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.     

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.     

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.     

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.     

How the great apes (Pan troglodytes, Pongo pygmaeus, Pan paniscus, Gorilla gorilla) perform on the reversed reward contingency task II: transfer to new quantities, long-term retention, and the impact of quantity ratios

We tested 6 chimpanzees (Pan troglodytes), 3 orangutans (Pongo pygmaeus), 4 bonobos (Pan paniscus), and 2 gorillas (Gorilla gorilla) in the reversed reward contingency task. Individuals were presented with pairs of quantities ranging between 0 and 6 food items. Prior to testing, some experienced apes had solved this task using 2 quantities while others were totally na?ve. Experienced apes transferred their ability to multiple-novel pairs after 6 to 19 months had elapsed since their initial testing. Two out of 6 na?ve apes (1 chimpanzee, 1 bonobo) solved the task--a proportion comparable to that of a previous study using 2 pairs of quantities. Their acquisition speed was also comparable to the successful subjects from that study. The ratio between quantities explained a large portion of the variance but affected na?ve and experienced individuals differently. For smaller ratios, na?ve individuals were well below 50% correct and experienced ones were well above 50%, yet both groups tended to converge toward 50% for larger ratios. Thus, some apes require no procedural modifications to overcome their strong bias for selecting the larger of 2 quantities.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Size matters: impact of item size and quantity on array choice by chimpanzees (Pan troglodytes)

The authors previously reported that chimpanzees (Pan troglodytes) showed a striking bias to select the larger of 2 candy arrays, despite a reversed reward contingency in which the animals received the smaller, nonselected array as a reward, except when Arabic numerals were used as stimuli. A perceptual or incentive-based interference occurred that was overcome by symbolic stimuli. The authors of the present study examined the impact of element size in choice arrays, using 1 to 5 large and small candies. Five test-sophisticated chimpanzees selected an array from the 2 presented during each trial. Their responses were not optimal, as animals generally selected arrays with larger total mass; thus, they received the smaller remaining array as a reward. When choice stimuli differed in size and quantity, element size was more heavily weighted, although choices reflected total candy mass. These results replicate previous findings showing chimpanzees' difficulties with quantity judgments under reverse reward contingencies and also show that individual item size exerts a more powerful interference effect.     

Summation in the chimpanzee (Pan troglodytes)

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.     

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.     

Time,number and length: Similarities and differences in discrimination in adults and children

The aim of this study was to focus on similarities in the discrimination of three different quantities—time, number, and line length—using a bisection task involving children aged 5 and 8 years and adults, when number and length were presented nonsequentially (Experiment 1) and sequentially (Experiment 2). In the nonsequential condition, for all age groups, although to a greater extent in the younger children, the psychophysical functions were flatter, and the Weber ratio higher for time than for number and length. Number and length yielded similar psychophysical functions. Thus, sensitivity to time was lower than that to the other quantities, whether continuous or not. However, when number and length were presented sequentially (Experiment 2), the differences in discrimination performance between time, number, and length disappeared. Furthermore, the Weber ratio values as well as the bisection points for all quantities presented sequentially appeared to be close to that found for duration in the nonsequential condition. The results are discussed within the framework of recent theories suggesting a common mechanism for all analogical quantities.     

Effects of processing fluency on comparative performance judgments

Research has shown that performance predictions are biased by the impact of processing fluency. However, existing data are inconclusive with regard to comparative judgments of performance. In five experiments, participants in an easy condition gave more favorable comparative judgments than participants in a difficult condition. Participants judged their performance more favorably if they named colors of non-color words rather than non-matching color words (Experiment 1), if they had to generate six words of a category rather than 12 words (Experiment 2), if they had to run in place for 15 s rather than 2 min (Experiment 3), but the latter result holds only true if participants were not active in sports (Experiment 4). When 67% of the items in a recognition test were old words, participants thought that their recognition performance was better than when 33% of the items were old words, although recognition performance did not differ between groups (Experiment 5). We discuss this result in the light of recent theories about effects of processing fluency on judgments.     

Direct versus indirect tests of memory for source: judgments of modality

We studied the relation between performance on direct versus indirect tests of memory for modality. Subjects read or heard words in a mixed list and then were tested by visual perceptual identification (the indirect test) and direct report of items as read, heard, or new. There was a dependent relation between perceptual identification performance and modality judgments, in accord with the hypothesis that subjects base their judgments of modality on relative perceptual fluency. In Experiment 2, we attempted to change the degree of dependence by providing subjects with an alternative basis for modality judgments. Subjects given a mnemonic to encode modality exhibited less dependence between perceptual identification performance and modality judgments than did subjects who encoded modality incidentally. The relation between direct and indirect tests of memory for source characteristics depends on the basis used for each.     

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.