Edited by: Michael Beran, Georgia State University, USA
Reviewed by: Stephen V. Shepherd, Princeton University, USA; Daniel J. Weiss, Penn State University, USA
*Correspondence: Jessica F. Cantlon, Department of Brain and Cognitive Sciences, University of Rochester, Meliora Hall, PO Box 270268, Rochester, NY 14627, USA. e-mail:
This article was submitted to Frontiers in Comparative Psychology, a specialty of Frontiers in Psychology.
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Strong evidence indicates that non-human primates possess a numerical representation system, but the inherent nature of that system is still debated. Two cognitive mechanisms have been proposed to account for non-human primate numerical performance: (1) a discrete object-file system limited to quantities <4, and (2) an analog system which represents quantities comparatively but is limited by the ratio between two quantities. To test the underlying nature of non-human primate quantification, we asked eight experiment-naive olive baboons (
From Euclid, who said, “The laws of nature are but the mathematical thoughts of God,” to the modern mathematical scholar Paul Dirac who stated, “If there is a God, he’s a great mathematician,” great thinkers have often associated abstract numerical thought with the divine. However, in contrast to human intuitions, cognitive science has demonstrated that the seemingly supernatural human capacity for symbolic mathematical thought – responsible for scientific measurement, architectural design, and economic exchange – likely arises from a primitive number representation system (or perhaps systems) that appear in creatures like beasts and babies. Evolutionarily and developmentally primitive numerical systems are well-documented. Non-linguistic infants can reason about small and large numerosities (for reviews on the extensive literature, see Feigenson et al.,
Non-linguistic numerical cognition in human infants is hypothesized to involve two different mechanisms: a precise object-file system and an analog magnitude system. The object-file system is thought to be an aspect of working memory, which individuates, enumerates, and tracks objects, and so, is inherently capable of tracking the number of objects (Trick and Pylyshyn,
The existences of the object-file system and the analog system are not controversial. The role of the object-file system in tracking objects is well established. The relevant research questions are if, when, and how the object-file system is spontaneously recruited to represent quantity. Infants appear to use both an analog and an object-file system to compare quantities spontaneously. With small numbers of objects (<4), infants are capable of making correct numerical judgments no matter the ratio between sets (Feigenson et al.,
The pattern of success and failure observed in infants is not observed in adults. When adults are asked to judge quantities while their verbal abilities are occupied by an articulatory suppression task, their number discrimination behavior exhibits the ratio signature of the analog system for small and large numbers alike (Whalen et al.,
The data from human infants and adults raise the question of whether the “two systems” view of quantity development also characterized the evolution of numerical cognition. Comparative studies of numerical cognition with non-human animals have yielded mixed results on the fundamental nature of number cognition in non-humans. In one study, Hauser et al. (
Growing evidence suggests that the analog magnitude system is the evolutionarily primitive number system shared across animal lineages. Less clear is whether the analog magnitude system is the primary mechanism that non-human animals recruit
In the current study, we tested quantity discrimination in experiment-naive olive baboons using a naturalistic food choice task that is similar to the Hauser et al. (
In Experiment 1, we examined the spontaneous quantity representations of eight olive baboons by analyzing their quantity choices on first exposure to each number pair. Subjects compared numerical values in pairs of both small (<5), both large (>4), and span sets (one small and one large value). This range of sets allowed us to test the object-file and analog magnitude hypotheses. If the baboons are successful only with contrasts of small sets, then the object-file hypothesis will be supported. If the baboons are successful with small and large, but not span sets, we can conclude that both the object-file and the analog magnitude systems are engaged by baboons, as in human infants, but that the object-file and analog magnitude representations are incompatible resulting in failure on span sets. Finally, prior research with infants found that infants succeeded at discriminating large and span pairs in simultaneous but not sequential presentations (Feigenson et al.,
Eight adult olive baboons (4–14 years old, three male) at the Seneca Park Zoo in Rochester, NY, USA served as subjects in this experiment. These baboons are housed as a social group and have access to large indoor and outdoor enclosures. In addition, these enclosures have multiple compartments that allow us to temporarily segregate one baboon from the rest of the troop for testing purposes. Primate chow and fresh fruits and vegetables are provided every morning, and water is available
The apparatus consisted of a small and short rectangular table (75 cm long × 35 cm deep × 17 cm high) that was a comfortable height for a seated baboon (Figure
All experimental manipulations were conducted on a sliding panel (75 cm long × 17 cm deep) that sat atop the table. The purpose of this panel, which was the same length as the table, but only half as deep, was to control a subject’s access to the experiment until the appropriate time. When the panel was close to the experimenter, the subject did not have access to the experimental items, however, when the panel was pushed forward, toward the subject, the subject could reach through a port in the plexiglass and indicate her choice. The contents of the panel were three identical, opaque, cardstock cylinders, placed upright on a circular end, each in front of one of the ports in the plexiglass shield. The cylinders were open on both circular ends so that the experimenter could drop items into a cylinder and also lift a cylinder up, leaving the contents of a cylinder on the panel. Once items were dropped into the cylinders the items were hidden from a subject. The items to be enumerated were unshelled half peanuts.
Each session was conducted by two experimenters. One experimenter worked the apparatus, while a second experimenter recorded the choices made by the subject, monitored the first experimenter for trial accuracy, and also operated a video camera which was used to record each session. Sessions were conducted when a subject could be temporarily isolated from the troop in an enclosure. Individuals were tested between one and three times a week.
Before testing began, the experimenters set up the apparatus: the plexiglass side of the table was placed flush with the subject’s enclosure, the sliding panel was placed on the experimenter’s side of the table, the three cylinders were set in place on the panel, and one experimenter sat opposite the subject. A trial could only be initiated if the subject was seated at and attentive to the apparatus. To initiate a trial, an experimenter showed the subject one or more peanuts; this was done by displaying peanuts in the palms of one or both hands, about 30 cm from the subject and above the experimental panel (Figure
After the cylinders had been baited with peanuts, the panel was pushed forward and the subject was allowed to make a choice from among the three cylinders (Figure
In the training phase, we exposed the subjects only to the numerical comparison 1 vs. 2, presented both simultaneously and sequentially. Subjects were given multiple sessions until they chose the larger reward set at above chance levels within a single session as determined by a cumulative binomial analysis (threshold = 24/36 correct). Each session consisted of 36 trials; these trials were counterbalanced for baiting locations, simultaneous vs. sequential conditions, and in the case of sequential trials, for which number set was baited first. Progress through the session was closely monitored. If a gap of 5 min occurred between two trials due to subject inattention, the session was terminated, and training resumed the next time the subject was available. Terminated sessions were rare and excluded from analyses. Once the subject passed the training criterion they immediately began the testing phase of the experiment. Subjects needed 1.5 sessions on average (54 trials) to reach our criterion.
Testing was conducted over 54 total test trials, across two 30-min sessions. The 27 different number pairs ranging from 1 to 8 items were tested (all possible pairs excluding 1 vs. 2 which was the training pair), with each number pair tested once in sequential and once in simultaneous presentation. The beginning of each testing session consisted of a warm-up of four 1 vs. 2 trials (two simultaneous, two sequential) to ensure the subject was oriented to the task. Two additional trials of 1 vs. 2 (one sequential, one simultaneous) were tested in each session but those trials were not analyzed as 1 vs. 2 was the training and warm-up pair. If the subject failed more than half of these first trials, testing with that subject was terminated for the day. The order of the test trials was randomized within and between subjects. Also, as in training, baiting locations, simultaneous vs. sequential conditions, and in the case of sequential trials, which baited first, were randomized. In addition, pair size, presentation type, and location of the larger quantity were never repeated on more than three consecutive trials. If a gap of 5 min occurred between two trials due to subject inattention, the session was stopped, and the remaining trials were resumed after a warm-up during the next testing day.
Data were coded and analyzed by an independent observer who coded responses from the recorded video files. Weber fractions were calculated using methods reported in Cantlon and Brannon (
Subjects took an average of 1.5 sessions to reach the training criterion of above-chance performance within a single session on 1 vs. 2 numerical comparisons according to a binomial test (range = 1–2 sessions).
Seven monkeys completed all 54 trials of testing, the eighth completed 21 of 27 sequential trials and 22 of 27 simultaneous trials. As a group, monkeys preferentially selected the larger quantity on the first exposure for simultaneous pairs [chance = 50%, one sample
We binned the numerical pairs by their numerical ratio and tested for a linear trend of numerical ratio. Monkeys showed a significant effect of ratio on their simultaneous trial performance indicating that they made choices on the basis of an analog quantity representation [Pearson’s
We calculated individual Weber fractions for the five animals that performed above chance overall on the first exposure task. Weber fractions on first exposure ranged from 0.51 to 0.91, which is comparable to the range of Weber fractions exhibited by young children on similar tasks (Halberda and Feigenson,
Subjects for Experiment 2 were two female baboons who participated in Experiment 1 (Pearl, Ursala).
In Experiment 2 we collected more data on numerical comparisons from two subjects in order to detect subtle performance signatures among pair types. We used the same apparatus and procedure as in Experiment 1. Three cups were presented on each trial as choices, two of the cups were baited. In this experiment, monkeys never chose the empty cup. The numerical values presented ranged from 1 to 8. Each session began with a five-trial 1 vs. 2 “warm-up.” The test immediately followed the warm-up and contained approximately eight of each small, large, and span test pairs (four each of simultaneous and sequential) and four 1 vs. 2 trials randomly interspersed throughout the test trials. Sessions were equated for mean numerical ratio across conditions. The numerical ratio was an average of approximately 0.5 for each pair type in each session. This meant that some pair types were tested more frequently than others. We tested the Experiment 2 subjects until they had multiple exposures to all contrasts in both presentation types. We completed 11 sessions with Pearl and 13 sessions with Ursala, as described in the procedure for Experiment 1. Extra sessions were required due to incomplete trials during some sessions. Ultimately, each animal completed approximately 130 trials per presentation format. There was a total average of approximately 4.5 trials per number pair, per presentation format.
It is important to note that the animals were not trained to select the larger quantity over the course of time. Instead, animals were always rewarded with the cache that they chose. The only way that a longer exposure period could possibly result in learning over time is if the animals are able to discriminate the quantities of the choices they were given. That is, because the animal was rewarded with their chosen food quantity on each trial, in order to learn that the quantity they chose was either greater or lesser than the alternative quantity, they would have to be able to discriminate and compare the quantities of the chosen vs. unchosen rewards.
In this longer exposure task, both monkeys significantly chose the larger food set for both sequential trials [binomial tests, Pearl (83/120 trials),
As discussed in the Introduction, failure on numerical pairs with one value greater than three has been taken as evidence for object-file representation in the literature on infant quantity development (Feigenson et al.,
Finally, in order to confirm that the animals were not learning these “predicted fail pairs” over time, we tested for trends of improving accuracy across the longer exposure period for the predicted fail pairs. Neither monkey showed a significant improvement in accuracy as a function of time for these pairs [Pearl
In Experiments 1 and 2 there is a possibility that animals used subconscious cues from the human experimenters to solve the task. This possibility seems unlikely for several reasons. First, we found evidence that the animals selected the larger quantity on their first exposure to the task and did not learn the task by trial-and-error, contrary to accounts of human cueing which are hypothesized to require associative learning over the course of training (i.e., Clever Hans; see Beran,
Subjects were the two female baboons who participated in Experiment 2 (Pearl, Ursala).
In the control condition, the two animals from Experiment 2 were tested by two experimenters, each of whom baited one of the two cups. Each experimenter was blind to the quantity of food items baited into the other’s cup and so was unaware of which cup contained the larger quantity. This ensured that the human experimenters could not give subconscious cues to the correct cup because they did not know which cup was correct. Monkeys were tested with approximately 55 trials of the number pairs 1 vs. 2 and 2 vs. 9 in the sequential presentation format. Each session was 24 trials. The procedure was otherwise identical to Experiments 1 and 2.
Both monkeys performed significantly above chance from the first session of testing with the control condition (Binomial tests; Pearl: 19/24,
Eight olive baboons without any prior experience discriminating quantities in experiments were tested on their ability to spontaneously discriminate quantities of food items. The monkeys were able to discriminate small, large, and most importantly, span number pairs, as evidenced by their ability to choose the larger quantity at a frequency significantly above chance. The data show that olive baboons can successfully discriminate quantities, as many other non-human species are known to do. Our data further demonstrate that non-human primates spontaneously discriminate quantities using analog quantity representations that are constrained by ratio and predicted by Weber’s Law.
We tested hypotheses that address the underlying nature of the spontaneous quantity representations of non-human primates. The three hypothetical possibilities we outlined in the Introduction were: (1) object-file numerical representation only, with success occurring only for small numbers, (2) dual incompatible object-file and analog magnitude representation, with success occurring for small and large numbers but not span pairs, and (3) analog magnitude representation only with success dependent on numerical ratio independently of set size. Reviewing the data, we find that the performance of these monkeys is best explained by a single-system analog representation model.
First, monkeys were able to discriminate small, span, and large number pairs presented simultaneously and small and span pairs presented sequentially – numerical discriminations which demonstrably exceed the capacity limit of the object-file system. Failures on sequential large sets were likely due to attentional constraints rather than object-file representations because simultaneous and span discriminations with large values were successful. Anecdotally, we observed that baboons were more distractible over the long sequential trials. This could suggest that failures on large sequential pairs were due to failures of sustained attention. Nonetheless, monkeys were capable of accurate discrimination of span pairs presented sequentially, indicating that they are capable of representing numbers larger than 3 or 4 during sequential presentation. Secondly, the finding that baboons successfully discriminated span pairs indicates that monkeys were not simultaneously using both the analog and object-file systems to perform this task as that hypothesis predicts failure on span pairs (but see Cordes and Brannon,
We also investigated the Weber fractions that characterize the numerical sensitivity of individual baboons. The Weber fractions on the first exposure trials were within the range of Weber fractions previously reported for non-verbal numerical discriminations in human children (Halberda and Feigenson,
On the longer exposure experiment with two monkeys, overall performance was significantly above chance for both simultaneous and sequential set presentations and quantity discriminations were modulated by ratio. Weber fractions on the longer exposure experiment were similar to those from the first exposure experiment and so they are also similar to Weber fractions reported for young children. The baboons did not exhibit substantial improvement in overall performance over these dozen or so sessions indicating that learning did not play a major role in baboons’ quantity judgments over across testing. Monkeys’ successful quantity choices during the control condition provides evidence that monkeys did not use subconscious cues by human experimenters to solve the food choice task.
A direct comparison of the baboon data with data previously reported for human infants (Feigenson et al.,
Our results are consistent with prior studies that have argued for spontaneous analog magnitude numerical judgments in many animal species (e.g., Meck and Church,
The overall success of these experiment-naive baboons on quantitative discriminations of food items indicates that non-human primates spontaneously represent and compare quantities to make adaptive choices. These discriminations can be made over simultaneously or sequentially presented sets of items. The discriminations can also be made over small numerical pairs, large numerical pairs, and pairs that include one small and one large value. Monkeys’ sensitivity in making these discriminations was determined by the ratio between the numerical values of the sets, a signature of analog magnitude representation. The only way to explain the monkeys’ successful performance in these experiments is by appealing to spontaneous quantitative abilities. Our data indicate that these spontaneous quantitative abilities in baboons are inherently analog in nature.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
We thank Stephen Ferrigno for conducting and analyzing the control condition. We thank Celia Litovsky, Sabina Noll, and Elizabeth Brown for assistance testing subjects and coding data. We also thank the Seneca Park Zoo for giving us permission to work with their animals. This research was supported by a grant from the James S. McDonnell Foundation to Jessica F. Cantlon.