Estimating and operating on discrete quantities in orangutans (Pongo pygmaeus)

Representational format determines numerical competence in monkeys

A range of animal species possess an evolutionarily ancient system for representing number, which provides the foundation for simple arithmetical operations such as addition and numerical comparisons. Surprisingly, non-human primates tested in ecologically, highly valid quantity discrimination tasks using edible items often show a relatively low performance, suggesting that stimulus salience interferes with rational decision making. Here we show that quantity discrimination was indeed significantly enhanced when monkeys were tested with inedible items compared with food items (84 versus 69% correct). More importantly, when monkeys were tested with food, but rewarded with other food items, the accuracy was equally high (86%). The results indicate that the internal representation of the stimuli, not their physical quality, determined performance. Reward replacement apparently facilitated representation of the food items as signifiers for other foods, which in turn supported a higher acuity in decision making.

Many animals can do simple quantity discrimination, but they often perform poorly when food is used. Here, the authors show that monkeys are good at food quantity discrimination when they are not allowed to eat it, suggesting that the mental representation of the stimuli is more important than the physical quality.

Can monkeys make investments based on maximized pay-off?

Animals can maximize benefits but it is not known if they adjust their investment according to expected pay-offs. We investigated whether monkeys can use different investment strategies in an exchange task. We tested eight capuchin monkeys (Cebus apella) and thirteen macaques (Macaca fascicularis, Macaca tonkeana) in an experiment where they could adapt their investment to the food amounts proposed by two different experimenters. One, the doubling partner, returned a reward that was twice the amount given by the subject, whereas the other, the fixed partner, always returned a constant amount regardless of the amount given. To maximize pay-offs, subjects should invest a maximal amount with the first partner and a minimal amount with the second. When tested with the fixed partner only, one third of monkeys learned to remove a maximal amount of food for immediate consumption before investing a minimal one. With both partners, most subjects failed to maximize pay-offs by using different decision rules with each partner' quality. A single Tonkean macaque succeeded in investing a maximal amount to one experimenter and a minimal amount to the other. The fact that only one of over 21 subjects learned to maximize benefits in adapting investment according to experimenters' quality indicates that such a task is difficult for monkeys, albeit not impossible.

Spatial attention determines the nature of nonverbal number representation

Coordinated studies of adults, infants, and nonhuman animals provide evidence for two systems of nonverbal number representation: a "parallel individuation" system that represents individual items and a "numerical magnitude" system that represents the approximate cardinal value of a group. However, there is considerable debate about the nature and functions of these systems, due largely to the fact that some studies show a dissociation between small (1-3) and large (>3) number representation, whereas others do not. Using event-related potentials, we show that it is possible to determine which system will represent the numerical value of a small number set (1-3 items) by manipulating spatial attention. Specifically, when attention can select individual objects, an early brain response (N1) scales with the cardinal value of the display, the signature of parallel individuation. In contrast, when attention cannot select individual objects or is occupied by another task, a later brain response (P2p) scales with ratio, the signature of the approximate numerical magnitude system. These results provide neural evidence that small numbers can be represented as approximate numerical magnitudes. Further, they empirically demonstrate the importance of early attentional processes to number representation by showing that the way in which attention disperses across a scene determines which numerical system will deploy in a given context.

Free-ranging dogs assess the quantity of opponents in intergroup conflicts

In conflicts between social groups, the decision of competitors whether to attack/retreat should be based on the assessment of the quantity of individuals in their own and the opposing group. Experimental studies on numerical cognition in animals suggest that they may represent both large and small numbers as noisy mental magnitudes subject to scalar variability, and small numbers (≤4) also as discrete object-files. Consequently, discriminating between large quantities, but not between smaller ones, should become easier as the asymmetry between quantities increases. Here, we tested these hypotheses by recording naturally occurring conflicts in a population of free-ranging dogs, Canis lupus familiaris, living in a suburban environment. The overall probability of at least one pack member approaching opponents aggressively increased with a decreasing ratio of the number of rivals to that of companions. Moreover, the probability that more than half of the pack members withdrew from a conflict increased when this ratio increased. The skill of dogs in correctly assessing relative group size appeared to improve with increasing the asymmetry in size when at least one pack comprised more than four individuals, and appeared affected to a lesser extent by group size asymmetries when dogs had to compare only small numbers. These results provide the first indications that a representation of quantity based on noisy mental magnitudes may be involved in the assessment of opponents in intergroup conflicts and leave open the possibility that an additional, more precise mechanism may operate with small numbers.

Chimpanzees (Pan troglodytes) accurately compare poured liquid quantities

Although many studies have shown that nonhuman animals can choose the larger of two discrete quantities of items, less emphasis has been given to discrimination of continuous quantity. These studies are necessary to discern the similarities and differences in discrimination performance as a function of the type of quantities that are compared. Chimpanzees made judgments between continuous quantities (liquids) in a series of three experiments. In the first experiment, chimpanzees first chose between two clear containers holding differing amounts of juice. Next, they watched as two liquid quantities were dispensed from opaque syringes held above opaque containers. In the second experiment, one liquid amount was presented by pouring it into an opaque container from an opaque syringe, whereas the other quantity was visible the entire time in a clear container. In the third experiment, the heights at which the opaque syringes were held above opaque containers differed for each set, so that sometimes sets with smaller amounts of juice were dropped from a greater height, providing a possible visual illusion as to the total amount. Chimpanzees succeeded in all tasks and showed many similarities in their continuous quantity estimation to how they performed previously in similar tasks with discrete quantities (for example, performance was constrained by the ratio between sets). Chimpanzees could compare visible sets to nonvisible sets, and they were not distracted by perceptual illusions created through various presentation styles that were not relevant to the actual amount of juice dispensed. This performance demonstrated a similarity in the quantitative discrimination skills of chimpanzees for continuous quantities that matches that previously shown for discrete quantities.

Perception of food amounts by chimpanzees (Pan troglodytes): the role of magnitude, contiguity, and wholeness

The authors investigated choice behavior by chimpanzees in five experiments involving choices between different amounts of food. Chimpanzees did not maximize the amount of food they obtained when choosing between a single 20-g banana piece and another option containing a 20-g piece and a 5-g piece. This was true even though they successfully discriminated between 20-g and 25-g banana pieces in other trials. When items in the mixed option were stacked, however, the chimpanzees chose the larger amount. Later experiments indicated that changing the magnitude of the two amounts did not change performance if the difference in magnitude between the two options remained the same (e.g., 40 g plus 10 g vs. 40 g). However, chimpanzees did improve when the two-item option was increased in its magnitude relative to the single slice (e.g., 20 g plus 10 g vs. 20 g). These results indicated that chimpanzees undervalued the total amount of food in sets when items differed in size and did not appear to be whole. Another experiment confirmed that it was this notion of wholeness that evoked suboptimal responding because chimpanzees were successful in the same comparisons with a different type of food that appeared less fractionated when presented as two pieces. These results provide evidence of suboptimal responding in some natural choice situations that prevents chimpanzees from maximizing food intake.

Natural Choice in Chimpanzees (Pan troglodytes): Perceptual and Temporal Effects on Selective Value

In three experiments, four chimpanzees made choices between two visible food options to assess the validity of the selective value effect (the assignment of value to only the most preferred type of food presented in a comparison). In Experiment 1, we established that all chimpanzees preferred single banana pieces to single apple pieces before presenting the critical test. In this test two chimpanzees preferred a mix of one banana piece and one apple piece to a single banana piece when both banana piece were approximately the same size, but two chimpanzees were indifferent between the two options, exhibiting the selective value effect. In Experiment 2, when the banana pieces in both options were more closely equated in size the chimpanzees then were biased to choose the single banana piece over the mixed array even though this was the smaller total amount of food. However, in Experiment 3, when we introduced longer intervals between each trial, the chimpanzees preferred the mixed set and thus the larger total amount of food. The results demonstrate that only some chimpanzees exhibit the choice pattern indicative of the selective value effect, and they do so only when item size is not carefully controlled and trials are presented quickly in succession. Thus, the behavior pattern originally labeled the selective value effect may actually be explained by a combination of chimpanzees' sensitivity to small differences in preferred food amount and chimpanzees tendency to avoid less preferred foods that would delay the acquisition of further preferred food items.

When in doubt, chimpanzees rely on estimates of past reward amounts

Many animals can repeatedly judge the larger of two sets of food items. However, it remains unclear as to what information might accrue regarding the relative rates of return from these repeated responses. Information about overall rates of return is, in fact, unnecessary to perform well at the task itself. However, if an uncertain situation arose, such as when the quantity in one set was unknown, that information would be useful in determining whether to select a known quantity or an unknown quantity. We gave chimpanzees this test. First, they made multiple judgements between two visible food sets that varied in the number of items across trials. Then, they were faced with the same combinations of set sizes, but only one set was revealed while the other remained unknown. Rather than using a specific quantity as a threshold for choosing the known or the unknown set, the chimpanzees' choice of the unknown set varied in relation to the rate of return from responses in the first phase (when both sets were known). This indicated that the chimpanzees' decisions in the face of uncertainty were guided by a sense of how well they were rewarded overall during the session.

Relative quantity judgment by Asian elephants (Elephas maximus)

This study investigated whether Asian elephants can make relative quantity judgment (RQJ), a dichotomous judgment of unequal quantities ordered in magnitude. In Experiment 1, elephants were simultaneously shown two baskets with differing quantities of bait (up to 6 items). In Experiment 2, elephants were sequentially presented with baits, which could not be seen by elephants in their total quantities. The task of elephants was to choose the larger quantity in both experiments. Results showed that the elephants chose the larger quantity with significantly greater frequency. Interestingly, the elephants did not exhibit disparity or magnitude effects, in which performance declines with a smaller difference between quantities in a two-choice task, or the total quantity increases, respectively. These findings appear to be inconsistent with the previous reports of RQJ in other animals, suggesting that elephants may be using a different mechanism to compare and represent quantities than previously suggested for other species.

The discrimination of discrete and continuous amounts in African grey parrots (Psittacus erithacus)

A wealth of research in infants and animals demonstrates discrimination of quantities, in some cases nonverbal numerical perception, and even elementary calculation capacities. We investigated the ability of three African grey parrots (Psittacus erithacus) to select the largest amount of food between two sets, either discrete food items (experiment 1) or as volume of a food substance (experiment 2). The two amounts were presented simultaneously and were visible at the time of choice. Parrots were tested several times for all possible combinations between 1 and 5 seeds or 0.2 and 1 ml of food substance. In both conditions, subjects performed above chance for almost all combinations. Accuracy was negatively correlated with the ratio, that is performance improved with greater differences between amounts. Therefore, these results with both individual items and volume discrimination suggest that parrots use an analogue of magnitude, rather than object-file mechanisms to quantify items and substances.

Perception of Food Amounts by Chimpanzees Based on the Number, Size, Contour Length and Visibility of Items

Nonhuman animals reliably select the largest of two or more sets of discrete items, particularly if those items are food items. However, many studies of these numerousness judgments fail to control for confounds between amount of food e.g., mass or volume) and number of food items. Stimulus dimensions other than number of items also may play a role in how animals perceive sets and make choices. Four chimpanzees (Pan troglodytes) completed a variety of tasks that involved comparisons of food items (graham crackers) that varied in terms of their number, size, and orientation. In Experiment 1, chimpanzees chose between two alternative sets of visible cracker pieces. In Experiment 2, the experimenters presented one set of crackers in a vertical orientation (stacked) and the other in a horizontal orientation. In Experiment 3, the experimenters presented all food items one-at-a-time by dropping them into opaque containers. Chimpanzees succeeded overall in choosing the largest amount of food. They did not rely on number or contour length as cues when making these judgments but instead primarily responded to the total amount of food in the sets. However, some errors reflected choices of the set with the smaller total amount of food but the individually largest single food item. Thus, responses were not optimal because of biases that were not related to the total amount of food in the sets.

Summation and quantity judgments of sequentially presented sets by capuchin monkeys (Cebus apella)

Capuchin monkeys (Cebus apella) were presented with two sets of food items, identical in food type but differing in number. Animals selected one set and were permitted to consume their choice. Set sizes ranged from 1 to 6 items. In experiment 1, each set was uncovered and recovered before a response was made, and the monkeys selected the larger set at high levels. Experiment 2 presented sets that had both visible and nonvisible food items in them at the time of the response, thus requiring the monkeys to sum the total amount of food that was available. The monkeys again selected the larger set with no decrement in performance. Overall, the data indicate that capuchins, like other more extensively studied primate species in this area of research, are responsive to quantitative differences between sets. Capuchins succeed in making these quantity judgments when sets are nonvisible at choice time and when summation of items must be performed, thus demonstrating coordination of quantification skills and memory. Capuchins also inhibit responses to visible food items when those items are only part of an overall smaller quantity of food compared with a completely nonvisible set.

Do capuchin monkeys (Cebus apella) use tokens as symbols?

In the absence of language, the comprehension of symbols is difficult to demonstrate. Tokens can be considered symbols since they arbitrarily stand for something else without having any iconic relation to their referent. We assessed whether capuchin monkeys (Cebus apella) can use tokens as symbols to represent and combine quantities. Our paradigm involved choices between various combinations of tokens A and B, worth one and three rewards, respectively. Pay-off maximization required the assessment of the value of each offer by (i) estimating token numerousness, (ii) representing what each token stands for and (iii) making simple computations. When one token B was presented against one to five tokens A (experiment 1), four out of ten capuchins relied on a flexible strategy that allowed to maximize their pay-off, i.e. they preferred one token B against one and two tokens A, and they preferred four or five tokens A against one token B. Moreover, when two tokens B were presented against three to six tokens A (experiment 2), two out of six capuchins performed summation over representation of quantities. These findings suggest that capuchins can use tokens as symbols to flexibly combine quantities.

Quantity representation in children and rhesus monkeys: linear versus logarithmic scales

The performances of 4- and 5-year-olds and rhesus monkeys were compared using a computerized task for quantity assessment. Participants first learned two quantity anchor values and then responded to intermediate values by classifying them as similar to either the large anchor or the small anchor. Of primary interest was an assessment of where the point of subjective equality (PSE) occurred for each species across four different sets of anchors to determine whether the PSE occurred at the arithmetic mean or the geometric mean. Both species produced PSEs that were closer to the geometric mean for three of four anchor sets. This indicates that monkeys and children access either a logarithmic scale for quantity representation or a linear scale that is subject to scalar variability, both of which are consistent with Weber's law and representation of quantity that takes the form of analog magnitudes.

Food and token quantity discrimination in capuchin monkeys (Cebus apella)

Quantity discrimination is adaptive in a variety of ecological contexts and different taxa discriminate stimuli differing in numerousness, both in the wild and in laboratory settings. Quantity discrimination between object arrays has been suggested to be more demanding than between food arrays but, to our knowledge, the same paradigm has never been used to directly compare them. We investigated to what extent capuchin monkeys' relative numerousness judgments (RNJs) with food and token are alike. Tokens are inherently non-valuable objects that acquire an associative value upon exchange with the experimenter. Our aims were (1) to assess capuchins' RNJs with food (Experiment 1) and with tokens (Experiment 2) by presenting all the possible pair-wise choices between one to five items, and (2) to evaluate on which of the two proposed non-verbal mechanisms underlying quantity discrimination (analogue magnitude and object file system) capuchins relied upon. In both conditions capuchins reliably selected the larger amount of items, although their performance was higher with food than with tokens. The influence of the ratio between arrays on performance indicates that capuchins relied on the same system for numerical representation, namely analogue magnitude, regardless of the type of stimuli (food or tokens) and across both the small and large number ranges.

Capuchin monkeys (Cebus apella) succeed in a test of quantity conservation

Nonhuman animals demonstrate a number of impressive quantitative skills such as counting sets of items, comparing sets on the basis of the number of items or amount of material, and even responding to simple arithmetic manipulations. In this experiment, capuchin monkeys were presented with a computerized task designed to assess conservation of discrete quantity. Monkeys first were trained to select from two horizontal arrays of stimuli the one with the larger number of items. On some trials, after a correct selection there was no feedback but instead an additional manipulation of one of those arrays. In some cases, this manipulation involved moving items closer together or farther apart to change the physical arrangement of the array but not 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 a second selection from the two arrays of items. Previous research had shown that rhesus monkeys (Macaca mulatta) succeeded with this task. However, there was no condition in that study in which items were added to the smaller array without increasing its quantity to a point where it became the new larger array. This new condition was added in the present experiment. Capuchin monkeys were sensitive to all of these manipulations, changing their selections when the manipulations changed which array contained the larger number of items but not when the manipulations changed the physical arrangement of items or increased the quantity in one array without also reversing which of the two arrays had more items. Therefore, capuchin monkeys responded on the basis of the quantity of items, and they were not distracted by non-quantitative manipulations of the arrays. The data indicate that capuchins are sensitive to simply arithmetic manipulations that involve addition of items to arrays and also that they can conserve quantity.

When quantity trumps number: discrimination experiments in cotton-top tamarins (Saguinus oedipus) and common marmosets (Callithrix jacchus)

The capacity for non-linguistic, numerical discrimination has been well characterized in non-human animals, with recent studies providing careful controls for non-numerical confounds such as continuous extent, density, and quantity. More poorly understood are the conditions under which animals use numerical versus non-numerical quantification, and the nature of the relation between these two systems. Here we test whether cotton-top tamarins and common marmosets can discriminate between two quantities on the basis of the amount of food rather than on number. In three experiments, we show that when choosing between arrays containing different numbers and sizes of food objects, both species based their decisions on the amount of food with only minor influences of numerical information. Further, we find that subjects successfully discriminated between two quantities differing by a 2:3 or greater ratio, which is consistent with the ratio limits found for numerical discrimination with this species. These studies demonstrate that non-human primates possess mechanisms that enable quantification of total amount, in addition to the numerical representations demonstrated in previous studies, with both types of quantification subject to similar processing limits.

Nonverbal estimation during numerosity judgements by adult humans

On an automated task, humans selected the larger of two sets of items, each created through the one-by-one addition of items. Participants repeated the alphabet out loud during trials so that they could not count the items. This manipulation disrupted counting without producing major effects on other cognitive capacities such as memory or attention, and performance of this experimental group was poorer than that of participants who counted the items. In Experiment 2, the size of individual items was varied, and performance remained stable when the larger numerical set contained a smaller total amount than the smaller numerical set (i.e., participants used numerical rather than nonnumerical quantity cues in making judgements). In Experiment 3, reports of the number of items in a single set showed scalar variability as accuracy decreased, and variability in responses increased with increases in true set size. These data indicate a mechanism for the approximate representation of numerosity in adult humans that might be shared with nonhuman animals.

Rhesus monkeys (Macaca mulatta) select Arabic numerals or visual quantities corresponding to a number of sequentially completed maze trials

Four number-trained rhesus monkeys were trained to enumerate their sequential responses. After completing a series of computerized maze trials, the monkeys were given a same/different discrimination involving a numerical stimulus (an Arabic numeral or a visual quantity) and the letter D. The goal was to choose the numerical stimulus if it matched the number ofjust-completed maze trials, and to choose the letter D if it did not. There were large individual differences in performance, but one animal performed above 70% when receiving randomly intermixed series of 1, 3, 5, and 9 maze trials. This indicates that the monkey was keeping track of the approximate number of maze trials completed in each series and using that numerical cue to respond during the same/different discrimination.

Rhesus monkeys (Macaca mulatta) enumerate large and small sequentially presented sets of items using analog numerical representations

Two rhesus monkeys selected the larger of two sequentially presented sets of items on a computer monitor. In Experiment 1, performance was related to the ratio of set sizes, and the monkeys discriminated between sets with up to 10 items. Performance was not disrupted when 1 set had fewer than 4 items and 1 set had more than 4 items, a critical trial type for differentiating object file and analog models of numerical representation. Experiment 2 controlled the interitem rate of presentation. Experiment 3 included some trials on which number and amount (visual surface area) offered conflicting cues. Experiment 4 varied the total duration of set presentation and the duration of item visibility. In all of the experiments, performance remained high, although total set presentation duration also acted as a partial cue for the monkeys. Overall, the data indicated that rhesus monkeys estimate the approximate number of items in sequentially presented sets and that they are not relying solely on nonnumerical cues such as rate, duration, or cumulative amount.

Apes know that hidden objects can affect the orientation of other objects

Four bonobos, seven gorillas, and six orangutans were presented with two small rectangular boards on a platform. One of the boards had a piece of food under it so that it acquired an inclined orientation whereas the other remained flat on the platform. Subjects preferentially selected the inclined board. In another experiment, subjects were initially presented with two inclined boards and a transformation took place in which one of the boards fell flat to the platform while the other remained inclined. Subjects also preferred the board that remained inclined. Two additional experiments highlighted some of the possible limitations of their reasoning in this task. Presented with two inclined boards, one of which was visibly supported by a piece of wood, they failed to systematically select the unsupported one whose only reason for being inclined was the presence of the reward. Another experiment presented two rewards in each trial (instead of the customary one) in one of the following two combinations: large banana vs. small carrot or small banana vs. large carrot. Prior to the test, E presented both rewards to the subject and then hid each of them under one of the boards so that both boards were differentially inclined due to the different sizes of the rewards involved. Although subjects selected the board that showed a greater inclination (thus securing the larger reward), they disregarded the type of food that was involved. This often meant that they chose the large carrot over the small banana even though they reversed such a choice when the rewards were not occluded by the boards. Providing subjects with a 'reminder' of the type of reward hidden under the boards did not alter the original results. There was no evidence of learning throughout the various experiments and control tests ruled out the possibility of inadvertent cuing by the experimenter, poor performance due to a lack of motivation, or good performance due to a predisposition to select objects with sloped surfaces. It is concluded that subjects made some inferences about the reason for the inclined orientation of the boards, and not simply associated an inclined orientation with the presence of the reward.

Quantity-based judgments in the domestic dog (Canis lupus familiaris)

We examined the ability of domestic dogs to choose the larger versus smaller quantity of food in two experiments. In experiment 1, we investigated the ability of 29 dogs (results from 18 dogs were used in the data analysis) to discriminate between two quantities of food presented in eight different combinations. Choices were simultaneously presented and visually available at the time of choice. Overall, subjects chose the larger quantity more often than the smaller quantity, but they found numerically close comparisons more difficult. In experiment 2, we tested two dogs from experiment 1 under three conditions. In condition 1, we used similar methods from experiment 1 and tested the dogs multiple times on the eight combinations from experiment 1 plus one additional combination. In conditions 2 and 3, the food was visually unavailable to the subjects at the time of choice, but in condition 2, food choices were viewed simultaneously before being made visually unavailable, and in condition 3, they were viewed successively. In these last two conditions, and especially in condition 3, the dogs had to keep track of quantities mentally in order to choose optimally. Subjects still chose the larger quantity more often than the smaller quantity when the food was not simultaneously visible at the time of choice. Olfactory cues and inadvertent cuing by the experimenter were excluded as mechanisms for choosing larger quantities. The results suggest that, like apes tested on similar tasks, some dogs can form internal representations and make mental comparisons of quantity.

Grey parrot numerical competence: a review

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.

Rhesus monkeys (Macaca mulatta) succeed on a computerized test designed to assess conservation of discrete quantity

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.

Understanding of the concept of numerically "less" by bottlenose dolphins (Tursiops truncatus)

In 2 experiments, bottlenose dolphins (Tursiops truncatus) judged the ordinal relationship between novel numerosities. The dolphins were first trained to choose the exemplar with the fewer number of items when presented with just a few specific comparisons (e.g., 2 vs. 6, 1 vs. 3, and 3 vs. 7). Generalization of this rule was then tested by presenting the dolphins with all possible pairwise comparisons between 1 and 8. The dolphins chose the exemplar with the fewer number of items at levels far above chance, showing that they could recognize and represent numerosities on an ordinal scale. Their pattern of errors was consistent with the idea of an underlying analog magnitude representation.

Relative numerousness judgment and summation in young and old Western lowland gorillas

The relationship between age, relative numerousness judgment, and summation was investigated in 11 Western lowland gorillas (Gorilla gorilla gorilla). Experiments 1 and 2 evaluated the gorillas' ability to select the larger of 2 food quantities before and with training. The majority of gorillas did not reliably select the larger quantity in Experiment 1 until receiving training to do so in Experiment 2. Experiment 3 evaluated their ability to select the larger of 2 pairs of quantities. All gorillas selected the larger pair more often than chance, and the old were less accurate and slower than were the young. For most gorillas, performance in relative numerousness judgment with training and summation was comparable with previous reports in chimpanzees and orangutans.

How the great apes (Pan troglodytes, Pongo pygmaeus, Pan paniscus, and Gorilla gorilla) perform on the reversed contingency task: The effects of food quantity and food visibility

S. T. Boysen and G. G. Berntson (1995) found that chimpanzees performed poorly on a reversed contingency task in which they had to point to the smaller of 2 food quantities to acquire the larger quantity. The authors compared the performance of 4 great ape species (Pan troglodytes, Pongo pygmaeus, Pan paniscus, and Gorilla gorilla) on the reversed contingency task while manipulating food quantity (0-4 or 1-4) and food visibility (visible pairs or covered pairs). Results showed no systematic species differences but large individual differences. Some individuals of each species were able to solve the reversed contingency task. Both quantity and visibility of the food items had a significant effect on performance. Subjects performed better when the disparity between quantities was smaller and the quantities were not directly visible.

Ordinal judgments and summation of nonvisible sets of food items by two chimpanzees and a rhesus macaque

Two chimpanzees and a rhesus macaque rapidly learned the ordinal relations between 5 colors of containers (plastic eggs) when all containers of a given color contained a specific number of identical food items. All 3 animals also performed at high levels when comparing sets of containers with sets of visible food items. This indicates that the animals learned the approximate quantity of food items in containers of a given color. However, all animals failed in a summation task, in which a single container was compared with a set of 2 containers of a lesser individual quantity but a greater combined quantity. This difficulty was not overcome by sequential presentation of containers into opaque receptacles, but performance improved if the quantitative difference between sizes was very large.

Ordinal representation of numeric quantities by brown capuchin monkeys (Cebus apella)

Using techniques established by E. M. Brannon and H. S. Terrace (2000) with rhesus macaques (Macaca mulatta), the authors tested the ability of brown capuchins (Cebus apella) to order arrays of items ranging in quantity from 1 to 9. Three monkeys were trained on a touch screen to select the quantities 1-4 in ascending order. The monkeys exhibited successful transfer of this ability to novel representations of the quantities 1-4 and to pairs of the novel quantities 5-9. Patterns of responding with respect to numeric distance and magnitude were similar to those seen in human subjects, suggesting the use of similar psychological processes. The capuchins demonstrated an ordinal representation of quantity equivalent to that shown in Old World monkeys.

Piagetian liquid conservation in the great apes (Pan paniscus, Pan troglodytes, and Pongo pygmaeus)

An understanding of Piagetian liquid conservation was investigated in 4 bonobos (Pan paniscus), 5 chimpanzees (Pan troglodytes), and 5 orangutans (Pongo pygmaeus). The apes were tested in the ability to track the larger of 2 quantities of juice that had undergone various kinds of transformations. The accuracy of the apes' judgment depended on the shape or number of containers into which the larger quantity was transferred. The apes made their choice mainly on the basis of visual estimation but showed modest success when the quantities were occluded. The results suggest that the apes rely to a greater extent on visual information, although they might have some appreciation of the constancy of liquid quantities.

Piagetian conservation of discrete quantities in bonobos (Pan paniscus), chimpanzees (Pan troglodytes), and orangutans (Pongo pygmaeus)

This study investigated whether physical discreteness helps apes to understand the concept of Piagetian conservation (i.e. the invariance of quantities). Subjects were four bonobos, three chimpanzees, and five orangutans. Apes were tested on their ability to conserve discrete/continuous quantities in an over-conservation procedure in which two unequal quantities of edible rewards underwent various transformations in front of subjects. Subjects were examined to determine whether they could track the larger quantity of reward after the transformation. Comparison between the two types of conservation revealed that tests with bonobos supported the discreteness hypothesis. Bonobos, but neither chimpanzees nor orangutans, performed significantly better with discrete quantities than with continuous ones. The results suggest that at least bonobos could benefit from the discreteness of stimuli in their acquisition of conservation skills.

Macaques’ (Macaca mulatta) use of numerical cues in maze trials

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.

Number Comprehension by a Grey Parrot (Psittacus erithacus), Including a Zero-Like Concept

A Grey parrot (Psittacus erithacus) that was able to quantify 6 item sets (including subsets of heterogeneous groups, e.g., blue blocks within groupings of blue and green blocks and balls) using English labels (I. M. Pepperberg, 1994a) was tested on comprehension of these labels, which is crucial for numerical competence (K. C. Fuson, 1988; see also record 1987-98811-000). He was, without training, asked "What color/object [number]?" for collections of various simultaneously presented quantities (e.g., subsets of 4, 5, and 6 blocks of 3 different colors; subsets of 2, 4, and 6 keys, corks, and sticks). Accuracy was greater than 80% and was unaffected by array quantity, mass, or contour. His results demonstrated numerical comprehension competence comparable to that of chimpanzees and very young children. He also demonstrated knowledge of absence of quantity, using "none" to designate zero.

Gorillas (Gorilla gorilla) and Orangutans (Pongo pygmaeus) Encode Relevant Problem Features in a Tool-Using Task

Two important elements in problem solving are the abilities to encode relevant task features and to combine multiple actions to achieve the goal. The authors investigated these 2 elements in a task in which gorillas (Gorilla gorilla) and orangutans (Pongo pygmaeus) had to use a tool to retrieve an out-of-reach reward. Subjects were able to select tools of an appropriate length to reach the reward even when the position of the reward and tools were not simultaneously visible. When presented with tools that were too short to retrieve the reward, subjects were more likely to refuse to use them than when tools were the appropriate length. Subjects were proficient at using tools in sequence to retrieve the reward.

Baby arithmetic: one object plus one tone

Recent studies using a violation-of-expectation task suggest that preverbal infants are capable of recognizing basic arithmetical operations involving visual objects. There is still debate, however, over whether their performance is based on any expectation of the arithmetical operations, or on a general perceptual tendency to prefer visually familiar and complex displays. Here we provide new evidence that 5-month-old infants recognize basic arithmetic operations across sensory modalities. Using a violation-of-expectation task that eliminated the possibility of the familiarity and complexity preference, 5-month-old infants were presented alternatively with two types of arithmetical events: the expected, correct outcomes of operations (1 object+1 tone=2 objects and 1 object+2 tones=3 objects) and the unexpected, incorrect ones (1 object+2 tones=2 objects and 1 object+1 tone=3 objects). Results showed that subjects looked significantly longer at the unexpected events than at the expected events, suggesting that infants are able to recognize basic arithmetic operations across sensory modalities.

Chimpanzees (Pan troglodytes) Respond to Nonvisible Sets After One-by-One Addition and Removal of Items

Two chimpanzees (Pan troglodytes) made numerousness judgments of nonvisible sets of items. In Experiment 1, 1-10 items were dropped 1 at a time into an opaque cup, and then an additional 1-10 items were dropped 1 at a time into another opaque cup. The chimpanzees' performance levels were high and were more dependent on factors indicative of an analogue-magnitude mechanism for representation of set size than on an object file mechanism. In Experiment 2, a 3rd visible set was made available after the sequential presentation of the first 2 sets. The chimpanzees again performed at high levels in selecting the largest of the 3 sets. In Experiment 3, 1 of the 2 initially presented sets was reduced in number by the sequential removal of 1, 2, or 3 items. Both chimpanzees performed above chance levels for the removal of 1, but not more than 1, item.

Evolutionary foundations of number: spontaneous representation of numerical magnitudes by cotton-top tamarins

Although animals of many species have been shown to discriminate between visual-spatial arrays or auditory-temporal sequences based on numerosity, most of the evidence for numerosity discrimination derives from experiments involving extensive laboratory training. Under these conditions, animals' discrimination of two numerosities depends on their ratio and is independent of their absolute value. It is an open question whether any untrained non-human animal spontaneously represents number in this way, as do human children and adults. We present the results of familiarization-discrimination experiments on cotton-top tamarin monkeys (Saguinus oedipus) that provide evidence for numerosity discrimination in the absence of training. Presented with auditory stimuli (speech syllables) controlled for the continuous variables of sequence duration, item duration, inter-stimulus interval and overall energy, tamarins readily discriminated sequences of 4 versus 8, 4 versus 6, and 8 versus 12 syllables. By contrast, tamarins failed to discriminate sequences of 4 versus 5 and 8 versus 10 syllables, providing evidence that their numerosity discrimination is approximate and shows the ratio signature of numerosity discrimination in humans and trained non-human animals. These results provide strong support for the hypothesis that representations of large, approximate numerosity are evolutionarily ancient and spontaneously available to non-human animals.

Object permanence in orangutans (Pongo pygmaeus), chimpanzees (Pan troglodytes), and children (Homo sapiens)

Juvenile and adult orangutans (n = 5; Pongo pygmaeus), chimpanzees (n = 7; Pan troglodytes), and 19- and 26-month-old children (n = 24; Homo sapiens) received visible and invisible displacements. Three containers were presented forming a straight line, and a small box was used to displace a reward under them. Subjects received 3 types of displacement: single (the box visited 1 container), double adjacent (the box visited 2 contiguous containers), and double nonadjacent (the box visited 2 noncontiguous containers). All species performed at comparable levels, solving all problems except the invisible nonadjacent displacements. Visible displacements were easier than invisible, and single were easier than double displacements. In a 2nd experiment, subjects saw the baiting of either 2 adjacent or 2 nonadjacent containers with no displacements. All species selected the empty container more often when the baited containers were nonadjacent than when they were adjacent. It is hypothesized that a response bias and inhibition problem were responsible for the poor performance in nonadjacent displacements.

Summation and numerousness judgments of sequentially presented sets of items by chimpanzees (Pan troglodytes)

Summation and numerousness judgments by 2 chimpanzees (Pan troglodytes) were investigated when 2 quantities of M&Ms were presented sequentially, and the quantities were never viewed in their totality. Each M&M was visible only before placement in 1 of 2 cups. In Experiment 1, sets of 1 to 9 M&Ms were presented. In Experiment 2, the quantities in each cup were presented as 2 smaller sets (e.g., 2 + 2 vs. 4 + 1). In Experiment 3, the quantities were presented as 3 smaller sets (e.g., 2 + 2 + 3 vs. 3 + 4 + 1). In Experiment 4, an M&M was removed from 1 set before the chimpanzees' selection. In Experiments 1 and 2, the chimpanzees selected the larger quantity on significantly more trials than would be predicted by chance. In Experiments 3 and 4, 1 chimpanzee performed at a level significantly better than chance. Therefore, chimpanzees mentally represent quantity and successfully combine and compare nonvisible, sequentially presented sets of items.