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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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Bayley, P., Martin, S., & Anson, M. (1975). Temperature-jump circular dichroism: observation of chiroptical relaxation processes at millisecond time resolution. Biochem Biophys Res Commun, 66(1), 303–308.
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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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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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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., & Terrace, H. S. (1998). Ordering of the numerosities 1 to 9 by monkeys. Science, 282(5389), 746–749.
Abstract: A fundamental question in cognitive science is whether animals can represent numerosity (a property of a stimulus that is defined by the number of discriminable elements it contains) and use numerical representations computationally. Here, it was shown that rhesus monkeys represent the numerosity of visual stimuli and detect their ordinal disparity. Two monkeys were first trained to respond to exemplars of the numerosities 1 to 4 in an ascending numerical order (1 --> 2 --> 3 --> 4). As a control for non-numerical cues, exemplars were varied with respect to size, shape, and color. The monkeys were later tested, without reward, on their ability to order stimulus pairs composed of the novel numerosities 5 to 9. Both monkeys responded in an ascending order to the novel numerosities. These results show that rhesus monkeys represent the numerosities 1 to 9 on an ordinal scale.
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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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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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Czerlinski, G. H., Erickson, J. O., & Theorell, H. (1979). Chemical relaxation studies on the horse liver alcohol dehydrogenase system. Physiol Chem Phys, 11(6), 537–569.
Abstract: Chemical relaxation studies on the system horse liver alcohol dehydrogenase, nicotinamide adenine dinucleotide, and ethanol were conducted observing fluorescence changes between 400 and 500 nm. Temperature-jump experiments were performed at pH 6.5, 7.0, 8.0, and 9.0; concentration-jump experiments at pH 9.0. The reciprocal of the slowest relaxation time was found to be linearly dependent upon the enzyme concentration for relatively low enzyme concentrations, as predicted earlier. Use of the wide pH-range necessitated expression of the four apparent dissociation constants of the catalytic reaction cycle in terms of pH-independent constants. The system was described in terms of only one (or two) catalysis-linked protons not associated with the electron transfer. Protonic steps in a buffered system are in rapid equilibrium, too fast to be measured with the equipment available. Assuming only two of the four bimolecular reaction steps in the four-step cycle are fast compared to the remaining two, six cases may be considered with six expressions for the reciprocal of the slowest relaxation time. Comparison with the experimental data revealed that the bimolecular reaction steps governing the slowest relaxation time change with pH. Above the effective time resolution of the temperature-lump instrument with fluorescence detection (0.1 msec) only one other relaxation time was detectable and only at pH 9. This relaxation time, found to be independent of the concentration of all reactants within experimental error (r = 10 +/- 5 msec), is most likely due to an interconversion among ternary complexes.
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