Brannon, E. M., & Terrace, H. S. (2000). Representation of the numerosities 1-9 by rhesus macaques (Macaca mulatta). J Exp Psychol Anim Behav Process, 26(1), 31–49.
Abstract: Three rhesus monkeys (Macaca mulatta) were trained to respond to exemplars of 1, 2, 3, and 4 in an ascending, descending, or a nonmonotonic numerical order (1-->2-->3-->4, 4-->3-->2--1, 3-->1-->4-->2). The monkeys were then tested on their ability to order pairs of the novel numerosities 5-9. In Experiment 1, all 3 monkeys ordered novel exemplars of the numerosities 1-4 in ascending or descending order. The attempt to train a nonmonotonic order (3-->1-->4-->2) failed. In Experiment 2A, the 2 monkeys who learned the ascending numerical rule ordered pairs of the novel numerosities 5-9 on unreinforced trials. The monkey who learned the descending numerical rule failed to extrapolate the descending rule to new numerosities. In Experiment 2B all 3 monkeys ordered novel exemplars of pairs of the numerosities 5-9. Accuracy and latency of responding revealed distance and magnitude effects analogous to previous findings with human participants (R. S. Moyer & T. K. Landaeur, 1967). Collectively these studies show that monkeys represent the numerosities 1-9 on at least an ordinal scale.
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Beran, M. J., Pate, J. L., Washburn, D. A., & Rumbaugh, D. M. (2004). Sequential responding and planning in chimpanzees (Pan troglodytes) and rhesus macaques (Macaca mulatta). J Exp Psychol Anim Behav Process, 30(3), 203–212.
Abstract: Chimpanzees (Pan troglodytes) and rhesus macaques (Macaca mulatta) selected either Arabic numerals or colored squares on a computer monitor in a learned sequence. On shift trials, the locations of 2 stimuli were interchanged at some point. More errors were made when this interchange occurred for the next 2 stimuli to be selected than when the interchange was for stimuli later in the sequence. On mask trials, all remaining stimuli were occluded after the 1st selection. Performance exceeded chance levels for only 1 selection after these masks were applied. There was no difference in performance for either stimulus type (numerals or colors). The data indicated that the animals planned only the next selection during these computerized tasks as opposed to planning the entire response 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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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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Kiltie, R. A., Fan, J., & Laine, A. F. (1995). A wavelet-based metric for visual texture discrimination with applications in evolutionary ecology. Math Biosci, 126(1), 21–39.
Abstract: Much work on natural and sexual selection is concerned with the conspicuousness of visual patterns (textures) on animal and plant surfaces. Previous attempts by evolutionary biologists to quantify apparency of such textures have involved subjective estimates of conspicuousness or statistical analyses based on transect samples. We present a method based on wavelet analysis that avoids subjectivity and that uses more of the information in image textures than transects do. Like the human visual system for texture discrimination, and probably like that of other vertebrates, this method is based on localized analysis of orientation and frequency components of the patterns composing visual textures. As examples of the metric's utility, we present analyses of crypsis for tigers, zebras, and peppered moth morphs.
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West, R. E., & Young, R. J. (2002). Do domestic dogs show any evidence of being able to count? Anim. Cogn., 5(3), 183–186.
Abstract: Numerical competence has been demonstrated in a wide range of animal species. The level of numerical abilities shown ranges from simple relative numerousness judgements to true counting. In this study we used the preferential looking technique to test whether 11 pet dogs could count. The dogs were presented with three simple calculations: “1+1=2”; “1+1=1”; and “1+1=3”. These calculations were performed by presenting the dogs with treats that were placed behind a screen that allowed manipulation of the outcome of the calculation. When the dogs expected the outcome they spent the same amount of time looking at the result of the calculation as they did on the initial presentation. However, when the result was unexpected dogs spent significantly longer looking at the outcome of the calculation. The results suggest that the dogs were anticipating the outcome of the calculations they observed, thus suggesting that dogs may have a rudimentary ability to count.
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Uller, C., Jaeger, R., Guidry, G., & Martin, C. (2003). Salamanders ( Plethodon cinereus) go for more: rudiments of number in an amphibian. Anim. Cogn., 6(2), 105–112.
Abstract: Techniques traditionally used in developmental research with infants have been widely used with nonhuman primates in the investigation of comparative cognitive abilities. Recently, researchers have shown that human infants and monkeys select the larger of two numerosities in a spontaneous forced-choice discrimination task. Here we adopt the same method to assess in a series of experiments spontaneous choice of the larger of two numerosities in a species of amphibian, red-backed salamanders ( Plethodon cinereus). The findings indicate that salamanders “go for more,” just like human babies and monkeys. This rudimentary capacity is a type of numerical discrimination that is spontaneously present in this amphibian.
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Beran, M. J. (2004). Long-term retention of the differential values of Arabic numerals by chimpanzees (Pan troglodytes). Anim. Cogn., 7(2), 86–92.
Abstract: As previously reported (Beran and Rumbaugh, 2001), two chimpanzees used a joystick to collect dots, one-at-a-time, on a computer monitor, and then ended a trial when the number of dots collected was equal to the Arabic numeral presented for the trial. Here, the chimpanzees were presented with the task again after an interval of 6 months and then again after an additional interval of 3.25 years. During each interval, the chimpanzees were not presented with the task, and this allowed an assessment of the extent to which both animals retained the values of each Arabic numeral. Despite lower performance at each retention interval compared to the original study, both chimpanzees performed above chance levels in collecting a quantity of dots equal to the target numeral, one chimpanzee for the numerals 1-7, and the second chimpanzee for the numerals 1-6. For the 3.25-year retention, errors were more dispersed around each target numeral than in the original study, but the chimpanzees' performances again appeared to be based on a continuous representation of magnitude rather than a discrete representation of number. These data provide an experimental demonstration of long-term retention of the differential values of Arabic numerals by chimpanzees.
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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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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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