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

Recruitment of the premotor cortex during arithmetic operations by the monkey

Arithmetic operations are complex mental processes rooted in the abstract concept of numerosity. Despite the significance, the neural architecture responsible for these operations has remained largely uncharted. In this study, we explored the presence of specific neuronal activity in the dorsal premotor cortex of the monkey dedicated to numerical addition and subtraction. Our findings reveal that many of these neural activities undergo a transformation, shifting their coding from arithmetic to motor representations. These motor representations include information about which hand to use and the number of steps involved in the action. We consistently observed that cells related to the right-hand encoded addition, while those linked to the left-hand encoded subtraction, suggesting that arithmetic operations and motor commands are intertwining with each other. Furthermore, we used a multivariate decoding technique to predict the monkey's behaviour based on the activity of these arithmetic-related cells. The classifier trained to discern arithmetic operations, including addition and subtraction, not only predicted the arithmetic decisions but also the subsequent motor actions of the right and left-hand. These findings imply a cognitive extension of the motor cortex's function, where inherent neural systems are repurposed to facilitate arithmetic operations.

Processing Individually Distinctive Schematic-Faces Supports Proto-Arithmetical Counting in the Young Domestic Chicken

Simple Summary

Baby chicks, like infants and other animals, are unable to distinguish 3 vs. 4 identical objects. Because infants and chicks discriminate among larger sets (e.g., 4 vs. 12; 6 vs. 9), the 3 vs. 4 limitation has been considered the key-signature of the counting cognitive system that processes small numerosities. Here, we explored if the experience with different bird-like faces as objects—which naturally trigger chicks’ attention—could make the 3 vs. 4 task easier. Chicks reared with seven different faces, characterized by two “eyes” and a “beak” as features, succeeded in the 1 + 1 + 1 vs. 1 + 1 + 1 + 1 operation (Exp. 1); while birds, reared and tested with seven identical copies of a same face, failed (Exp. 2). Processing different individuals, and not experience with copies of one single individual per se, increased proto-arithmetic performance. Surprisingly, chicks, after being reared with seven identical faces, succeeded in the proto-arithmetic task when presented with seven completely novel faces (Exp. 3). On the contrary, similar experience with seven identical and featureless faces did not allow discrimination of novel faces (Exp. 4). Experience of one face probably helps to focus on the facial features which are later used to individually process new faces. In turn, individual processing enhances proto-arithmetical calculation.

Abstract

A key signature of small-number processing is the difficulty in discriminating between three and four objects, as reported in infants and animals. Five-day-old chicks overcome this limit if individually distinctive features characterize each object. In this study, we have investigated whether processing individually different face-like objects can also support discrimination between three and four objects. Chicks were reared with seven face-like stimuli and tested in the proto-arithmetic comparison 1 + 1 + 1 vs. 1 + 1 + 1 + 1. Birds reared and tested with all different faces discriminated and approached the larger group (Exp. 1), whereas new birds reared and tested with seven identical copies of one same face failed (Exp. 2). The presence at test of individually different faces allowed discrimination even when chicks were reared with copies of one face (Exp. 3). To clarify the role of the previous experience of at least one specific arrangement of facial features, in Experiment 4, featureless faces were employed during rearing. During testing, chicks were unable to discriminate between three and four individually distinct faces. Results highlight the importance of having experienced at least one “face” in prompting individual processing and proto-arithmetical calculation later during testing. We speculate that mechanisms effective at the non-symbolic level may positively affect numerical performance.

Acknowledging the Relevance of Elephant Sensory Perception to Human–Elephant Conflict Mitigation

Simple Summary

Elephants have a unique sensory perspective of the world, using their complex olfactory and auditory systems to make foraging and social decisions. All three species of elephants are endangered and inhabit environments, which are being affected rapidly by human development. Anthropogenic disturbances can have significant effects on elephants’ abilities to perceive sensory information and communicate with one another, potentially further endangering their survival. Conflicts over high-quality resources also arise from the overlapping habitation of humans and elephants. While many different methods have been employed to reduce this conflict, we propose that elephants’ unique olfactory and acoustic sensory strengths be considered in future mitigation strategies to achieve coexistence.

Abstract

Elephants are well known for their socio-cognitive abilities and capacity for multi-modal sensory perception and communication. Their highly developed olfactory and acoustic senses provide them with a unique non-visual perspective of their physical and social worlds. The use of these complex sensory signals is important not only for communication between conspecifics, but also for decisions about foraging and navigation. These decisions have grown increasingly risky given the exponential increase in unpredictable anthropogenic change in elephants’ natural habitats. Risk taking often develops from the overlap of human and elephant habitat in Asian and African range countries, where elephants forage for food in human habitat and crop fields, leading to conflict over high-quality resources. To mitigate this conflict, a better understanding of the elephants’ sensory world and its impact on their decision-making process should be considered seriously in the development of long-term strategies for promoting coexistence between humans and elephants. In this review, we explore the elephants’ sensory systems for audition and olfaction, their multi-modal capacities for communication, and the anthropogenic changes that are affecting their behavior, as well as the need for greater consideration of elephant behavior in elephant conservation efforts.

Cichlids and stingrays can add and subtract 'one' in the number space from one to five

The numerical understanding of cichlids and stingrays was examined regarding addition and subtraction abilities within the number space of one to five. Experiments were conducted as two-alternative forced-choice experiments, using a delayed matching to sample technique. On each trial, fish had to perform either an addition or subtraction, based on the presentation of two-dimensional objects in two distinct colors, with the color signaling a particular arithmetic process. Six cichlids and four stingrays successfully completed training and recognized specific colors as symbols for addition and subtraction. Cichlids needed more sessions than stingrays to reach the learning criterion. Transfer tests showed that learning was independent of straightforward symbol memorization. Individuals did not just learn to pick the highest or lowest number presented based on the respective color; instead, learning was specific to adding or subtracting ‘one’. Although group results were significant for both species in all tests, individual results varied. Addition was learned more easily than subtraction by both species. While cichlids learned faster than stingrays, and more cichlids than stingrays learned the task, individual performance of stingrays exceeded that of cichlids. Previous studies have provided ample evidence that fish have numerical abilities on par with those of other vertebrate and invertebrate species tested, a result that is further supported by the findings of the current study.

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

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 into two containers (Nonvisible condition), and in one condition they could also see the food on top of the containers (Visible condition). Elephants received sets of varying ratios and magnitudes. We found that the elephants chose the greater quantity of food significantly above chance in both the Visible and Nonvisible conditions. Additionally, we found the elephants' ability to discriminate between quantities decreased as the ratio, and not the absolute difference, between the quantities increased, which is predicted by the accumulator model. We also compare our findings to those from a study using the same methods with African savanna elephants and found that the two species performed at similar levels, but given our small sample size it is difficult to make strong species-level conclusions. In discussing our results, we consider differences between the two species' wild environments as well as the types of sensory cues provided in human care, and we provide recommendations for extensions of this work.

Achieving arithmetic learning in honeybees and examining how individuals learn

In recent years honeybees have demonstrated intriguing numerical capacities, leading to the recent discovery of their ability to perform simple arithmetic by learning to add or subtract ‘one’ using symbolic representations of operators. When training an insect with a miniature brain containing less than one million neurons to understand a conceptual rule, the procedure is of vital importance. We explain in detail the controls and process of designing an experiment to test for complex behaviors in a relatively simple brained animal. Furthermore, we will discuss the finding that individual honeybees do not demonstrate a consistent learning scenario when trained to perform the same tasks, rather they appear to acquire arithmetic rules through individual processes.

Elephants have a nose for quantity

Animals often face situations that require making decisions based on quantity. Many species, including humans, rely on an ability to differentiate between more and less to make judgments about social relationships, territories, and food. Habitat-related choices require animals to decide between areas with greater and lesser quantities of food while also weighing relative risk of danger based on group size and predation risk. Such decisions can have a significant impact on survival for an animal and its social group. Many species have demonstrated a capacity for differentiating between two quantities of food and choosing the greater of the two, but they have done so based on information provided primarily in the visual domain. Using an object-choice task, we demonstrate that elephants are able to discriminate between two distinct quantities using their olfactory sense alone. We presented the elephants with choices between two containers of sunflower seeds. The relationship between the amount of seeds within the two containers was represented by 11 different ratios. Overall, the elephants chose the larger quantity of food by smelling for it. The elephants' performance was better when the relative difference between the quantities increased and worse when the ratio between the quantities of food increased, but was not affected by the overall quantity of food presented. These results are consistent with the performance of animals tested in the visual domain. This work has implications for the design of future, cross-phylogenetic cognitive comparisons that ought to account for differences in how animals sense their world.

Any reward will do: Effects of a reverse-reward contingency on size preference with pet dogs (Canis lupus familiaris)

The reverse-reward contingency (RRC) task involves presenting subjects with a choice between one plate containing a large amount of food and a second plate containing a small amount of food. Subjects are then required to select the smaller of the two options in order to receive the larger-magnitude reward. The RRC task is a commonly used paradigm for assessing complex cognition, such as inhibitory control, in subjects. To date, the RRC task has not been tested with pet dogs as subjects, and it may provide insights to their ability to perceive quantities of differing magnitudes. Nine dogs were tested in an RRC task involving three conditions. In Condition 1, plates of food were presented, and the dogs were allowed to consume their choice. In Condition 2, plates with different-sized symbols resembling the quantities of food in Condition 1 were presented, and dogs received food quantities of the same size as their choice (e.g., a larger-magnitude reward for selecting the plate with the larger shape). In Condition 3, the same plates were presented, but dogs received a reverse-sized quantity of food, relative to their choice (e.g., a smaller-magnitude reward for selecting the plate with the larger shape). A novel addition here to the traditional RRC task was the inclusion of a third, empty (control) plate that was present throughout all conditions, and no programmed consequences were provided when that plate was selected. Our results were consistent with the previous RRC literature: All dogs developed and maintained a preference for the larger stimulus option across conditions. The use of symbolic representations did not ameliorate performance on the RRC task. Applied implications are discussed.

Precise relative-quantity judgement in the striped field mouse Apodemus agrarius Pallas

Applying the classical experimental scheme of training animals with food rewards to discriminate between quantities of visual stimuli, we demonstrated that not only can striped field mice Apodemus agrarius discriminate between clearly distinctive quantities such as 5 and 10, but some of these mice also exhibit high accuracy in discriminating between quantities that differ only by one. The latter include both small (such as 2 versus 3) and relatively large (such as 5 versus 6, and 8 versus 9) quantities of elements. This is the first evidence of precise relative-quantity judgement in wild rodents. We found striking individual variation in cognitive performance among striped field mice, which possibly reflects individual cognitive variation in natural populations. We speculate that high accuracy in differentiating large quantities is based on the adaptive ability of wild rodents to capture subtle changes in their environment. We suggest that the striped field mouse may be a powerful model species to develop advanced cognitive tests for comparative studies of numerical competence in animals and for understanding evolutionary roots of quantity processing.

Numerical cognition in honeybees enables addition and subtraction

Many animals understand numbers at a basic level for use in essential tasks such as foraging, shoaling, and resource management. However, complex arithmetic operations, such as addition and subtraction, using symbols and/or labeling have only been demonstrated in a limited number of nonhuman vertebrates. We show that honeybees, with a miniature brain, can learn to use blue and yellow as symbolic representations for addition or subtraction. In a free-flying environment, individual bees used this information to solve unfamiliar problems involving adding or subtracting one element from a group of elements. This display of numerosity requires bees to acquire long-term rules and use short-term working memory. Given that honeybees and humans are separated by over 400 million years of evolution, our findings suggest that advanced numerical cognition may be more accessible to nonhuman animals than previously suspected.

Towards numerical cognition's origin: insights from day-old domestic chicks

Instead of the scepticism on animal numerical understanding that characterized the first half of the twentieth century, in recent decades, a large and increasing body of the literature has shown that adult animals can master a variety of non-symbolic (in the absence of symbols such as mathematical words) numerical tasks. Nonetheless, evidence proving early numerical abilities in non-human animals was sparse. In this paper, I report the ongoing work to investigate numerical cognition in the day-old domestic chick (Gallus gallus). Unlike previous studies on adult animals, chicks can be tested very early in life, which gives us the opportunity to discover the origins of numerical comprehension. Here, I discuss studies revealing that day-old domestic chicks can: (i) discriminate between different numbers of objects; (ii) solve rudimentary arithmetic operations; and (iii) use ordinal information, identifying a target element (e.g. the fourth) in a series of identical elements, on the basis of its serial-numerical position. Some of these abilities are number-specific, while others underlie the interplay between number and continuous extents (continuous-quantity cues that covary with number, such as area and perimeter). These data are discussed in terms of ontogenetic development of mathematical comprehension.This article is part of a discussion meeting issue 'The origins of numerical abilities'.

Intuitive statistical inferences in chimpanzees and humans follow Weber's law

Humans and nonhuman great apes share a sense for intuitive statistical reasoning, making intuitive probability judgments based on proportional information. This ability is of fundamental importance, in particular for inferring general regularities from finite numbers of observations and, vice versa, for predicting the outcome of single events using prior information. To date it remains unclear which cognitive mechanism underlies and enables this capacity. The aim of the present study was to gain deeper insights into the cognitive structure of intuitive statistics by probing its signatures in chimpanzees and humans. We tested 24 sanctuary-living chimpanzees in a previously established paradigm which required them to reason from populations of food items with different ratios of preferred (peanuts) and non-preferred items (carrot pieces) to randomly drawn samples. In a series of eight test conditions, the ratio between the two ratios to be discriminated (ROR) was systematically varied ranging from 1 (same proportions in both populations) to 16 (high magnitude of difference between populations). One hundred and forty-four human adults were tested in a computerized version of the same task. The main result was that both chimpanzee and human performance varied as a function of the log(ROR) and thus followed Weber's law. This suggests that intuitive statistical reasoning relies on the same cognitive mechanism that is used for comparing absolute quantities, namely the analogue magnitude system.

More evidence that less is better: Sub-optimal choice in dogs

The less-is-better effect is a preference for the lesser of two alternatives sometimes observed when they are evaluated separately. For example, a dinner service of 24 intact pieces might be judged to be more valuable than a 40-piece dinner service containing nine broken pieces. Pattison and Zentall (Animal Cognition, 17: 1019-1022, 2014) reported similar sub-optimal choice behavior in dogs using a simultaneous choice procedure. Given a choice between a single high-value food item (cheese) or an equivalent high-value item plus a lower-value food item (carrot), their dogs chose the individual item. In a subsequent test, the dogs preferred two high-value items to a single high-value item, suggesting that avoidance of multiple items did not cause the sub-optimal choice behavior. In two experiments, we replicated Pattison and Zentall's procedure while including additional controls. In Experiment 1, habituation of neophobia for multiple items was controlled for by intermixing the two types of test trial within a single experimental session. In Experiment 2, we controlled for avoidance of heterogeneous rewards by including test trials in which a choice was offered between the combination of items and a single low-value item. In both experiments we observed sub-optimal choice behavior which could not be explained by either of these putative mechanisms. Our results, as well as those of Pattison and Zentall, are consistent with the suggestion that dogs' assessment of the total value of multiple items is based, at least partly, on their average quality.

A strategy to improve arithmetical performance in four day-old domestic chicks (Gallus gallus)

A large body of literature shows that non-human animals master numerical discriminations, but a limit has been reported in a variety of species in the comparison 3vs.4. Little is known regarding the possibility of using “cognitive strategies” to enable this discrimination. The aims of this study were to investigate: whether domestic chicks discriminated 3vs.4, and if changes in stimuli presentation could improve chicks’ numerical performance. Newly hatched chicks were reared with seven identical objects. On day 4, they underwent 20 consecutive testing trials to assess their capability to discriminate 3vs.4. The objects were presented, one-by-one, to the chicks and hidden behind one of two identical panels. As expected, the chicks did not discriminate (Experiment 1). When objects were presented and hidden in groups comprising one or two objects (2 + 1)vs.(2 + 2), the chicks succeeded (Experiment 2). The grouping strategy did not help in the case of a harder discrimination of (3 + 1)vs.(3 + 2) (Experiment 3), unless chicks were allowed to rest for two hours between testing sessions (Experiment 4). Our results suggest that in some cases, the limits reported for numerical performance in animals do not depend on cognitive limitations but on attentional or motivational factors, which can be overcome employing simple procedural adjustments.

Dealing with interference: Chimpanzees respond to conflicting cues in a food-choice memory task

Interference effects emerge when responding on the basis of task-relevant features is directly pitted against task-irrelevant cues that could lead to errors. To study potential interference effects in a food-choice memory test, 3 chimpanzees were presented with conflicting information in a magnitude judgment task. In Experiment 1, chimpanzees were presented with an ordinal series of colored containers that they sequenced on the basis of relative preference for the different foods that were consistently hidden under the containers. Chimpanzees also were presented with a relative quantity judgment task in which they saw identical containers cover different amounts of a consistent food type. Then, the ordinal and quantity tasks were combined such that the colored containers from the ordinal task were used as covers for the consistent food type from the quantity task. This created instances of congruency (e.g., a highly preferred colored container placed over the largest food quantity) and incongruency (e.g., a highly preferred colored container placed over a small food quantity) between task-relevant and task-irrelevant features. Interference effects were evident when chimpanzees responded on the basis of task-irrelevant features (i.e., container value) rather than task-relevant features (i.e., food quantity), sometimes leading to suboptimal responses in incongruent trial types. Chimpanzees also demonstrated some evidence of the cognitive control needed to inhibit responding based solely on the learned values of the containers. (PsycINFO Database Record

Are great apes able to reason from multi-item samples to populations of food items?

Inductive learning from limited observations is a cognitive capacity of fundamental importance. In humans, it is underwritten by our intuitive statistics, the ability to draw systematic inferences from populations to randomly drawn samples and vice versa. According to recent research in cognitive development, human intuitive statistics develops early in infancy. Recent work in comparative psychology has produced first evidence for analogous cognitive capacities in great apes who flexibly drew inferences from populations to samples. In the present study, we investigated whether great apes (Pongo abelii, Pan troglodytes, Pan paniscus, Gorilla gorilla) also draw inductive inferences in the opposite direction, from samples to populations. In two experiments, apes saw an experimenter randomly drawing one multi-item sample from each of two populations of food items. The populations differed in their proportion of preferred to neutral items (24:6 vs. 6:24) but apes saw only the distribution of food items in the samples that reflected the distribution of the respective populations (e.g., 4:1 vs. 1:4). Based on this observation they were then allowed to choose between the two populations. Results show that apes seemed to make inferences from samples to populations and thus chose the population from which the more favorable (4:1) sample was drawn in Experiment 1. In this experiment, the more attractive sample not only contained proportionally but also absolutely more preferred food items than the less attractive sample. Experiment 2, however, revealed that when absolute and relative frequencies were disentangled, apes performed at chance level. Whether these limitations in apes' performance reflect true limits of cognitive competence or merely performance limitations due to accessory task demands is still an open question.

Zebrafish prefer larger to smaller shoals: analysis of quantity estimation in a genetically tractable model organism

Numerical abilities have been demonstrated in a variety of non-human vertebrates. However, underlying biological mechanisms have been difficult to study due to a paucity of experimental tools. Powerful genetic and neurobiological tools already exist for the zebrafish, but numerical abilities remain scarcely explored with this species. Here, we investigate the choice made by single experimental zebrafish between numerically different shoals of conspecifics presented concurrently on opposite sides of the experimental tank. We examined this choice using the AB strain and pet store zebrafish. We found zebrafish of both populations to generally prefer the numerically larger shoal to the smaller one. This preference was significant for contrasted ratios above or equalling 2:1 (i.e. 4 vs. 0, 4 vs. 1, 8 vs. 2, 6 vs. 2 and 6 vs. 3). Interestingly, zebrafish showed no significant preference when each of the two contrasted shoals had at least 4 members, e.g. in a contrast 8 versus 4. These results confirm that zebrafish possess the ability to distinguish larger numbers of items from smaller number of items, in a shoaling context, with a potential limit above 4. Our findings confirm the utility of the zebrafish for the exploration of both the behavioural and the biological mechanisms underlying numerical abilities in vertebrates.

Thinking chickens: a review of cognition, emotion, and behavior in the domestic chicken

Domestic chickens are members of an order, Aves, which has been the focus of a revolution in our understanding of neuroanatomical, cognitive, and social complexity. At least some birds are now known to be on par with many mammals in terms of their level of intelligence, emotional sophistication, and social interaction. Yet, views of chickens have largely remained unrevised by this new evidence. In this paper, I examine the peer-reviewed scientific data on the leading edge of cognition, emotions, personality, and sociality in chickens, exploring such areas as self-awareness, cognitive bias, social learning and self-control, and comparing their abilities in these areas with other birds and other vertebrates, particularly mammals. My overall conclusion is that chickens are just as cognitively, emotionally and socially complex as most other birds and mammals in many areas, and that there is a need for further noninvasive comparative behavioral research with chickens as well as a re-framing of current views about their intelligence.

Chimpanzees Remember the Results of One-by-One Addition of Food Items to Sets Over Extended Time Periods

Four chimpanzees were highly accurate in selecting the larger of two concurrent accumulations of bananas in two opaque containers over a span of 20 min. One at a time, bananas were placed into the containers, which were outside the chimpanzees' cages. The chimpanzees never saw more than one banana at a time, and there were no cues indicating the locations of the bananas after they were placed into the containers. The performance of these animals matched that of human infants and young children in similar tests. The chimpanzees were successful even when the sets to be compared were sufficiently large (5 vs. 8, 5 vs. 10, and 6 vs. 10) to cast doubt on the possibility that the chimpanzees were using an object file mechanism. These chimpanzees are the first nonhuman animals to demonstrate extended memory for accumulated quantity.

When maths trumps logic: probabilistic judgements in chimpanzees

When searching for hidden food, do chimpanzees take into account both the number of hidden items and the number of potential hiding locations? We presented chimpanzees with two trays, each of them containing a different food/cup ratio and therefore a different likelihood of finding a baited cup among empty alternatives. Subjects' performance was directly influenced by the relative difference (probability ratio (PR)) between the two given probabilities. Interestingly, however, they did not appreciate the special value of a truly safe option (with P = 1.0). Instead, they seemed to 'blindly' rely on the PR between the two options, systematically preferring the more likely one once a certain threshold had been reached. A control condition ruled out the possibility of low-level learning explanations for the observed performance.

Quantification acuity in spontaneous shoaling decisions of three-spined sticklebacks

The ability to discriminate between different quantities is widespread throughout the animal kingdom, and the underlying mechanisms of quantity discrimination are currently intensely discussed. In contrast, questions elucidating the limits of quantity estimation received rather little attention so far. Here, we examined fine-tuned quantity estimation in the three-spined stickleback (Gasterosteus aculeatus) in a natural context, i.e. during shoaling decisions. Wild-caught focal fish were given the spontaneous choice between two shoals which differed in group size by 1 fish (0 vs. 1, 1 vs. 2, 2 vs. 3, 3 vs. 4, 4 vs. 5, 5 vs. 6 and 6 vs. 7), based on visual assessment. The results show that sticklebacks generally prefer to shoal with the larger group. They discriminated numerical contrasts up to 6 versus 7, equalling a numerical ratio of 0.86. Preference patterns followed Weber's law, i.e. decreased with increasing numerical ratio. This pattern was found across all numerical conditions as well as within the small number range (ranging from 1 vs. 2 to 3 vs. 4). The results suggest that wild-caught three-spined sticklebacks are spontaneously able (i.e. without prior learning) to detect subtle differences in shoal sizes. Further, they confirm findings of previous studies highlighting the contribution of the analogue magnitude system to quantity estimation in fishes.

The use of proportion by young domestic chicks (Gallus gallus)

We investigated whether 4-day-old domestic chicks can discriminate proportions. Chicks were trained to respond, via food reinforcement, to one of the two stimuli, each characterized by different proportions of red and green areas (¼ vs. ¾). In Experiment 1, chicks approached the proportion associated with food, even if at test the spatial dispositions of the two areas were novel. In Experiment 2, chicks responded on the basis of proportion even when the testing stimuli were of enlarged dimensions, creating a conflict between the absolute positive area experienced during training and the relative proportion of the two areas. However, chicks could have responded on the basis of the overall colour (red or green) of the figures rather than proportion per se. To control for this objection, in Experiment 3, we used new pairs of testing stimuli, each depicting a different number of small squares on a white background (i.e. 1 green and 3 red vs. 3 green and 1 red or 5 green and 15 red vs. 5 red and 15 green). Chicks were again able to respond to the correct proportion, showing they discriminated on the basis of proportion of continuous quantities and not on the basis of the prevalent colour or on the absolute amount of it. Data indicate that chicks can track continuous quantities through various manipulations, suggesting that proportions are information that can be processed by very young animals.

Defining value through quantity and quality-Chimpanzees (Pan troglodytes) undervalue food quantities when items are broken

Decision-making largely is influenced by the relative value of choice options, and the value of such options can be determined by a combination of different factors (e.g., the quantity, size, or quality of a stimulus). In this study, we examined the competing influences of quantity (i.e., the number of food items in a set) and quality (i.e., the original state of a food item) of choice items on chimpanzees' food preferences in a two-option natural choice paradigm. In Experiment 1, chimpanzees chose between sets of food items that were either entirely whole or included items that were broken into pieces before being shown to the chimpanzees. Chimpanzees exhibited a bias for whole food items even when such choice options consisted of a smaller overall quantity of food than the sets containing broken items. In Experiment 2, chimpanzees chose between sets of entirely whole food items and sets of initially whole items that were subsequently broken in view of the chimpanzees just before choice time. Chimpanzees continued to exhibit a bias for sets of whole items. In Experiment 3, chimpanzees chose between sets of new food items that were initially discrete but were subsequently transformed into a larger cohesive unit. Here, chimpanzees were biased to choose the discrete sets that retained their original qualitative state rather than toward the cohesive or clumped sets. These results demonstrate that beyond a food set's quantity (i.e., the value dimension that accounts for maximization in terms of caloric intake), other seemingly non-relevant features (i.e., quality in terms of a set's original state) affect how chimpanzees assign value to their choice options.

Numerical discrimination by frogs (Bombina orientalis)

Evidence has been reported for quantity discrimination in mammals and birds and, to a lesser extent, fish and amphibians. For the latter species, however, whether quantity discrimination would reflect sensitivity to number or to the continuous physical variables that covary with number is unclear. Here we reported a series of experiments with frogs (Bombina orientalis) tested in free-choice experiments for their preferences for different amounts of preys (Tenebrio molitor larvae) with systematic controls for variables such as surface area, volume, weight, and movement. Frogs showed quantity discrimination in the range of both small (1 vs. 2, 2 vs. 3, but not 3 vs. 4) and large numerousness (3 vs. 6, 4 vs. 8, but not 4 vs. 6), with clear evidence of being able to discriminate numerousness even when continuous physical variables were controlled for in the case of small numerousness (i.e., 1 vs. 2), whereas in the case of large numerousness it remains unclear whether the number or surface areas were dominant. We suggested that task demands are likely to be responsible for the activation of different systems for small and large numerousness and for their relative susceptibility to quantitative stimulus variables.

Visual nesting of stimuli affects rhesus monkeys' (Macaca mulatta) quantity judgments in a bisection task

Nonhuman animals are highly proficient at judging relative quantities presented in a variety of formats, including visual, auditory, and even cross-modal formats. Performance typically is constrained by the ratio between sets, as would be expected under Weber's law and as is described in the approximate number system (ANS) hypothesis. In most cases, tests are designed to avoid any perceptual confusion for animals regarding the stimulus sets, but despite this, animals show some of the perceptual biases that humans show based on organization of stimuli. Here, we demonstrate an additional perceptual bias that emerges from the illusion of nested sets. When arrays of circles were presented on a computer screen and were to be classified as larger than or smaller than an established central value, rhesus monkeys (Macaca mulatta) underestimated quantities when circles were nested within each other. This matched a previous report with adult humans (Chesney & Gelman, Attention, Perception, & Psychophysics 24:1104-1113, 2012), indicating that macaques, like humans, show the pattern of biased perception predicted by ANS estimation. Although some macaques overcame this perceptual bias, demonstrating that they could come to view nested stimuli as individual elements to be included in the estimates of quantity used for classifying arrays, the majority of the monkeys showed the bias of underestimating nested arrays throughout the experiment.

Spontaneous versus trained numerical abilities. A comparison between the two main tools to study numerical competence in non-human animals

A large body of experimental evidence shows that animals as diverse as mammals, birds, and fish are capable of processing numerical information. Considerable differences have been reported in some cases among species and a wide debate currently surrounds the issue of whether all vertebrates share the same numerical systems or not. Part of the problem is due to the fact that these studies often use different methods, a circumstance that potentially introduces confounding factors in a comparative analysis. In most studies, two main methodological approaches have been used: spontaneous choice tests and training procedures. The former approach consists of presenting to the subjects two groups of biologically-relevant stimuli (e.g., food items or social companions) differing in numerosity with the assumption that if they are able to discriminate between the two quantities, they are expected to spontaneously select the larger/smaller quantity. In the latter approach, subjects undergo extensive training in which some neutral stimuli (e.g., a quantity of dots) are associated with a reward and the capacity to learn a numerical rule is taken as evidence of numerical abilities. We review the literature on this topic, highlighting the relevance, and potential weaknesses in controlling confounding factors obtained with either approach.

Lateralized mechanisms for encoding of object. Behavioral evidence from an animal model: the domestic chick (Gallus gallus)

In our previous research we reported a leftward-asymmetry in domestic chicks required to identify a target element, on the basis of its ordinal position, in a series of identical elements. Here we re-coded behavioral data collected in previous studies from chicks tested in a task involving a different kind of numerical ability, to study lateralization in dealing with an arithmetic task. Chicks were reared with a set of identical objects representing artificial social companions. On day 4, chicks underwent a free-choice test in which two sets, each composed of a different number of identical objects (5 vs.10 or 6 vs. 9, Experiment 1), were hidden behind two opaque screens placed in front of the chick, one on the left and one on the right side. Objects disappeared, one by one, behind either screen, so that, for example, one screen occluded 5 objects and the other 10 objects. The left-right position of the larger set was counterbalanced between trials. Results show that chicks, in the attempt to rejoin the set with the higher number of social companions, performed better when this was located to the right. However, when the number of elements in the two sets was identical (2 vs. 2, in Experiment 2) and they differed only in the coloration of the objects, this bias was not observed, suggesting a predisposition to map the numerical magnitude from left to right. Future studies should be devoted to the direct investigation of this phenomenon, possibly employing an identical number of mono-chromatic imprinting stimuli in both conditions involving a numerical discrimination and conditions not involving any numerosity difference.

Numerical abstraction in young domestic chicks (Gallus gallus)

In a variety of circumstances animals can represent numerical values per se, although it is unclear how salient numbers are relative to non-numerical properties. The question is then: are numbers intrinsically distinguished or are they processed as a last resort only when no other properties differentiate stimuli? The last resort hypothesis is supported by findings pertaining to animal studies characterized by extensive training procedures. Animals may, nevertheless, spontaneously and routinely discriminate numerical attributes in their natural habitat, but data available on spontaneous numerical competence usually emerge from studies not disentangling numerical from quantitative cues. In the study being outlined here, we tested animals' discrimination of a large number of elements utilizing a paradigm that did not require any training procedures. During rearing, newborn chicks were presented with two stimuli, each characterized by a different number of heterogeneous (for colour, size and shape) elements and food was found in proximity of one of the two stimuli. At testing 3 day-old chicks were presented with stimuli depicting novel elements (for colour, size and shape) representing either the numerosity associated or not associated with food. The chicks approached the number associated with food in the 5vs.10 and 10vs.20 comparisons both when quantitative cues were unavailable (stimuli were of random sizes) or being controlled. The findings emerging from the study support the hypothesis that numbers are salient information promptly processed even by very young animals.

What counts for 'counting'? Chimpanzees, Pan troglodytes, respond appropriately to relevant and irrelevant information in a quantity judgment task

Nonhuman animals quantify all manner of things, and the way in which this is done is fairly well understood. However, little research has been conducted to determine how they know what is or is not relevant in the instances in which they quantify stimuli. We assessed how four chimpanzees chose between two sets of food items when the items were distributed across separate spatial arrays. Each item was covered by a container, and then was revealed in sequence so that neither whole set was visible at one time. After all containers were revealed, some were revealed again. The chimpanzees should have ignored items that were seen a second time and instead enumerated each item only once. In another test, some of the items were transposed in location and then uncovered again. Here, the chimpanzees needed to recognize that the newly shown food items were ones they already had seen. Overall, the chimpanzees were successful in selecting the truly larger array of items despite these potential distracting re-presentations of items. Discrimination performance also reflected analogue magnitude estimation because comparisons of sets that differed by larger amounts were easier than comparisons that differed by smaller amounts. Thus, chimpanzee quantity judgments for nonvisible sets of items are inexact, but they include an aspect of control for determining when items are uniquely presented versus re-presented.

Quantity judgments in the context of risk/reward decision making in striped field mice: first "count," then hunt

We simulated the situation of risky hunting in the striped field mouse Apodemus agrarius in order to examine whether these animals are able to make a choice between small and large quantities of live prey (ants). In the first (preliminary) experiment we investigated to what extent mice were interested in ants as a live prey and how their hunting activity depended on the quantity of these edible but rather aggressive insects. We placed mice one by one into arenas together with ant groups of different quantities, from 10 to 60. Surprisingly, animals, both wild-caught and laboratory-reared, displayed rather skilled predatory attacks: mice killed and ate from 0.37 ± 003 to 4 ± 0.5 ants per minute. However, there was a threshold number of ants in the arenas when rodents expressed signs of discomfort and started to panic, likely because ants bit them. This threshold corresponds to the dynamic density (about 400 individuals per m² per min) in the vicinity of anthills and ants' routes in natural environment. In the second experiment mice had to choose between different quantities of ants placed in two transparent tunnels. Ants here served both as food items and as a source of danger. As far as we know, this is the first experimental paradigm based on evaluation of quantity judgments in the context of risk/reward decision making where the animals face a trade-off between the hedonistic value of the prey and the danger it presents. We found that when mice have to choose between 5 vs. 15, 5 vs. 30, and 10 vs. 30 ants, they always tend to prefer the smaller quantity, thus displaying the capacity for distinguishing more from less in order to ensure comfortable hunting. The results of this study are ecologically relevant as they reflect situations and challenges faced by free-living small rodents.

1 < 2 and 2 < 3: non-linguistic appreciations of numerical order

Ordinal understanding is involved in understanding social hierarchies, series of actions, and everyday events. Moreover, an appreciation of numerical order is critical to understanding number at a highly abstract, conceptual level. In this paper, we review findings concerning the development and expression of ordinal numerical knowledge in preverbal human infants in light of literature about the same cognitive abilities in non-human animals. We attempt to reconcile seemingly contradictory evidence, provide new directions for prospective research, and evaluate the shared basis of ordinal knowledge among non-verbal organisms. Our review of the research leads us to conclude that both infants and non-human animals are adapted to respond to monotonic progressions in numerical order, consonant with mathematical definitions of numerical order. Further, we suggest that patterns in the way that infants and non-human animals process numerical order can be accounted for by changes across development, the conditions under which representations are generated, or both.

Do Social Conditions Affect Capuchin Monkeys' (Cebus apella) Choices in a Quantity Judgment Task?

Beran et al. (2012) reported that capuchin monkeys closely matched the performance of humans in a quantity judgment test in which information was incomplete but a judgment still had to be made. In each test session, subjects first made quantity judgments between two known options. Then, they made choices where only one option was visible. Both humans and capuchin monkeys were guided by past outcomes, as they shifted from selecting a known option to selecting an unknown option at the point at which the known option went from being more than the average rate of return to less than the average rate of return from earlier choices in the test session. Here, we expanded this assessment of what guides quantity judgment choice behavior in the face of incomplete information to include manipulations to the unselected quantity. We manipulated the unchosen set in two ways: first, we showed the monkeys what they did not get (the unchosen set), anticipating that "losses" would weigh heavily on subsequent trials in which the same known quantity was presented. Second, we sometimes gave the unchosen set to another monkey, anticipating that this social manipulation might influence the risk-taking responses of the focal monkey when faced with incomplete information. However, neither manipulation caused difficulty for the monkeys who instead continued to use the rational strategy of choosing known sets when they were as large as or larger than the average rate of return in the session, and choosing the unknown (riskier) set when the known set was not sufficiently large. As in past experiments, this was true across a variety of daily ranges of quantities, indicating that monkeys were not using some absolute quantity as a threshold for selecting (or not) the known set, but instead continued to use the daily average rate of return to determine when to choose the known versus the unknown quantity.

A shared system of representation governing quantity discrimination in canids

One way to investigate the evolution of cognition is to compare the abilities of phylogenetically related species. The domestic dog (Canis lupus familiaris), for example, still shares cognitive abilities with the coyote (Canis latrans). Both of these canids possess the ability to make psychophysical "less/more" discriminations of food based on quantity. Like many other species including humans, this ability is mediated by Weber's Law: discrimination of continuous quantities is dependent on the ratio between the two quantities. As two simultaneously presented quantities of food become more similar, choice of the large or small option becomes random in both dogs and coyotes. It remains unknown, however, whether these closely related species within the same family - one domesticated, and one wild - make such quantitative comparisons with comparable accuracy. Has domestication honed or diminished this quantitative ability? Might different selective and ecological pressures facing coyotes drive them to be more or less able to accurately represent and discriminate food quantity than domesticated dogs? This study is an effort to elucidate this question concerning the evolution of non-verbal quantitative cognition. Here, we tested the quantitative discrimination ability of 16 domesticated dogs. Each animal was given nine trials in which two different quantities of food were simultaneously displayed to them. The domesticated dogs' performance on this task was then compared directly to the data from 16 coyotes' performance on this same task reported by Baker et al. (2011). The quantitative discrimination abilities between the two species were strikingly similar. Domesticated dogs demonstrated similar quantitative sensitivity as coyotes, suggesting that domestication may not have significantly altered the psychophysical discrimination abilities of canids. Instead, this study provides further evidence for similar non-verbal quantitative abilities across multiple species.

Humans and monkeys show similar skill in estimating uncertain outcomes

When information is incomplete but a choice must be made, individuals sometimes can rely on past experiences to help them assess uncertain outcomes in terms of the probabilities of payoffs. Monkeys (Cebus apella) and humans (Homo sapiens) were presented with a test in which they first made quantity judgments between two clear options. Then they made choices in which only one option was visible, and they had to estimate the quantity for the other option. Both species were guided by the past outcomes, as they shifted from selecting the known option to selecting the unknown option at the point at which the known option went from being greater than the average rate of return to being less than the average rate of return. This comparability across species suggests that tallying ongoing average rates of return from repeated choices occurs spontaneously and likely serves an adaptive purpose when dealing with uncertainty in the environment.

Summation by Asian Elephants (Elephas maximus)

Recent empirical evidence for complex cognition in elephants suggests that greater attention to comparative studies between non-human primates and other animals is warranted. We have previously shown that elephants possess the ability to judge the difference between two discrete quantities, and unlike other animals, their choice does not appear to be affected by distance or overall quantity. In this study, we investigated Asian elephants’ ability to perform summation, as exemplified by the ability to combine four quantities into two sums and subsequently compare them. We presented two discrete sums (3–7) to the elephants by baiting two buckets; they were loaded sequentially with two discrete quantities (1–5 pieces) of food per bucket. All three elephants selected the larger grand sum significantly more often than the smaller grand sum. Moreover, their performance was not affected by either distance to the bait or the overall quantity evaluated. Studies report that the performance of other animal species on similar tasks declines as distance to the bait decreases and as the overall quantities evaluated increase. These results suggest that the numerical cognition of Asian elephants may be different from that of other animals, but further study is required to elucidate the differences precisely.

Tracking of food quantity by coyotes (Canis latrans)

Previous studies have demonstrated that Weber's Law mediates quantitative discrimination abilities across various species. Here, we tested coyotes' (Canis latrans) ability to discriminate between various quantities of food and investigated whether this ability conforms to predictions of Weber's Law. We demonstrate herein that coyotes are capable of reliably discriminating large versus small quantities of discrete food items. As predicted by Weber's Law, coyotes' quantitative discrimination abilities are mediated by the ratio between the large and small quantities of food and exhibit scalar variability. Furthermore, in this task coyotes were not discriminating large versus small quantities based on olfactory cues alone.

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.

Relative quantity judgments in South American sea lions (Otaria flavescens)

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.

Monkeys (macaca mulatta and cebus apella) and human adults and children (homo sapiens) compare subsets of moving stimuli based on numerosity

Two monkey species (Macaca mulatta and Cebus apella) and human children and adults judged the numerousness of two subsets of moving stimuli on a computer screen. Two sets of colored dots that varied in number and size were intermixed in an array in which all dots moved in random directions and speeds. Participants had to indicate which dot color was more numerous within the array. All species performed at high and comparable levels, including on trials in which the subset with the larger number of items had a smaller total area of coloration. This indicated a similarity across species to use the number of items in the subsets, and not dimensions such as area or volume, to guide decision making. Discrimination performance was constrained by the ratio between the subsets, consistent with other reports of numerousness judgments of stationary stimuli. These results indicate a similarity in numerical estimation ability for moving stimuli across primate species, and this capacity may be necessary for naturally occurring experiences in which moving stimuli must be summed.