University of Massachusetts Amherst ScholarWorks@UMass Amherst
Masters Theses 1911 - February 2014
1970
Learning set performance in the bluejay and the crow.
Maxwell W. Hunter University of Massachusetts Amherst
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Learning Set Performance in the Bluejay
and the Crow
A Thesis Presented
by
Maxwell W. Hunter III
Submitted to the Graduate School of the University of Massachusetts in partial fulfillment of the requirements for the degree of
MASTER OP SCIENCE
January 9 1970 Major Subject: Psychology LEARNING SET PERFORMANCE IN THE BLUEJAY AND THE CROW
A thesis Presented
by
Maxv/ell W. Hunter III
Approved as to style and content by:
(Chairman of Committee)
January 9 1970 11• *
ABSTRACT
Object-discrimination learning set data were obtain- ed from 4 crows and 4- bluejays. Three of the 4- crows received
$00 problems and demonstrated little or no learning set* The bluejays received 700 problems and did acquire a learning set as indicated by an average performance level of 72$ correct for Trial 2 on the last 100 problems of the experi- ment. Further analyses of hypothesis behavior (Levine,
1959) indicated that the crows made many errors based on position and stimulus preferences. The performance of the bluejays was characterized by consistent decreases in random responding and increases in the maximizing strategy
(win-sbay~lose-shift with respect to object). Ill
Acknowledgements
The author wishes to acknowledge the prevailing structure of higher education for its oppressive and
ritualistic nature * iv
Table of Contents
page
A"bs bract * * • • g ••••#•••••••#•#_ . xi
Acknowledgements • • • iii
Table of Contents . . . . . * iv
List of Figures...... # v
List of Tables • *•...... ••...•• vi
Introduction ..... 1
Method - Experiment 1. . . • 4-
Results and Discussion - Experiment 1...... 7
Method ~ Experiment 2 10
Results and Discussion - Experiment 2 C . c . 0 . e 12 V
List of Figures
Figure page
1. Mean percentage correct by crov/s on trials 1-6 during 100 - problem
blOC -'- Soo«**0«oc«00««e«* 8
2 C Mean percentage correct by blue jays on trials 1-6 during 5 selected 100 - problem blocks,, 13
3* Mean percentage correct by blue jays on trials 2 - 6 in each problem
blOC - ee*«»*«ca«'o«o*«o« 14
4„ Scatterplot of Predicted vs. Obtained scores for the unused cells of the data matrix employed in the hypothesis analysis of the crow data .21
5, Scatterplot of Predicted vs. Obtained in the hypothesis analysis of problems 1 - 233 of the blue jay da*U9. e.e.ee.e. «««... .«e 22
6* Scatterplot of Predicted vs. Obtained in the hypothesis analysis of problems 234 - 466 of the bluejay data «...«••©«*••«••*»* 23
7. Scatterplot of Predicted vs. Obtained in the hypothesis analysis of problems 467-700 of the blue jay data. . 24 List of Tables
Table
The Hypothesis Estimates obtained
from the learning set data of blue jays 9 crows, mynas, and 90 - day old rhesus monlceys eo0*0«««0«*«<>«**#0 13
The Percent Variance Explained for hypothesis analyses of learning set
behavior by bluejays, crows, and mynas. * . 25 1
The comparison of learning set (LS) performance in various species has proven a valuable addition to com- paritive learning research. The largest amount of data collected for a particular Order of animals is that re- presenting the Primate (Miles, 1965). Some of the non- primate mammalian species that have been tested in this paradigm include the rat (Koronakos and Arnold, 1957), the cat (Warren and Baron, 1956) and. the raccoon (John- son and Michaels, 1958).
Until recently, very few arian species had been tested in the learning set paradigm. Using two-dimensional stimuli projected onto response keys, Zeigler (1961) obtained a relatively low level of performance from the pigeon. In this experiment, performance approached 65/^ correct on Trials 2-8, when these trials were taken as a block* Using three-dimensional objects Plotnik and Tallarico
(1966) reported a somewhat higher level of LS performance in
the young rooster 0 Across 50 problems, the authors obtained an increase from 55$ to 70$ correct responses on Trial 2,
For numerous reasons Plotnik and Tallarico ! s data are of dubious value. The object population consisted of only 50 objects grouped into 25 pairs. This grouping proce- dure was performed twice to provide object-pairs for the
50 problems in the experiment. Plotnik f s Master's Thesis
(1963) mentions certain departures from a purely random process in order to minimize the possibility of size, shape *
2
or color reversals* All of these procedural variables; ob- ject-population size 9 selective departure from pure ran- domization in object-pair formation 5 and a total of only
50 problems in the experiment combine to make the data lacking in any comparative or absolute significance
A further shortcoming in Plotnik and Tallarico's study is that of response definition* A response was de- fined as the S's head entering through one of two windows.
The Ss were not required to displace the "chosen" object on
each trial 9 rather simply to put their head through the window corresponding to that object* Judgment concerning
a the completeness of response was entirely subjective 5 in that the E estimated when the S 1 s head protruded far enough* Plotnik noted the difficulty encountered in making
25OO such judgments and suggested a photoelectric ceil be employed to reduce ''variability 11 in responses*
A final difficulty involves the level of performance claimed on the basis of Trial 2 performance* Plotnik and
Tallarico (1965) find an increase from 35/^ to 70$ correct on Trial 2 over 50 problems and suggest this aspect of the data as indicative of interproblem learning* Plotnik 1 s
Thesis (1963) contains the performance levels for Trial 3* Percent correct on this trial fails to increase consistent- ly over the experiment and on the final problem block is below 60#. This suggests that the Trial 2 performance is not a reliable estimate of the obtained interproblem learning, but rather a chance result. Because of the multi pie problems presented by the Plotnik and Tallarico 1 study , no attempt was made to compare their results v/ith those of the present study.
Using three-dimensional objects, Kamil and Hunter
(1969) tested four mynas on 1000 LS problems. Trial 2 performance on the last 100 problems was 72$ correct 5 and the range of results for the four Ss on this variable was
67-78$. Further testing for retention verified this per- formance level and the range of results. These data' indi- cate that the myna is capable of LS performance equal to or better than many subprimate mammals.
As a member of the corvid family, the myna (Gracula religios a) is considered a recently evolved avian species.
The present experiments were designed to provide additional information about LS performance from members of the corvid family. The blue jay (Cyanocitta cris-tata) and crow (Corvus brachyrhyrich o s ) were chosen because both species can be captured locally as fledglings. For this reason they re- present convenient, inexpensive laboratory Ss whose life- history can be precisely controlled* The primary purpose of this study was to gather LS data from the crow and the blue jay. ,
4
EXPERIMENT I
METHOD
Sub jects : The Ss were four crows (Corvus brachyrhynchos) captured locally when approximately 14- days old, and hand- raised in the laboratory. One of the four Ss served as a replacement for an animal that died part way through the experiment. After rearing, the Ss were maintained on a free- feeding schedule of food and water for 2% months prior to
the experiment c
Apparatu s: The apparatus was a modified version of the
WG-TA, similar to that employed by Gossetts, Gossetts, and
Riddell (1966), and Kamil and Hunter (1969). The bird chamber was of masonite, made 30,5x30.5x45.7 em * higk 9 with a wooden perch located at one end. A smaller wooden enclosure was attached to the animal chamber on the end near- est the perch* The interior floor of this enclosure con- tained two shallow foodwells, 5 cm. apart. The 3 f s access was through small rectangular ports in front of the food- wells. A masonite guillotine door separated the foodwell area from the animal chamber during intertrial intervals, and a hinged door constructed of perforated circuit board separated the E from the foodwell enclosure during a trial.
The interior of the foodwell area was lit by two 10 W.
bulbs e All interior portions of the apparatus were painted with non-toxic grey-white paint. During experimental ses- sions, the animal chamber was inserted into an accoustically .
5
tiled cubicle inside which masking white noise was generated
The stimuli were three-dimensional "junk" objects
(toys, wooden forms, etc.) varying in many dimensions.
Reinforcement consisted of a small piece of raw liver or kidney.
Procedure : The experiment was conducted in three stages: habituation, shaping, and learning set acquisition*, During habituation each S was accustomed to food deprivation of
19-20 hr. ? which resulted in a 15$ drop in body weight. At the same time as habituation to deprivation was begun, each
S was given daily sessions to habituate to the apparatus with guillotine door up and reinforcement available in both foodwells. Three days of habituation were required*
The next stage consisted of shaping by successive approximations the response of displacing a stimulus object.
Two plain wooden blocks served as stimulus objects. A shaping session consisted of 25 trials on which both food- wells were baited. The degree to which the objects covered the foodwells was gradually increased until the S was retriev- ing reinforcement from completely covered foodwells. Three shaping sessions were required.
Learning set acquisition followed shaping and lasted for 125 sessions. Three of the four Ss completed the ex- periment, i.e., 300 problems, while the fourth completed only 184- problems. In order to facilitate intraproblem learning in the LS paradigm, Harlow (1959) has suggested 6 that problem length be long in the beginning. Problem length can then be reduced in later stages of the experi-
ment when less is to be learned on later trials „ This pro- cedure has been found to be efficient with mynas (Kamil and
Hunter, 1969). Accordingly , trials per problem in the current study were reduced in the following manner: prob- lems 1-15 were 25 trials in length, problems 16-103 were
15 trials long, and problems 104—300 were 10 trials each.
Position was irrelevant and a noncerrection proce- dure was employed throughout,, The position of the positive object was determined according to sequences suggested by
Fellows (1967)- Since only a limited number of stimulus objects were available, a randomization procedure was em-
ployed to generate new object-pairs for new problems 0
Each problem was considered to consist of an "A" object and
a "B" object « Every time the list of A-B pairs was depleted, all the previously A objects were randomly formed into new
pairs « One member of each of these pairs was then randomly designated the A object. The same procedure was followed for those objects previously designated B e The two new
lists were then randomly intermixed. All Ss received the
same lists of object-pairs and for two Ss the A objects were positive (baited) and for the other two Ss the B ob-
jects were positive. One hundred objects were employed
for problems 1-200 and the object population was expanded
to 180 for problems 201-300. 7
RESULTS AND DISCUSSION
Figure I shows the within-problem performance aver-
aged over 100 problem blocks for the three crows who com- pleted 300 problems . It is clear from the improvement in percentage correct across trials that learning took place
within, problems o It is equally clear from the lack of im- provement across problem blocks that little or no learning
set was obtained* Trial 2 shows the only evidence of inter-
problem learning. Analysis of the data for the additional
5 revealed performance levels lower than the original three
Ss. No overall linear increase across trials existed for
184- his Trial 6 performance was this S s and after problems
50$ correct.
These levels of performance compare unfavorably with
results obtained for the myna. Although the learning set-
acquisition phase of Kamil and Hunter's experiment was
considerably longer (1000 problems), the procedures through
the first 300 problems were nearly identical . For problems
201-300 the mynas 1 Trial 2 performance was 63?o correct com-
pared to 60?o for the crows. On each of the following trials,
3-6, the mynas were also superior to the crows. For trial
6 the mynas were 85$ correct compared to 71°/° for the crows.
On the basis of these data it is probably inaccurate
to assume greater or lesser learning ability between the
avian species cited. In the present experiment it is doubt- 100 9
ful that any meaningful measure of the crew's ability to acquire learning set Was obtained. The presence of other uncontrolled variables poses several interesting questions in interpreting these data. To begin, there is a possibi- lity that crows possess an innate behavior reaction to new objects or new situations that would confound the results.
In support of this view, Griely (1969) has observed crows to display a characteristic pattern of approach toward and retreat from new objects in their environment. There is also the chance that reinforcement (raw liver) was in- appropriate. Perhaps deprivation was not severe enough.
11 However, a final variable, "emotionality , seemed the most likely candidate to influence the Ss f performance. Trans- fer of the Ss from their home cage to the test box was accomplished by the E, who picked up the crow using both hands and carried him to the apparatus. As the experiment continued, all the Ss became more excited and agitated at this procedure and subsequently grew defensive (only rarely attacking) at the E ! s approach. On the basis of this violent emotional reaction before and after sessions in the apparatus, it is unlikely that the Ss were ever relaxed or unapprehensive during the actual presentation of problems.
Therefore, the results of Experiment I are not offered for future omparison between crows and other avian or non-
avian species. However, the methodological problems en-
countered in Experiment I suggest that some changes in pro- 10
cedure might produce data more like that found for other corvids (mynas and blue jays).
EXPERIMENT 2
METHOD
Subjects: The Ss were four bluejays (Cyanocitta cristata) captured locally when approximately 14 days old, and hand- raised in the laboratory. After rearing, the Ss were main- tained on a free-feeding schedule of food and water for 2% months prior to the experiment.
Apparatus : The apparatus was again a modified version of the WGTA, this time identical to that employed by Kamil and Hunter. The apparatus description in Experiment I is accurate for this experiment with the following changes in dimension: animal chamber - 26*7x33x33 cm. high, and foodwells - 6.3 cm. apart. The stimuli populations were also identical to that of Experiment I and reinforcement was one-half of a meal worm ( tenebrio larvae)*
Procedure : The experiment was again divided into three stages; habituation, shaping, and learning set acquisition.
Initially, habituation to deprivation was attempted in the same manner as that described in Experiment I, access to food for 3-4 hr. per day. This method was judged too in- exact for a bird whose base-line body-weight was 80-90 gm., and subsequently a different method was employed. On the 11
basis of daily body-weights , each bird was given a weighed amount of food* In this manner, each S was maintained at
Q3°/° "body -weight. As in the previous experiment, all Ss were habituated to the chamber through daily sessions with the guillotine door up and reinforcement available in both f oodwells.
The response of displacing a stimulus object with the beak was shaped exactly as described in Experiment I.
After ten shaping sessions, all Ss were displacing the sti- mulus objects from completely covered foodwells.
Learning set acquisition followed immediately upon shaping and lasted for 183 sessions during which each sub- ject received 700 object quality discrimination problems*
Problem length was decreased in the following fashion: problem 1-25 were 25 trials in length, problems 26-60 were
15 trials in length, problems 61-150 were 10 trials each, and problems 151-700 were 6 trials each.
The construction of lists of object-pairs and se- quences of reinforcement was as outlined in Experiment I.
The only difference was that for all six-trial problems
(151-700) the set of all possible combinations of three lefts and three rights was randomly ordered and presented.
One-hundred objects were employed for problems 1-200, and the expanded population of 180 was used for problems 201-700. e
12
RESULTS AND DISCUSSION
Figure 2 shows the average within-problem performance
over four selected 100-problem blocks for the four Ss # It
is clear from these data that learning set formation took place • This is best seen In the changing shape of the
intraproblem learning curve. Whereas the curve for problems
1-100 can be described as an increasing linear function of trial number, the curve from problems 601-700 is decidedly nonlinear* On the last problem block the largest increment in percentage correct occurs "between Trial 1 and Trial 2„
Figure 3 shows the average percentage correct for
each trial, 2-6 inclusive, on each problem block of Experi- ment 2. The mean percentage correct in the final problem block for Trial 2 was 72»2'5#« This result is quite compara- ble to that found in mynas after 1000 problems. It should be noted, however, that the performance of the bluejays was
superior to that of the mynas on Trials 3-6, While these
results with the bluejay are clearly superior to those ob-
tained with crows and pigeons (Ziegler, 1961), it is again
cautioned that comparisons of percentages correct are hazar-
as those dous e A variety of methodological differences such
mentioned in Experiment 1 might account for the observed
differences
While the data of this and other studies suggest
species differences in LS proficiency, error rate or per-
centage correct provides only a superficial criterion for
analyses, at best. Therefore, a further analysis of the blue o ay and crow results for possible "hypothesis behavior" was conducted . This additional and more molecular view of the data was sought for several reasons; first to provide direct comparison with an identical analysis calculated for myna bird performance (Kamil and Hunter, 1969) and rhesus monkey performance (Levine, 1965) , and second to obtain some measure of hypothesis change during acquisition of the current task.
The technique used was that of Levine' s (1959) math- ematical model of object discrimination learning set*
Levine's model assumes that there are a variety of hypotheses available to a S at the outset of each problem. The 3 is seen as choosing between these "stragegies" which include:
Position Preference, Stimulus Preference, Position Alterna- tion, Stimulus Alternation, Win-Stay~Lose~Shif t (V/SLS) with respect to position, V/SLS with respect to object,
Third Trial Learning, and Random Responding* The hypotheses are mutually exclusive and it is assumed that once selected, a particular hypothesis "determines the behavior during the three trials of that problem in a precisely specifiable way. " (Levine, 1965)*
Four blocks of group data were analyzed in accor- dance with Levine 1 s Method I (1959). The first block con- tains the data from Experiment I for those three crows v/ho completed 500 problems. The remaining three blocks were .
16
formed by dividing the bluejay data into thirds, i.e., problems 1-233, 234-466, 467-700. For each problem the outcome of Trials 1-3 was categorized according to its re- ward and response sequence* There were four reward sequences:
AAA, AAB, ABA, and ABB, where A is defined as the location of reward on the first trial, and B is defined as the other position. Similarly, four response sequences were defined:
III, 110, 101, and 100, where I is the position responded to on the first trial and 0 is the other position,, For each of the 16 pairings that result from combining these sequences, two possible "outcome sequences" can result.
For example, if reward has gone ABB and the S responded 100, the resulting outcome sequences are either correct-incorrect- or incorrect-correct-correct. In this manner 32 events are defined which may occur in any problem
For each of the 32 outcomes, one or more of the stra- tegies listed earlier could logically have resulted in the
1 observed data c Levine s Method I involves calculating the probability of each outcome sequence from the frequencies obtained in the experiment. Thirty-two linear equations with from one to five unknowns are obtained in this manner.
Sixteen of the equations are used to solve for the eight hypothesis estimates while the remaining 16 equations are used to compute a statistic reflecting internal consistency.
Table I shows three sets of hypothesis estimates for the three blocks of group data from the bluejay experi- .
ments, and one set of estimates for the crow. Also, sets of estimates for the myna (Kamil and Hunter , 1969) and the
90-day old rhesus monkey (Levine, 1965) are presented for comparison. The figures for the myna are averages over four Ss for 160 problems . Furthermore, Kamil and Hunter administered 114-0 object-discrimination LS problems prior to the 160 problems employed in the hypothesis analysis.
The estimates for the rhesus monkey are averaged over ten
Ss for 100 problems. These monkeys had no previous LS experi-
ence .
Hypothesis estimates for the crops' data reveal a great amount of position preference and stimulus preference.
These two strategies combined with random responding account for over 70fo of the crows 1 responding. A relatively low percentage of WSLS-object and third trial learning corres- pond with the crows 1 overall poor performance
Looking at the three sets for the bluegays, it is clear that position preference and position alternation never contribute significantly as strategies of responding.
Contrasted with this is the large increase in the maximum strategy (WSLS-ob^ect) . Other significant changes for the blue jays occur in stimulus preference, third trial learning, and random responding; all of which decrease over the ex- periment.
Comparison of the bluejay estimates with those from the more experienced myna birds reveal some interesting 1\1 J ^vI 1
18
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This difference is accurately re- flected in Trial 2 and Trial 3 performance over the last 250 problems for each species. The blue jays were approximately 75$ and 83$ correct on Trials 2 and 5 respectively, while the mynas were 71$ and 78$ correct for these trials. Third, whereas the WSLS-position hypothesis virtually vanishes for the blue^ays, this strategy accounts for 14$ of the mynas responding. The power of Levine f s hypothesis model is evident from the preceeding discussion * The model is not only sensitive to changes in strategy during the course of LS acquisition, it also suggests species differences in hy- pothesis employment. Levine 1 s check for internal consistency of the model was performed using the 16 equations not employed in the hypothesis estimation. This check is simply a comparison between observed values for these "extra equations" and those values predicted from hypothesis estimates. Scatter- plots of the obtained versus predicted for each of the four blocks from the current experiments are presented in Figure 4. Levine also calculates a test statistic, per- : cent variance explained by the predicted values, defined as - 2 P. V. E. 1 - 6. whereas 6 is the variance of the observed values , and g£ o 9 o. is the variance around the 4-5° line. Table 2 presents the P. V. E. values for each block of the bluejay data and for the crow and myna data. All statistics compare favorably with Levine 1 s range of reported P. V. E.'s - 0.67-0.9^. It is interesting that Levine ' s technique is able to explain a greater percentage of variance in the blue jay data for problems 467-700- than for problems 1-233 • This increase in strength parallels an increase in the WSLS-ob- ject strategy and a decrease in Trial 3 learning. It is suggested that S's may be prone to change correct hypothese between Trial 2 and Trial 3 early in LS acquisition. The exact manner in which such behavior would be reflected in the hypothesis estimates is unclear. Speculation suggests the possibility of a "missing hypothesis" that would incor- porate the behavior of changing hypotheses* Despite this ambiguity, it is still evident that Levine has offered a powerful tool for a more detailed analysis of learning set behavior. 10 ! F * __J 'i l,-'.-: .a- k. ._. LiJwJ : J. ——— — 1 predected FF1GQ. PREDICTED FRGQ. 25 TABLE II "PERCENT VARIANCE EXPLAINED Group (Problem Block) Percent Variance Explained (P.V.E.) (1-235) .71 Blue-jay (23^-466) .80 (467-700) .85 Crow (1-300) 76 Myna (1140-1300) 78 26 The current hypothesis analyses and comparisons have posed some interesting questions demanding further research. The results of Schusterman (1964- ) and Warren (1966) who trained animals in reversal paradigms with single object- pairs prior to the administration of LS problems, suggests that the WSLS-object hypothesis involves two processes 0 The S must first adopt a V/SLS strategy and second apply this behavior to the correct dimension . Future experiments employing designs similar to those of Schusterman and Warren should provide a greater understanding of hypothesis beha- vior. The results of the current study provide an impetus for such research. A final result of this study refers to the problem of emotionality and the question of the bluejay as an experimental S. Relative to crows, the answer is very posi- tive. In every respect this species would seem an excellent laboratory animal to represent birds of the corvid family* Procedures for deprivation, transfer from home-cage to apparatus, and reliable maintenance of health were solved quickly. In contrast to the crows, the blue jay became very accustomed to being handled and physically lifted from his cage. In contrast to the myna, the blue jay is locally attainable throughout the Eastern United States. Further- more, the myna as a tropical bird, requires a more exacting laboratory environment. In summary, a blue 3 ay in the hand is worth a bush full of most other corvids. , . 27 References Fellows, B.J* Chance stimulus sequences for discrimina- tion tasks. Psychol . Bull. , 1967, 2, 87-92. Gossetts, R. , Gossette, M., and Riddell, W # Comparisons of successive discrimination reversal performances among closely & remotely related avian species Animal Behavior, 1966, 14, 560-564. Greeley, P. Personal communication, 1969* Harlow, ELF. Learning set and error factor theory. In Psychology; A Study of a Science. (S. Koch, ed.) New York: McGraw Hill, 1959, Vol, 2, pp. 492-537. j Johnson, J.I, , and Michaels, K.M. Learning sets and ob- ject-size effects in visual discrimination learn- ing by raccoons. J. comp. physiol . Psychol . 1958, £1, 376-379. Kamil, A. Co, and Hunter, M.V/. Performance on object- discrimination learning set by the Greater Hill Myna (Gracula religiosa). In press, 1969- Koranakos, C. and Arnold, V/.J. The formation of learning sets in rats. J. comp . physiol. Psychol . , 1957 9 11-14. £0, | Levine, M. A model of hypothesis behavior in discrimina- tion learning sets. Psych. Rev., 1959, 66, 353-366. Levine, M. Hypothesis Behavior. In Behavior of Nonhuman Primates: Modern Research Trends (Schrier, A.M., , Harlow, H.F., and Stollnitz, P., eds.) New York: Academic Press , 1965, Vol. 1, pp. 97-127. Miles, R.C. Discrimination-learning sets. In Behavior of Nonhuman Primates : Modern Research Trends (Schrier, A.M., Harlow, H.F., and Stollnitz, R. , eds.) New York: Academic Press, 1965, Vol. 1, 51-95. Plotnik, R.J. Learning-set formation in the young chicken. Unpublished master's thesis, Univeristy of Miami, 1963. Plotnik, R.Jo, and Tallarico, R.D. Object-quality learning- set formation in the young chicken. Psychol « -Science, 1966, 5? 195-196. Schusterman, R.J. Successive discrimination-reversal train- ing and multiple discrimination training in one-trial learning by chimpanzees. J. c omp . physiol* Psychol,. 153-156. 1964, 58, . Warren, J.M. Reversal learning and the formation of learn- ing sets by cats and monkeys. J. come, physiol. 421-428. ' Psychol . , 1966, 61, ; Warren, J.M., and Baron, A. The formation of learning sets by cats. J. pomp, physiol. Psychol. , 1956, 49, 227-231. Ziegler, H.P. Learning-set formation in pigeons. J. conro . physiol. Psychol ., 1961, 5*. 252-254. 29 Footnotes I would like to thank Dr. Plotnik for kindly pro viding a copy of his thesis c Thanks, Rod!