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Jones, J. E., Antoniadis, E., Shettleworth, S. J., & Kamil, A. C. (2002). A comparative study of geometric rule learning by nutcrackers (Nucifraga columbiana), pigeons (Columba livia), and jackdaws (Corvus monedula). J Comp Psychol, 116(4), 350–356.
Abstract: Three avian species, a seed-caching corvid (Clark's nutcrackers; Nucifraga columbiana), a non-seed-caching corvid (jackdaws; Corvus monedula), and a non-seed-caching columbid (pigeons; Columba livia), were tested for ability to learn to find a goal halfway between 2 landmarks when distance between the landmarks varied during training. All 3 species learned, but jackdaws took much longer than either pigeons or nutcrackers. The nutcrackers searched more accurately than either pigeons or jackdaws. Both nutcrackers and pigeons showed good transfer to novel landmark arrays in which interlandmark distances were novel, but inconclusive results were obtained from jackdaws. Species differences in this spatial task appear quantitative rather than qualitative and are associated with differences in natural history rather than phylogeny.
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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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Gonzalez-Fernandez, J. M., & Atta, S. E. (1982). Facilitated transport of oxygen in the presence of membranes in the diffusion path. Biophys J, 38(2), 133–141.
Abstract: Most of the experimental observations on facilitated transport have been done with millipore filters, and all the theoretical studies have assumed homogeneous spatial properties. In striated muscle there exist membranes that may impede the diffusion of the carrier myoglobin. In this paper a theoretical study is undertaken to analyze the transport in the presence of membranes in the diffusion path. For the numerical computations physiologically relevant values of the parameters were chosen. The numerical results indicate that the presence of membranes tends to decrease the facilitation. For the nonlinear chemical kinetics of the reaction of oxygen with the carrier, this decrement also depends on the location of the membranes. At the higher oxygen concentration side of each membrane the flow of combined oxygen is transferred to the flow of dissolved oxygen. The reverse process occurs at the lower concentration side. Jump discontinuities of the concentration of the oxygen-carrier compound at each membrane are associated with these transfers. The decrement of facilitation is due to the cumulative effect of these jump discontinuities.
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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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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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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. (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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Wilson, M. T., Ranson, R. J., Masiakowski, P., Czarnecka, E., & Brunori, M. (1977). A kinetic study of the pH-dependent properties of the ferric undecapeptide of cytochrome c (microperoxidase). Eur J Biochem, 77(1), 193–199.
Abstract: The ferric form of the haem undecapeptide, derived from horse cytochrome c by peptic digestion, undergoes at least three pH-induced transitions with pK values of 3.4, 5.8 and 7.6. Temperature-jump experiments suggest that the first of these is due to the binding of a deprotonated imidazole group to the feric iron while the second and third arise from the binding of the two available amino groups present (the alpha-NH2 of valine and the epsilon-NH2 of lysine). Molecular models indicate that steric retraints on the peptide dictate that these amino groups may only coordinate to iron atoms via intermolecular bonds, thus leading to the polymerization of the peptide. Cyanide binding studies are in agreement with these conclusions and also yield a value of 3.6 X 10(6) M-1 s-1 for the intrinsic combination constant of CN- anion with the haem. A model is proposed which describes the pH-dependent properties of the ferric undecapeptide.
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