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Lewis, K. P., Jaffe, S., & Brannon, E. M. (2005). Analog number representations in mongoose lemurs (Eulemur mongoz): evidence from a search task. Anim. Cogn., 8(4), 247–252.
Abstract: A wealth of data demonstrating that monkeys and apes represent number have been interpreted as suggesting that sensitivity to number emerged early in primate evolution, if not before. Here we examine the numerical capacities of the mongoose lemur (Eulemur mongoz), a member of the prosimian suborder of primates that split from the common ancestor of monkeys, apes and humans approximately 47-54 million years ago. Subjects observed as an experimenter sequentially placed grapes into an opaque bucket. On half of the trials the experimenter placed a subset of the grapes into a false bottom such that they were inaccessible to the lemur. The critical question was whether lemurs would spend more time searching the bucket when food should have remained in the bucket, compared to when they had retrieved all of the food. We found that the amount of time lemurs spent searching was indicative of whether grapes should have remained in the bucket, and furthermore that lemur search time reliably differentiated numerosities that differed by a 1:2 ratio, but not those that differed by a 2:3 or 3:4 ratio. Finally, two control conditions determined that lemurs represented the number of food items, and neither the odor of the grapes, nor the amount of grape (e.g., area) in the bucket. These results suggest that mongoose lemurs have numerical representations that are modulated by Weber's Law.
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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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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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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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Staniar, W. B., Kronfeld, D. S., Hoffman, R. M., Wilson, J. A., & Harris, P. A. (2004). Weight prediction from linear measures of growing Thoroughbreds. Equine Vet J, 36(2), 149–154.
Abstract: REASON FOR PERFORMING STUDY: Monitoring weight of foals is a useful management practice to aid in maximising athletic potential while minimising risks associated with deviations from normal growth. OBJECTIVE: To develop predictive equations for weight, based on linear measurements of growing Thoroughbreds (TBs). METHODS: Morphometric equations predicting weight from measurements of the trunk and legs were developed from data of 153 foals. The accuracy, precision and bias of the best fitting equation were compared to published equations using a naive data set of 22 foals. RESULTS: Accuracy and precision were maximised with a broken line relating calculated volumes (V(t + l)) to measured weights. Use of the broken line is a 2 step process. V(t + l) is calculated from linear measures (m) of girth (G), carpus circumference (C), and length of body (B) and left forelimb (F). V(t + I) = ([G2 x B] + 4[C2 x F]) 4pi. If V(t + l) < 0.27 m3, weight is estimated: Weight (kg) = V(t + l) x 1093. If V(t + l) > or = 0.27 m3: Weight (kg) = V(t + l) x 984 + 24. The broken line was more accurate and precise than 3 published equations predicting the weight of young TBs. CONCLUSIONS: Estimation of weight using morphometric equations requires attention to temporal changes in body shape and density; hence, a broken line is needed. Including calculated leg volume in the broken line model is another contributing factor to improvement in predictive capability. POTENTIAL RELEVANCE: The broken line maximises its value to equine professionals through its accuracy, precision and convenience.
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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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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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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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