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Mathematical models of delayed reactions in rats
LEAHNISC
ASD
hlOTIVATIOK
Mathematical
4, 445-458
(1973)
Models
of
Delayed
Reactions
in Rats’
ARNOLDPOWELL Columbus
College
AND WILLIAM University
J. ARNOLD of Nebraska
Two models of delayed reactions, the Uncertain Trace and the Linear Trace-Decay mode!s, were proposed and tested in a delayed-reaction T maze. Ss trained with a short delay attained lower asymptotic performance !evels than did Ss trained on the same discrimination, hut with no delay between stimulus and response. This was interpreted as reflecting the greater probability that Ss forget the cue during a delay interval, and three additional findings eliminated an alternative explanation that the cue is not attended to in the delay condition. The Linear Trace-Decay model provided a more accurate description of quantitative aspects of the data; however, neither model provided a completely adequate fit to the data.
Ever since Hunter’s (1913) original investigation of the delayed reaction paradigm, delayed reactions have been investigated in a variety of situations and species, but there have been relatively few explicit theoretical models of learning and performance is such situations. Cowles’ (1940, 1941) early discrimination model and Fletcher’s (1965) more recent intratrial, orienting response analysis are among the few explicit theoretical treatments of delayed reactions. According to Fletcher’s (1965) model, an orienting-response chain is evoked by stimulus presentation, and the instrumental response at the end of the delay interval is the terminal member of the response chain. Performance decrements as a function of delay interval result from events occurring during the delay ‘This research was supported by an NSF Predoctoral Traineeship awarded to the first author, and is based upon a dissertation submitted to the Graduate College in the University of Nebraska in partial fulfill ment of the requirements of the degree of Doctor of Philosophy. The thesis was submitted by the first author and supervised by the second author. A portion of the data were included in a paper presented at the meeting of the Rocky Mountain Psychological Association, Denver, May 1971. Requests for reprints should be sent to Arnold Powell, Department of Psychology, Columbus College, Columbus, Georgia 31907. Copyright All rights
@ 1973 by Academic Press, of reproduction in any form
445 Inc. reserved.
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interval which disrupt the response chain. An important assumption of this model is that imposing a delay between stimulus and response influences performance but not learning. Performance decrements arc’ COW sidered intratrial phenomena; the probability that the correct response does not occur, as a result of intradelay events, is a set parameter and does not vary as a function of trial number. Fletcher did not propose any explicit mathematical interpretation of his model, but there are several alternatives that stem from his analysis. A couple of alternative models are investigated in the present study that assume that responses become conditioned to the traces of stimuli presented earlier, as was postulated in by the models of delayed reactions investigated by Smith (1951, see also, Hull, 1951) and Konorski and Lawicka (1959). Th ere is a theoretical controversy concerning whether to conceptualize the processes that intervene between stimulus reception and response evocation in terms of stimulus traces, orienting responses, or memory storage and retrieval (e.g., Blough, 1959; Cumming, Berryman, & Cohen, 1965; Powell, 1972). However, the present study is not concerned with this issue but focuses, instead, upon the intratrial interpretation and its various implications. According to the Uncertain Trace model the discriminandum can be represented by a single stimulus element that is sampled with a probability of 1.0 on each trial. The trace of the sampled element continues through a delay interval with a probability of r, and becomes conditioned to the correct response with a probability of c. The memory parameter, 7, is assumed to be a function of the length of the delay interval, and both T and c are assumed to be independent of trial number. In other words, the Uncertain Trace model assumes that S attends to the cue whenever it is presented, and there is some probability that the cue will be remembered until there is an opportunity to respond. If S forgets the cue, or if it is remembered but still in the unconditioned state, then he guessesand makes a correct response with a probability of 0.50. It can be shown (Lynn, 1969) that the probability of a correct response on trial N ( P( R,-) N ) will equal P(Rc)X
= >2[(1 + r) - Y(l - cV)“-‘].
(1) The last term in Eq. ( 1)) ( 1 - CP)“~~, is the probability that the trace of a sampled element remains in an unconditioned state after N - I trials. As the trial number increases, the term approaches zero, and the probability of a correct response approaches W(I + r) : hence, the model predicts that asymptotic performance will vary as a function of the memory parameter, 7. An alternative to the Uncertain Trace model is the Linear TraceDecay model, which assumes that learning is an incremental process,
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and that the strength of a trace of a sampled element varies inversely with the length of delay. The Linear Trace-Decay model is a modification (cf. Lynn, 1969) of Bush and Mosteller’s (1959) Single Operator Linear model (see also, Bower, 1961; Atkinson, Bower, & Crothers, 1966), according to which the probability of a correct response on trial N + 1 is equal to the probability of being correct on trial N, plus a fraction, (1 - (Y), of the remaining portion (1 - PN) of the level to which P, can grow (1.0) (cf. Atkinson et al., 1966). However, the Linear Trace-Decay model assumes that the limit of P, is an additional parameter, 1L1,that varies inversely with the length of delay. Therefore, the probability of a correct response on trial N will equal (cf. Lynn, 1969) P(Rc)X
= IIT - (AZ - ?/$)((y)-‘.
(2)
The Linear Trace-Decay model is a stochastic analog to Hull’s (1952) incremental model in which the limit of the growth of Reaction Potential was postulated to vary inversely with the intensity of the Molar Stimulus Trace. Equations (1) and (2) predict the same learning curves, since (Y = (1 - CT) and M = X(1 + r), and both models make similar predict&s with regard to the effects of several variables upon delayed reaction performance. It is assumed that r and M vary with the length of delay and that both are equal to 1.0 when there is no delay. Therefore, both models predict that asymptotic performance will vary inversely as a function of length of delay and that perfect performance will be attained as an asymptote when there is no delay between stimulus and response. The models also predict that any increase in the length of delay with which Ss are being trained will produce an immediate and reliable decrement in performance. Since the memory, or asymptotic, parameters are independent of trial number, or prior experience, it is predicted that there will be no difference between the asymptotic performance of Ss given discrimination training prior to their training under conditions of delay and the asymptotic performance of Ss trained only under conditions of delay. Although Ss given prior discrimination training should demonstrate some stimulus generalization on the early trials of the transfer stage, their performance should approach the same asymptote. The Uncertain Trace and Linear-Decay models make similar predictions with regard to the above hypotheses, but they can be differentiated in terms of their quantitative fit to the data.” ‘It should be pointed out that although Uncertain ‘Trace and Linear TraceDecay make different assumptions with regard to the duration of the traces of sampled elements (all-or-none versus decay), these assumptions are not tested in the present study.
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POWELL
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Roth of the above models interpret differences in performance as a function of delay interval in terms of the tendency of S to forget the cue during the delay interval. However, there is evidence that perceptual or attentional variables are involved in performance in some variations of the delayed reaction paradigm (Fletcher, 1965). Therefore, any difference between performance in delay and nondelay conditions could be attributed to the probability the Ss fail to attend the cue when a delay is involved. If failure to attend to the cue is an important factor, then giving prior discrimination training would be expected to improve performance in the delay condition. Furthermore, feeding S in front of the cue would be expected to increase the probability that he attends to it and, hence, should also improve performance in the delay condition. The present study was designed to test the following hypotheses: (a) imposing a short delay between stimulus and response occasions will lead to a decrease in asymptotic performance; and (b) administering prior discrimination training will not improve asymptotic performance under conditions of a short delay; (c) increasing the length of delay will result in an immediate and reliable decrement in performance; and (d) feeding Ss in front of the discriminandum under conditions of a short delay will not influence asymptotic performance. These hypotheses are tested in a T-maze in which “length” of delay is defined in terms of the distance between a stimulus chamber and the choice point of the maze. This apparatus incorporates several improvements upon earlier employed in studies by apparatus. For example, in the apparatus McAllister ( 1932) and Wilson (1934a,b) the delay interval was confounded with amount of effort, delay of reinforcement, or both, whereas both of these variables are held constant in the apparatus employed in the present study. METHOD
Subjects. Ss were 20 male albino rats obtained from the Charles Rivers CD strain. All Ss were approximately 90-110 days old at the beginning of the study and were housed individually throughout the investigation. Apparatus. The apparatus was a T-maze with a 2.9 m long x 11 cm wide X 17 cm high alley and a 1.2 m X 13 cm X 14 cm high arm. The stimulus which indicated a correct response was a white circle, 9 cm in diameter, cut from white enamel Con-Tact paper. In the no-delay condition the stimulus was placed on the appropriate goal box door. In the delay conditions, however, the stimulus was presented at either of two points between the start box and the choice point. Short sections of the
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flush alley walls were removed and walls, which extended at a 60” angle outside of the alley walls, were inserted in their place. The stimulus was then placed on the back wall, extending outside the normal alley walls and in clear view as S approached from the start box. When short and long delays were imposed, the stimulus was placed 1.1 m or .4 m, respectively, in front of the choice point, and was not present on the goal box door. A guillotine door was at the entrance to the alley and the goal boxes were entered by pushing open masonite doors that were hinged at the top. The entire maze was painted flat black and covered with hardware cloth doors. Design and procedure. During the first 10 days of the study Ss were placed on a 11-13 g per day maintenance diet, with water available ad lib., and maintained on this schedule for the remainder of the study. Adaptation to the experimental apparatus and shaping of Ss to push open the goal box doors were conducted on days 11 and 12. For all Ss the first phase of experimental training involved 150 acquisition trials and was begun on day 13; one trial was administered on days 13 and 14, two on days 15 and 16 and, then eight per day except for the last day which required 10 trials. Ss were run in squads of 10 and all Ss in a squad were given a single trial before any S received a second trial. The average intertrial interval was approximately 10 min. Correct responses were rewarded with three 45-mg Noyes pellets, a noncorrection procedure was employed, and the correct response was alternated according to a RLLRLRRLLRRLRLLR counterbalanced sequence. Ss were randomly assigned to group DIS or DEL. A summary of the experimental design is presented in Table 1. Group DIS received 150 training trials on a black-white discrimination, with no delay, while Ss in DEL received 150 trials on the same task with a short delay imposed between the stimulus and response. During the second phase of experimental training, Ss in DIS were given 150 trials (8 per day; with 6 on the last day) under conditions of short delay (hereafter referred to as group Ds-DEL). Following acquisition, Ss in group DEL were randomly assigned to two subgroups. During the second phase, 5 Ss in group NO-F (DEL) were continued under the same conditions of short delay for an additional 60 trials (8 per day; 4 on the last day), Five Ss in FED (DEL) were given 20 placements (10 per day) in front of the discriminandum, with a single 45-mg Noyes pellet available on each of these placements. S was removed as soon as the pellet was consumed. Then, 60 additional short trials were given with a single pellet available in front of the discriminandum on each of these trials. Group Ds-DEL was subdivided for purposes of a third phase of training. Five Ss were continued under the same conditions of a short delay [group SH-DEL
Description
Treatment
Description
Treatment
-
-.
One
Short-delay
DEL
DIS
t’raining
__-
Discrimination training
-__~-__
subdivided
NO-F
(DEL)
Short-delay testing
Group
or
Ds-DEL
Two
of training
Design
Short-delay testing with prefeeding FED (DEL)
either ~-
testing
and given
training
and
TABLE 1 of Experiment.al
Short-delay
Phase
Summary
subdivided
-
-
Short-delay testing SH-DEL (DIS)
Group
or
Three and
I&-DEL -
(DIS,
eit’her Long-delay testing
given
~
:! u
5
5 d
z 8 m F
DELAYED
(DIS)] [group
REACTIONS
IN
and 5 Ss were given an additional LG-DEL ( DIS ) ] .3
451
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60 trials
under
long delay
RESULTS
Acquisition. Response correctness was recorded on each trial and the number of correct responses summed for blocks of 10 trials each. The mean proportion of correct responses by groups DIS and DEL have been plotted as data points in Fig, 1. The smooth curves in Fig. 1 graph the expected mean learning curves and are discussed below. As can be seen in Fig. 1, the groups were responding about the same at the outset, but their performances tended to diverge across subsequent trial blocks. Group DIS was 100% correct on the last three blocks of trials, whereas group DEL was only 65-70% correct on these trial blocks. The effects of delay on number of correct responses on 15 blocks of trials were evaluated in a 2 X 15’ X 10 analysis of variance. In this analysis and subsequent ones, statistical significance was evaluated at the .05 level. Delay, trial blocks, and the delay by trial blocks interaction were all significant.
BLOCKS
FIG. 1. Mean learning curves for circles), and Ds-DEL (solid squares). performance of group DIS on trials imposed. Smooth curves show predicted
OF IO TRIALS
groups DIS (open squares ), DEL (open The data for group Ds-DEL represent the 151300, during which a short delay was mean learning curves.
‘Because of a severe blizzard Ss could not be middle of the study. In order to get Ss back on additional days. The g-day interruption occurred of testing on the short delay for group Ds-DEL, day of training for groups FED (DEL) and NO-F
fed or run for 2 days during the schedule, they were not run for 3 between the second and third day and between the second and third (DEL).
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POWELL
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AHNOLD
Di,scrimination trcmyfcr. The number of correct responses made by group Ds-DEL were summed for blocks of ten trials each and the mean proportions of correct responses on each block have been plotted as filled squares in Fig. 1. As can be seen there, group Ds-DEL responded more correctly on earlier trial blocks than did group DEL, but both groups were responding about the same at the end of training. The effects of prior discrimination training upon number of correct responses on 15 blocks of trials were evaluated in 2 X 15 X 10 analysis of variance. Prior discrimination training and trial blocks were significant, but the treatments by trial blocks interaction was not. A comparison of groups Ds-DEL and DEL on the last four trials blocks showed the difference to be nonsignificant. These results indicate that, whereas prior discrimination training facilitated performance on the earlier trials of short-delay training, it did not influence asymptotic performance under the short delay. Length of delay. The number of correct responses by groups SH-DEL (01s) and LG-DEL (01s) were summed for blocks of ten trials each, and the mean proportions of correct responses on each trial block have been plotted in Fig. 2. As can be seen, the introduction of a longer delay led to an immediate and reliable decrement in correct responding. Group SH-DEL (DIS) continued to respond correctly about 70% of the time, whereas group LG-DEL (DIS) was correct only about S747 of the time. The effects of length of delay on number of correct responses on six blocks of trials were evaluated in a 2 X 6 x 5 analysis of variance. The main effect of length of delay was marginally significant ( p < .06), but trial blocks and the treatments by trial blocks interaction were nonsignificant. Although group LG-DEL ( DIS ) wzs responding 2 ‘: lo2 i
.90-
i
eo-
----
g70-
u
26’3-
@- -\
SH-DEL LG-DEL
(DIS) (Dl.9
&----a.,
-. .a----*---
‘73
B 50B E 40-
$3 QLOCKS
OF
IO TRIALS
FIG. 2. Mean performance on trials on which vening training on a short-delay) were continued DEL; solid lines) or switched to a longer delay
Ss in group DIS under short-delay (LG-DEL; broken
(following conditions lines).
inter( SH-
DELAYED
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IN
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close to chance level, a test of the difference between the average number of correct responses across all 60 trials and the nunlber expected by chance (i.e., 30), was significant (t( 4) = 3.62). Prefeeding. The number of correct responses by groups NO-F (DEL) were summed for blocks of ten trials each on the and FED (DEL) mean proportions of correct responses on each trial block have been plotted in Fig. 3. As can be seen, feeding Ss in front of the cue had a disruptive effect on their performance on the first trial block but had little or no effect on subsequent trial blocks. The effects of prefeeding upon number of correct responses on six blocks of trials were evaluated in a 2 x 6 X 5 analysis of variance. Prefeeding, trial blocks and the treatments by trial blocks interaction were all nonsignificant. The simple main effect of prefeeding on the first trial block was significant. Quantitative fit. According to the nonincremental assumption of learning made by the Uncertain Trace model, the sampled element must be in an unconditioned state prior to the occurrence of the last error in the no delay condition, and therefore, the probability of a correct response occurring on any presolution trial should remain constant, and equal to the probability of guessing correctly. The number of correct responses for group DIS on all presolution trials were summed for Vincentized tenths and, although there was a tendency for the probability of a correct response to remain stable (and equal to one-half) over the first few tenths, there was an obvious increase over the last few tenths. The difference between the average number of correct responses on the first five and last five Vincentized-tenths was significant ( wra&re&t( 9) = 2 2 2 l.O2 E .90P IT BO8 u 70zi i 60P 0 soE z 40-
/’ d’ ----
9T, 1
,
,
,
,
,
2
3
4
5
G
BLOCKS
FIG. in front without
NO-F (DELI FED (DEL)
OF IO TRIALS
3. Mean performance on trials on which S’s in group of the cue (FED; broken lines) or continued under feeding in front of the cue (NO-F; solid lines ).
DEL short
were delay
either fed conditions
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POWELL
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2.73). Therefore, learning in the present study is best described as an incremental process. The conditioning parameter, c, was estimated by dividing the average total number of errors made by group DIS into .5 (cf. Atkinson et al., 1966). As a result, the empirical estimate of c was found to equal .02. The data from all 210 trials on which Ss in DEL were trained under a short delay (10 Ss received 150 acquisition and, then, half of them received another 60 trials under the same condition) were used to find an estimate of the memory parameter, T. By substituting 0.2 for c into an expression for the total error data the empirical estimate of r was found to equal .46. The smooth functions in Fig. 1 are the predicted mean learning curves. As can be seen, the data points for groups DIS and DEL formed a slightly more sigmoid-shaped curve than the predicted mean learning curves, which are negative growth functions. The fit of the predicted mean learning curves to the obtained data was evaluated using the procedure outlined by Grant (1962). Although the covariation (F correspondence) between the obtained and predicted values was significant for groups DIS and DEL, the deviations of obtained from predicted values were nonsignificant in the case of group DIS and significant in the case of DEL. These results indicate that although the models account for most of the variance in the mean learning curves there is a small amount of variance left unaccounted for. Lynn (1969) has derived a number of sequential statistics from models that are mathematically equivalent to the Uncertain Trace and Linear Trace-Decay models, and these statistics were used to further evaluate the quantitative fit of the models. The obtained and predicted values for the SD of total errors for groups DIS and DEL are presented in Table 1, the predicted values being determined by appropriate substitutions for c and r in the equations presented in Lynn (1969). The obtained and predicted values for four response bigrams (where V;j is the number of occurrences, in 150 trials, of response i on trial N and response i on trial N + 1) are also presented in Table 2. As can be seen in Table 2, the Linear Trace-Decay model provided a better fit to the data than did the Uncertain Trace model, A goodness of fit test found the discrepancies between the obtained values and those predicted by the latter model to be significant for both groups DIS, x2( 2) = 13.61, and DEL, x”( 2) = 6.02. The values predicted by the Linear Trace-Decay model were not significantly different from obtained values. This is consistent with the findings, reported above, that learning in group DIS failed to support the assumption of stationarity of performance on presolution trials. However, as can be seen in Table 1, there were rather large discrepancies between the obtained and predicted values for the
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TABLE 2 Observed and Predict,ed Values for Standard Deviation of Total Errors and Response Bigrams of Groups DIS and DEL Group DIS
DEL Predicted
Variable -____ Standard deviation of total errors __- _~Response bigram@ voo 81, VOl VII
Predicted
Observed
UTY
8.66
24.37
13.46
7.67 __~~.
12 12 12 114
6 18 1X 108
22 41 42 45
7 20 20 I 03
-~-
LTD
Observed
UTa
LTDa
32.35
21.46
26 34 34 56
24 35 36 55
a UT refers to t,he IJnrertain Trace model and LTT) to the Linear Trace-Decay model. * An incorrect response is signified by 0 and a correct response by 1.
standard deviations of total errors, the discrepancy being largest in the case of group DIS. DISCUSSION
According to the models of delayed reactions that were investigated, the difference between the asymptotic performance levels of Ss trained under delay and nondelay conditions can be attributed to a given probability that the cue is forgotten during the interval. Three findings of the study lend support to this interpretation and eliminate an alternative explanation that 5’s do not attend to (or “sample”) the stimulus element as well when there is delay between the stimulus and response occasions. (a) While administering discrimination training prior to the introduction of a delay facilitated performance on the early delay trials, it did not influence asymptotic performance. (b) Feeding in front of the discriminandum did not improve the asymptotic performance of Ss being tested with a short delay imposed. (c) Increasing the length of delay led to an immediate and reliable decrement in performance. It has been generally assumedthat prior discrimination training is necessary in order for any learning or nonchance performance to occur when a delay is imposed between stimulus and response occasions. Most studies of short-term memory in animals using the delayed reaction paradigm
456
POWELL
AND
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have followed the procedure of trainin, CTss on a nondelay discrimination task, and then gradually introducing increasingly longer clehy~. HOWever, this procedure confounds stage of practice with retention interval, and the results of the present study and studies that have departed from this procedure (e.g., Blough, 1959) demonstrate that learning can occur under delay conditions, Although performance may be impaired by the decrease in the stimulus truce or loss of information from a shortterm memory store, learning still occurs. There is experimental evidence that perceptual or attentional variables are involved in some variations of the delayed reaction paradigm (Bliss, 1960; Cowles, 1940, 1941; Handlon, 1950). In fact, failure to attend to the cue can account for some of the difference between the performance of rats in delay and non-delay conditions in Hunter’s (1913) original study. That is, in Hunter’s early investigation when a delay was imposed Ss could only view the discriminandum from a distance, whereas they could approach it directly under conditions of no delay. A recent study by Harlow, Blomquist, and Deets (1971) provides another example of the importance of perceptual of attentional variables. Harlow’s et al. study of rhesus monkeys found that performance under various intervals of delay was improved if the food could be seen during the baiting stage of each trial, a finding that was interpreted as lending support to Fletcher’s (1965) orienting response analysis of delayed reactions. The mathematical models did not adequately predict all of the quantitative aspects of the data. Although an analysis of the presolution data and selected sequential statistics indicated that the Linear TraceDecay model provided a more accurate description of the data than did the Uncertain Trace model, a still more complex model is needed in order to adequately account for the quantitative aspects of delayedreaction performance. In both the delay and nondelay conditions, the empirical learning curves were slightly sigmoid-shaped, whereas the Linear Trace-Decay model predicts a negative growth function. It is not uncommon to find sigmoid-shaped curves in studies of animal discrimination learning, and this finding suggests that a more complex model is needed to account for the learning that occurs in such situations. Tests of the mathematical models did provide some support for the assumption that the effect of delay is restricted to the asymptote of learning and that acquisition occurs at the same rate in delay and nondelay conditions. The conditioning parameter, c (which is also equal to 1 - (y) was estimated from the total error data of group DIS. When this estimate was used in predicting the mean learning curve of group DEL, a reasonable fit was obtained to the mean learning data. Although there was a significant discrepancy between the observed and predicted
DELAYED
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values, it is still reasonable to assume that acquisition occurred at the same rate in the delay and nondelay conditions, since a similar discrepancy arose in predicting the mean learning data of group DIS. Although the Linear Trace-Decay model did not satisfactorily account for all the quantitative aspects of the data, it provided a better fit to the data than the Uncertain Trace model. The incremental nature of learning that occurs in simple discrimination training with rats, whether or not short-term memory processes are involved by imposing a delay, could be given further emphasis by models that assume that the attributes of relevant stimuli become conditioned gradually while attributes of irrelevant stimuli are gradually adapted (e.g., Restle, 1955). Such models should be investigated further in simple discrimination situations and considered for their ability to accomodate “memory” parameters. REFERENCES ATKINSON, R. C., BOXER, G. H., & CROTHERS, E. J. Introduction to mathematical learning theory. New York: Wiley, 1966. BLISS, W. D. C. The role of perceptual cues in the delayed reaction. Journrll of Comparative and Physiological Psychology, 1960, 53, 176-179. BLOUGH, 0. S. Delayed matching in the pigeon. Journal of the Experiment& Analysis of Behavior, 1959, 2, 151-160. BOWER, G. H. Application of a model to paired-associate learning. Psychometrika, 1961, 26, 255-280. BUSH, R. R., & MOSTELLER, F. A comparison of eight models. In R. R. Bush & W. K. Estes (Eds.) Studies in mathematical learning theory. Stanford: Stanford Univrer. Press, 1959. COWLES, J. T. “Delayed response” as tested by three methods and its relationship to other learning situations. Journal of Psychology, 1940, 9, 103-130. COWLES, J. T. Discrimination learning and pre-delay reinforcement in “delayed response.” Psychological Review, 1941, 48, 225-234. CUMIIIISG, W. W., BERRYAIAN, R., & COHEN, L. R. Acquisition and transfer of zerodelay matching. Psychological Reports, 1965, 17, 435-445. FLETCHER, H. J. The delayed-response problem. In A. M. Schrier, H. F. Harlow, & F. Stollnitz (Eds.) Behavior of nonhuman primafes: Modern research trends. Vol. 1. New York: Academic Press, 1965. GRANT, D. A. Testing the null hypotheses and the strategy and tactics of investigating theoretical models. Psychological Review, 1962, 69, 54-61. HANDLOS, J. H. Perceptual factors in the delayed response. University of California Publications in Psychology, 1950, 5, 289-320. HARLOW, H. F., BLOMQUIST. A. J., & DEETS, A. C. Effects of manipulating incentive visibility during the baiting phase of delayed-response problems. Learning and Motitiation, 1971, 2. 67-74. HULL, C. L. E.ssentiab of behavior. New Haven: Yale Univer. Press, 1951. HULL, C. L. A behavior .s@enz. New Haven: Yale Univer. Press, 1952. HUNTER, W. S. In delayed reaction in animals and children. Behavior Monographs, 1913, 2, l-86.
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KONORSKI, J., & LAWICKA, W. Physiologicai
AND
ARNOLD
mechanisms of delayed reactions: I. The analysis and classification of delayed reactions. Acta Biologiue Expe~imentaks (Warsaw), 1959, 19, 175-197. LYCT, E. A stimulus sampling model for stimultaneous discrimination learning. Journal of Mathematical Psychology, 1969, 6, 277-285. MCALLISTER, W. G. A further study of the delayed reaction in the albino rat. Compamtive Psychological Monogruphs, 1932, 8 (Whole No. 2), l-103. POWELL, A. Cognitive processes in animal learning and memory. Paper presented at the meeting of the Southern Society for Philosophy and Psychology, St. Louis, April, 1972. RESTLE, F. A theory of discrimination learning. Psychological Review, 1955, 62, 11-19. SMITH, M. P. The stimulus trace gradient in visual discrimination learning. Journal of Comparative and Physiological Psychology, 1951, 44, 154-161. WILSON, M. 0. Symbolic behavior in the white rat: 1. Relation of amount of interpolated activity to adequacy of delayed response. Jowd of Comparative Psychology, 1934, 18, 2949. (a) WILSON, M. 0. Symbolic behavior in the white rat: II. Relation of quality of interpolated activity on the adequacy of the delayed response. Journal of Comparative Psychology, 1934, 18, 367-384. (b) (Received
November
22, 1971)
ASD
hlOTIVATIOK
Mathematical
4, 445-458
(1973)
Models
of
Delayed
Reactions
in Rats’
ARNOLDPOWELL Columbus
College
AND WILLIAM University
J. ARNOLD of Nebraska
Two models of delayed reactions, the Uncertain Trace and the Linear Trace-Decay mode!s, were proposed and tested in a delayed-reaction T maze. Ss trained with a short delay attained lower asymptotic performance !evels than did Ss trained on the same discrimination, hut with no delay between stimulus and response. This was interpreted as reflecting the greater probability that Ss forget the cue during a delay interval, and three additional findings eliminated an alternative explanation that the cue is not attended to in the delay condition. The Linear Trace-Decay model provided a more accurate description of quantitative aspects of the data; however, neither model provided a completely adequate fit to the data.
Ever since Hunter’s (1913) original investigation of the delayed reaction paradigm, delayed reactions have been investigated in a variety of situations and species, but there have been relatively few explicit theoretical models of learning and performance is such situations. Cowles’ (1940, 1941) early discrimination model and Fletcher’s (1965) more recent intratrial, orienting response analysis are among the few explicit theoretical treatments of delayed reactions. According to Fletcher’s (1965) model, an orienting-response chain is evoked by stimulus presentation, and the instrumental response at the end of the delay interval is the terminal member of the response chain. Performance decrements as a function of delay interval result from events occurring during the delay ‘This research was supported by an NSF Predoctoral Traineeship awarded to the first author, and is based upon a dissertation submitted to the Graduate College in the University of Nebraska in partial fulfill ment of the requirements of the degree of Doctor of Philosophy. The thesis was submitted by the first author and supervised by the second author. A portion of the data were included in a paper presented at the meeting of the Rocky Mountain Psychological Association, Denver, May 1971. Requests for reprints should be sent to Arnold Powell, Department of Psychology, Columbus College, Columbus, Georgia 31907. Copyright All rights
@ 1973 by Academic Press, of reproduction in any form
445 Inc. reserved.
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POWELL
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interval which disrupt the response chain. An important assumption of this model is that imposing a delay between stimulus and response influences performance but not learning. Performance decrements arc’ COW sidered intratrial phenomena; the probability that the correct response does not occur, as a result of intradelay events, is a set parameter and does not vary as a function of trial number. Fletcher did not propose any explicit mathematical interpretation of his model, but there are several alternatives that stem from his analysis. A couple of alternative models are investigated in the present study that assume that responses become conditioned to the traces of stimuli presented earlier, as was postulated in by the models of delayed reactions investigated by Smith (1951, see also, Hull, 1951) and Konorski and Lawicka (1959). Th ere is a theoretical controversy concerning whether to conceptualize the processes that intervene between stimulus reception and response evocation in terms of stimulus traces, orienting responses, or memory storage and retrieval (e.g., Blough, 1959; Cumming, Berryman, & Cohen, 1965; Powell, 1972). However, the present study is not concerned with this issue but focuses, instead, upon the intratrial interpretation and its various implications. According to the Uncertain Trace model the discriminandum can be represented by a single stimulus element that is sampled with a probability of 1.0 on each trial. The trace of the sampled element continues through a delay interval with a probability of r, and becomes conditioned to the correct response with a probability of c. The memory parameter, 7, is assumed to be a function of the length of the delay interval, and both T and c are assumed to be independent of trial number. In other words, the Uncertain Trace model assumes that S attends to the cue whenever it is presented, and there is some probability that the cue will be remembered until there is an opportunity to respond. If S forgets the cue, or if it is remembered but still in the unconditioned state, then he guessesand makes a correct response with a probability of 0.50. It can be shown (Lynn, 1969) that the probability of a correct response on trial N ( P( R,-) N ) will equal P(Rc)X
= >2[(1 + r) - Y(l - cV)“-‘].
(1) The last term in Eq. ( 1)) ( 1 - CP)“~~, is the probability that the trace of a sampled element remains in an unconditioned state after N - I trials. As the trial number increases, the term approaches zero, and the probability of a correct response approaches W(I + r) : hence, the model predicts that asymptotic performance will vary as a function of the memory parameter, 7. An alternative to the Uncertain Trace model is the Linear TraceDecay model, which assumes that learning is an incremental process,
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and that the strength of a trace of a sampled element varies inversely with the length of delay. The Linear Trace-Decay model is a modification (cf. Lynn, 1969) of Bush and Mosteller’s (1959) Single Operator Linear model (see also, Bower, 1961; Atkinson, Bower, & Crothers, 1966), according to which the probability of a correct response on trial N + 1 is equal to the probability of being correct on trial N, plus a fraction, (1 - (Y), of the remaining portion (1 - PN) of the level to which P, can grow (1.0) (cf. Atkinson et al., 1966). However, the Linear Trace-Decay model assumes that the limit of P, is an additional parameter, 1L1,that varies inversely with the length of delay. Therefore, the probability of a correct response on trial N will equal (cf. Lynn, 1969) P(Rc)X
= IIT - (AZ - ?/$)((y)-‘.
(2)
The Linear Trace-Decay model is a stochastic analog to Hull’s (1952) incremental model in which the limit of the growth of Reaction Potential was postulated to vary inversely with the intensity of the Molar Stimulus Trace. Equations (1) and (2) predict the same learning curves, since (Y = (1 - CT) and M = X(1 + r), and both models make similar predict&s with regard to the effects of several variables upon delayed reaction performance. It is assumed that r and M vary with the length of delay and that both are equal to 1.0 when there is no delay. Therefore, both models predict that asymptotic performance will vary inversely as a function of length of delay and that perfect performance will be attained as an asymptote when there is no delay between stimulus and response. The models also predict that any increase in the length of delay with which Ss are being trained will produce an immediate and reliable decrement in performance. Since the memory, or asymptotic, parameters are independent of trial number, or prior experience, it is predicted that there will be no difference between the asymptotic performance of Ss given discrimination training prior to their training under conditions of delay and the asymptotic performance of Ss trained only under conditions of delay. Although Ss given prior discrimination training should demonstrate some stimulus generalization on the early trials of the transfer stage, their performance should approach the same asymptote. The Uncertain Trace and Linear-Decay models make similar predictions with regard to the above hypotheses, but they can be differentiated in terms of their quantitative fit to the data.” ‘It should be pointed out that although Uncertain ‘Trace and Linear TraceDecay make different assumptions with regard to the duration of the traces of sampled elements (all-or-none versus decay), these assumptions are not tested in the present study.
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Roth of the above models interpret differences in performance as a function of delay interval in terms of the tendency of S to forget the cue during the delay interval. However, there is evidence that perceptual or attentional variables are involved in performance in some variations of the delayed reaction paradigm (Fletcher, 1965). Therefore, any difference between performance in delay and nondelay conditions could be attributed to the probability the Ss fail to attend the cue when a delay is involved. If failure to attend to the cue is an important factor, then giving prior discrimination training would be expected to improve performance in the delay condition. Furthermore, feeding S in front of the cue would be expected to increase the probability that he attends to it and, hence, should also improve performance in the delay condition. The present study was designed to test the following hypotheses: (a) imposing a short delay between stimulus and response occasions will lead to a decrease in asymptotic performance; and (b) administering prior discrimination training will not improve asymptotic performance under conditions of a short delay; (c) increasing the length of delay will result in an immediate and reliable decrement in performance; and (d) feeding Ss in front of the discriminandum under conditions of a short delay will not influence asymptotic performance. These hypotheses are tested in a T-maze in which “length” of delay is defined in terms of the distance between a stimulus chamber and the choice point of the maze. This apparatus incorporates several improvements upon earlier employed in studies by apparatus. For example, in the apparatus McAllister ( 1932) and Wilson (1934a,b) the delay interval was confounded with amount of effort, delay of reinforcement, or both, whereas both of these variables are held constant in the apparatus employed in the present study. METHOD
Subjects. Ss were 20 male albino rats obtained from the Charles Rivers CD strain. All Ss were approximately 90-110 days old at the beginning of the study and were housed individually throughout the investigation. Apparatus. The apparatus was a T-maze with a 2.9 m long x 11 cm wide X 17 cm high alley and a 1.2 m X 13 cm X 14 cm high arm. The stimulus which indicated a correct response was a white circle, 9 cm in diameter, cut from white enamel Con-Tact paper. In the no-delay condition the stimulus was placed on the appropriate goal box door. In the delay conditions, however, the stimulus was presented at either of two points between the start box and the choice point. Short sections of the
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flush alley walls were removed and walls, which extended at a 60” angle outside of the alley walls, were inserted in their place. The stimulus was then placed on the back wall, extending outside the normal alley walls and in clear view as S approached from the start box. When short and long delays were imposed, the stimulus was placed 1.1 m or .4 m, respectively, in front of the choice point, and was not present on the goal box door. A guillotine door was at the entrance to the alley and the goal boxes were entered by pushing open masonite doors that were hinged at the top. The entire maze was painted flat black and covered with hardware cloth doors. Design and procedure. During the first 10 days of the study Ss were placed on a 11-13 g per day maintenance diet, with water available ad lib., and maintained on this schedule for the remainder of the study. Adaptation to the experimental apparatus and shaping of Ss to push open the goal box doors were conducted on days 11 and 12. For all Ss the first phase of experimental training involved 150 acquisition trials and was begun on day 13; one trial was administered on days 13 and 14, two on days 15 and 16 and, then eight per day except for the last day which required 10 trials. Ss were run in squads of 10 and all Ss in a squad were given a single trial before any S received a second trial. The average intertrial interval was approximately 10 min. Correct responses were rewarded with three 45-mg Noyes pellets, a noncorrection procedure was employed, and the correct response was alternated according to a RLLRLRRLLRRLRLLR counterbalanced sequence. Ss were randomly assigned to group DIS or DEL. A summary of the experimental design is presented in Table 1. Group DIS received 150 training trials on a black-white discrimination, with no delay, while Ss in DEL received 150 trials on the same task with a short delay imposed between the stimulus and response. During the second phase of experimental training, Ss in DIS were given 150 trials (8 per day; with 6 on the last day) under conditions of short delay (hereafter referred to as group Ds-DEL). Following acquisition, Ss in group DEL were randomly assigned to two subgroups. During the second phase, 5 Ss in group NO-F (DEL) were continued under the same conditions of short delay for an additional 60 trials (8 per day; 4 on the last day), Five Ss in FED (DEL) were given 20 placements (10 per day) in front of the discriminandum, with a single 45-mg Noyes pellet available on each of these placements. S was removed as soon as the pellet was consumed. Then, 60 additional short trials were given with a single pellet available in front of the discriminandum on each of these trials. Group Ds-DEL was subdivided for purposes of a third phase of training. Five Ss were continued under the same conditions of a short delay [group SH-DEL
Description
Treatment
Description
Treatment
-
-.
One
Short-delay
DEL
DIS
t’raining
__-
Discrimination training
-__~-__
subdivided
NO-F
(DEL)
Short-delay testing
Group
or
Ds-DEL
Two
of training
Design
Short-delay testing with prefeeding FED (DEL)
either ~-
testing
and given
training
and
TABLE 1 of Experiment.al
Short-delay
Phase
Summary
subdivided
-
-
Short-delay testing SH-DEL (DIS)
Group
or
Three and
I&-DEL -
(DIS,
eit’her Long-delay testing
given
~
:! u
5
5 d
z 8 m F
DELAYED
(DIS)] [group
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IN
and 5 Ss were given an additional LG-DEL ( DIS ) ] .3
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60 trials
under
long delay
RESULTS
Acquisition. Response correctness was recorded on each trial and the number of correct responses summed for blocks of 10 trials each. The mean proportion of correct responses by groups DIS and DEL have been plotted as data points in Fig, 1. The smooth curves in Fig. 1 graph the expected mean learning curves and are discussed below. As can be seen in Fig. 1, the groups were responding about the same at the outset, but their performances tended to diverge across subsequent trial blocks. Group DIS was 100% correct on the last three blocks of trials, whereas group DEL was only 65-70% correct on these trial blocks. The effects of delay on number of correct responses on 15 blocks of trials were evaluated in a 2 X 15’ X 10 analysis of variance. In this analysis and subsequent ones, statistical significance was evaluated at the .05 level. Delay, trial blocks, and the delay by trial blocks interaction were all significant.
BLOCKS
FIG. 1. Mean learning curves for circles), and Ds-DEL (solid squares). performance of group DIS on trials imposed. Smooth curves show predicted
OF IO TRIALS
groups DIS (open squares ), DEL (open The data for group Ds-DEL represent the 151300, during which a short delay was mean learning curves.
‘Because of a severe blizzard Ss could not be middle of the study. In order to get Ss back on additional days. The g-day interruption occurred of testing on the short delay for group Ds-DEL, day of training for groups FED (DEL) and NO-F
fed or run for 2 days during the schedule, they were not run for 3 between the second and third day and between the second and third (DEL).
452
POWELL
ASI)
AHNOLD
Di,scrimination trcmyfcr. The number of correct responses made by group Ds-DEL were summed for blocks of ten trials each and the mean proportions of correct responses on each block have been plotted as filled squares in Fig. 1. As can be seen there, group Ds-DEL responded more correctly on earlier trial blocks than did group DEL, but both groups were responding about the same at the end of training. The effects of prior discrimination training upon number of correct responses on 15 blocks of trials were evaluated in 2 X 15 X 10 analysis of variance. Prior discrimination training and trial blocks were significant, but the treatments by trial blocks interaction was not. A comparison of groups Ds-DEL and DEL on the last four trials blocks showed the difference to be nonsignificant. These results indicate that, whereas prior discrimination training facilitated performance on the earlier trials of short-delay training, it did not influence asymptotic performance under the short delay. Length of delay. The number of correct responses by groups SH-DEL (01s) and LG-DEL (01s) were summed for blocks of ten trials each, and the mean proportions of correct responses on each trial block have been plotted in Fig. 2. As can be seen, the introduction of a longer delay led to an immediate and reliable decrement in correct responding. Group SH-DEL (DIS) continued to respond correctly about 70% of the time, whereas group LG-DEL (DIS) was correct only about S747 of the time. The effects of length of delay on number of correct responses on six blocks of trials were evaluated in a 2 X 6 x 5 analysis of variance. The main effect of length of delay was marginally significant ( p < .06), but trial blocks and the treatments by trial blocks interaction were nonsignificant. Although group LG-DEL ( DIS ) wzs responding 2 ‘: lo2 i
.90-
i
eo-
----
g70-
u
26’3-
@- -\
SH-DEL LG-DEL
(DIS) (Dl.9
&----a.,
-. .a----*---
‘73
B 50B E 40-
$3 QLOCKS
OF
IO TRIALS
FIG. 2. Mean performance on trials on which vening training on a short-delay) were continued DEL; solid lines) or switched to a longer delay
Ss in group DIS under short-delay (LG-DEL; broken
(following conditions lines).
inter( SH-
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close to chance level, a test of the difference between the average number of correct responses across all 60 trials and the nunlber expected by chance (i.e., 30), was significant (t( 4) = 3.62). Prefeeding. The number of correct responses by groups NO-F (DEL) were summed for blocks of ten trials each on the and FED (DEL) mean proportions of correct responses on each trial block have been plotted in Fig. 3. As can be seen, feeding Ss in front of the cue had a disruptive effect on their performance on the first trial block but had little or no effect on subsequent trial blocks. The effects of prefeeding upon number of correct responses on six blocks of trials were evaluated in a 2 x 6 X 5 analysis of variance. Prefeeding, trial blocks and the treatments by trial blocks interaction were all nonsignificant. The simple main effect of prefeeding on the first trial block was significant. Quantitative fit. According to the nonincremental assumption of learning made by the Uncertain Trace model, the sampled element must be in an unconditioned state prior to the occurrence of the last error in the no delay condition, and therefore, the probability of a correct response occurring on any presolution trial should remain constant, and equal to the probability of guessing correctly. The number of correct responses for group DIS on all presolution trials were summed for Vincentized tenths and, although there was a tendency for the probability of a correct response to remain stable (and equal to one-half) over the first few tenths, there was an obvious increase over the last few tenths. The difference between the average number of correct responses on the first five and last five Vincentized-tenths was significant ( wra&re&t( 9) = 2 2 2 l.O2 E .90P IT BO8 u 70zi i 60P 0 soE z 40-
/’ d’ ----
9T, 1
,
,
,
,
,
2
3
4
5
G
BLOCKS
FIG. in front without
NO-F (DELI FED (DEL)
OF IO TRIALS
3. Mean performance on trials on which S’s in group of the cue (FED; broken lines) or continued under feeding in front of the cue (NO-F; solid lines ).
DEL short
were delay
either fed conditions
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2.73). Therefore, learning in the present study is best described as an incremental process. The conditioning parameter, c, was estimated by dividing the average total number of errors made by group DIS into .5 (cf. Atkinson et al., 1966). As a result, the empirical estimate of c was found to equal .02. The data from all 210 trials on which Ss in DEL were trained under a short delay (10 Ss received 150 acquisition and, then, half of them received another 60 trials under the same condition) were used to find an estimate of the memory parameter, T. By substituting 0.2 for c into an expression for the total error data the empirical estimate of r was found to equal .46. The smooth functions in Fig. 1 are the predicted mean learning curves. As can be seen, the data points for groups DIS and DEL formed a slightly more sigmoid-shaped curve than the predicted mean learning curves, which are negative growth functions. The fit of the predicted mean learning curves to the obtained data was evaluated using the procedure outlined by Grant (1962). Although the covariation (F correspondence) between the obtained and predicted values was significant for groups DIS and DEL, the deviations of obtained from predicted values were nonsignificant in the case of group DIS and significant in the case of DEL. These results indicate that although the models account for most of the variance in the mean learning curves there is a small amount of variance left unaccounted for. Lynn (1969) has derived a number of sequential statistics from models that are mathematically equivalent to the Uncertain Trace and Linear Trace-Decay models, and these statistics were used to further evaluate the quantitative fit of the models. The obtained and predicted values for the SD of total errors for groups DIS and DEL are presented in Table 1, the predicted values being determined by appropriate substitutions for c and r in the equations presented in Lynn (1969). The obtained and predicted values for four response bigrams (where V;j is the number of occurrences, in 150 trials, of response i on trial N and response i on trial N + 1) are also presented in Table 2. As can be seen in Table 2, the Linear Trace-Decay model provided a better fit to the data than did the Uncertain Trace model, A goodness of fit test found the discrepancies between the obtained values and those predicted by the latter model to be significant for both groups DIS, x2( 2) = 13.61, and DEL, x”( 2) = 6.02. The values predicted by the Linear Trace-Decay model were not significantly different from obtained values. This is consistent with the findings, reported above, that learning in group DIS failed to support the assumption of stationarity of performance on presolution trials. However, as can be seen in Table 1, there were rather large discrepancies between the obtained and predicted values for the
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TABLE 2 Observed and Predict,ed Values for Standard Deviation of Total Errors and Response Bigrams of Groups DIS and DEL Group DIS
DEL Predicted
Variable -____ Standard deviation of total errors __- _~Response bigram@ voo 81, VOl VII
Predicted
Observed
UTY
8.66
24.37
13.46
7.67 __~~.
12 12 12 114
6 18 1X 108
22 41 42 45
7 20 20 I 03
-~-
LTD
Observed
UTa
LTDa
32.35
21.46
26 34 34 56
24 35 36 55
a UT refers to t,he IJnrertain Trace model and LTT) to the Linear Trace-Decay model. * An incorrect response is signified by 0 and a correct response by 1.
standard deviations of total errors, the discrepancy being largest in the case of group DIS. DISCUSSION
According to the models of delayed reactions that were investigated, the difference between the asymptotic performance levels of Ss trained under delay and nondelay conditions can be attributed to a given probability that the cue is forgotten during the interval. Three findings of the study lend support to this interpretation and eliminate an alternative explanation that 5’s do not attend to (or “sample”) the stimulus element as well when there is delay between the stimulus and response occasions. (a) While administering discrimination training prior to the introduction of a delay facilitated performance on the early delay trials, it did not influence asymptotic performance. (b) Feeding in front of the discriminandum did not improve the asymptotic performance of Ss being tested with a short delay imposed. (c) Increasing the length of delay led to an immediate and reliable decrement in performance. It has been generally assumedthat prior discrimination training is necessary in order for any learning or nonchance performance to occur when a delay is imposed between stimulus and response occasions. Most studies of short-term memory in animals using the delayed reaction paradigm
456
POWELL
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have followed the procedure of trainin, CTss on a nondelay discrimination task, and then gradually introducing increasingly longer clehy~. HOWever, this procedure confounds stage of practice with retention interval, and the results of the present study and studies that have departed from this procedure (e.g., Blough, 1959) demonstrate that learning can occur under delay conditions, Although performance may be impaired by the decrease in the stimulus truce or loss of information from a shortterm memory store, learning still occurs. There is experimental evidence that perceptual or attentional variables are involved in some variations of the delayed reaction paradigm (Bliss, 1960; Cowles, 1940, 1941; Handlon, 1950). In fact, failure to attend to the cue can account for some of the difference between the performance of rats in delay and non-delay conditions in Hunter’s (1913) original study. That is, in Hunter’s early investigation when a delay was imposed Ss could only view the discriminandum from a distance, whereas they could approach it directly under conditions of no delay. A recent study by Harlow, Blomquist, and Deets (1971) provides another example of the importance of perceptual of attentional variables. Harlow’s et al. study of rhesus monkeys found that performance under various intervals of delay was improved if the food could be seen during the baiting stage of each trial, a finding that was interpreted as lending support to Fletcher’s (1965) orienting response analysis of delayed reactions. The mathematical models did not adequately predict all of the quantitative aspects of the data. Although an analysis of the presolution data and selected sequential statistics indicated that the Linear TraceDecay model provided a more accurate description of the data than did the Uncertain Trace model, a still more complex model is needed in order to adequately account for the quantitative aspects of delayedreaction performance. In both the delay and nondelay conditions, the empirical learning curves were slightly sigmoid-shaped, whereas the Linear Trace-Decay model predicts a negative growth function. It is not uncommon to find sigmoid-shaped curves in studies of animal discrimination learning, and this finding suggests that a more complex model is needed to account for the learning that occurs in such situations. Tests of the mathematical models did provide some support for the assumption that the effect of delay is restricted to the asymptote of learning and that acquisition occurs at the same rate in delay and nondelay conditions. The conditioning parameter, c (which is also equal to 1 - (y) was estimated from the total error data of group DIS. When this estimate was used in predicting the mean learning curve of group DEL, a reasonable fit was obtained to the mean learning data. Although there was a significant discrepancy between the observed and predicted
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values, it is still reasonable to assume that acquisition occurred at the same rate in the delay and nondelay conditions, since a similar discrepancy arose in predicting the mean learning data of group DIS. Although the Linear Trace-Decay model did not satisfactorily account for all the quantitative aspects of the data, it provided a better fit to the data than the Uncertain Trace model. The incremental nature of learning that occurs in simple discrimination training with rats, whether or not short-term memory processes are involved by imposing a delay, could be given further emphasis by models that assume that the attributes of relevant stimuli become conditioned gradually while attributes of irrelevant stimuli are gradually adapted (e.g., Restle, 1955). Such models should be investigated further in simple discrimination situations and considered for their ability to accomodate “memory” parameters. REFERENCES ATKINSON, R. C., BOXER, G. H., & CROTHERS, E. J. Introduction to mathematical learning theory. New York: Wiley, 1966. BLISS, W. D. C. The role of perceptual cues in the delayed reaction. Journrll of Comparative and Physiological Psychology, 1960, 53, 176-179. BLOUGH, 0. S. Delayed matching in the pigeon. Journal of the Experiment& Analysis of Behavior, 1959, 2, 151-160. BOWER, G. H. Application of a model to paired-associate learning. Psychometrika, 1961, 26, 255-280. BUSH, R. R., & MOSTELLER, F. A comparison of eight models. In R. R. Bush & W. K. Estes (Eds.) Studies in mathematical learning theory. Stanford: Stanford Univrer. Press, 1959. COWLES, J. T. “Delayed response” as tested by three methods and its relationship to other learning situations. Journal of Psychology, 1940, 9, 103-130. COWLES, J. T. Discrimination learning and pre-delay reinforcement in “delayed response.” Psychological Review, 1941, 48, 225-234. CUMIIIISG, W. W., BERRYAIAN, R., & COHEN, L. R. Acquisition and transfer of zerodelay matching. Psychological Reports, 1965, 17, 435-445. FLETCHER, H. J. The delayed-response problem. In A. M. Schrier, H. F. Harlow, & F. Stollnitz (Eds.) Behavior of nonhuman primafes: Modern research trends. Vol. 1. New York: Academic Press, 1965. GRANT, D. A. Testing the null hypotheses and the strategy and tactics of investigating theoretical models. Psychological Review, 1962, 69, 54-61. HANDLOS, J. H. Perceptual factors in the delayed response. University of California Publications in Psychology, 1950, 5, 289-320. HARLOW, H. F., BLOMQUIST. A. J., & DEETS, A. C. Effects of manipulating incentive visibility during the baiting phase of delayed-response problems. Learning and Motitiation, 1971, 2. 67-74. HULL, C. L. E.ssentiab of behavior. New Haven: Yale Univer. Press, 1951. HULL, C. L. A behavior .s@enz. New Haven: Yale Univer. Press, 1952. HUNTER, W. S. In delayed reaction in animals and children. Behavior Monographs, 1913, 2, l-86.
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KONORSKI, J., & LAWICKA, W. Physiologicai
AND
ARNOLD
mechanisms of delayed reactions: I. The analysis and classification of delayed reactions. Acta Biologiue Expe~imentaks (Warsaw), 1959, 19, 175-197. LYCT, E. A stimulus sampling model for stimultaneous discrimination learning. Journal of Mathematical Psychology, 1969, 6, 277-285. MCALLISTER, W. G. A further study of the delayed reaction in the albino rat. Compamtive Psychological Monogruphs, 1932, 8 (Whole No. 2), l-103. POWELL, A. Cognitive processes in animal learning and memory. Paper presented at the meeting of the Southern Society for Philosophy and Psychology, St. Louis, April, 1972. RESTLE, F. A theory of discrimination learning. Psychological Review, 1955, 62, 11-19. SMITH, M. P. The stimulus trace gradient in visual discrimination learning. Journal of Comparative and Physiological Psychology, 1951, 44, 154-161. WILSON, M. 0. Symbolic behavior in the white rat: 1. Relation of amount of interpolated activity to adequacy of delayed response. Jowd of Comparative Psychology, 1934, 18, 2949. (a) WILSON, M. 0. Symbolic behavior in the white rat: II. Relation of quality of interpolated activity on the adequacy of the delayed response. Journal of Comparative Psychology, 1934, 18, 367-384. (b) (Received
November
22, 1971)