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A conditional numerical discrimination based on qualitatively different reinforcers
LEARNING
AND MOTIVATION
20,
48-59
(1989)
A Conditional Numerical Discrimination Based on Qualitatively Different Reinforcers E. J. CAPALDI, DANIEL J. MILLER, Purdue
AND
SUZAN
ALPTEKIN
University
An animal able to count but unable to conditionalize its count on some other cue would not possess a useful sense of number because numerical discriminations are often conditional ones. Accordingly, we examined here in two runway investigations the ability of rats to learn a conditional numerical discrimination of the form: count this many Xs and that many Ys, the Xs and Ys being qualitatively different food items which in the normal environment would correspond to different prey items. In each investigation, the rat learned the conditional numerical discrimination, running slowly on nonreinforced trials which were signaled by different numbers of successively presented food reinforcements, running being rapid to food items. In Experiment 1, nonreinforcement was signaled by two successive food events of one type, e.g., Noyes sucrose pellets, and a single food event of another type, e.g., Noyes plain pellets. In Experiment 2, nonreinforcement was signaled by two successive food events of one type and three such events of another type. That rats were able to conditionalize their count on type of food item indicates that their numerical capacity is far from primitive and may be complex. But further tests are required to determine how complex the numerical Capacity of rats may be. Q 1989 Academic Press, IIK
Recent evidence indicates that rats are able to employ numbers of events of various sorts as a discriminative cue, events ranging from visual and auditory stimuli to food reinforcement (e.g., Capaldi & Miller, 1988a; Church & Meek, 1987; Davis & Bradford. 1986). In the preparation employed by Capaldi and Miller (1988a), rats were able to employ as a discriminative cue numbers of successively presented food reinforcements, each of which was contingent upon an instrumental running response in a straight-alley runway. For example, rats were able to anticipate, as indicated by slow running, a nonreinforced trial which was preceded by three reinforced trials, running being rapid on each of the reinforced trials. Call this a 3R series. Various control procedures indicated that This research was supported in part by NSF Grant BNS-8515831 to E. J. Capaldi. Address correspondence and reprint requests to Dr. E. J. Capaldi, Department of Psychological Sciences, Purdue University, West Lafayette, IN 47907. 48 0023-9690189 Copyright All rights
$3.00 0 1989 by Academic Press. of reproduction in any form
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discriminative responding under the 3R series was based upon enumerating number of reinforcing events independently of a variety of other cues: other number cues, various temporal cues, and the amount of food ingested. It seems particularly appropriate to have rats enumerate food reinforcements because food events are obviously of great importance to animals, whether in various laboratory learning situations or in the natural environment. Thus, food events seem as likely as any events as candidates for enumeration by animals. A variety of approaches have been employed to determine how competent animals may be at forming numerical discriminations, some of which will be mentioned in the general discussion section. An examination of the various conditions under which numerical information may be employed by either people or animals is at the basis of the approach employed by the two investigations reported here. It seems quite clear that numerical discriminations rather than being simple in nature are very often conditional. That is, the number of events to be enumerated (n) differs depending upon the presence of some other cue (c) or n/c. For example, a child may be asked to place two blocks in the red box and three blocks in the blue box, while an animal may learn that more prey items of a particular description are available at one location than at another location. The conditionalization here, of course, is that the number of events enumerated (blocks, prey items of a given sort) depend upon something else (box color, location). Interestingly, rats have been shown to be able to form a conditional discrimination of the n/c sort described above. Bums and Sanders (1987), employing the same sort of experimental procedures as Capaldi and Miller (1988a), reported that rats are capable of anticipating simultaneously a nonreinforced trial which follows two reinforced trials in a runway of one brightness and texture, a 2R series, and three reinforced trials in a runway of another brightness and texture, a 3R series. Another sort of conditional numerical discrimination was of concern here. In this sort of problem, which is also quite common, number depends upon the event (e) being enumerated or n/e. Thus, a child might be required to distinguish two apples from three oranges; an animal might have to discriminate that at a given location more prey items of type X are available than of type Y. To investigate the n/e sort of conditional numerical discrimination, we employed here two qualitatively different reinforcing events: 0.045-g Noyes sucrose pellets (S) and plain pellets (P). Experiment 1 asked if rats could learn to anticipate nonreinforcement (N) when if followed one reinforcer of one type, a 1R series, and two successive reinforcers of the other type, a 2R series. That is, the series was either PN or SSN (or vice versa), the 1R and 2R series being irregularly presented in a gray runway. Previous findings indicate that
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ALPTEKIN
when rats are trained only under the 2R series they learn that two successive reinforced trials signal nonreinforcement, despite the fact that many other cues are confounded with number of reinforcers, e.g., number or duration of intertrial intervals (see Capaldi & Miller, 1988a, Experiment 3). Thus, on the basis of the Capaldi and Miller (1988a) findings, anticipating nonreinforcement in the IR and 2R series in Experiment 1 could be taken to indicate that rats are able to apply different counts to two different events simultaneously. In any case, to establish more firmly that rats can apply different counts to two different events simultaneously, Experiment 2 employed somewhat more elaborate, if not necessary, control procedures than Experiment 1. Experiment 2 asked if rats could learn to anticipate nonreinforcement when it followed two successive reinforcers of one type, a 2R series, and three successive reinforcers of another type, a 3R series. Half the 2R and 3R series were preceded, on an irregular basis, by a nonreinforced trial to rule out the possibility that the rats were counting or summing the duration of other events, e.g., intertrial intervals. EXPERIMENT
1
Method Subjects. The subjects were eight experimentally naive, male albino rats obtained from Holtzman Co., Madison, Wisconsin. All rats were 77 days old upon arrival at the laboratory and were placed on ad fibitum food for 14 days prior to the start of the experiment. The rats were randomly assigned in equal number to each of two subgroups. Two experimenters were employed, each running four rats, two from each subgroup. Two runways were employed. Apparatus. For the rats run by Experimenter 1, a straight gray runway was used measuring 208.67 cm long, 10.2 cm wide, and enclosed by 22.75-cm sides covered by a wire-mesh top on a hinged frame. The startbox and goalbox were 20.8 and 29.7 cm long, respectively, closed off by wooden guillotine doors. Raising the startbox door started a completely silent 0.01-s digital clock, which was stopped when a photobeam located 175.27 cm beyond the startbox door and 7.5 cm in front of the goalcup was broken by the rat. Pellets (0.045-g Noyes, Formula Atraditional plain, P; Formula F-sucrose, S) could be placed in a brass rectangular goalcup (4.2 x 3.0 cm and 1.85 cm in depth) located within a metal insert measuring 5.1 x 10.2 x 4.3 cm. Upon interruption of the photobeam, the wooden doors were lowered, confining the rat to the goalbox. For the rats run by Experimenter 2, a similar apparatus was employed, except it was slightly shorter (197.10 cm), slightly narrower (10.1 cm), and was enclosed by shorter sides (13.85 cm). The photobeam was located 158.13 cm beyond the startbox door and 9.5 cm in front of the circular
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goalcup, which was 4.0 cm in diameter and I.5 cm deep (cut into a 6.2 X 10.6 x 4.0-cm wooden block). Also the startbox and goalbox doors were made of metal. Pretruining. On Day 1 of pretraining, all rats began deprivation consisting of 15 g of Wayne Lab Chow fed in the home cage minus any amount eaten in the apparatus. On Days 1-6, all rats were handled individually for l-2 min. On Day 7, rats were given three plain and three sucrose pellets in the home cage prior to receiving the daily ration. On Days 79. each rat was allowed to explore the runway for 3 min, three plain pellets and three sucrose pellets being scattered about the runway. The rats were then returned to the home cage where they were fed the daily ration. Water was freely available in the home cage and in the running room throughout the experiment. On Days 10-12, each rat received two, two, and four series, respectively, in the runway. Trials terminated either in six 0.045-g plain pellets (P), six 0.045-g sucrose pellets (S), or nonreinforcement (N). Each rat received a 1R series, a single reinforced trial followed by nonreinforcement (N), and a 2R series, two successive reinforced trials followed by an N trial. Two of the rats trained by each experimenter received the series PN and SSN; the other two received the series SN and PPN. On Day 10, each rat received its 1R series, followed about 10 min later by its 2R series, the 1R series following the 2R series on Day 11. On Day 12, the rats received the series in the order lR, 2R, lR, 2R. Experimental training. On each of the 22 days of experimental training, each rat received its 1R series three times and its 2R series three times. On odd days, the series were presented in the order lR, 2R, 2R, lR, lR, 2R, and on even days the order was 2R, lR, lR, 2R, 2R, 1R. The experimenter brought the four rats she was running into the experimental room, with the home cages serving as the individual holding cages where they were confined between trials. Rats were run in a varied order each day. Each rat received its first scheduled series before another rat received its second series. This method produced an intertrial interval of about 15-30 s and an interseries interval of about 5-10 min. The rats were confined to the goalbox for 15 s on reinforced trials and for 60 s on nonreinforced trials. If a rat had not entered the goalbox within 60 s, it was placed in the goalbox where it received the reinforcing event scheduled on that trial. Following the last trial of the day, the rats were returned to the colony room where they were fed the daily ration about 5-10 min later. Results Figure 1 shows speed of running on each trial of the 1R series (PN and SN rats combined) and on each trial of the 2R series (PPN and SSN rats combined) in blocks of 2 days. Quite clearly, with training the rats
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CAPALDI,
2
20--2R
$
o-
MILLER,
AND ALPTEKIN
I,,l,,l,,111111111111l1111111111, 5 6 7 6 1 2 3 4 BLOCKS OF 2 DAYS
9
10
11
FIG. 1. Speed of running on each trial of the lR series (PN and SN rats combined) and on each trial of the 2R series (PPN and SSN rats combined) in blocks of 2 days in Experiment 1.
developed the capacity correctly to anticipate all reinforcement outcomes of both series. For example, on the last two blocks of trials, speeds were equally rapid on the R trials of both series and slow on the N trials of both series. Too, speeds were slower on the N trials of the IR series than on those of the 2R series, a tendency which began its emergence on Block 5 of training. Three separate analyses were applied to the data in Fig. 1. First, because the 1R and the 2R series contained different numbers of trials, each series was analyzed separately. A third analysis compared the N trials of the two series. The R trials of the two series were not compared statistically because it is obvious from inspection of the data that R-trial differences either within or between series were either small or practically nonexistent. An analysis of variance over the data shown in Fig. 1 for the 1R series indicated that differences were significant due to trials [F(l, 7) = 42.49, p < .OOl] and the Trials x Blocks interaction [F(lO, 70) = 13.73, p < .OOl]. A similar analysis applied to the 2R series likewise produced significant differences due to trials [F(2, 14) = 17.62, p < .OOl] and the Trials x Blocks interaction [F(lO, 140) = 9.26, p < .OOl]. Subsequent Newman-Keuls tests based on each of the significant Trials x Blocks interactions revealed the following. In neither the 1R series nor the 2R series was the difference due to trials significant on Blocks 1 and 2; but by the later blocks, e.g., 10 and II, running was slower on the N trials than on the R trials @s < .Ol). The R trials of the 2R series failed to differ. Finally, an analysis comparing N trials of the 1R and 2R series over the last 5 blocks of training produced a significant difference
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[F(l, 7) = 12.43, p < .Ol]. A similar analysis on Blocks to produce a significant difference (F < 1).
53
1 and 2 failed
Discussion
In Experiment 1, rats were trained under both a 1R series and a 2R series. Each event of each series was correctly anticipated. That is, the rats ultimately ran fast to the R event of the 1R series, equally fast to both R events of the 2R series, and slow to the terminal N event of both series. Running was slower to the terminal N event of the 1R series than to that of the 2R series. Capaldi and Miller (1988a, 1988b), employing series similar to those employed here, supplied evidence consistent with the following view. Rats possess internal, abstract representations corresponding to number of events. We call these internal representations number tags. Transfer data indicated that the tags are abstract. For example, in transfer, despite the introduction of entirely novel reinforcers, discriminative responding was maintained. People, of course, employ conventional, abstract verbal number tags of the form “one,” “two,” “three,” etc. The nature of animal number tags is not known. In any event, the findings obtained in Experiment I may be interpreted as follows. Rats learned an n/e numerical discrimination in which the signal capacity of a number tag was conditional upon the event being enumerated. That is, in Experiment 1 the rats learned that the cue for nonreinforcement was either a single reinforcement of one type (IR series) or two successive reinforcements of another type (2R series). A number of alternative interpretations of the results obtained in Experiment 1 are available, however. For example, it is possible that the rats of Experiment 1 anticipated nonreinforcement by counting or timing inter-trial intervals which, of course, were perfectly confounded with number of R events. We reject alternatives of the sort mentioned because data supplied by Capaldi and Miller (1988a) clearly indicated that, when other events are confounded with number of R events under the particular experimental conditions employed here, rats nevertheless enumerate the R events. For example, rats having learned correctly to anticipate the events of the 2R series, RRN, were shifted to two somewhat different series, irregularly presented, RRN and NRRN (Capaldi & Miller, 1988a, Experiment 3). Practically from the outset of the shift, the rats correctly anticipated the R events and the terminal N events of both series. Such anticipation would not have occurred in the NRRN series had the animals been counting or timing intertrial intervals to the exclusion of counting R events because, of course, whereas two inter-trial intervals had preceded the terminal N trial in initial training (RRN series), in shift three inter-trial intervals preceded the terminal N event in the NRRN series. Too, in
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MILLER,
AND
ALPTEKIN
Experiment 3 of Capaldi and Miller (1988a), animals originally trained under a NRRN series likewise showed almost immediate transfer when shifted to the two series RRN and NRRN. Since Experiment 1 represented an initial attempt to determine if rats could form an n/e numerical discrimination, the simplest form of that sort of conditional numerical discrimination was employed: the animal being provided with a 1R and a 2R series. Experiment 2 differed from Experiment 1 in two notable respects. First, a different and presumably more difficult n/e numerical conditional discrimination learning problem was employed: rats being given a 2R and a 3R series. Second, on half the occasions, irregularly determined, the 2R and 3R series were preceded by an N trial. Thus, each rat received four series, e.g., PPN. NPPN, SSSN and NSSSN, each series occurring once each day in experimental training. EXPERIMENT
2
Method Subjects. The subjects were five rats of the same description as employed in Experiment 1. Apparatus. The same runway was employed in Experiment 2 as was employed in Experiment 1 by the first experimenter. Pretraining. Pretraining in Experiment 2 was identical to that employed in Experiment 1 except for the following differences. The rats were handled on Days l-7, alley exploration being given on Days 8-10. Each rat received a 2R series and a 3R series administered by a single experimenter. Half the 2R and half the 3R series began with an N trial. For three rats the 2R series was (A) PPN and (B) NPPN, the 3R series being (C) SSSN and (D) NSSSN; for two rats the 2R series was (A) SSN and (B) NSSN, the 3R series being (C) PPPN and (D) NPPPN. On Day 11, each rat received the A series; on Day 12 the D series; on Day 13 the C series, followed about 20 min later by the B series; on Day 14 the B series followed by the C series; and on Day 15 the D series followed by the A series. Experimental training. Experimental training in Experiment 2 was identifical to that in Experiment 1 except for the following differences. Each rat received one presentation each day of the A, B, C, and D series described above. On Days 1-4, the series occurred each day in the order (1) ABCD, (2) BADC, (3) CDAB, and (4) DCBA, respectively. On Days 5-8, the order of series presentation was 4, 3, 2, 1, respectively. The series were administered in the order 1-2-3-4-4-3-2-1 over the next 8 days, and SO on. The interseries interval was lo-15 min. Experimental training lasted for 34 days.
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Results
Figure 2 shows speed of running on each trial of the 2R series for the short series (S; PPN and SSN rats combined) and for the long series (L; NPPN and NSSN rats combined) in blocks of 2 days in Experiment 2. The unconnected points show speed of running on the initial N trial of the long series. Figure 3 presents data for the 3R series exactly as Fig. 2 for the 2R series. By the end of training, the rats had developed the tendency correctly to anticipate all reinforcement outcomes of both series, except, of course, the initial N trial which occurred irregularly. Thus, by the last two blocks of trials, the rats were running fast on all trials except the terminal N trials of each series. Because the 2R and 3R series contained different numbers of trials, each series was analyzed separately. The analyses were performed over the common trials of the two types of 2R series (e.g., SSN) and the common trials of the two types of 3R series (e.g., PPPN), i.e., the initial N trial was excluded and analyzed separately. Analyses applied to the data shown in each figure for the 2R and 3R series revealed the following. Differences due to trials were significant both for the 2R series [F(2, 8) = 24.02, p < .OOl] and the 3R series [F(3, 12) = 65.92, p < .OOl]. The Trials x Blocks interaction produced significant differences both for the 2R series [F(32, 128) = 3.64, p < .OOl] and the 3R series [F(48, 192) = 5.20, p < .OOl]. A breakdown of the significant Trials x Blocks interactions using NewmanKeuls tests revealed the following. On Block 1 running did not differ over trials either for the 2R series or the 3R series; but, by the last two blocks of trials, both for the 2R and the 3R series, running was slower on the terminal N trials than on each of the reinforced trials which did not differ (ps < .05).
FIG. 2. Speed of running on each trial of the 2R series for the short series (S; PPN and SSN rats combined) and for the long series (L; NPPN and NSSN rats combined) in blocks of 2 days in Experiment 2. The unconnected points show speed of running on the initial N trial of the long series.
CAPALDI,
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MILLER,
AND ALPTEKIN
i!40u1
-3RS
2 20 -
---.3RL
2
o-
FIG. 3. Speed of running on each trial of the 3R series for the short series (S: PPPN and SSSN rats combined) and for the long series (L; NPPPN and NSSSN rats combined) in blocks of 2 days in Experiment 2. The unconnected points show speed of running on the initial N trial of the log series.
A separate analysis comparing the initial N trials of the 2R and 3R series with the initial reinforced trial of the other 2R and 3R series, respectively, revealed that the rats ran equally rapidly on both types of trials [F(3, 12) = 1.89, p > .05]. The final analysis applied to the data was a 2 x 2 factorial employing the terminal N trials of the 2R and 3R series. The analysis revealed that, while the rats ran more slowly on the terminal N trial of the long series of both 2R and 3R series [F(l, 4) = 7.92, p < .05], running speed did not differ on the terminal N trials of the 2R and 3R series (F < 1). Examining Figs. 2 and 3, it will be seen that while overall the rats ran more slowly on the terminal N trial of the long series, this difference was not a consistent one over blocks, being large on some blocks, nonexistent on others, and even reversed on others. Discussion
In Experiment 2, as in Experiment 1, rats learned an n/e discrimination in which the signal capacity of a number tag was conditional upon the event being enumerated. There were two major differences between Experiments 1 and 2. First, in Experiment 2, unlike in Experiment 1, and N trial preceded each series on half the occasions randomly determined. This procedure made it impossible for the rats to anticipate the terminal N trial of each series by, e.g., counting or timing intertrial intervals. Second, Experiment 2 employed 2R and 3R series rather than the IR and 2R series of Experiment 1. Thus, the ability of rats to form n/e discriminations is not limited to the most simple 1R and 2R series but extends to the more complicated, or at least greater number, 2R and 3R series. In Experiment 1, the rats ran more slowly on the terminal N trial of the IR series than on that of the 2R series. However, in Experiment
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2, running was not slower on the terminal N trial of the 2R series than on that of the 3R series. It was found in Experiment 2 that running was slower on the terminal N trial of the series having the initial N trial (longer series) than on the terminal N trial of the series lacking the initial N trial (shorter series). This comparison was made as well in a number of previous studies from this laboratory (Capaldi & Miller, 1988a, 1988b). In some of the previous studies, the effect (i.e., slower running on the terminal N trial of the longer series) was as in Experiment 2 here, and in others, the effect was present on an absolute basis but was not statistically significant. Our opinion is that the effect is a real one-but small and unstable. It may reflect the fact that while the rat’s primary attention is directed at counting reinforcing events, it also counts trials. As is perhaps clear, the number cue applied to the last trial of the longer series always signals nonreinforcement, whereas that applied to the last trial of the shorter series sometimes signals nonreinforcement and sometimes reinforcement. Thus, the rat may be relatively more confident of nonreinforcement on the terminal N trial of the longer series than on that of the shorter series. It may be objected that, in Experiments 1 and 2, the rats formed a conditional discrimination in which reinforcers were timed rather than enumerated. The timing reinforcement alternative to the counting reinforcements alternative has been completely ruled out in prior investigations by Capaldi and Miller (1988a), under conditions like those employed here. First, neither doubling nor halving confinement times on reinforced trials had any effect on discriminative responding in prior investigations (Experiments 1 and 2). Second, rats trained on R’RRN (Experiment 5), where R’ and R are qualitatively different reinforcers, continued to respond discriminatively-running fast to R events, slow to terminal N eventswhen shifted either to RRN and NRRN (count to two) or to RRRN and NRRRN (count to three). Shift findings of that sort would be impossible if rats were merely timing reinforcing events. Rather, Capaldi and Miller (1988a) concluded under the R’RRN series, the rats counted one R’ event, two R events, and three reinforcing events (a superordinate category containing R’ and R events), an interpretation entirely consistent with the general hypothesis being advanced here: that rats are capable of n/e numerical discriminations (see also Capaldi & Miller, 1988b). GENERAL DISCUSSION
A number of different approaches have been employed to investigate counting in animals, the complexity of counting, and the role of counting in animal learning and behavior. For example, Capaldi and Miller (1988a) showed that the numerical discriminations formed by rats meet formal criteria of counting contained in a highly lauded model suggested by Gelman and Gallistel (1978) to explain counting in children. As another
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example, Church and co-workers (e.g., Church & Meek, 1984) have advanced and tested an information-processing model of counting which has much in common with a model of timing behavior in animals. Each of the two approaches described, as well as others, have value (see e.g., Capaldi & Miller, 1988a; Davis & Memmott, 1982). Let us briefly outline some benefits of the approach employed here. An animal unable to form a conditional numerical discrimination of either the form n/c or n/e would not possess a highly useful sense of number. For example, an animal unable to form an n/c discriminationin effect, an animal unable to conditionalize its enumeration of some event X upon some other cue-would lack the prerequisite for determining that Xs are more numerous, e.g., here than there. By the same token, an animal unable to form an n/e discrimination, or one unable to conditionalize the enumeration of events on the events being enumerated, would lack the prerequisite for determining, e.g., that some events at some location are more numerous than other events at that location. Of course, establishing that animals can form conditional discriminations of the n/c or n/e sort is not to demonstrate that animals having formed those discriminations will select the better alternative if given a choice, as they were not here nor in the investigation of Bums and Sanders (1987), which employed the n/e discrimination. But, clearly, animals could not select the better numerical alternative if they were unable to form either n/c or n/e conditional numerical discriminations in the first place. Thus, demonstrating that animals can form n/c and n/e conditional numerical discriminations is but the first step, an important first step, in determining how useful the number capacity of animals may turn out to be. But quite aside from the question of how adept a particular animal might be in translating its conditional numerical information into appropriate action under various conditions, there are, at present, a variety of prior determinations which need to be made as well. For example, on the basis of what sorts of cues is a particular animal able to conditionalize its enumeration of events, and do some cues provide a better source of conditional cues than others? A modest first step has been taken in this report. If rats were unable to pass the test they were given here, it would be obvious that their number sense is quite primitive; that their ability to count could only be employed under highly restricted conditions. But they did pass the test; and so other steps are indicated, steps which will provide a fuller understanding of the complexity and usefulness of rat numerical abilities and, of course, those of other animals as well. REFERENCES Burns, R. A., & Sanders, R. E. (1987). Concurrent counting of two and three events in a serial anticipation paradigm. Bulletin of the Ps.ychonomic Society, 25, 479-48 1.
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Capaldi, E. J., & Miller, D. J. (1988a). Counting in rats: Its functional significance and the independent cognitive processes which comprise it. Journal ofExperimenfa/ Psychology: Animal Behavior Processes, 14, 3-17. Capaldi, E. J., & Miller, D. J. (1988b). Number tags applied by rats to reinforcers are general and exert powerful control over responding. The Quarterly Journal of Experimental Psychology, 4OB, 279-291. Church, R. M., & Meek, W. H., (1984). The numerical attribute of stimuli. In H. L. Roitblat, T. G. Bever, & H. S. Terrace (Eds.), Animal cognition (pp. 445-464). Hillsdale, NJ: Erlbaum. Davis, H., & Bradford, S. A. (1986). Counting behavior by rats in a simulated natural environment. Ethology. 73, 265-280. Davis, H., & Memmott, J. (1982). Counting behavior in animals: A critical evaluation. Psychological
Buifefin,
92, 547-571.
Gelman, R., & Gallistel, C. R. (1978). The child’s MA: Harvard Univ. Press. Received January 29, 1988 Revised June 15, 1988
understanding
of number.
Cambridge,
AND MOTIVATION
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(1989)
A Conditional Numerical Discrimination Based on Qualitatively Different Reinforcers E. J. CAPALDI, DANIEL J. MILLER, Purdue
AND
SUZAN
ALPTEKIN
University
An animal able to count but unable to conditionalize its count on some other cue would not possess a useful sense of number because numerical discriminations are often conditional ones. Accordingly, we examined here in two runway investigations the ability of rats to learn a conditional numerical discrimination of the form: count this many Xs and that many Ys, the Xs and Ys being qualitatively different food items which in the normal environment would correspond to different prey items. In each investigation, the rat learned the conditional numerical discrimination, running slowly on nonreinforced trials which were signaled by different numbers of successively presented food reinforcements, running being rapid to food items. In Experiment 1, nonreinforcement was signaled by two successive food events of one type, e.g., Noyes sucrose pellets, and a single food event of another type, e.g., Noyes plain pellets. In Experiment 2, nonreinforcement was signaled by two successive food events of one type and three such events of another type. That rats were able to conditionalize their count on type of food item indicates that their numerical capacity is far from primitive and may be complex. But further tests are required to determine how complex the numerical Capacity of rats may be. Q 1989 Academic Press, IIK
Recent evidence indicates that rats are able to employ numbers of events of various sorts as a discriminative cue, events ranging from visual and auditory stimuli to food reinforcement (e.g., Capaldi & Miller, 1988a; Church & Meek, 1987; Davis & Bradford. 1986). In the preparation employed by Capaldi and Miller (1988a), rats were able to employ as a discriminative cue numbers of successively presented food reinforcements, each of which was contingent upon an instrumental running response in a straight-alley runway. For example, rats were able to anticipate, as indicated by slow running, a nonreinforced trial which was preceded by three reinforced trials, running being rapid on each of the reinforced trials. Call this a 3R series. Various control procedures indicated that This research was supported in part by NSF Grant BNS-8515831 to E. J. Capaldi. Address correspondence and reprint requests to Dr. E. J. Capaldi, Department of Psychological Sciences, Purdue University, West Lafayette, IN 47907. 48 0023-9690189 Copyright All rights
$3.00 0 1989 by Academic Press. of reproduction in any form
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discriminative responding under the 3R series was based upon enumerating number of reinforcing events independently of a variety of other cues: other number cues, various temporal cues, and the amount of food ingested. It seems particularly appropriate to have rats enumerate food reinforcements because food events are obviously of great importance to animals, whether in various laboratory learning situations or in the natural environment. Thus, food events seem as likely as any events as candidates for enumeration by animals. A variety of approaches have been employed to determine how competent animals may be at forming numerical discriminations, some of which will be mentioned in the general discussion section. An examination of the various conditions under which numerical information may be employed by either people or animals is at the basis of the approach employed by the two investigations reported here. It seems quite clear that numerical discriminations rather than being simple in nature are very often conditional. That is, the number of events to be enumerated (n) differs depending upon the presence of some other cue (c) or n/c. For example, a child may be asked to place two blocks in the red box and three blocks in the blue box, while an animal may learn that more prey items of a particular description are available at one location than at another location. The conditionalization here, of course, is that the number of events enumerated (blocks, prey items of a given sort) depend upon something else (box color, location). Interestingly, rats have been shown to be able to form a conditional discrimination of the n/c sort described above. Bums and Sanders (1987), employing the same sort of experimental procedures as Capaldi and Miller (1988a), reported that rats are capable of anticipating simultaneously a nonreinforced trial which follows two reinforced trials in a runway of one brightness and texture, a 2R series, and three reinforced trials in a runway of another brightness and texture, a 3R series. Another sort of conditional numerical discrimination was of concern here. In this sort of problem, which is also quite common, number depends upon the event (e) being enumerated or n/e. Thus, a child might be required to distinguish two apples from three oranges; an animal might have to discriminate that at a given location more prey items of type X are available than of type Y. To investigate the n/e sort of conditional numerical discrimination, we employed here two qualitatively different reinforcing events: 0.045-g Noyes sucrose pellets (S) and plain pellets (P). Experiment 1 asked if rats could learn to anticipate nonreinforcement (N) when if followed one reinforcer of one type, a 1R series, and two successive reinforcers of the other type, a 2R series. That is, the series was either PN or SSN (or vice versa), the 1R and 2R series being irregularly presented in a gray runway. Previous findings indicate that
50
CAPALDI,
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when rats are trained only under the 2R series they learn that two successive reinforced trials signal nonreinforcement, despite the fact that many other cues are confounded with number of reinforcers, e.g., number or duration of intertrial intervals (see Capaldi & Miller, 1988a, Experiment 3). Thus, on the basis of the Capaldi and Miller (1988a) findings, anticipating nonreinforcement in the IR and 2R series in Experiment 1 could be taken to indicate that rats are able to apply different counts to two different events simultaneously. In any case, to establish more firmly that rats can apply different counts to two different events simultaneously, Experiment 2 employed somewhat more elaborate, if not necessary, control procedures than Experiment 1. Experiment 2 asked if rats could learn to anticipate nonreinforcement when it followed two successive reinforcers of one type, a 2R series, and three successive reinforcers of another type, a 3R series. Half the 2R and 3R series were preceded, on an irregular basis, by a nonreinforced trial to rule out the possibility that the rats were counting or summing the duration of other events, e.g., intertrial intervals. EXPERIMENT
1
Method Subjects. The subjects were eight experimentally naive, male albino rats obtained from Holtzman Co., Madison, Wisconsin. All rats were 77 days old upon arrival at the laboratory and were placed on ad fibitum food for 14 days prior to the start of the experiment. The rats were randomly assigned in equal number to each of two subgroups. Two experimenters were employed, each running four rats, two from each subgroup. Two runways were employed. Apparatus. For the rats run by Experimenter 1, a straight gray runway was used measuring 208.67 cm long, 10.2 cm wide, and enclosed by 22.75-cm sides covered by a wire-mesh top on a hinged frame. The startbox and goalbox were 20.8 and 29.7 cm long, respectively, closed off by wooden guillotine doors. Raising the startbox door started a completely silent 0.01-s digital clock, which was stopped when a photobeam located 175.27 cm beyond the startbox door and 7.5 cm in front of the goalcup was broken by the rat. Pellets (0.045-g Noyes, Formula Atraditional plain, P; Formula F-sucrose, S) could be placed in a brass rectangular goalcup (4.2 x 3.0 cm and 1.85 cm in depth) located within a metal insert measuring 5.1 x 10.2 x 4.3 cm. Upon interruption of the photobeam, the wooden doors were lowered, confining the rat to the goalbox. For the rats run by Experimenter 2, a similar apparatus was employed, except it was slightly shorter (197.10 cm), slightly narrower (10.1 cm), and was enclosed by shorter sides (13.85 cm). The photobeam was located 158.13 cm beyond the startbox door and 9.5 cm in front of the circular
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goalcup, which was 4.0 cm in diameter and I.5 cm deep (cut into a 6.2 X 10.6 x 4.0-cm wooden block). Also the startbox and goalbox doors were made of metal. Pretruining. On Day 1 of pretraining, all rats began deprivation consisting of 15 g of Wayne Lab Chow fed in the home cage minus any amount eaten in the apparatus. On Days 1-6, all rats were handled individually for l-2 min. On Day 7, rats were given three plain and three sucrose pellets in the home cage prior to receiving the daily ration. On Days 79. each rat was allowed to explore the runway for 3 min, three plain pellets and three sucrose pellets being scattered about the runway. The rats were then returned to the home cage where they were fed the daily ration. Water was freely available in the home cage and in the running room throughout the experiment. On Days 10-12, each rat received two, two, and four series, respectively, in the runway. Trials terminated either in six 0.045-g plain pellets (P), six 0.045-g sucrose pellets (S), or nonreinforcement (N). Each rat received a 1R series, a single reinforced trial followed by nonreinforcement (N), and a 2R series, two successive reinforced trials followed by an N trial. Two of the rats trained by each experimenter received the series PN and SSN; the other two received the series SN and PPN. On Day 10, each rat received its 1R series, followed about 10 min later by its 2R series, the 1R series following the 2R series on Day 11. On Day 12, the rats received the series in the order lR, 2R, lR, 2R. Experimental training. On each of the 22 days of experimental training, each rat received its 1R series three times and its 2R series three times. On odd days, the series were presented in the order lR, 2R, 2R, lR, lR, 2R, and on even days the order was 2R, lR, lR, 2R, 2R, 1R. The experimenter brought the four rats she was running into the experimental room, with the home cages serving as the individual holding cages where they were confined between trials. Rats were run in a varied order each day. Each rat received its first scheduled series before another rat received its second series. This method produced an intertrial interval of about 15-30 s and an interseries interval of about 5-10 min. The rats were confined to the goalbox for 15 s on reinforced trials and for 60 s on nonreinforced trials. If a rat had not entered the goalbox within 60 s, it was placed in the goalbox where it received the reinforcing event scheduled on that trial. Following the last trial of the day, the rats were returned to the colony room where they were fed the daily ration about 5-10 min later. Results Figure 1 shows speed of running on each trial of the 1R series (PN and SN rats combined) and on each trial of the 2R series (PPN and SSN rats combined) in blocks of 2 days. Quite clearly, with training the rats
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2
20--2R
$
o-
MILLER,
AND ALPTEKIN
I,,l,,l,,111111111111l1111111111, 5 6 7 6 1 2 3 4 BLOCKS OF 2 DAYS
9
10
11
FIG. 1. Speed of running on each trial of the lR series (PN and SN rats combined) and on each trial of the 2R series (PPN and SSN rats combined) in blocks of 2 days in Experiment 1.
developed the capacity correctly to anticipate all reinforcement outcomes of both series. For example, on the last two blocks of trials, speeds were equally rapid on the R trials of both series and slow on the N trials of both series. Too, speeds were slower on the N trials of the IR series than on those of the 2R series, a tendency which began its emergence on Block 5 of training. Three separate analyses were applied to the data in Fig. 1. First, because the 1R and the 2R series contained different numbers of trials, each series was analyzed separately. A third analysis compared the N trials of the two series. The R trials of the two series were not compared statistically because it is obvious from inspection of the data that R-trial differences either within or between series were either small or practically nonexistent. An analysis of variance over the data shown in Fig. 1 for the 1R series indicated that differences were significant due to trials [F(l, 7) = 42.49, p < .OOl] and the Trials x Blocks interaction [F(lO, 70) = 13.73, p < .OOl]. A similar analysis applied to the 2R series likewise produced significant differences due to trials [F(2, 14) = 17.62, p < .OOl] and the Trials x Blocks interaction [F(lO, 140) = 9.26, p < .OOl]. Subsequent Newman-Keuls tests based on each of the significant Trials x Blocks interactions revealed the following. In neither the 1R series nor the 2R series was the difference due to trials significant on Blocks 1 and 2; but by the later blocks, e.g., 10 and II, running was slower on the N trials than on the R trials @s < .Ol). The R trials of the 2R series failed to differ. Finally, an analysis comparing N trials of the 1R and 2R series over the last 5 blocks of training produced a significant difference
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[F(l, 7) = 12.43, p < .Ol]. A similar analysis on Blocks to produce a significant difference (F < 1).
53
1 and 2 failed
Discussion
In Experiment 1, rats were trained under both a 1R series and a 2R series. Each event of each series was correctly anticipated. That is, the rats ultimately ran fast to the R event of the 1R series, equally fast to both R events of the 2R series, and slow to the terminal N event of both series. Running was slower to the terminal N event of the 1R series than to that of the 2R series. Capaldi and Miller (1988a, 1988b), employing series similar to those employed here, supplied evidence consistent with the following view. Rats possess internal, abstract representations corresponding to number of events. We call these internal representations number tags. Transfer data indicated that the tags are abstract. For example, in transfer, despite the introduction of entirely novel reinforcers, discriminative responding was maintained. People, of course, employ conventional, abstract verbal number tags of the form “one,” “two,” “three,” etc. The nature of animal number tags is not known. In any event, the findings obtained in Experiment I may be interpreted as follows. Rats learned an n/e numerical discrimination in which the signal capacity of a number tag was conditional upon the event being enumerated. That is, in Experiment 1 the rats learned that the cue for nonreinforcement was either a single reinforcement of one type (IR series) or two successive reinforcements of another type (2R series). A number of alternative interpretations of the results obtained in Experiment 1 are available, however. For example, it is possible that the rats of Experiment 1 anticipated nonreinforcement by counting or timing inter-trial intervals which, of course, were perfectly confounded with number of R events. We reject alternatives of the sort mentioned because data supplied by Capaldi and Miller (1988a) clearly indicated that, when other events are confounded with number of R events under the particular experimental conditions employed here, rats nevertheless enumerate the R events. For example, rats having learned correctly to anticipate the events of the 2R series, RRN, were shifted to two somewhat different series, irregularly presented, RRN and NRRN (Capaldi & Miller, 1988a, Experiment 3). Practically from the outset of the shift, the rats correctly anticipated the R events and the terminal N events of both series. Such anticipation would not have occurred in the NRRN series had the animals been counting or timing intertrial intervals to the exclusion of counting R events because, of course, whereas two inter-trial intervals had preceded the terminal N trial in initial training (RRN series), in shift three inter-trial intervals preceded the terminal N event in the NRRN series. Too, in
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Experiment 3 of Capaldi and Miller (1988a), animals originally trained under a NRRN series likewise showed almost immediate transfer when shifted to the two series RRN and NRRN. Since Experiment 1 represented an initial attempt to determine if rats could form an n/e numerical discrimination, the simplest form of that sort of conditional numerical discrimination was employed: the animal being provided with a 1R and a 2R series. Experiment 2 differed from Experiment 1 in two notable respects. First, a different and presumably more difficult n/e numerical conditional discrimination learning problem was employed: rats being given a 2R and a 3R series. Second, on half the occasions, irregularly determined, the 2R and 3R series were preceded by an N trial. Thus, each rat received four series, e.g., PPN. NPPN, SSSN and NSSSN, each series occurring once each day in experimental training. EXPERIMENT
2
Method Subjects. The subjects were five rats of the same description as employed in Experiment 1. Apparatus. The same runway was employed in Experiment 2 as was employed in Experiment 1 by the first experimenter. Pretraining. Pretraining in Experiment 2 was identical to that employed in Experiment 1 except for the following differences. The rats were handled on Days l-7, alley exploration being given on Days 8-10. Each rat received a 2R series and a 3R series administered by a single experimenter. Half the 2R and half the 3R series began with an N trial. For three rats the 2R series was (A) PPN and (B) NPPN, the 3R series being (C) SSSN and (D) NSSSN; for two rats the 2R series was (A) SSN and (B) NSSN, the 3R series being (C) PPPN and (D) NPPPN. On Day 11, each rat received the A series; on Day 12 the D series; on Day 13 the C series, followed about 20 min later by the B series; on Day 14 the B series followed by the C series; and on Day 15 the D series followed by the A series. Experimental training. Experimental training in Experiment 2 was identifical to that in Experiment 1 except for the following differences. Each rat received one presentation each day of the A, B, C, and D series described above. On Days 1-4, the series occurred each day in the order (1) ABCD, (2) BADC, (3) CDAB, and (4) DCBA, respectively. On Days 5-8, the order of series presentation was 4, 3, 2, 1, respectively. The series were administered in the order 1-2-3-4-4-3-2-1 over the next 8 days, and SO on. The interseries interval was lo-15 min. Experimental training lasted for 34 days.
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Results
Figure 2 shows speed of running on each trial of the 2R series for the short series (S; PPN and SSN rats combined) and for the long series (L; NPPN and NSSN rats combined) in blocks of 2 days in Experiment 2. The unconnected points show speed of running on the initial N trial of the long series. Figure 3 presents data for the 3R series exactly as Fig. 2 for the 2R series. By the end of training, the rats had developed the tendency correctly to anticipate all reinforcement outcomes of both series, except, of course, the initial N trial which occurred irregularly. Thus, by the last two blocks of trials, the rats were running fast on all trials except the terminal N trials of each series. Because the 2R and 3R series contained different numbers of trials, each series was analyzed separately. The analyses were performed over the common trials of the two types of 2R series (e.g., SSN) and the common trials of the two types of 3R series (e.g., PPPN), i.e., the initial N trial was excluded and analyzed separately. Analyses applied to the data shown in each figure for the 2R and 3R series revealed the following. Differences due to trials were significant both for the 2R series [F(2, 8) = 24.02, p < .OOl] and the 3R series [F(3, 12) = 65.92, p < .OOl]. The Trials x Blocks interaction produced significant differences both for the 2R series [F(32, 128) = 3.64, p < .OOl] and the 3R series [F(48, 192) = 5.20, p < .OOl]. A breakdown of the significant Trials x Blocks interactions using NewmanKeuls tests revealed the following. On Block 1 running did not differ over trials either for the 2R series or the 3R series; but, by the last two blocks of trials, both for the 2R and the 3R series, running was slower on the terminal N trials than on each of the reinforced trials which did not differ (ps < .05).
FIG. 2. Speed of running on each trial of the 2R series for the short series (S; PPN and SSN rats combined) and for the long series (L; NPPN and NSSN rats combined) in blocks of 2 days in Experiment 2. The unconnected points show speed of running on the initial N trial of the long series.
CAPALDI,
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i!40u1
-3RS
2 20 -
---.3RL
2
o-
FIG. 3. Speed of running on each trial of the 3R series for the short series (S: PPPN and SSSN rats combined) and for the long series (L; NPPPN and NSSSN rats combined) in blocks of 2 days in Experiment 2. The unconnected points show speed of running on the initial N trial of the log series.
A separate analysis comparing the initial N trials of the 2R and 3R series with the initial reinforced trial of the other 2R and 3R series, respectively, revealed that the rats ran equally rapidly on both types of trials [F(3, 12) = 1.89, p > .05]. The final analysis applied to the data was a 2 x 2 factorial employing the terminal N trials of the 2R and 3R series. The analysis revealed that, while the rats ran more slowly on the terminal N trial of the long series of both 2R and 3R series [F(l, 4) = 7.92, p < .05], running speed did not differ on the terminal N trials of the 2R and 3R series (F < 1). Examining Figs. 2 and 3, it will be seen that while overall the rats ran more slowly on the terminal N trial of the long series, this difference was not a consistent one over blocks, being large on some blocks, nonexistent on others, and even reversed on others. Discussion
In Experiment 2, as in Experiment 1, rats learned an n/e discrimination in which the signal capacity of a number tag was conditional upon the event being enumerated. There were two major differences between Experiments 1 and 2. First, in Experiment 2, unlike in Experiment 1, and N trial preceded each series on half the occasions randomly determined. This procedure made it impossible for the rats to anticipate the terminal N trial of each series by, e.g., counting or timing intertrial intervals. Second, Experiment 2 employed 2R and 3R series rather than the IR and 2R series of Experiment 1. Thus, the ability of rats to form n/e discriminations is not limited to the most simple 1R and 2R series but extends to the more complicated, or at least greater number, 2R and 3R series. In Experiment 1, the rats ran more slowly on the terminal N trial of the IR series than on that of the 2R series. However, in Experiment
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2, running was not slower on the terminal N trial of the 2R series than on that of the 3R series. It was found in Experiment 2 that running was slower on the terminal N trial of the series having the initial N trial (longer series) than on the terminal N trial of the series lacking the initial N trial (shorter series). This comparison was made as well in a number of previous studies from this laboratory (Capaldi & Miller, 1988a, 1988b). In some of the previous studies, the effect (i.e., slower running on the terminal N trial of the longer series) was as in Experiment 2 here, and in others, the effect was present on an absolute basis but was not statistically significant. Our opinion is that the effect is a real one-but small and unstable. It may reflect the fact that while the rat’s primary attention is directed at counting reinforcing events, it also counts trials. As is perhaps clear, the number cue applied to the last trial of the longer series always signals nonreinforcement, whereas that applied to the last trial of the shorter series sometimes signals nonreinforcement and sometimes reinforcement. Thus, the rat may be relatively more confident of nonreinforcement on the terminal N trial of the longer series than on that of the shorter series. It may be objected that, in Experiments 1 and 2, the rats formed a conditional discrimination in which reinforcers were timed rather than enumerated. The timing reinforcement alternative to the counting reinforcements alternative has been completely ruled out in prior investigations by Capaldi and Miller (1988a), under conditions like those employed here. First, neither doubling nor halving confinement times on reinforced trials had any effect on discriminative responding in prior investigations (Experiments 1 and 2). Second, rats trained on R’RRN (Experiment 5), where R’ and R are qualitatively different reinforcers, continued to respond discriminatively-running fast to R events, slow to terminal N eventswhen shifted either to RRN and NRRN (count to two) or to RRRN and NRRRN (count to three). Shift findings of that sort would be impossible if rats were merely timing reinforcing events. Rather, Capaldi and Miller (1988a) concluded under the R’RRN series, the rats counted one R’ event, two R events, and three reinforcing events (a superordinate category containing R’ and R events), an interpretation entirely consistent with the general hypothesis being advanced here: that rats are capable of n/e numerical discriminations (see also Capaldi & Miller, 1988b). GENERAL DISCUSSION
A number of different approaches have been employed to investigate counting in animals, the complexity of counting, and the role of counting in animal learning and behavior. For example, Capaldi and Miller (1988a) showed that the numerical discriminations formed by rats meet formal criteria of counting contained in a highly lauded model suggested by Gelman and Gallistel (1978) to explain counting in children. As another
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example, Church and co-workers (e.g., Church & Meek, 1984) have advanced and tested an information-processing model of counting which has much in common with a model of timing behavior in animals. Each of the two approaches described, as well as others, have value (see e.g., Capaldi & Miller, 1988a; Davis & Memmott, 1982). Let us briefly outline some benefits of the approach employed here. An animal unable to form a conditional numerical discrimination of either the form n/c or n/e would not possess a highly useful sense of number. For example, an animal unable to form an n/c discriminationin effect, an animal unable to conditionalize its enumeration of some event X upon some other cue-would lack the prerequisite for determining that Xs are more numerous, e.g., here than there. By the same token, an animal unable to form an n/e discrimination, or one unable to conditionalize the enumeration of events on the events being enumerated, would lack the prerequisite for determining, e.g., that some events at some location are more numerous than other events at that location. Of course, establishing that animals can form conditional discriminations of the n/c or n/e sort is not to demonstrate that animals having formed those discriminations will select the better alternative if given a choice, as they were not here nor in the investigation of Bums and Sanders (1987), which employed the n/e discrimination. But, clearly, animals could not select the better numerical alternative if they were unable to form either n/c or n/e conditional numerical discriminations in the first place. Thus, demonstrating that animals can form n/c and n/e conditional numerical discriminations is but the first step, an important first step, in determining how useful the number capacity of animals may turn out to be. But quite aside from the question of how adept a particular animal might be in translating its conditional numerical information into appropriate action under various conditions, there are, at present, a variety of prior determinations which need to be made as well. For example, on the basis of what sorts of cues is a particular animal able to conditionalize its enumeration of events, and do some cues provide a better source of conditional cues than others? A modest first step has been taken in this report. If rats were unable to pass the test they were given here, it would be obvious that their number sense is quite primitive; that their ability to count could only be employed under highly restricted conditions. But they did pass the test; and so other steps are indicated, steps which will provide a fuller understanding of the complexity and usefulness of rat numerical abilities and, of course, those of other animals as well. REFERENCES Burns, R. A., & Sanders, R. E. (1987). Concurrent counting of two and three events in a serial anticipation paradigm. Bulletin of the Ps.ychonomic Society, 25, 479-48 1.
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Capaldi, E. J., & Miller, D. J. (1988a). Counting in rats: Its functional significance and the independent cognitive processes which comprise it. Journal ofExperimenfa/ Psychology: Animal Behavior Processes, 14, 3-17. Capaldi, E. J., & Miller, D. J. (1988b). Number tags applied by rats to reinforcers are general and exert powerful control over responding. The Quarterly Journal of Experimental Psychology, 4OB, 279-291. Church, R. M., & Meek, W. H., (1984). The numerical attribute of stimuli. In H. L. Roitblat, T. G. Bever, & H. S. Terrace (Eds.), Animal cognition (pp. 445-464). Hillsdale, NJ: Erlbaum. Davis, H., & Bradford, S. A. (1986). Counting behavior by rats in a simulated natural environment. Ethology. 73, 265-280. Davis, H., & Memmott, J. (1982). Counting behavior in animals: A critical evaluation. Psychological
Buifefin,
92, 547-571.
Gelman, R., & Gallistel, C. R. (1978). The child’s MA: Harvard Univ. Press. Received January 29, 1988 Revised June 15, 1988
understanding
of number.
Cambridge,