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

Quantity misperception by hymenopteran insects observing the solitaire illusion

Visual illusions are errors in signal perception and inform us about the visual and cognitive processes of different animals. Invertebrates are relatively less studied for their illusionary perception, despite the insight that comparative data provides on the evolution of common perceptual mechanisms. The Solitaire Illusion is a numerosity illusion where a viewer typically misperceives the relative quantities of two items of different colors consisting of identical quantity, with more centrally clustered items appearing more numerous. We trained European honeybees (Apis mellifera) and European wasps (Vespula vulgaris) to select stimuli containing a higher quantity of yellow dots in arrays of blue and yellow dots and then presented them with the Solitaire Illusion. Insects learnt to discriminate between dot quantities and showed evidence of perceiving the Solitaire Illusion. Further work should determine whether the illusion is caused by numerical cues only or by both quantity and non-numerical spatial cues.

Chimpanzees engage in competitive altruism in a triadic ultimatum game

Partner choice promotes competition among individuals to be selected as a cooperative partner, a phenomenon referred to as competitive altruism. We explored whether chimpanzees engage in competitive altruism in a triadic Ultimatum Game where two proposers can send offers simultaneously or consecutively to a responder who can only accept one of the two competing offers. In a dyadic control condition only one proposer at a time could send an offer to the responder. Chimpanzees increased their offers across trials in the competitive triadic, but not in the dyadic control condition. Chimpanzees also increased their offers after being rejected in previous triadic trials. Furthermore, we found that chimpanzees, under specific conditions, outcompete first proposers in triadic consecutive trials before the responder could choose which offer to accept by offering more than what is expected if they acted randomly or simply offered the smallest possible amount. These results suggest that competitive altruism in chimpanzees did not emerge just as a by-product of them trying to increase over previous losses. Chimpanzees might consider how others' interactions affect their outcomes and engage in strategies to maximize their chances of being selected as cooperative partners.

Crows flexibly apply statistical inferences based on previous experience

Statistical inference, the ability to use limited information to draw conclusions about the likelihood of an event, is critical for decision-making during uncertainty. The ability to make statistical inferences was thought to be a uniquely human skill requiring verbal instruction and mathematical reasoning.1 However, basic inferences have been demonstrated in both preliterate and pre-numerate individuals,2,3,4,5,6,7 as well as non-human primates.8 More recently, the ability to make statistical inferences has been extended to members outside of the primate lineage in birds.9,10 True statistical inference requires subjects use relative rather than absolute frequency of previously experienced events. Here, we show that crows can relate memorized reward probabilities to infer reward-maximizing decisions. Two crows were trained to associate multiple reward probabilities ranging from 10% to 90% to arbitrary stimuli. When later faced with the choice between various stimulus combinations, crows retrieved the reward probabilities associated with individual stimuli from memory and used them to gain maximum reward. The crows showed behavioral distance and size effects when judging reward values, indicating that the crows represented probabilities as abstract magnitudes. When controlling for absolute reward frequency, crows still made reward-maximizing choices, which is the signature of true statistical inference. Our study provides compelling evidence of decision-making by relative reward frequency in a statistical inference task.

Great ape cognition is structured by stable cognitive abilities and predicted by developmental conditions

Great ape cognition is used as a reference point to specify the evolutionary origins of complex cognitive abilities, including in humans. This research often assumes that great ape cognition consists of cognitive abilities (traits) that account for stable differences between individuals, which change and develop in response to experience. Here, we test the validity of these assumptions by assessing repeatability of cognitive performance among captive great apes (Gorilla gorilla, Pongo abelii, Pan paniscus, Pan troglodytes) in five tasks covering a range of cognitive domains. We examine whether individual characteristics (age, group, test experience) or transient situational factors (life events, testing arrangements or sociality) influence cognitive performance. Our results show that task-level performance is generally stable over time; four of the five tasks were reliable measurement tools. Performance in the tasks was best explained by stable differences in cognitive abilities (traits) between individuals. Cognitive abilities were further correlated, suggesting shared cognitive processes. Finally, when predicting cognitive performance, we found stable individual characteristics to be more important than variables capturing transient experience. Taken together, this study shows that great ape cognition is structured by stable cognitive abilities that respond to different developmental conditions.

Numerical cognition in black-handed spider monkeys (Ateles geoffroyi)

We assessed two aspects of numerical cognition in a group of nine captive spider monkeys (Ateles geoffroyi). Petri dishes with varying amounts of food were used to assess relative quantity discrimination, and boxes fitted with dotted cards were used to assess discrete number discrimination with equally-sized dots and various-sized dots, respectively. We found that all animals succeeded in all three tasks and, as a group, reached the learning criterion of 70% correct responses within 110 trials in the quantity discrimination task, 160 trials in the numerosity task with equally-sized dots, and 30 trials in the numerosity task with various-sized dots. In all three tasks, the animals displayed a significant correlation between performance in terms of success rate and task difficulty in terms of numerical similarity of the stimuli and thus a ratio effect. The spider monkeys performed clearly better compared to strepsirrhine, catarrhine, and other platyrrhine primates tested previously on both types of numerical cognition tasks and at the same level as chimpanzees, bonobos, and orangutans. Our results support the notion that ecological traits such as a high degree of frugivory and/or social traits such as a high degree of fission-fusion dynamics may underlie between-species differences in cognitive abilities.

On the Working Memory of Humans and Great Apes: Strikingly Similar or Remarkably Different?

In this article we review publications relevant to addressing widely reported claims in both the academic and popular press that chimpanzees working memory (WM) is comparable to, if not exceeding, that of humans. WM is a complex multidimensional construct with strong parallels in humans to prefrontal cortex and cognitive development. These parallels occur in chimpanzees, but to a lesser degree. We review empirical evidence and conclude that the size of WM in chimpanzees is 2 ± 1 versus Miller's famous 7 ± 2 in humans. Comparable differences occur in experiments on chimpanzees relating to strategic and attentional WM subsystems. Regardless of the domain, chimpanzee WM performance is comparable to that of humans around the age of 4 or 5. Next, we review evidence showing parallels among the evolution of WM capacity in hominins ancestral to Homo sapiens, the phylogenetic evolution of hominins leading to Homo sapiens, and evolution in the complexity of stone tool technology over this time period.

Does quantity matter to a stingless bee?

Quantitative information is omnipresent in the world and a wide range of species has been shown to use quantities to optimize their decisions. While most studies have focused on vertebrates, a growing body of research demonstrates that also insects such as honeybees possess basic quantitative abilities that might aid them in finding profitable flower patches. However, it remains unclear if for insects, quantity is a salient feature relative to other stimulus dimensions, or if it is only used as a “last resort” strategy in case other stimulus dimensions are inconclusive. Here, we tested the stingless bee Trigona fuscipennis, a species representative of a vastly understudied group of tropical pollinators, in a quantity discrimination task. In four experiments, we trained wild, free-flying bees on stimuli that depicted either one or four elements. Subsequently, bees were confronted with a choice between stimuli that matched the training stimulus either in terms of quantity or another stimulus dimension. We found that bees were able to discriminate between the two quantities, but performance differed depending on which quantity was rewarded. Furthermore, quantity was more salient than was shape. However, quantity did not measurably influence the bees' decisions when contrasted with color or surface area. Our results demonstrate that just as honeybees, small-brained stingless bees also possess basic quantitative abilities. Moreover, invertebrate pollinators seem to utilize quantity not only as "last resort" but as a salient stimulus dimension. Our study contributes to the growing body of knowledge on quantitative cognition in invertebrate species and adds to our understanding of the evolution of numerical cognition.

Chimpanzees and bonobos use social leverage in an ultimatum game

The ultimatum game (UG) is widely used to investigate our sense of fairness, a key characteristic that differentiates us from our closest living relatives, bonobos and chimpanzees. Previous studies found that, in general, great apes behave as rational maximizers in the UG. Proposers tend to choose self-maximizing offers, while responders accept most non-zero offers. These studies do not rule out the possibility that apes can behave prosocially to improve the returns for themselves and others. However, this has never been well studied. In this study, we offer chimpanzee and bonobo proposers the possibility of taking into account the leverage of responders over the offers they receive. This leverage takes the form of access to alternatives for responders. We find that proposers tend to propose fairer offers when responders have the option to access alternatives. Furthermore, we find that both species use their leverage to reject unequal offers. Our results suggest that great apes mostly act as rational maximizers in an UG, yet access to alternatives can lead them to change their strategies such as not choosing the self-maximizing offer as proposers and not accepting every offer higher than zero as responders.

Superior continuous quantity discrimination in a freshwater turtle

BACKGROUND

Quantity discrimination, the ability to discriminate a magnitude of difference or discrete numerical information, plays a key role in animal behavior. While quantitative ability has been well documented in fishes, birds, mammals, and even in previously unstudied invertebrates and amphibians, it is still poorly understood in reptiles and has never been tested in an aquatic turtle despite the fact that evidence is accumulating that reptiles possess cognitive skills and learning ability. To help address this deficiency in reptiles, we investigated the quantitative ability of an Asian freshwater turtle, Mauremys sinensis, using red cubes on a white background in a trained quantity discrimination task. While spontaneous quantity discrimination methods are thought to be more ecologically relevant, training animals on a quantity discrimination task allows more comparability across taxa.

RESULTS

We assessed the turtles' quantitative performance in a series of tests with increasing quantity ratios and numerosities. Surprisingly, the turtles were able to discriminate quantities of up to 9 versus 10 (ratio = 0.9), which shows a good quantitative ability that is comparable to some endotherms. Our results showed that the turtles' quantitative performance followed Weber's law, in which success rate decreased with increasing quantity ratio across a wide range of numerosities. Furthermore, the gradual improvement of their success rate across different experiments and phases suggested that the turtles possess learning ability.

CONCLUSIONS

Reptile quantitative ability has long been ignored and therefore is likely under-estimated. More comparative research on numerical cognition across a diversity of species will greatly contribute to a clearer understanding of quantitative ability in animals and whether it has evolved convergently in diverse taxa.

Quantitative abilities of invertebrates: a methodological review

Quantitative abilities are widely recognized to play important roles in several ecological contexts, such as foraging, mate choice, and social interaction. Indeed, such abilities are widespread among vertebrates, in particular mammals, birds, and fish. Recently, there has been an increasing number of studies on the quantitative abilities of invertebrates. In this review, we present the current knowledge in this field, especially focusing on the ecological relevance of the capacity to process quantitative information, the similarities with vertebrates, and the different methods adopted to investigate this cognitive skill. The literature argues, beyond methodological differences, a substantial similarity between the quantitative abilities of invertebrates and those of vertebrates, supporting the idea that similar ecological pressures may determine the emergence of similar cognitive systems even in distantly related species.

Towards a standardization of non-symbolic numerical experiments: GeNEsIS, a flexible and user-friendly tool to generate controlled stimuli

Several studies have suggested that vertebrate and invertebrate species may possess a number sense, i.e. an ability to process in a non-symbolic and non-verbal way the numerousness of a set of items. However, this hypothesis has been challenged by the presence of other non-numerical continuous physical variables, which vary along with numerosity (i.e., any change in the number of visual physical elements in a set naturally involves a related change in visual features such as area, density, contour length and convex hull of the stimulus). It is therefore necessary to control and manipulate the continuous physical information when investigating the ability of humans and other animals to perceive numerousness. During decades of research, different methods have been implemented in order to address this issue, which has implications for experiment replicability and inter-species comparisons, since no general standardized procedure is currently being used. Here we present the ‘Generation of Numerical Elements Images Software’ (GeNEsIS) for the creation of non-symbolic numerical arrays in a standardized and user-friendly environment. The main aim of this tool is to provide researchers in the field of numerical cognition a manageable and precise instrument to produce visual numerical arrays controlled for all the continuous variables. Additionally, we implemented the ability to actively guide stimuli presentation during habituation/dishabituation and dual-choice comparison tasks used in human and comparative research.

Gibbon strategies in a food competition task

Social primates face conflicts of interest with other partners when their individual and collective interests collide. Despite living in small, primarily bonded, groups compared to other social primates, gibbons are not exempt from these conflicts in their everyday lives. In the current task, we asked whether dyads of gibbons would solve a conflict of interest over food rewards. We presented dyads of gibbons with a situation in which they could decide whether to take an active role and pull a handle to release food rewards at a distance or take a passive role and avoid action. In this situation, the passive partner could take an advantageous position to obtain the rewards over the active partner. Gibbons participated in three conditions: a control condition with no food rewards, a test condition with indirect food rewards and a test condition with direct food rewards. In both test conditions, five rewards were released at a distance from the handle. In addition, the active individual could obtain one extra food reward from the handle in the direct food condition. We found that gibbons acted more often in the two conditions involving food rewards, and waited longer in the indirect compared to the direct food condition, thus suggesting that they understood the task contingencies. Surprisingly, we found that in a majority of dyads, individuals in the active role obtained most of the payoff compared to individuals in the passive role in both food conditions. Furthermore, in some occasions individuals in the active role did not approach the location where the food was released. These results suggest that while gibbons may strategize to maximize benefits in a competitive food task, they often allowed their partners to obtain better rewards. Our results highlight the importance of social tolerance and motivation as drivers promoting cooperation in these species.

Estimating on the fly: The approximate number system in rufous hummingbirds (Selasphorus rufus)

When presented with resources that differ in quantity, many animals use a numerosity system to discriminate between them. One taxonomically widespread system is the approximate number system. This is a numerosity system that allows the rapid evaluation of the number of objects in a group and which is regulated by Weber's Law. Here we investigated whether wild, free-living rufous hummingbirds (Selasphorus rufus) possess an approximate number system. The hummingbirds were presented with two experiments. In the first we investigated whether hummingbirds spontaneously chose an array containing more flowers than an alternate array. In the second we asked whether the hummingbirds could learn to use numerosity as a cue to which of two arrays contained the better reward. The birds did not spontaneously prefer an array containing more flowers. After minimal training, however, they learned to choose the more numerous array and could differentiate between arrays of five and seven flowers. These data support the presence of an approximate number system in the rufous hummingbird. It seems plausible that having such a system would enable much more efficient foraging in this species.

Continuous versus discrete quantity discrimination in dune snail (Mollusca: Gastropoda) seeking thermal refuges

The ability of invertebrates to discriminate quantities is poorly studied, and it is unknown whether other phyla possess the same richness and sophistication of quantification mechanisms observed in vertebrates. The dune snail, Theba pisana, occupies a harsh habitat characterised by sparse vegetation and diurnal soil temperatures well above the thermal tolerance of this species. To survive, a snail must locate and climb one of the rare tall herbs each dawn and spend the daytime hours in an elevated refuge position. Based on their ecology, we predicted that dune snails would prefer larger to smaller groups of refuges. We simulated shelter choice under controlled laboratory conditions. Snails’ acuity in discriminating quantity of shelters was comparable to that of mammals and birds, reaching the 4 versus 5 item discrimination, suggesting that natural selection could drive the evolution of advanced cognitive abilities even in small-brained animals if these functions have a high survival value. In a subsequent series of experiments, we investigated whether snails used numerical information or based their decisions upon continuous quantities, such as cumulative surface, density or convex hull, which co-varies with number. Though our results tend to underplay the role of these continuous cues, behavioural data alone are insufficient to determine if dune snails were using numerical information, leaving open the question of whether gastropod molluscans possess elementary abilities for numerical processing.

Non-human primates use combined rules when deciding under ambiguity

Decision outcomes in unpredictable environments may not have exact known probabilities. Yet the predictability level of outcomes matters in decisions, and animals, including humans, generally avoid ambiguous options. Managing ambiguity may be more challenging and requires stronger cognitive skills than decision-making under risk, where decisions involve known probabilities. Here we compare decision-making in capuchins, macaques, orangutans, gorillas, chimpanzees and bonobos in risky and ambiguous contexts. Subjects were shown lotteries (a tray of potential rewards, some large, some small) and could gamble a medium-sized food item to obtain one of the displayed rewards. The odds of winning and losing varied and were accessible in the risky context (all rewards were visible) or partially available in the ambiguous context (some rewards were covered). In the latter case, the level of information varied from fully ambiguous (individuals could not guess what was under the covers) to predictable (individuals could guess). None of the species avoided gambling in ambiguous lotteries and gambling rates were high if at least two large rewards were visible. Capuchins and bonobos ignored the covered items and gorillas and macaques took the presence of potential rewards into account, but only chimpanzees and orangutans could consistently build correct expectations about the size of the covered rewards. Chimpanzees and orangutans combined decision rules according to the number of large visible rewards and the level of predictability, a process resembling conditional probabilities assessment in humans. Despite a low sample size, this is the first evidence in non-human primates that a combination of several rules can underlie choices made in an unpredictable environment. Our finding that non-human primates can deal with the uncertainty of an outcome when exchanging one food item for another is a key element to the understanding of the evolutionary origins of economic behaviour. This article is part of the theme issue 'Existence and prevalence of economic behaviours among non-human primates'.

A sense of number in invertebrates

Non-symbolic numerical abilities are widespread among vertebrates due to their important adaptive value. Moreover, these abilities were considered peculiar of vertebrate species as numerical competence is regarded as cognitively sophisticated. However, recent evidence convincingly showed that this is not the case: invertebrates, with their limited number of neurons, proved able to successfully discriminate different quantities (e.g., of prey), to use the ordinal property of numbers, to solve arithmetic operations as addition and subtraction and even to master the concept of zero numerosity. To date, though, the debate is still open on the presence and the nature of a «sense of number» in invertebrates. Whether this is peculiar for discrete countable quantities (numerosities) or whether this is part of a more general magnitude system dealing with both discrete and continuous quantities, as hypothesized for humans and other vertebrates. Here we reviewed the main studies on numerical abilities of invertebrates, discussing in particular the recent findings supporting the hypothesis of a general mechanism that allows for processing of both discrete (i.e., number) and continuous dimensions (e.g., space).

Comparative performance of orangutans (Pongo spp.), gorillas (Gorilla gorilla gorilla), and drills (Mandrillus leucophaeus), in an ephemeral foraging task

A goal of the comparative approach is to test a variety of species on the same task. Here, we examined whether the factors that helped capuchin monkeys improve their performance in a dichotomous choice task would generalize to three other primate species: orangutans, gorillas, and drill monkeys. In this task, subjects have access to two options, each resulting in an identical food, but one (the ephemeral option) is only available if it is chosen first, whereas the other one (the permanent option) is always available. Therefore, the food-maximizing solution is to choose the ephemeral option first, followed by the permanent option for an additional reward. On the original version (plate task), the options were discriminated by the color and pattern of the plates holding the food, while on two subsequent versions we used altered cues that we predicted would improve performance: (1) the color of the foods themselves (color task), which we hypothesized was relevant to primates, who choose foods rather than substrates on which foods are found when foraging, and (2) patterned cups covering the foods (cup task), which we hypothesized would help primates avoid the prepotent response associated with visible food. Like capuchins, all three species initially failed to solve the plate task. However, while orangutans improved their performance from the plate to the color task, they did not for the cup task, and only a few gorillas and no drills succeeded in either task. Unfortunately, our ability to interpret these data was obscured by differences in the subjects' level of experience with cognitive testing and practical constraints that precluded the use of completely identical procedures across species. Nonetheless, we consider what these results can tell us, and discuss the value of conducting studies across multiple sites despite unavoidable differences.

Learning in non-avian reptiles 40 years on: advances and promising new directions

Recently, there has been a surge in cognition research using non-avian reptile systems. As a diverse group of animals, non-avian reptiles [turtles, the tuatara, crocodylians, and squamates (lizards, snakes and amphisbaenids)] are good model systems for answering questions related to cognitive ecology, from the role of the environment on the brain, behaviour and learning, to how social and life-history factors correlate with learning ability. Furthermore, given their variable social structure and degree of sociality, studies on reptiles have shown that group living is not a pre-condition for social learning. Past research has demonstrated that non-avian reptiles are capable of more than just instinctive reactions and basic cognition. Despite their ability to provide answers to fundamental questions in cognitive ecology, and a growing literature, there have been no recent systematic syntheses of research in this group. Here, we systematically, and comprehensively review studies on reptile learning. We identify 92 new studies investigating learning in reptiles not included in previous reviews on this topic - affording a unique opportunity to provide a more in-depth synthesis of existing work, its taxonomic distribution, the types of cognitive domains tested and methodologies that have been used. Our review therefore provides a major update on our current state of knowledge and ties the collective evidence together under nine umbrella research areas: (i) habituation of behaviour, (ii) animal training through conditioning, (iii) avoiding aversive stimuli, (iv) spatial learning and memory, (v) learning during foraging, (vi) quality and quantity discrimination, (vii) responding to change, (viii) solving novel problems, and (ix) social learning. Importantly, we identify knowledge gaps and propose themes which offer important future research opportunities including how cognitive ability might influence fitness and survival, testing cognition in ecologically relevant situations, comparing cognition in invasive and non-invasive populations of species, and social learning. To move the field forward, it will be immensely important to build upon the descriptive approach of testing whether a species can learn a task with experimental studies elucidating causal reasons for cognitive variation within and among species. With the appropriate methodology, this young but rapidly growing field of research should advance greatly in the coming years providing significant opportunities for addressing general questions in cognitive ecology and beyond.

Poor numerical performance of guppies tested in a Skinner box

We tested the hypothesis that part of the gap in numerical competence between fish and warm-blooded vertebrates might be related to the more efficient procedures (e.g. automated conditioning chambers) used to investigate the former and could be filled by adopting an adapted version of the Skinner box in fish. We trained guppies in a visual numerosity discrimination task, featuring two difficulty levels (3 vs. 5 and 3 vs. 4) and three conditions of congruency between numerical and non-numerical cues. Unexpectedly, guppies trained with the automated device showed a much worse performance compared to previous investigations employing more “ecological” procedures. Statistical analysis indicated that the guppies overall chose the correct stimulus more often than chance; however, their average accuracy did not exceed 60% correct responses. Learning measured as performance improvement over training was significant only for the stimuli with larger numerical difference. Additionally, the target numerosity was selected more often than chance level only for the set of stimuli in which area and number were fully congruent. Re-analysis of prior studies indicate that the gap between training with the Skinner box and with a naturalistic setting was present only for numerical discriminations, but not for colour and shape discriminations. We suggest that applying automated conditioning chambers to fish might increase cognitive load and therefore interfere with achievement of numerosity discriminations.

Food Quantity Discrimination in Angelfish (Pterophyllum scalare): The Role of Number, Density, Size and Area Occupied by the Food Items

Quantity discrimination, the ability to identify, process, and respond to differences in number, has been shown in a variety of animal species and may have fitness value. In fish, the ability to distinguish between numerically different shoals has been well studied. However, little work has been devoted to the investigation of such ability in a foraging context. Nevertheless, angelfish (Pterophyllum scalare) have been previously shown to be able to discriminate numerically different sets of food items, with variables such as size and density of the food items playing important roles in making the choice. Here, we examine the possible role of other numerical and non-numerical variables. Using a spontaneous binary choice task, we contrasted sets of food items differing in specifically controlled ways: (1) different numerical size but equal inter-item distance; (2) different numerical size and different inter-item distance; and (3) identical total contour length and area occupied but different individual food size and inter-food distance between the contrasted food sets. In Experiment 1, angelfish were found to prefer the sets with a large number of food items. In Experiment 2, they preferred the numerically smaller sets with clustered items to the numerically larger sets with scattered items, but only when the sets were in the large number range (10 vs. 5 food items). Finally, in Experiment 3 fish preferred numerically smaller sets with large-sized and scattered food items in the large number range sets. We conclude that food item number, density, and size may not be considered individually by angelfish, but instead, the fish respond to all these factors attempting to maximize energy gained from eating the food while minimizing energy expenditure collecting and/or protecting the food.

Use of numerical and spatial information in ordinal counting by zebrafish

The use of non-symbolic numerical information is widespread throughout the animal kingdom, providing adaptive benefits in several ecological contexts. Here we provide the possible evidence of ordinal numerical skills in zebrafish (Danio rerio). Zebrafish were trained to identify the second exit in a series of five identically-spaced exits along a corridor. When at test the total length of the corridor (Exp. 1) or the distance between exits (Exp. 2) was changed, zebrafish appeared not to use the absolute spatial distance. However, zebrafish relied both on ordinal as well as spatial cues when the number of exits was increased (from 5 to 9) and the inter-exit distance was reduced (Exp. 3), suggesting that they also take into account relative spatial information. These results highlight that zebrafish may provide a useful model organism for the study of the genetic bases of non-symbolic numerical and spatial cognition, and of their interaction.

The role of item size on choosing contrasted food quantities in angelfish (Pterophyllum scalare)

Comparative studies on quantity discrimination in animals are important for understanding potential evolutionary roots of numerical competence. A previous study with angelfish has shown that they discriminate numerically different sets of same-sized food items and prefer the larger set. However, variables that covary with number were not controlled and choice could have been influenced by variables such as size or density of the food items rather than numerical attributes. Here using a recently developed approach, we examined whether contour length of the food items affects choice in a spontaneous binary choice task. In Experiment 1, a contrast of 1 vs. 1 food item was presented, but the ratio between the size (diameter) of the food items was varied. In Experiment 2, numerically different food sets were equated in overall size by increasing the size (diameter) of the items in the numerically small sets. In both Experiments, subjects showed a preference for the larger sized food items with a discrimination limit. These results show that item size plays a prominent role in foraging decisions in angelfish. Experiment 3 placed numerical and size attributes of the sets in conflict by presenting one larger-sized food item in the numerically smaller set that also had smaller overall size (diameter) of food items. Angelfish showed no preference in any of the contrasts, suggesting that they could not make optimal foraging decisions when these attributes were in conflict. Maximization of energy return is central to optimal foraging. Accordingly, here item size was also found to be a key feature of the sets, although the numerical attributes of the sets also influenced the choice.

Surpassing the subitizing threshold: appetitive–aversive conditioning improves discrimination of numerosities in honeybees

Animals including humans, fish and honeybees have demonstrated a quantity discrimination threshold at four objects, often known as subitizing elements. Discrimination between numerosities at or above the subitizing range is considered a complex capacity. In the current study, we trained and tested two groups of bees on their ability to differentiate between quantities (4 versus 5 through to 4 versus 8) when trained with different conditioning procedures. Bees trained with appetitive (reward) differential conditioning demonstrated no significant learning of this task, and limited discrimination above the subitizing range. In contrast, bees trained using appetitive–aversive (reward–aversion) differential conditioning demonstrated significant learning and subsequent discrimination of all tested comparisons from 4 versus 5 to 4 versus 8. Our results show conditioning procedure is vital to performance on numerically challenging tasks, and may inform future research on numerical abilities in other animals.

Impact of stimulus format and reward value on quantity discrimination in capuchin and squirrel monkeys

Quantity discrimination abilities are seen in a diverse range of species with similarities in performance patterns, suggesting common underlying cognitive mechanisms. However, methodological factors that impact performance make it difficult to draw broad phylogenetic comparisons of numerical cognition across studies. For example, some Old World monkeys selected a higher quantity stimulus more frequently when choosing between inedible (pebbles) than edible (food) stimuli. In Experiment 1 we presented brown capuchin (Cebus [Sapajus] paella) and squirrel monkeys (Saimiri sciureus) with the same two-choice quantity discrimination task in three different stimulus conditions: edible, inedible, and edible replaced (in which choice stimuli were food items that stood in for the same quantity of food items that were given as a reward). Unlike Old World monkeys, capuchins selected the higher quantity stimulus more in the edible condition and squirrel monkeys showed generally poor performance across all stimulus types. Performance patterns suggested that differences in subjective reward value might motivate differences in choice behavior between and within species. In Experiment 2 we manipulated the subjective reinforcement value of the reward by varying reward type and delay to reinforcement and found that delay to reinforcement had no impact on choice behavior, while increasing the value of the reward significantly improved performance by both species. The results of this study indicate that species presented with identical tasks may respond differently to methodological factors such as stimulus and reward types, resulting in significant differences in choice behavior that may lead to spurious suggestions of species differences in cognitive abilities.

Chimpanzees' understanding of social leverage

Social primates can influence others through the control of resources. For instance, dominant male chimpanzees might allow subordinates access to mate with females in exchange for social support. However, little is known about how chimpanzees strategically use a position of leverage to maximize their own benefits. We address this question by presenting dyads of captive chimpanzee (N = 6) with a task resulting in an unequal reward distribution. To gain the higher reward each individual should wait for their partner to act. In addition, one participant had leverage: access to an alternative secure reward. By varying the presence and value of the leverage we tested whether individuals used it strategically (e.g. by waiting longer for partners to act when they had leverage in the form of alternatives). Additionally, non-social controls served to show if chimpanzees understood the social dilemma. We measured the likelihood to choose the leverage and their latencies to act. The final decision made by the chimpanzees did not differ as a function of condition (test versus non-social control) or the value of the leverage, but they did wait longer to act when the leverage was smaller—particularly in test (versus non-social control) trials suggesting that they understood the conflict of interest involved. The chimpanzees thus recognized the existence of social leverage, but did not use it strategically to maximize their rewards.

Comparing chimpanzees' preparatory responses to known and unknown future outcomes

When humans plan for the future, we recognize not only that one particular event may occur, but that the future can have different, mutually exclusive possible outcomes. A recent study by Suddendorf et al (Suddendorf 2017 Biol. Lett. 13, 20170170 (doi:10.1098/rsbl.2017.0170)) suggests that young children (less than 3 years) and apes lack this capacity, as demonstrated by their failure to cover each of two tube openings to ensure catching an object that would drop randomly from one of the tubes. Before drawing conclusions based on these negative results, however, it is important to assess subjects' failures and test the reliability of the task itself. To explore whether the apes' performance resulted from an inability to represent mutually exclusive futures or from extraneous factors related to the task, we replicated the methods of Suddendorf et al (Suddendorf 2017 Biol. Lett. 13, 20170170 (doi:10.1098/rsbl.2017.0170)) with a group of six chimpanzees but included a key control condition in which subjects were expected to cover both tubes on every trial (i.e. the rewards would consistently emerge from both tubes). We show that even in this straightforward condition in which the outcome of the trial was known, only four of the six subjects ever covered both tubes, typically doing so after a minimum of 17 trials, and often reverting back to covering one tube on later trials. We conclude that this task is not valid for testing the ability to represent mutually exclusive futures. We discuss what potential factors may explain the results and outline a new suggested method to continue testing for this capacity in the future.

Numerical assessment in the wild: insights from social carnivores

Playback experiments have proved to be a useful tool to investigate the extent to which wild animals understand numerical concepts and the factors that play into their decisions to respond to different numbers of vocalizing conspecifics. In particular, playback experiments have broadened our understanding of the cognitive abilities of historically understudied species that are challenging to test in the traditional laboratory, such as members of the Order Carnivora. Additionally, playback experiments allow us to assess the importance of numerical information versus other ecologically important variables when animals are making adaptive decisions in their natural habitats. Here, we begin by reviewing what we know about quantity discrimination in carnivores from studies conducted in captivity. We then review a series of playback experiments conducted with wild social carnivores, including African lions, spotted hyenas and wolves, which demonstrate that these animals can assess the number of conspecifics calling and respond based on numerical advantage. We discuss how the wild studies complement those conducted in captivity and allow us to gain insights into why wild animals may not always respond based solely on differences in quantity. We then consider the key roles that individual discrimination and cross-modal recognition play in the ability of animals to assess the number of conspecifics vocalizing nearby. Finally, we explore new directions for future research in this area, highlighting in particular the need for further work on the cognitive basis of numerical assessment skills and experimental paradigms that can be effective in both captive and wild settings.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.

Why Cross-Cultural Psychology Is Incomplete Without Comparative and Developmental Perspectives

We argue that comparing adult behavior and cognition across cultures is insufficient to capture the multifaceted complexity of cultural variation. We champion a multidisciplinary perspective that draws on biological and psychological theory and methods. We provide examples for ways in which cross-cultural, developmental, and comparative studies might be combined to unravel the interplay between universal species-typical behaviors and behavioral variation across groups and, at the same time, to explain uniquely human cultural diversity by identifying the unique and universal patterns of human behavior and cognition in early childhood that create, structure, and maintain variation across groups. Such a perspective adds depth to explanations of cultural variation and universality and firmly roots accounts of human culture in a broader, biological framework. We believe that, therefore, the field of cross-cultural psychology may benefit from combining efforts with comparative and developmental psychologists.

Is There Really an Evolved Capacity for Number?

Humans and other species have biologically endowed abilities for discriminating quantities. A widely accepted view sees such abilities as an evolved capacity specific for number and arithmetic. This view, however, is based on an implicit teleological rationale, builds on inaccurate conceptions of biological evolution, downplays human data from non-industrialized cultures, overinterprets results from trained animals, and is enabled by loose terminology that facilitates teleological argumentation. A distinction between quantical (e.g., quantity discrimination) and numerical (exact, symbolic) cognition is needed: quantical cognition provides biologically evolved preconditions for numerical cognition but it does not scale up to number and arithmetic, which require cultural mediation. The argument has implications for debates about the origins of other special capacities - geometry, music, art, and language.

Spatial Arrangement and Set Size Influence the Coding of Non-symbolic Quantities in the Intraparietal Sulcus

Performance in visual quantification tasks shows two characteristic patterns as a function of set size. A precise subitizing process for small sets (up to four) was contrasted with an approximate estimation process for larger sets. The spatial arrangement of elements in a set also influences visual quantification performance, with frequently perceived arrangements (e.g., dice patterns) being faster enumerated than random arrangements. Neuropsychological and imaging studies identified the intraparietal sulcus (IPS), as key brain area for quantification, both within and above the subitizing range. However, it is not yet clear if and how set size and spatial arrangement of elements in a set modulate IPS activity during quantification. In an fMRI study, participants enumerated briefly presented dot patterns with random, canonical or dice arrangement within and above the subitizing range. We evaluated how activity amplitude and pattern in the IPS were influenced by size and spatial arrangement of a set. We found a discontinuity in the amplitude of IPS response between subitizing and estimation range, with steep activity increase for sets exceeding four elements. In the estimation range, random dot arrangements elicited stronger IPS response than canonical arrangements which in turn elicited stronger response than dice arrangements. Furthermore, IPS activity patterns differed systematically between arrangements. We found a signature in the IPS response for a transition between subitizing and estimation processes during quantification. Differences in amplitude and pattern of IPS activity for different spatial arrangements indicated a more precise representation of non-symbolic numerical magnitude for dice and canonical than for random arrangements. These findings challenge the idea of an abstract coding of numerosity in the IPS even within a single notation.

Capuchin monkeys (Cebus apella) treat small and large numbers of items similarly during a relative quantity judgment task

A key issue in understanding the evolutionary and developmental emergence of numerical cognition is to learn what mechanism(s) support perception and representation of quantitative information. Two such systems have been proposed, one for dealing with approximate representation of sets of items across an extended numerical range and another for highly precise representation of only small numbers of items. Evidence for the first system is abundant across species and in many tests with human adults and children, whereas the second system is primarily evident in research with children and in some tests with non-human animals. A recent paper (Choo & Franconeri, Psychonomic Bulletin & Review, 21, 93-99, 2014) with adult humans also reported "superprecise" representation of small sets of items in comparison to large sets of items, which would provide more support for the presence of a second system in human adults. We first presented capuchin monkeys with a test similar to that of Choo and Franconeri in which small or large sets with the same ratios had to be discriminated. We then presented the same monkeys with an expanded range of comparisons in the small number range (all comparisons of 1-9 items) and the large number range (all comparisons of 10-90 items in 10-item increments). Capuchin monkeys showed no increased precision for small over large sets in making these discriminations in either experiment. These data indicate a difference in the performance of monkeys to that of adult humans, and specifically that monkeys do not show improved discrimination performance for small sets relative to large sets when the relative numerical differences are held constant.

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.

Quantity discrimination in angelfish (Pterophyllum scalare) is maintained after a 30-s retention interval in the large but not in the small number range

The ability to discriminate between sets that differ in the number of elements can be useful in different contexts and may have survival and fitness consequences. As such, numerical/quantity discrimination has been demonstrated in a diversity of animal species. In the laboratory, this ability has been analyzed, for example, using binary choice tests. Furthermore, when the different number of items first presented to the subjects are subsequently obscured, i.e., are not visible at the moment of making a choice, the task requires memory for the size of the sets. In previous work, angelfish (Pterophyllum scalare) have been found to be able to discriminate shoals differing in the number of shoal members both in the small (less than 4) and the large (4 or more) number range, and they were able to perform well even when a short memory retention interval (2-15 s) was imposed. In the current study, we increased the retention interval to 30 s during which the shoals to choose between were obscured, and investigated whether angelfish could show preference for the larger shoal they saw before this interval. Subjects were faced with a discrimination between numerically small shoals (≤4 fish) and also between numerically large (≥4 fish) shoals of conspecifics. We found angelfish not to be able to remember the location of larger versus smaller shoals in the small number range, but to exhibit significant memory for the larger shoal in the large number range as long as the ratio between these shoals was at least 2:1. These results, together with prior findings, suggest the existence of two separate quantity estimation systems, the object file system for small number of items that does not work with the longer retention interval and the analogue magnitude system for larger number of items that does.

Quantitative abilities in a reptile (Podarcis sicula)

The ability to identify the largest amount of prey available is fundamental for optimizing foraging behaviour in several species. To date, this cognitive skill has been observed in all vertebrate groups except reptiles. In this study we investigated the spontaneous ability of ruin lizards to select the larger amount of food items. In Experiment 1, lizards proved able to select the larger food item when presented with two alternatives differing in size (0.25, 0.50, 0.67 and 0.75 ratio). In Experiment 2 lizards presented with two groups of food items (1 versus 4, 2 versus 4, 2 versus 3 and 3 versus 4 items) were unable to select the larger group in any contrast. The lack of discrimination in the presence of multiple items represents an exception in numerical cognition studies, raising the question as to whether reptiles' quantitative abilities are different from those of other vertebrate groups.

Understanding the origin of number sense: a review of fish studies

The ability to use quantitative information is thought to be adaptive in a wide range of ecological contexts. For nearly a century, the numerical abilities of mammals and birds have been extensively studied using a variety of approaches. However, in the last two decades, there has been increasing interest in investigating the numerical abilities of teleosts (i.e. a large group of ray-finned fish), mainly due to the practical advantages of using fish species as models in laboratory research. Here, we review the current state of the art in this field. In the first part, we highlight some potential ecological functions of numerical abilities in fish and summarize the existing literature that demonstrates numerical abilities in different fish species. In many cases, surprising similarities have been reported among the numerical performance of mammals, birds and fish, raising the question as to whether vertebrates' numerical systems have been inherited from a common ancestor. In the second part, we will focus on what we still need to investigate, specifically the research fields in which the use of fish would be particularly beneficial, such as the genetic bases of numerical abilities, the development of these abilities and the evolutionary foundation of vertebrate number sense.This article is part of a discussion meeting issue 'The origins of numerical abilities'.

Primitive Concepts of Number and the Developing Human Brain

Counting is an evolutionarily recent cultural invention of the human species. In order for humans to have conceived of counting in the first place, certain representational and logical abilities must have already been in place. The focus of this review is the origins and nature of those fundamental mechanisms that promoted the emergence of the human number concept. Five claims are presented that support an evolutionary view of numerical development: 1) number is an abstract concept with an innate basis in humans, 2) maturational processes constrain the development of humans' numerical representations between infancy and adulthood, 3) there is evolutionary continuity in the neural processes of numerical cognition in primates, 4) primitive logical abilities support verbal counting development in humans, and 5) primitive neural processes provide the foundation for symbolic numerical development in the human brain. We support these claims by examining current evidence from animal cognition, child development, and human brain function. The data show that at the basis of human numerical concepts are primitive perceptual and logical mechanisms that have evolutionary homologs in other primates and form the basis of numerical development in the human brain. In the final section of the review, we discuss some hypotheses for what makes human numerical reasoning unique by drawing on evidence from human and non-human primate neuroimaging research.

Numerosity representations in crows obey the Weber-Fechner law

The ability to estimate number is widespread throughout the animal kingdom. Based on the relative close phylogenetic relationship (and thus equivalent brain structures), non-verbal numerical representations in human and non-human primates show almost identical behavioural signatures that obey the Weber-Fechner law. However, whether numerosity discriminations of vertebrates with a very different endbrain organization show the same behavioural signatures remains unknown. Therefore, we tested the numerical discrimination performance of two carrion crows (Corvus corone) to a broad range of numerosities from 1 to 30 in a delayed match-to-sample task similar to the one used previously with primates. The crows' discrimination was based on an analogue number system and showed the Weber-fraction signature (i.e. the 'just noticeable difference' between numerosity pairs increased in proportion to the numerical magnitudes). The detailed analysis of the performance indicates that numerosity representations in crows are scaled on a logarithmically compressed 'number line'. Because the same psychophysical characteristics are found in primates, these findings suggest fundamentally similar number representations between primates and birds. This study helps to resolve a classical debate in psychophysics: the mental number line seems to be logarithmic rather than linear, and not just in primates, but across vertebrates.

Short-Term Memory Effects on Crossing the Boundary: Discrimination between Large and Small Quantities in Angelfish (Pterophyllum scalare)

Rudimentary quantification abilities are found in numerous animal species and in human infants all demonstrating the ability to discriminate between quantities differing in numerical size. An open question is whether individuals rely on different underlying systems to discriminate between large (analogue magnitude system (AMS) for number of items exceeding 3) and small quantities (object-file system (OFS) for number of items below 4), or they use only one system (AMS) for the entire number range. The two-system hypothesis has been supported by finding reduced ability to discriminate between quantities that cross the large-small boundary in several species. Recently, the role of cognitive representation, i.e., memory, in quantity discrimination has also been recognized. Here, we investigated whether angelfish can discriminate quantities across the boundary under two memory conditions. In a binary choice test, single angelfish were allowed to see groups (shoals) of conspecifics of different numerical size on the two sides of their test tank. In Experiment 1, their choice was recorded after a 2-sec retention interval during which shoal size information was unavailable. Angelfish were able to discriminate the larger shoal across the boundary when the shoals differed by a 2:1 or higher ratio, but not when the ratio was lower. In Experiment 2, however, with a 15-sec retention interval, angelfish could only detect a four-fold difference in ratio but failed to detect a three- or a two-fold difference across the boundary. These results suggest that angelfish can remember smaller differences for a short (2 sec) but not for a longer (15 sec) period. Together with previous findings, the current results support the idea that angelfish use two distinct systems for representing quantity, but they may recruit the AMS even for the small number range under some circumstances, e.g., when higher memory demand is imposed by a greater retention interval.

Experimental setting affects the performance of guppies in a numerical discrimination task

A recent study found that guppies (Poecilia reticulata) can be trained to discriminate 4 versus 5 objects, a numerical discrimination typically achieved only by some mammals and birds. In that study, guppies were required to discriminate between two patches of small objects on the bottom of the tank that they could remove to find a food reward. It is not clear whether this species possesses exceptional numerical accuracy compared with the other ectothermic vertebrates or whether its remarkable performance was due to a specific predisposition to discriminate between differences in the quality of patches while foraging. To disentangle these possibilities, we trained guppies to the same numerical discriminations with a more conventional two-choice discrimination task. Stimuli were sets of dots presented on a computer screen, and the subjects received a food reward upon approaching the set with the larger numerosity. Though the cognitive problem was identical in the two experiments, the change in the experimental setting led to a much poorer performance as most fish failed even the 2 versus 3 discrimination. In four additional experiments, we varied the duration of the decision time, the type of stimuli, the length of training, and whether correction was allowed in order to identify the factors responsible for the difference. None of these parameters succeeded in increasing the performance to the level of the previous study, although the group trained with three-dimensional stimuli learned the easiest numerical task. We suggest that the different results with the two experimental settings might be due to constraints on learning and that guppies might be prepared to accurately estimate patch quality during foraging but not to learn an abstract stimulus-reward association.