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Harris, E. H., & Washburn, D. A. (2005). Macaques' (Macaca mulatta) use of numerical cues in maze trials. Anim. Cogn., 8(3), 190–199.
Abstract: We tested the ability of number-trained rhesus monkeys to use Arabic numeral cues to discriminate between different series of maze trials and anticipate the final trial in each series. The monkeys' prior experience with numerals also allowed us to investigate spontaneous transfer between series. A total of four monkeys were tested in two experiments. In both experiments, the monkeys were trained on a computerized task consisting of three reinforced maze trials followed by one nonreinforced trial. The goal of the maze was an Arabic numeral 3, which corresponded to the number of reinforced maze trials in the series. In experiment 1 (n=2), the monkeys were given probe trials of the numerals 2 and 4 and in experiment 2 (n=2), they were given probe trials of the numerals 2-8. The monkeys receiving the probe trials 2 and 4 showed some generalization to the new numerals and developed a pattern of performing more slowly on the nonreinforced trial than the reinforced trial before it for most series, indicating the use of the changing numeral cues to anticipate the nonreinforced trial. The monkeys receiving probe trials of the numerals 2-8 did not predict precisely when the nonreinforced trial would occur in each series, but they did incorporate the changing numerals into their strategy for performing the task. This study provides the first evidence that number-trained monkeys can use Arabic numerals to perform a task involving sequential presentations.
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Ferkin, M. H., Pierce, A. A., Sealand, R. O., & Delbarco-Trillo, J. (2005). Meadow voles, Microtus pennsylvanicus, can distinguish more over-marks from fewer over-marks. Anim. Cogn., 8(3), 182–189.
Abstract: Is it possible that voles have a sense of number? To address this question, we determined whether voles discriminate between two different scent-marking individuals and identify the individual whose scent marks was on top more often than the other individual. We tested whether voles show a preference for the individual whose scent marks was on top most often. If so, the simplest explanation was that voles can make a relative size judgement-such as distinguishing an area containing more of one individual's over-marks as compared to less of another individual's over-marks. We found that voles respond preferentially to the donor that provided a greater number of over-marks as compared to the donor that provided a lesser number of over-marks. Thus, we concluded that voles might display the capacity for relative numerousness. Interestingly, female voles were better able than male voles to distinguish between small differences in the relative number of over-marks by the two scent donors.
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Pepperberg, I. M. (2006). Grey parrot numerical competence: a review. Anim. Cogn., 9(4), 377–391.
Abstract: The extent to which humans and nonhumans share numerical competency is a matter of debate. Some researchers argue that nonhumans, lacking human language, possess only a simple understanding of small quantities, generally less than four. Animals that have, however, received some training in human communication systems might demonstrate abilities intermediate between those of untrained nonhumans and humans. Here I review data for a Grey parrot (Psittacus erithacus) that has been shown to quantify sets of up to and including six items (including heterogeneous subsets) using vocal English labels, to comprehend these labels fully, and to have a zero-like concept. Recent research demonstrates that he can also sum small quantities. His success shows that he understands number symbols as abstract representations of real-world collections, and that his sense of number compares favorably to that of chimpanzees and young human children.
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Jordan, K. E., & Brannon, E. M. (2006). Weber's Law influences numerical representations in rhesus macaques (Macaca mulatta). Anim. Cogn., 9(3), 159–172.
Abstract: We present the results of two experiments that probe the ability of rhesus macaques to match visual arrays based on number. Three monkeys were first trained on a delayed match-to-sample paradigm (DMTS) to match stimuli on the basis of number and ignore continuous dimensions such as element size, cumulative surface area, and density. Monkeys were then tested in a numerical bisection experiment that required them to indicate whether a sample numerosity was closer to a small or large anchor value. Results indicated that, for two sets of anchor values with the same ratio, the probability of choosing the larger anchor value systematically increased with the sample number and the psychometric functions superimposed. A second experiment employed a numerical DMTS task in which the choice values contained an exact numerical match to the sample and a distracter that varied in number. Both accuracy and reaction time were modulated by the ratio between the correct numerical match and the distracter, as predicted by Weber's Law.
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Brannon, E. M., Cantlon, J. F., & Terrace, H. S. (2006). The role of reference points in ordinal numerical comparisons by rhesus macaques (Macaca mulatta). J Exp Psychol Anim Behav Process, 32(2), 120–134.
Abstract: Two experiments examined ordinal numerical knowledge in rhesus macaques (Macaca mulatta). Experiment 1 replicated the finding (E. M. Brannon & H. S. Terrace, 2000) that monkeys trained to respond in descending numerical order (4-->3-->2-->1) did not generalize the descending rule to the novel values 5-9 in contrast to monkeys trained to respond in ascending order. Experiment 2 examined whether the failure to generalize a descending rule was due to the direction of the training sequence or to the specific values used in the training sequence. Results implicated 3 factors that characterize a monkey's numerical comparison process: Weber's law, knowledge of ordinal direction, and a comparison of each value in a test pair with the reference point established by the first value of the training sequence.
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Beran, M. J., Smith, J. D., Redford, J. S., & Washburn, D. A. (2006). Rhesus macaques (Macaca mulatta) monitor uncertainty during numerosity judgments. J Exp Psychol Anim Behav Process, 32(2), 111–119.
Abstract: Two rhesus macaques (Macaca mulatta) judged arrays of dots on a computer screen as having more or fewer dots than a center value that was never presented in trials. After learning a center value, monkeys were given an uncertainty response that let them decline to make the numerosity judgment on that trial. Across center values (3-7), errors occurred most often for sets adjacent in numerosity to the center value. The monkeys also used the uncertainty response most frequently on these difficult trials. A 2nd experiment showed that monkeys' responses reflected numerical magnitude and not the surface-area illumination of the displays. This research shows that monkeys' uncertainty-monitoring capacity extends to the domain of numerical cognition. It also shows monkeys' use of the purest uncertainty response possible, uncontaminated by any secondary motivator.
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Agrillo, C., Dadda, M., & Bisazza, A. (2007). Quantity discrimination in female mosquitofish. Anim. Cogn., 10(1), 63–70.
Abstract: The ability in animals to count and represent different numbers of objects has received a great deal of attention in the past few decades. Cumulative evidence from comparative studies on number discriminations report obvious analogies among human babies, non-human primates and birds and are consistent with the hypothesis of two distinct and widespread mechanisms, one for counting small numbers (<4) precisely, and one for quantifying large numbers approximately. We investigated the ability to discriminate among different numerosities, in a distantly related species, the mosquitofish, by using the spontaneous choice of a gravid female to join large groups of females as protection from a sexually harassing male. In one experiment, we found that females were able to discriminate between two shoals with a 1:2 numerosity ratio (2 vs. 4, 4 vs. 8 and 8 vs. 16 fish) but failed to discriminate a 2:3 ratio (8 vs. 12 fish). In the second experiment, we studied the ability to discriminate between shoals that differed by one element; females were able to select the larger shoal when the paired numbers were 2 vs. 3 or 3 vs. 4 but not 4 vs. 5 or 5 vs. 6. Our study indicates that numerical abilities in fish are comparable with those of other non-verbal creatures studied; results are in agreement with the hypothesis of the existence of two distinct systems for quantity discrimination in vertebrates.
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Beran, M. J. (2007). Rhesus monkeys (Macaca mulatta) succeed on a computerized test designed to assess conservation of discrete quantity. Anim. Cogn., 10(1), 37–45.
Abstract: Conservation of quantity occurs through recognition that changes in the physical arrangement of a set of items do not change the quantity of items in that set. Rhesus monkeys (Macaca mulatta) were presented with a computerized quantity judgment task. Monkeys were rewarded for selecting the greater quantity of items in one of two horizontal arrays of items on the screen. On some trials, after a correct selection, no reward was given but one of the arrays was manipulated. In some cases, this manipulation involved moving items closer together or farther apart to change the physical arrangement of the array without changing the quantity of items in the array. In other cases, additional items were added to the initially smaller array so that it became quantitatively larger. Monkeys then made another selection from the two rows of items. Monkeys were sensitive to these manipulations, changing their selections when the number of items in the rows changed but not when the arrangement only was changed. Therefore, monkeys responded on the basis of the quantity of items, and they were not distracted by non-quantitative manipulations of the sets.
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