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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.
Keywords: Animals; *Cognition; Macaca mulatta/*psychology; *Mathematics; Perception; Reaction Time
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Rumbaugh, D. M., Savage-Rumbaugh, S., & Hegel, M. T. (1987). Summation in the chimpanzee (Pan troglodytes). J Exp Psychol Anim Behav Process, 13(2), 107–115.
Abstract: In this research, we asked whether 2 chimpanzee (Pan troglodytes) subjects could reliably sum across pairs of quantities to select the greater total. Subjects were allowed to choose between two trays of chocolates. Each tray contained two food wells. To select the tray containing the greater number of chocolates, it was necessary to sum the contents of the food wells on each tray. In experiments where food wells contained from zero to four chocolates, the chimpanzees chose the greater value of the summed wells on more than 90% of the trials. In the final experiment, the maximum number of chocolates assigned to a food well was increased to five. Choice of the tray containing the greater sum still remained above 90%. In all experiments, subjects reliably chose the greater sum, even though on many trials a food well on the “incorrect” tray held more chocolates than either single well on the “correct” tray. It was concluded that without any known ability to count, these chimpanzees used some process of summation to combine spatially separated quantities. Speculation regarding the basis for summation includes consideration of perceptual fusion of pairs of quantities and subitization.
Keywords: Animals; Choice Behavior; *Cognition; Male; *Mathematics; *Pan troglodytes; Visual Perception
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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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Matsuzawa, T. (1985). Use of numbers by a chimpanzee. Nature, 315(6014), 57–59.
Abstract: Recent studies have examined linguistic abilities in apes. However, although human mathematical abilities seem to be derived from the same foundation as those in language, we have little evidence for mathematical abilities in apes (but for exceptions see refs 7-10). In the present study, a 5-yr-old female chimpanzee (Pan troglodytes), 'Ai', was trained to use Arabic numerals to name the number of items in a display. Ai mastered numerical naming from one to six and was able to name the number, colour and object of 300 types of samples. Although no particular sequence of describing samples was required, the chimpanzee favoured two sequences (colour/object/number and object/colour/number). The present study demonstrates that the chimpanzee was able to describe the three attributes of the sample items and spontaneously organized the 'word order'.
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Kaplan, A. I., & Borodovskii, M. I. (1989). [Alternative animal behavior: a model and its statistical characteristics]. Nauchnye Doki Vyss Shkoly Biol Nauki, (3), 29–32.
Abstract: The rats' alternative behaviour in T-maze at simultaneous two-sided food refreshment in 13 trials a day during 6 days has been studied. It has been found that in the first testing days the indexes of alternative behaviour of animals correspond to the characteristics of the random alternation. However, on the 5-6th day of testing in the overwhelming majority of rats the true deviation of alternation index above or below than the theoretical values has been revealed. A question on the existence of two strategies of cognitive behaviour alteration and perseveration in rat population is under discussion.
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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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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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Real, L. A. (1991). Animal choice behavior and the evolution of cognitive architecture. Science, 253(5023), 980–986.
Abstract: Animals process sensory information according to specific computational rules and, subsequently, form representations of their environments that form the basis for decisions and choices. The specific computational rules used by organisms will often be evolutionarily adaptive by generating higher probabilities of survival, reproduction, and resource acquisition. Experiments with enclosed colonies of bumblebees constrained to foraging on artificial flowers suggest that the bumblebee's cognitive architecture is designed to efficiently exploit floral resources from spatially structured environments given limits on memory and the neuronal processing of information. A non-linear relationship between the biomechanics of nectar extraction and rates of net energetic gain by individual bees may account for sensitivities to both the arithmetic mean and variance in reward distributions in flowers. Heuristic rules that lead to efficient resource exploitation may also lead to subjective misperception of likelihoods. Subjective probability formation may then be viewed as a problem in pattern recognition subject to specific sampling schemes and memory constraints.
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