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 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.

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 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.     

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.     

Is your choice my choice? The owners’ effect on pet dogs’ (Canis lupus familiaris) performance in a food choice task

This study investigates the influence of owners on their dogs’ performance in a food choice task using either different or equal quantities of food. Fifty-four pet dogs were tested in three different conditions. In Condition 1 we evaluated their ability to choose between a large and small amount of food (quantity discrimination task). In Condition 2 dogs were again presented with a choice between the large and small food quantity, but only after having witnessed their owner favouring the small quantity. In Condition 3 dogs were given a choice between two equally small quantities of food having witnessed their owner favouring either one or the other. A strong effect of the owner on the dogs’ performance was observed. In Condition 1 dogs as a group chose significantly more often the large food quantity, thus showing their ability to solve the quantity discrimination task. After observing their owner expressing a preference for the small food quantity they chose the large quantity of food significantly less than in the independent choice situation. The tendency to conform to the owner’s choice was higher when the dogs had to choose between equally small quantities of food (Condition 3) rather than between a large and a small one (Condition 2). These results provide evidence that dogs can be influenced by their owners even when their indications are clearly in contrast with direct perceptual information, thus leading dogs to ultimately make counterproductive choices.     

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.     

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.     

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.     

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.     

When quantity trumps number: discrimination experiments in cotton-top tamarins (<Emphasis Type="Italic">Saguinus oedipus</Emphasis>) and common marmosets (<Emphasis Type="Italic">Callithrix jacchus</Emphasis>)

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.     

Quantity-based judgments in the domestic dog (<Emphasis Type="Italic">Canis lupus familiaris</Emphasis>)

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.     

Mangabeys (<Emphasis Type="Italic">Cercocebus torquatus lunulatus</Emphasis>) solve the reverse contingency task without a modified procedure

Problem solving often relies on generating new responses while inhibiting others, particularly prepotent ones. A paradigm to study inhibitory abilities is the reverse contingency task (Boysen and Berntson in J Exp Psychol Anim Behav Process 21:82–86, 1995), in which two different quantities of food are offered to an individual who receives the array he did not choose. Therefore, mastery of the task demands selecting the smaller quantity to obtain the larger one. Several non-human primates have been tested in the reverse contingency task. To date, only great apes and rhesus monkeys (Macaca mulatta) have succeeded in the original task, with no need of procedural modifications as the large-or-none contingency, correction trials or symbolic stimuli substituting for actual food quantities. Here, four mangabeys were presented with two stimulus arrays of one and four raisins in the context of the reverse contingency task. Three of them learned to perform the task well above chance without a modified procedure. They also reached above-chance performance when presented with two stimulus arrays of zero and four raisins, despite the initial difficulty of choosing a null quantity. After a period of 7–10 months, in which the animals were not tested on any task, all three subjects continued to perform well, even when presented with novel quantity pairs.     

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.     

Horses (Equus caballus) select the greater of two quantities in small numerical contrasts

The ability to select the greater numerosity over another in small sets seems to stem from the calculation of which set contains more, and has been taken as evidence of a primordial representation at the roots of the primate numerical system. We tested 56 horses (Equus caballus) in a paradigm previously used with human infants and nonhuman primates. Horses saw two quantities paired in contrasts—2 versus 1, 3 versus 2, 6 versus 4 and a control for volume, 2 versus 1 big—and had to make a choice by snout touching the container holding the numerosity selected. The horses spontaneously selected the greater of the two quantities when the numerosities were small. These results add to evidence showing spontaneous quantity assessment in a variety of species. To my brother Marcelo Uller (1964–2008), for whom the understanding of animals, through biomimetics, was the only way to understand man-made engineering.     

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.     

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.     

Objects,pictures and words. Effects of representational format on four-year-olds’ quantity knowledge / Objetos,imágenes y palabras. Efectos del formato representacional en el conocimiento de la cantidad a los cuatro años

Abstract

This study explores whether and how different external representations of quantity influence the performance of four-year-old children when constructing sets of a given cardinal number. Three representations of quantity were presented (objects, pictures and number words) in an adaptation of the ‘Give-a-number’ task, in sets that contained 2–6 items. The results show that the use of pictures facilitated children’s performance with quantities of three and four. These results are discussed by analysing the cognitive demands of representational formats, in terms of dual representation and iconicity, and according to the magnitude of the quantities involved.     

Performance of Asian elephants (Elephas maximus) on a quantity discrimination task is similar to that of African savanna elephants (Loxodonta africana)

Animal Cognition - Using an object-choice task, we measured the relative quantity discrimination ability of Asian elephants. Two zoo-housed elephants were given auditory cues of food being dropped...