Discrete quantity judgments in the great apes (Pan paniscus, Pan troglodytes, Gorilla gorilla, Pongo pygmaeus): the effect of presenting whole sets versus item-by-item

The authors examined quantity-based judgments for up to 10 items for simultaneous and sequential whole sets as well as for sequentially dropped items in chimpanzees (Pan troglodytes), gorillas (Gorilla gorilla), bonobos (Pan paniscus), and orangutans (Pongo pygmaeus). In Experiment 1, subjects had to choose the larger of 2 quantities presented in 2 separate dishes either simultaneously or 1 dish after the other. Representatives of all species were capable of selecting the larger of 2 quantities in both conditions, even when the quantities were large and the numerical distance between them was small. In Experiment 2, subjects had to select between the same food quantities sequentially dropped into 2 opaque cups so that none of the quantities were ever viewed as a whole. The authors found some evidence (albeit weaker) that subjects were able to select the larger quantity of items. Furthermore, the authors found no performance breakdown with the inclusion of certain quantities. Instead, the ratio between quantities was the best performance predictor. The authors conclude that quantity-based judgments rely on an analogical system, not a discrete object file model or perceptual estimation mechanism, such as subitizing.     

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.     

Quantity judgments of sequentially presented food items by capuchin monkeys (Cebus apella)

Recent assessments have shown that capuchin monkeys, like chimpanzees and other Old World primate species, are sensitive to quantitative differences between sets of visible stimuli. In the present study, we examined capuchins’ performance in a more sophisticated quantity judgment task that required the ability to form representations of food quantities while viewing the quantities only one piece at a time. In three experiments, we presented monkeys with the choice between two sets of discrete homogeneous food items and allowed the monkeys to consume the set of their choice. In Experiments 1 and 2, monkeys compared an entirely visible food set to a second set, presented item-by-item into an opaque container. All monkeys exhibited high accuracy in choosing the larger set, even when the entirely visible set was presented last, preventing the use of one-to-one item correspondence to compare quantities. In Experiment 3, monkeys compared two sets that were each presented item-by-item into opaque containers, but at different rates to control for temporal cues. Some monkeys performed well in this experiment, though others exhibited near-chance performance, suggesting that this species’ ability to form representations of food quantities may be limited compared to previously tested species such as chimpanzees. Overall, these findings support the analog magnitude model of quantity representation as an explanation for capuchin monkeys’ quantification of sequentially presented food items.

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.     

Large quantity discrimination by North Island robins (Petroica longipes)

While numerosity—representation and enumeration of different numbers of objects—and quantity discrimination in particular have been studied in a wide range of species, very little is known about the numerical abilities of animals in the wild. This study examined spontaneous relative quantity judgments (RQJs) by wild North Island robins (Petroica longipes) of New Zealand. In Experiment 1, robins were tested on a range of numerical values of up to 14 versus 16 items, which were sequentially presented and hidden. In Experiment 2, the same numerical contrasts were tested on a different group of subjects but quantities were presented as whole visible sets. Experiment 3 involved whole visible sets that comprised of exceedingly large quantities of up to 56 versus 64 items. While robins shared with other species a ratio-based representation system for representing very large values, they also appeared to have developed an object indexing system with an extended upper limit (well beyond 4) that may be an evolutionary response to ecological challenges faced by scatter-hoarding birds. These results suggest that cognitive mechanism influencing an understanding of physical quantity may be deployed more flexibly in some contexts than previously thought, and are discussed in light of findings across other mammalian and avian species.     

More or less: spontaneous quantity discrimination in the domestic cat

We examined spontaneous quantity discrimination in untrained domestic cats in three food choice experiments. In Experiment 1, we presented the cats with two different quantities of food in eight numerical combinations. Overall, the subjects chose the larger quantity more often than the smaller one, and significantly so when the ratio between the quantities was less than 0.5. In Experiment 2, we presented the cats with two pieces of food in four different size combinations. Again, subjects chose the larger piece above chance, although not in the combination where the largest item was presented. In Experiment 3, a subset of the cats was presented multiple times with two different quantities of food, which were hidden from view. In this case, the cats did not choose the larger quantity more often than the smaller one, suggesting that in the present experiments they mainly used visual cues when comparing quantities. We conclude that domestic cats are capable of spontaneously discriminating quantities when faced with different numbers or sizes of food items, and we suggest why they may not always be motivated to choose the larger quantity. In doing so, we highlight the advantages of testing spontaneous choice behavior, which is more likely to reflect animals’ everyday manner of responding than is the case when training them in order to test their absolute limits of performance which may not always coincide with their daily needs.     

Chimpanzee responding during matching to sample: control by exclusion

Three chimpanzees performed a computerized matching-to-sample task in which samples were photographs of items and comparison stimuli were geometric symbols called lexigrams. In Experiment 1, samples were either defined (i.e., they represented items that were associated already with a specific lexigram label by the chimpanzees) or undefined (i.e., they did not have an already learned association with a specific lexigram). On each trial, the foil (incorrect) comparison could be either a defined or an undefined lexigram. All 3 chimpanzees selected the correct comparison for undefined samples at a level significantly better than chance only when the foil comparison was defined. In Experiment 2, three comparisons were presented on each trial, and in Experiment 3, four comparisons were presented on each trial. For Experiments 2 and 3, the foil comparisons consisted of either defined or undefined comparisons or a mixture of both. For these two experiments, when the chimpanzees were presented with an undefined sample, they typically made selections of only undefined comparisons. These data indicate that the chimpanzees responded through use of exclusion. A final experiment, however, indicated that, despite the use of exclusion to complete trials with undefined samples correctly, the chimpanzees did not learn new associations between undefined samples and comparisons.     

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.     

Quantity judgments of auditory and visual stimuli by chimpanzees (Pan troglodytes)

Many species can choose between two visual sets of stimuli on the basis of quantity. This is true when sets are both visible, or are presented one set at a time or even one item at a time. However, we know comparatively little about how well nonhuman animals can compare auditory quantities. Here, three chimpanzees (Pan troglodytes) chose between two sets of food items when they only heard each item fall into different containers rather than seeing those items. This method prevented the chimpanzees from summing the amount of visible food they saw because there were no visual cues. Chimpanzees performed well, and their performance matched that of previous experiments with regard to obeying Weber's law. They also performed well with comparisons between a sequentially presented auditory set and a fully visible set, demonstrating that duration of presentation was not being used as a cue. In addition, they accommodated empty sets into these judgments, although not perfectly. Thus, chimpanzees can judge auditory quantities in flexible ways that show many similarities to how they compare visual quantities.     

Spontaneous use of tools as straws in great apes

Great apes can use multiple tools to extract food embedded in substrates and can invent new ways to exploit those resources. We tested five bonobos, five chimpanzees, and six orangutans in a task in which they had to use (and modify) a tool as a straw to drink the juice located inside a container. Experiment 1 showed that four orangutans and one chimpanzee invented the use of a piece of electric cable to get the juice. Experiment 2 investigated whether subjects could transform a non-functional hose into a functional one by removing blockages that impeded the free flow of juice. Orangutans outperformed chimpanzees and bonobos by differentially removing those blockages that prevented the flow of juice, often doing so before attempting to extract the juice. In Experiment 3, we presented chimpanzees and orangutans with four 3-tool sets (each tool set contained a single straw-like tool) and allowed them to select one tool. Unlike chimpanzees, orangutans succeeded in selecting the straw-like tool above chance levels without having to physically manipulate it. We suggest that orangutans’ superior performance is related to their greater reliance on mouth actions during foraging. Experiment 4 investigated whether orangutans were also capable of selecting the suitable tool not by its appearance, but by the effects that it produced. After witnessing the experimenter blow bubbles or absorb liquid with a functional tool but fail to accomplish the same thing with the non-functional tool, orangutans failed to select the functional tool above chance levels.     

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

This study investigated the ability of 3 male orangutans (Pongo pygmaeus; 1 subadult, 2 adults) to estimate, compare, and operate on 2 sets of small quantities (1-6 cereal bits). Experiment 1 investigated the orangutans' ability to choose the larger of 2 quantities when they were presented successively as opposed to simultaneously, thus being perceptually unavailable at the time of choice. Experiment 2 investigated the orangutans' ability to select the larger quantity after the original quantities were augmented or reduced. Orangutans were capable of selecting the larger of 2 quantities in Experiment 1. There was also some evidence from Experiment 2, albeit weaker, that orangutans may mentally combine quantities (but not dissociate) to obtain the larger of 2 quantities. This study suggests that orangutans use a representational mechanism (especially when comparing quantities) to select the larger of 2 sets of items.     

Can dogs count?

Numerical competencies have been thoroughly examined in several species, yet relatively few studies have examined such processes in the domestic dog. In an initial experiment, procedures from numerical studies of chimpanzees (0010 and 0015) were adapted for use with 27 domestic dogs. Subjects in these experiments watched as different quantities of food were sequentially dropped into each of two bowls. The subjects were then allowed to select and consume the contents of one of the bowls. Although dogs excelled in a 1 vs 0 condition, their performance failed to significantly surpass chance across all other ratios. In a second experiment with a single subject (a rough collie named Sedona), the procedure was revised so that non-food stimuli were presented simultaneously to the dog on two magnet boards. If Sedona chose the board with the majority of the items, she was rewarded with a piece of food hidden underneath the board. If she made an incorrect choice, she received no reinforcement. Interestingly, Sedona's performance far exceeded that of the dogs in Experiment 1. Implications of these findings for the study of domestic dogs are discussed.     

Spatial memory and monitoring of hidden items through spatial displacements by chimpanzees (Pan troglodytes)

This study examined chimpanzee (Pan troglodytes) short-term memory for food location in near space. In Experiments 1 and 2, either 1 or 2 items (chocolate pieces) were hidden in an array of 3 or 5 containers that either remained stationary or were rotated 180 degrees or 360 degrees. When the array remained stationary, the chimpanzees remembered both item locations. When arrays were rotated, however, chimpanzees found only 1 item. In Experiment 3, 2 items were hidden in an array of 7 cups. Both items were found at levels significantly better than chance. Ninety percent of errors were made after the 1st item was found, and errors reflected memory failure rather than a failure of inhibitory control.     

Erratum to: 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.     

Shetland ponies (Equus caballus) show quantity discrimination in a matching-to-sample design

Numerical competence is one of the aspects of animal cognition with a long history of research interest, but few results are available for the horse. In the present study, we investigated the ability of three Shetland ponies to discriminate between different quantities of geometric symbols presented on a computer screen in a matching-to-sample arrangement. In Experiment 1, the ponies had to relate two similar quantities to another, paired in contrasts (1 vs. 2, 3 vs. 4 and 4 vs. 5) of the same stimulus (dot). Specific pairs of quantities (all differing by one) of up to five different geometrical symbols were displayed in Experiment 2. In each session, both quantities (more and less) were used as sample in such a way that each of the two quantities presented in one test served as positive and as negative stimulus, respectively. The three Shetland ponies were able to discriminate between the given quantities of dots by showing more than 80 % correct responses in two consecutive sessions. Only one of the ponies distinguished different shapes of geometric symbols at a level of 4 versus 5 items. The results show that all ponies were capable of visual quantity discrimination in the present matching-to-sample design, but task solving seemed more difficult when quantities were composed of heterogeneous stimuli. The present results confirm our hypothesis that the ponies based their decision on the matching concept of sameness and were not biased by a spontaneous preference for higher quantities.     

Scale-model comprehension by chimpanzees (Pan troglodytes)

The ability of chimpanzees (Pan troglodytes) to recognize the correspondence between a scale model and its real-world referent was examined. In Experiments 1 and 2, an adult female and a young adult male watched as an experimenter hid a miniature model food in 1 of 4 sites in a scale model. Then, the chimpanzees were given the opportunity to find the real food item that had been hidden in the analogous location in the real room. The female performed significantly above chance, whereas the male performed at chance level. Experiments 3 and 4 tested 5 adult and 2 adolescent chimpanzees in a similar paradigm, using a scale model of the chimpanzees' outdoor area. Results indicate that some adult chimpanzees were able to reliably demonstrate an understanding of the relationship between a scale model and the larger space it represented, whereas other subjects were constrained by inefficient and unsuccessful search patterns.     

Relative quantity judgments in South American sea lions (<Emphasis Type="Italic">Otaria flavescens</Emphasis>)

There is accumulating evidence that a variety of species possess quantitative abilities although their cognitive substrate is still unclear. This study is the first to investigate whether sea lions (Otaria flavescens), in the absence of training, are able to assess and select the larger of two sets of quantities. In Experiment 1, the two sets of quantities were presented simultaneously as whole sets, that is, the subjects could compare them directly. In Experiment 2, the two sets of quantities were presented item-by-item, and the totality of items was never visually available at the time of choice. For each type of presentation, we analysed the effect of the ratio between quantities, the difference between quantities and the total number of items presented. The results showed that (1) sea lions can make relative quantity judgments successfully and (2) there is a predominant influence of the ratio between quantities on the subjects’ performance. The latter supports the idea that an analogue representational mechanism is responsible for sea lions’ relative quantities judgments. These findings are consistent with previous reports of relative quantities judgments in other species such as monkeys and apes and suggest that sea lions might share a similar mechanism to compare and represent quantities.     

Toddler subtraction with large sets: further evidence for an analog-magnitude representation of number

Two experiments were conducted to test the hypothesis that toddlers have access to an analog-magnitude number representation that supports numerical reasoning about relatively large numbers. Three-year-olds were presented with subtraction problems in which initial set size and proportions subtracted were systematically varied. Two sets of cookies were presented and then covered. The experimenter visibly subtracted cookies from the hidden sets, and the children were asked to choose which of the resulting sets had more. In Experiment 1, performance was above chance when high proportions of objects (3 versus 6) were subtracted from large sets (of 9) and for the subset of older participants (older than 3 years, 5 months; n = 15), performance was also above chance when high proportions (10 versus 20) were subtracted from the very large sets (of 30). In Experiment 2, which was conducted exclusively with older 3-year-olds and incorporated an important methodological control, the pattern of results for the subtraction tasks was replicated. In both experiments, success on the tasks was not related to counting ability. The results of these experiments support the hypothesis that young children have access to an analog-magnitude system for representing large approximate quantities, as performance on these subtraction tasks showed a Weber's Law signature, and was independent of conventional number knowledge.     

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.     

Rats’ visual-spatial working memory: New object choice accuracy as a function of number of objects in the study array

When rats had to find new (jackpot) objects for rewards from among previously sampled baited objects, increasing the number of objects in the sample (study) segment of a trial from 3 to 5 and then to 7 (Experiment 1) or from 3 to 6 and 9 (Experiments 2 and 3) or from 6 to 9 and 12 (Experiment 4) did not reduce rats’ test segment performance. Increasing study segment size improved test segment performance contrary the limited-capacity hypothesis concerning rats’ spatial working memory. This effect occurred when objects either differed visually (Experiments 1, 2, 4) or only by odor (Experiment 3). Rats performed no better than chance in finding a jackpot on their first choice from among three visually different objects in Experiments 1 and 2. Furthermore, results from Experiments 2 and 3 indicate that differences in the probability of finding a jackpot by chance in Experiment 1 were not responsible for failure to find the predicted inverse relationship. Results from Experiment 4 indicate that those from Experiments 2 and 3 were not solely due to size of test arrays. We discussed whether our findings could be attributed to innate foraging or perceptual isolation processes during testing or to perceptual encoding processes during exposure to study segment arrays.