe trials minimizes the prblem f learning during manipulated trials. EXPERIMENT 2 During Experiment 1, the birds in each grup were trained with fur specific interlandmark distances. Experiment 2 was designed t determine perfrmance with nvel interlandmark distances. Tw types f nvel inter- landmark distances can be tested, thse within the testing range (interplated) and thse utside the testing range (extraplated). Results frm ur previus research have shwn that birds trained either t find a gal lcated directly between tw landmarks r t find a gal with a cnstant directinal relatinship t tw landmarks (as in the cntrl grup f Experiment 1) generalized interplated as well as extraplated interlandmark distances. In cntrast, nutcrackers trained t find a gal withut a cnstant directinal relatinship t tw landmarks generalized nly t interplated distances (Kamil & Jnes, 2000). As Biegler et al. (1999) have pinted ut, this failure t generalize t extraplated distances suggests that these birds may have learned the prblem by memrizing fur vectrs that crrespnd t the training interlandmark distances-as fur separate prblems rather than as a single prblem. Therefre, it was f cnsiderable interest t determine whether birds trained with relative bearings culd generalize search t bth interplated and extraplated interlandmark distances. Methd Prcedure. The secnd experiment began immediately fllwing Experiment 1: The same subjects, assignments t grups, and materials and methds were used. Each day the birds received three buried seed trials and ne prbe trial. Training interlandmark distances (36, 60, 84, and 108 cm) were used fr all buried-seed trials. Fr the entire training, interlandmark distances and five new interlandmark distances 24, 48, 72, 96, and 120 cm apart were used as prbe trials. A prbe trial was randmly assigned t Trial 2, three Unrtated Rtated E u -- :I... t=20 W... cts I- 10 L Interlandmark Distance (cm) Figure 4. Mean ttal errr distance between the lcatin f the first five digs and the gal lcatin n prbe trials thrughut transfer. Each interlandmark distance cntains three prbe trials fr each bird. Dashed line: rtated grup's predicted line. Brken dashed line: unrtated grup's predicted line. Predicted lines were calculated using training interlandmark distance prbe trials frm Experiment 1.

8 126 JONES AND KAMIL r fur each day. Acrss the 27-day experiment each bird received three prbe trials at each f the nine interlandmark distances in a randmized blck design. Fr the rtated grup, interlandmark distance was cunterbalanced acrss rtatin psitin fr the grup. Results We analyzed errr distance during transfer testing with a grup X interlandmark distance mixed ANOVA. The unrtated grup perfrmed significantly better than the rtated grup [F(1,7) = 18.3,p <.05]. As the interlandmark distance increased, the birds' accuracy decreased [F(8,56) = 9.8, p <.05], but there was n significant interactin [F(8,56) = 1.45, p >.05; Figure 4]. The rtated grup was very inaccurate at the shrtest interlandmark distance. Therefre, we ran independent ANOVAs n the effect f interlandmark distance fr each grup. Fr the rtated grup, there was a significant effect f interlandmark distance [F(8,32) = 6.81,p <.05]. A subsequent Fisher's LSD test was carried ut in which the ttal errr at each interlandmark distance was cmpared with the ttal errr with the next greater interlandmark distance. Only the difference between 24 and 36 cm was significant. There was als an effect f interlandmark distance fr the unrtated grup [F(8,24) = 5.97, p <.05]. A similar Fisher's LSD analysis revealed n differences in ttal errr between any adjacent pairs f interlandmark distances. It has been demnstrated in this experiment and previus experiments (Kamil & Jnes, 1997,2000) that as interlandmark distance increases, search accuracy decreases. In rder t examine the magnitude f errr with this general trend remved, we selected the data frm Experiment 1, which cnsisted f the training interlandmark distances (36, 60, 84, and 108 cm), and calculated the linear equatin fr each grup. The unrtated grup's linear equatin was Y = X while the rtated grup's linear equatin was Y = X (Figure 4). Frm the linear equatins we calculated the predicted errr distance fr each new interlandmark distance (24,48, 72, 96, and 120 cm) and analyzed the deviatins frm the predicted line with a tw-way mixed ANOVA with grup and cnditin as factrs. Deviatins were calculated as fllws: Bth training and transfer prbe test data fr each trial were subtracted frm the predicted line at the apprpriate interlandmark distance. This errr term was used as the respnse variable in the AN OVA. The levels f cnditin were cntrl (training), interplated, and extraplated interlandmark distances. The rtated grup had mre deviatin frm its predicted line than the unrtated grup [F(1,7) = 59.32,p <.05]. When the landmarks were placed at the extraplated interlandmark distances errr distance was mre deviant frm the predicted line than n training r interplated cnditins [F(2,14) = 14.62,p <.05] and there was a grup X cnditin interactin [F(2,14) = 7.43,p <.05]. A subsequent Fisher's LSD revealed that the effect Qf interlandmark distances was due t the decrease in accuracy fr the rtated grup at the smallest interlandmark distance (which was an extraplated distance). Discussin Our previus research with generalizatin t nvel interlandmark distances suggests that ne f tw utcmes shuld have resulted. Either the birds shuld have generalized nly t interplated distances r they shuld have generalized t all nvel distances. Hwever, while bth grups clearly generalized accurately t interplated distances, the results frm the extraplated distances (24 and 120 cm) were mre cmplicated. Search errr and deviatin frm the predicted line increased when the 24- cm interlandmark distance was presented t the rtated grup but nt the unrtated grup. Hwever, fr bth grups there was n difference in perfrmance measured at the 108-cm distance r an increase in deviatin frm the predicted line, even thugh such a difference might be expected n the basis f increasing interlandmark distance alne. Thus the results suggest that the birds transferred t the extraplated interlandmark distance that was lnger than any training distance, but nt t the shrter extraplated distance. While it is pssible that these results demnstrate a failure t generalize t extraplated distances, it is als pssible that the pr perfrmance at the 24-cm interlandmark distance may have been a mre specific effect. When the landmarks were 24 cm apart, the gal-landmark distance was nly cm and the birds appeared reluctant t search this clse t the landmarks. If this hypthesis is crrect, then birds trained with interlandmark distances f 48 t 144 cm wuld perfrm accurately when presented with an extraplated interlandmark distance f 36 cm. Then the transfer shwn by bth grups during Experiment 2 wuld be due t the acquisitin f a general principle based n bearings. In the case f the unrtated grup, this principle culd have been based n the use f either abslute r relative bearings, whereas the principle fr the rtated grup culd have been based slely n relative bearings. EXPERIMENT 3 It is apparent that the birds in bth grups were able t generalize t new interlandmark distances; yet, the ability t generalize t nvel rientatins within the rm has thus far nt been tested. In previus experiments (Kamil & Jnes, 1997, 2000), nutcrackers were trained with the landmark array in a fixed rientatin, and prbe tests were perfrmed in which the array was rtated away frm the training rientatin frm 22 t 180. Results indicated that when the landmark array was slightly rtated (22 0), the birds tended t fllw the rtatin, suggesting the use f relative bearings. Hwever, when the landmark array rtatin was greater than 45, the birds tended t use abslute bearings. This leads t the predictin that the birds

9 RELATIVE AND ABSOLUTE BEARING APPLIED TO A GEOMETRIC PROBLEM 127 in the rtated grup wuld generalize t nvel rientatins because they have learned t use relative bearings. In cntrast, the birds in the unrtated grup shuld nt generalize when nvel rientatins are presented because they tend t favr the use f abslute bearings. The purpse f Experiment 3 was t test this predictin. Methd Prcedure. The third experiment began immediately after Experiment 2 and the same subjects, assignments t grups, and materials and methds were used as thse in Experiment 1. The birds received fur trials a day with each interlandmark distance (36, 60, 84, and 108 cm) presented nce, including ne prbe trial, randmly scheduled fr Trial 2, 3, r 4. There were three stages t this experiment. During the first stage (24 days), the landmarks were presented either in a cntrl psitin r in a rtated psitin n each prbe trial. There were six rtated test psitins that were new t bth grups. These psitins were 15, 45, r 75, bth clckwise and cunterclckwise frm the 0 rtatin rientatin. The cntrl psitin was 0 fr the unrtated grup. Fr the rtated grup the cntrl psitins were the five rientatins used during training. Each bird received a ttal f tw prbe trials at each new rientatin at the interlandmark distance f 84 cm. During the secnd stage (32 days), interlandmark distances f60 and 84 cm were used fr large rtatin prbe trials. The birds experienced cntrl, 90 rtatin (clckwise and cunterclckwise) and a 180 rtatin twice at each f the tw interlandmark distances. In the third stage (8 days), each bird experienced tw prbe trials with the blue landmark remved and tw prbe trials with the red landmark remved. These prbe trials were presented every ther day, in randm rder. On the alternate days withut a single-landmark prbe trial, prbe cntrl trials at riginal training interlandmark distances were presented. Results Small rtatin (15, 45, 75 ). Fr the fllwing set f analyses, we assumed that the birds were applying ne f tw strategies when presented with a nvel rientatin. The first assumptin is based n the idea that the birds were applying abslute bearing infrmatin t the situatin, whereas the secnd assumptin is that the birds were utilizing relative bearings t lcate the gal. Fr the fllwing analysis, errr was calculated frm the relative rule lcatin, which signifies the predicted placement f the gal determined by relative bearings. Thus, if the birds were applying the abslute bearing strategy, then errr distance frm the relative rule lcatin shuld increase as degree f rtatin increases. In rder t test whether the directin f rtatin had an effect n errr distance, a grup X directin f rtatin ANOVA was perfrmed n ttal errr distance (as measured frm the relative rule lcatin), and there was n effect f directin f rtatin (clckwise r cunterclckwise) [F(2,14) = 2.15,p >.05]. Therefre we cllapsed acrss directin f rtatin fr the remaining analyses. The effect f rtatin n ttal errr distance frm the relative rule lcatin was analyzed with a grup X degree f rtatin (cntrl, 15,45, and 75 ) ANOVA. Overall, the rtated grup searched clser t the relative rule lcatin than did the unrtated grup [F(1,21) = 50.3, p <.05]. The rtated grup's errr distance frm the relative rule lcatin stayed cnsistent acrss newly presented rtated psitins relative t the cntrl trials. In cntrast, the unrtated grup's errr distance increased as 80,.--.. E u '-"'" 60 t- O t- t- W 40 - CO +-' _ Unrtated 1 _ Rtated I r I I I, I Cntrl 15CW 15CCW 45CW 45CCW 75CW 75CCW Rtatin f the Landmark Array - r Figure 5. Mean ttal errr distance ±SE frm the crrect lcatin f search predicted by relative bearings. Black bars: unrtated grup's ttal errr distance. Gray bars: rtated grup's ttal errr distance.

10 128 JONES AND KAMIL the degree f rtatin increased, resulting in bth a significant main effect f rtatin [F(3,21) = 22.09, p <.05] and a significant grup X degree f rtatin interactin [F(3,21) = 18.88,p <.05; Figure 5]. Large rtatin (90 ). We first analyzed the results f the large rtatin experiment n ttal errr distance frm the relative rule lcatin with a grup X interlandmark distance X cnditin repeated measures ANOYA. The levels f cnditin were cntrl and 90 rtated. The unrtated grup searched further away frm the relative rule lcatin than did the rtated grup [F(l,7) = 14.59, p <.05], and there was n effect f interlandmark distance [F(l, 7) = 1.94, p >.05]. Bth grups were mre accurate n cntrl trials than n trials during which nvel rientatins were presented [F(l,7) = ,p <.05]. There was als a significant grup X cnditin interactin [F(l,7) = 18.5,p <.05] and a significant landmark X cnditin interactin [F(l,7) = 6.25,p <.05]. The search patterns f the tw grups appeared t differ qualitatively when the landmark array was rtated 90 either clckwise r cunterclckwise. In particular, the search pattern f the unrtated grup appeared t be riented tward the west landmark (Figure 6). Therefre, we perfrmed a separate analysis fr the unrtated grup. We calculated the errr distance frm tw predicted abslute bearings, nrthwest and suthwest frm the west landmark, and selected the lwer errr distance (per dig) fr analysis. A cnditin (cntrl vs. 90 rtatin) X interlandmark distance repeated measures ANOYA was perfrmed n these errr distances. The unrtated grup was clser t the predicted abslute bearing n cntrl trials than n rtated trials [F(l,3) = 20.73,p <.05], and there was n effect f interlandmark distance [F( 1,3) < 1] nr any interactin [F( 1,3) < 1]. Psitin reversal (180 ). When the landmarks were rtated 180 there were tw pssible strategies that the nutcrackers culd use. The first wuld be t use relative bearings, which wuld invlve searching nrtheast frm the red landmark and sutheast frm the blue landmark. The secnd wuld be t rely n abslute bearings, searching nrthwest frm the red landmark and suthwest frm the blue landmark. The effect f the 180 rtatin n search accuracy was analyzed with a grup X interlandmark distance by predicted lcatin (relative vs. abslute) ANOYA. Errr distance was measured as the distance f search t the crrect gemetric lcatin. The grups did nt differ in errr distance [F(l,7) = 2.63,p >.05]. The birds searched clser t the lcatin predicted by the use f abslute rather than relative bearings [F( 1,7) = , p <.05]. This pattern f search was nt affected by interlandmark distance [F(l,7) = 2.42, p <.05; Figure 7]. Nne f the interactins were significant. A c E -L e L.. W -110 '-----' '--'..c +-' :::J en I..c t Z B "- 70 ':. / f X D "-.. X.'0-50 -/ /.. / East-West Errr (em) Figure 6. Maps f trial placement f search n 90 rtated (clckwise and cunterclckwise) trials at the interlandmark distances f60 and 84 cm apart. Filled circles: red landmark. Unfilled circles: blue landmark. Crss: gal lcatin predicted by relative bearings. Squares: mean search lcatin fr each bird in the un rtated grup. Triangle: mean search lcatin fr each bird in the rtated grup. Dashed line: predicted abslute bearing. Interlandmark distance and rientatin: (A) 90 rtated clckwise, 60 cm. (B) 90 rtated clckwise, 84 cm. (C) 90 rtated cunterclckwise, 60 cm. (D) 90 rtated cunterclckwise, 84 cm.

11 RELATIVE AND ABSOLUTE BEARING APPLIED TO A GEOMETRIC PROBLEM A ( E () J. 10 J X W r:. B D... 0 C/) I.r: e 10 ti! 0 Z 10 r,. X C East-West Errr (em) Figure 7. Maps ftrial placement f search n cntrl and rtated trials at the interlandmark distances f 60 and 84 cm apart. Filled circle: red landmark. Unfilled circle: blue landmark. Crss: gal lcatin predicted by relative bearings. Square: mean search lcatin fr each bird in the un rtated grup. Triangle: mean search lcatin fr each bird in the rtated grup. Interlandmark distance and rientatin: (A) 0 rtated, 60 cm. (8) 0 rtated, 84 cm. (C) rtated, 60 cm. (0) rtated, 84 cm. Since it appears that the animals did nt fllw the rtatin tests, we wanted t determine whether search accuracy (frm the lcatin where the seed wuld be buried if the landmark array was nt rtated) changed between the rtatin and a cntrl prbe trial (in this case the landmarks were placed at 0 0 rtatin). Thus, we cmpared ttal errr distance (frm the lcatin predicted by the use f abslute bearings) frm trials during which the landmark array was rtated with the ttal errr distance during cntrl trials with a grup X cnditin ANOVA. There was neither a significant difference between the grups [F(l,7) = 3.92,p >.05] nr an effect f the rtatin [F(1,7) = 1.7,p>.05]. There was als n grup X cnditin interactin [F( 1,7) = 2.64, p >.05]. Single landmark. We analyzed the single landmark prbe data by calculating the errr distance between each dig and each f tw predicted bearings: (1) the crrect directin frm the presented landmark (nrthwest frm the blue landmark and suthwest frm the red landmark); and (2) the ppsite bearing (suthwest frm the blue and nrthwest frm the red landmark). Distance frm bth bearings was calculated, because if the birds did nt use the clr f the landmark as a cue, then search alng either abslute bearing is a pssibility. Thus, errr distance t each bearing was calculated fr each dig, and the lwer errr distance was used fr analysis. We carried ut a similar calculatin fr cntrl trials, n the basis f the distance frm each dig t the abslute bearing. Data were analyzed with a grup X cnditin (cntrl vs. single landmark) ANOVA. The single landmark level was cllapsed acrss landmark clr, and the cntrl trial level was cllapsed acrss the interlandmark distances f 60 and 84 cm. The unrtated grup searched with higher accuracy than the rtated grup [F(1,7) = 10.52, p <.05], and bth grups searched clser t the predicted lines n cntrl trials than n single landmark trials [F(1,7) = 12.12,p <.05], but there was n grup X cnditin interactin [F(1,7) = 3.58,p>.05; Figure 8]. Discussin It has been previusly demnstrated that when nutcrackers are trained with tw landmarks always presented nrth and suth f each ther and then tested with small rtatins f the array, the birds use bth relative and abslute bearings (Kamil & Jnes, 1997,2000). The search behavir f the unrtated grup during small rtatin prbe trials was cnsistent with this pattern. In cntrast, the rtated grup appeared t use relative bearings when tested with nvel rientatins within 15 0 f training psitins (Figure 5). Hwever, the rtated grup did nt generalize search t new rientatins greater than 15 0 This suggests a limitatin in the birds' ability t generalize rel-

12 RELATIVE AND ABSOLUTE BEARING APPLIED TO A GEOMETRIC PROBLEM 131 n clustering f search r cmmn search pattern when a landmark was remved, nr was there a cnsistent search pattern between the tw landmark clrs. Whereas the rtated grup learned a gemetric principle based n relative bearings (which require tw landmarks), the unrtated grup learned a gemetric principle based n abslute bearings (which can be applied t a single landmark). GENERAL DISCUSSION When Clark's nutcrackers stre seeds, they must encde infrmatin abut the lcatin f the fd in rder t relcate the cache mnths later. The results f previus studies using cache recvery prcedures (e.g., Kamil & Balda, 1995; Vander Wall, 1982) have suggested that nutcrackers use bth glbal and lcal cues in rder t lcate buried seeds. Hwever, because it is extremely difficult t cntrl the gemetric relatinship between gal and landmarks when a bird chses cache sites, buriedseed prcedures in which the experimenter determines the gal lcatin are als needed t study the mechanisms that nutcrackers use t find a specific lcatin. Results frm such studies (e.g., Guld-Beierle & Kamil, 1996) are cnsistent with the cache recvery studies, indicating that nutcrackers use bth glbal and lcal cues. The buried-seed studies have als demnstrated that nutcrackers relcate the gal by remembering relatinships (distance and directin) between the gal lcatin and ne r mre landmarks. In tw previus studies (Kamil & Jnes, 1997, 2000), Clark's nutcrackers demnstrated the ability t utilize abslute and relative bearings t learn a gemetric relatinship amng tw landmarks and a gal. In these studies, the rientatin f the landmark array was fixed with respect t the walls, and the birds culd have either fcused n directinal infrmatin that was cnsistent with glbal cues (abslute bearings) r fcused n directinal infrmatin that was taken slely frm the landmark array (relative bearings). Results demnstrated that the birds utilized a gemetric principle based n bth abslute bearings and relative bearings, but when the tw were put in cnflict, the birds always chse t use abslute bearings. The main questin psed in the present experiment was whether these birds culd learn a gemetric task that was dependent n the use f relative bearings. The perfrmance fthe rtated grup during the present experiments demnstrated that nutcrackers culd learn a gemetric principle based n relative bearings and generalize the principle t many new cnditins during which the landmarks were presented at nvel interlandmark distances r rientatins. Hwever, they did nt generalize well when the landmarks were rtated 90 r mre, and the reasns fr this failure are nt clear. When the landmarks were rtated 90, sme f the birds searched in lcatins ther than that defined by relative bearings. This indicates that the birds learned sme relatinship between the lcatin f the gal and landmarks in additin t relative bearings. One pssibility is directinal infrmatin. Althugh the landmark array was rtated ver a range f 150, during training the red landmark was always nrth f the blue landmark, and the gal lcatin was always west f the hypthetical line between landmarks. If the birds depended n this type f directinal rule, then these directinal cues were invalid when the landmark array was rtated 90. Thus, it appears that even the birds in the rtated grup encded sme directinal infrmatin due t the lack f training rientatins. Hence, if the birds had been trained with a greater range flandmark rientatins, then this might have frced the nutcrackers t rely exclusively n relative bearings. In additin t increasing the degree landmark array rtatin during training, anther pssibility is using landmarks that are distinctly different in appearance. This might be beneficial because nutcrackers pay mre attentin t the spatial rientatin f features in their envirnment than t the appearance f the landmarks. Anther pssibility wuld be t cnduct the experiment in a rm that had n directinal cues. Therefre testing the effects f training with rtating landmark arrays might prduce exclusive reliance n relative bearings. REFERENCES BALDA. R. P. (1980). Recvery f cached seeds by a captive Nuc(fraga carytactes. Zeitschrififiir Tierpsychlgie, 52, BENNETT, A. T. D. (1993). Spatial memry in a fd string crvid. Jurnal f Cmparative Physilgll, 173A, BIEGLER, R., MCGREGOR. A., & HEALY. S. D. (1999). Hw d animals "d" gemetry? 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13 132 JONES AND KAMIL SPETCH, M. L., CHENG, K., & MACDNALD, S. E. (1996). Learning the cnfiguratin f a landmark array: I. Tuch screen studies with pigens and humans. Jurnal f Cmparative Psychlgy, 110, SPETCH, M. L., CHENG, K.. MACDNALD, S. E., LINKENHOKER, B., KELLY, D., & DOERKSON, S. (1997). Use f landmark cnfiguratin by pigens and humans: II. Generality acrss search tasks. Jurnal f Cmparative Psychlgy, 111, VANDER WALL, S. B. (1982). An experimental analysis f cache recvery in Clark's nutcrackers. Animal Behaviur, 30, WILSON, B., MACKINTOSH, N. J., & BOAKES, R. A. (1985). Transfer f relatinal rules in matching and ddity learning by pigens and crvids. Quarterly Jurnal f Experimental Psychlgy, 37B, (Manuscript received September 15,2000; revisin accepted fr publicatin February 13,200 I.)