Putting the elephant back in the herd: elephant relative quantity judgments match those of other species

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.

Visual number sense for real-world scenes shared by deep neural networks and humans

Recently, visual number sense has been identified from deep neural networks (DNNs). However, whether DNNs have the same capacity for real-world scenes, rather than the simple geometric figures that are often tested, is unclear. In this study, we explore the number perception of scenes using AlexNet and find that numerosity can be represented by the pattern of group activation of the category layer units. The global activation of these units increases with the number of objects in the scene, and the variations in their activation decrease accordingly. By decoding the numerosity from this pattern, we reveal that the embedding coefficient of a scene determines the likelihood of potential objects to contribute to numerical perception. This was demonstrated by the more optimized performance for pictures with relatively high embedding coefficients in both DNNs and humans. This study for the first time shows that a distinct feature in visual environments, revealed by DNNs, can modulate human perception, supported by a group-coding mechanism.

Passive Grouping Enhances Proto-Arithmetic Calculation for Leftward Correct Responses

Baby chicks and other animals including human infants master simple arithmetic. They discriminate 2 vs. 3 (1 + 1 vs. 1 + 1 + 1) but fail with 3 vs. 4 (1 + 1 + 1 vs. 1 + 1 + 1 + 1). Performance is restored when elements are grouped as 2 + 1 vs. 2 + 2. Here, we address whether grouping could lead to asymmetric response bias. We recoded behavioural data from a previous study, in which separate groups of four-day-old domestic chicks underwent an arithmetic task: when the objects were presented one-by-one (1 + 1 + 1 vs. 1 + 1 + 1 + 1), chicks failed in locating the larger group irrespective of its position and did not show any side bias; Experiment 1. When the objects were presented as grouped (2 + 1 vs. 2 + 2), chicks succeeded, performing better when the larger set was on their left; Experiment 2. A similar leftward bias was also observed with harder discriminations (4 vs. 5: 3  +  1 vs. 3  +  2), with baby chicks succeeding in the task only when the larger set was on the left (Experiments 3 and 4). A previous study showed a rightward bias, with tasks enhancing individual processing. Despite a similar effect in boosting proto-arithmetic calculations, individual processing (eliciting a right bias) and grouping (eliciting a left bias) seem to depend on distinct cognitive mechanisms.

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.

Characterizing ontogeny of quantity discrimination in zebrafish

A sense of non-symbolic numerical magnitudes is widespread in the animal kingdom and has been documented in adult zebrafish. Here, we investigated the ontogeny of this ability using a group size preference (GSP) task in juvenile zebrafish. Fish showed GSP from 21 days post-fertilization and reliably chose the larger group when presented with discriminations of between 1 versus 3, 2 versus 5 and 2 versus 3 conspecifics but not 2 versus 4 conspecifics. When the ratio between the number of conspecifics in each group was maintained at 1 : 2, fish could discriminate between 1 versus 2 individuals and 3 versus 6, but again, not when given a choice between 2 versus 4 individuals. These findings are in agreement with studies in other species, suggesting the systems involved in quantity representation do not operate separately from other cognitive mechanisms. Rather they suggest quantity processing in fishes may be the result of an interplay between attentional, cognitive and memory-related mechanisms as in humans and other animals. Our results emphasize the potential of the use of zebrafish to explore the genetic and neural processes underlying the ontogeny and function of number cognition.

Archerfish number discrimination

Debates have arisen as to whether non-human animals actually can learn abstract non-symbolic numerousness or whether they always rely on some continuous physical aspect of the stimuli, covarying with number. Here, we investigated archerfish (Toxotes jaculatrix) non-symbolic numerical discrimination with accurate control for covarying continuous physical stimulus attributes. Archerfish were trained to select one of two groups of black dots (Exp. 1: 3 vs 6 elements; Exp. 2: 2 vs 3 elements); these were controlled for several combinations of physical variables (elements' size, overall area, overall perimeter, density, and sparsity), ensuring that only numerical information was available. Generalization tests with novel numerical comparisons (2 vs 3, 5 vs 8, and 6 vs 9 in Exp. 1; 3 vs 4, 3 vs 6 in Exp. 2) revealed choice for the largest or smallest numerical group according to the relative number that was rewarded at training. None of the continuous physical variables, including spatial frequency, were affecting archerfish performance. Results provide evidence that archerfish spontaneously use abstract relative numerical information for both small and large numbers when only numerical cues are available.

Neurons in the Dorso-Central Division of Zebrafish Pallium Respond to Change in Visual Numerosity

We found a region of the zebrafish pallium that shows selective activation upon change in the numerosity of visual stimuli. Zebrafish were habituated to sets of small dots that changed in individual size, position, and density, while maintaining their numerousness and overall surface. During dishabituation tests, zebrafish faced a change in number (with the same overall surface), in shape (with the same overall surface and number), or in size (with the same shape and number) of the dots, whereas, in a control group, zebrafish faced the same stimuli as during the habituation. Modulation of the expression of the immediate early genes c-fos and egr-1 and in situ hybridization revealed a selective activation of the caudal part of the dorso-central division of the zebrafish pallium upon change in numerosity. These findings support the existence of an evolutionarily conserved mechanism for approximate magnitude and provide an avenue for understanding its underlying molecular correlates.

Cooperating elephants mitigate competition until the stakes get too high

Cooperation is ubiquitous in the animal kingdom as it aims to maximize benefits through joint action. Selection, however, may also favor competitive behaviors that could violate cooperation. How animals mitigate competition is hotly debated, with particular interest in primates and little attention paid thus far to nonprimates. Using a loose-string pulling apparatus, we explored cooperative and competitive behavior, as well as mitigation of the latter, in semi-wild Asian elephants (Elephas maximus). Our results showed that elephants first maintained a very high cooperation rate (average = 80.8% across 45 sessions). Elephants applied “block,” “fight back,” “leave,” “move side,” and “submission” as mitigation strategies and adjusted these strategies according to their affiliation and rank difference with competition initiators. They usually applied a “fight back” mitigation strategy as a sanction when competition initiators were low ranking or when they had a close affiliation, but were submissive if the initiators were high ranking or when they were not closely affiliated. However, when the food reward was limited, the costly competitive behaviors (“monopoly” and “fight”) increased significantly, leading to a rapid breakdown in cooperation. The instability of elephant cooperation as a result of benefit reduction mirrors that of human society, suggesting that similar fundamental principles may underlie the evolution of cooperation across species.

This study shows that in a task requiring coordinated pulling, elephants compete for access to food but work to mitigate competition in order to maintain cooperation. If the cost of competition becomes too high, however, cooperation breaks down entirely. This behavior mirrors that seen in humans and other great apes, suggesting that certain cooperative mechanisms are not unique to primates.

The Evolutionary History of Brains for Numbers

Humans and other animals share a number sense', an intuitive understanding of countable quantities. Having evolved independent from one another for hundreds of millions of years, the brains of these diverse species, including monkeys, crows, zebrafishes, bees, and squids, differ radically. However, in all vertebrates investigated, the pallium of the telencephalon has been implicated in number processing. This suggests that properties of the telencephalon make it ideally suited to host number representations that evolved by convergent evolution as a result of common selection pressures. In addition, promising candidate regions in the brains of invertebrates, such as insects, spiders, and cephalopods, can be identified, opening the possibility of even deeper commonalities for number sense.

Numerosities and Other Magnitudes in the Brains: A Comparative View

The ability to represent, discriminate, and perform arithmetic operations on discrete quantities (numerosities) has been documented in a variety of species of different taxonomic groups, both vertebrates and invertebrates. We do not know, however, to what extent similarity in behavioral data corresponds to basic similarity in underlying neural mechanisms. Here, we review evidence for magnitude representation, both discrete (countable) and continuous, following the sensory input path from primary sensory systems to associative pallial territories in the vertebrate brains. We also speculate on possible underlying mechanisms in invertebrate brains and on the role played by modeling with artificial neural networks. This may provide a general overview on the nervous system involvement in approximating quantity in different animal species, and a general theoretical framework to future comparative studies on the neurobiology of number cognition.

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.

Giraffes go for more: a quantity discrimination study in giraffes (Giraffa camelopardalis)

Many species, including humans, rely on an ability to differentiate between quantities to make decisions about social relationships, territories, and food. This study is the first to investigate whether giraffes (Giraffa camelopardalis) are able to select the larger of two sets of quantities in different conditions, and how size and density affect these decisions. In Task 1, we presented five captive giraffes with two sets containing a different quantity of identical foods items. In Tasks 2 and 3, we also modified the size and density of the food reward distribution. The results showed that giraffes (i) can successfully make quantity judgments following Weber's law, (ii) can reliably rely on size to maximize their food income, and (iii) are more successful when comparing sparser than denser distributions. More studies on different taxa are needed to understand whether specific selective pressures have favored the evolution of these skills in certain taxa.

Food quantity discrimination in puppies (Canis lupus familiaris)

There is considerable evidence that animals are able to discriminate between quantities. Despite the fact that quantitative skills have been extensively studied in adult individuals, research on their development in early life is restricted to a limited number of species. We, therefore, investigated whether 2-month-old puppies could spontaneously discriminate between different quantities of food items. We used a simultaneous two-choice task in which puppies were presented with three numerical combinations of pieces of food (1 vs. 8, 1 vs. 6 and 1 vs. 4), and they were allowed to select only one option. The subjects chose the larger of the two quantities in the 1 vs. 8 and the 1 vs. 6 combinations but not in the 1 vs. 4 combination. Furthermore, the last quantity the puppies looked at before making their choice and the time spent looking at the larger/smaller amounts of food were predictive of the choices they made. Since adult dogs are capable of discriminating between more difficult numerical contrasts when tested with similar tasks, our findings suggest that the capacity to discriminate between quantities is already present at an early age, but that it is limited to very easy discriminations.

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.

Motion Illusions as Environmental Enrichment for Zoo Animals: A Preliminary Investigation on Lions (Panthera leo)

Investigating perceptual and cognitive abilities of zoo animals might help to improve their husbandry and enrich their daily life with new stimuli. Developing new environmental enrichment programs and devices is hence necessary to promote species-specific behaviors that need to be maintained in controlled environments. As far as we are aware, no study has ever tested the potential benefits of motion illusions as visual enrichment for zoo animals. Starting from a recent study showing that domestic cats are spontaneously attracted by a well-known motion illusion, the Rotating Snake (RS) illusion, we studied whether this illusion could be used as a visual enrichment for big cats. We observed the spontaneous behavior of three lionesses when three different visual stimuli were placed in their environment: the RS illusion and two control stimuli. The study involved two different periods: the baseline and the RS period, in which the visual stimuli were provided to the lionesses. To assess whether the lionesses were specifically attracted by the RS illusion, we collected data on the number of interactions with the stimuli, as well as on the total time spent interacting with them. To investigate the effect of the illusion on the animals' welfare, individual and social behaviors were studied, and compared between the two periods. The results showed that two lionesses out of three interacted more with the RS stimulus than with the two control stimuli. The fact that the lionesses seemed to be more inclined to interact with the RS stimulus indirectly suggests the intriguing possibility that they were attracted by the illusory motion. Moreover, behavioral changes between the two periods were reported for one of the lionesses, highlighting a reduction in self-directed behaviors and an increase in attentive behaviors, and suggesting positive welfare implications. Thus, behavioral observations made before and during the presentation of the stimuli showed that our visual enrichment actually provided positive effects in lionesses. These results call for the development of future studies on the use of visual illusions in the enrichment programs of zoo animals.

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.

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'.

Quantity Discrimination in Trained Lizards (Podarcis sicula)

Quantitative abilities have been reported in many animal species. Two main methods have been extensively used: spontaneous choice tests and training procedures. A recent study showed that ruin lizards are capable of spontaneously discriminating between the surface area of two food items of different size, but failed when food was presented in sets of discrete items differing in number. In the present study, we used a training procedure to further investigate quantitative abilities in ruin lizards. Subjects were presented with two sets of yellow disks differing either in number (Experiment 1) or in area (Experiment 2) and were trained on different discriminations of increasing difficulty (1 vs. 4, 2 vs. 4, and 2 vs. 3). Results showed that lizards were more accurate in discriminating sets of discrete items differing in number than the area of two individual items, in contrast to what had earlier been observed in spontaneous choice tests. Although we cannot exclude other factors that affected the performance of ruin lizards, the poor accuracy here observed in both experiments might reflect a true limit in lizards' quantitative abilities.

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.

Quantity discrimination in canids: Dogs (Canis familiaris) and wolves (Canis lupus) compared

Accumulating evidence indicates that animals are able to discriminate between quantities. Recent studies have shown that dogs' and coyotes' ability to discriminate between quantities of food items decreases with increasing numerical ratio. Conversely, wolves' performance is not affected by numerical ratio. Cross-species comparisons are difficult because of differences in the methodologies employed, and hence it is still unclear whether domestication altered quantitative abilities in canids. Here we used the same procedure to compare pet dogs and wolves in a spontaneous food choice task. Subjects were presented with two quantities of food items and allowed to choose only one option. Four numerical contrasts of increasing difficulty (range 1-4) were used to assess the influence of numerical ratio on the performance of the two species. Dogs' accuracy was affected by numerical ratio, while no ratio effect was observed in wolves. These results align with previous findings and reinforce the idea of different quantitative competences in dogs and wolves. Although we cannot exclude that other variables might have played a role in shaping quantitative abilities in these two species, our results might suggest that the interspecific differences here reported may have arisen as a result of domestication.

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.

Cross-Modal Correspondences in Non-human Mammal Communication

For both humans and other animals, the ability to combine information obtained through different senses is fundamental to the perception of the environment. It is well established that humans form systematic cross-modal correspondences between stimulus features that can facilitate the accurate combination of sensory percepts. However, the evolutionary origins of the perceptual and cognitive mechanisms involved in these cross-modal associations remain surprisingly underexplored. In this review we outline recent comparative studies investigating how non-human mammals naturally combine information encoded in different sensory modalities during communication. The results of these behavioural studies demonstrate that various mammalian species are able to combine signals from different sensory channels when they are perceived to share the same basic features, either because they can be redundantly sensed and/or because they are processed in the same way. Moreover, evidence that a wide range of mammals form complex cognitive representations about signallers, both within and across species, suggests that animals also learn to associate different sensory features which regularly co-occur. Further research is now necessary to determine how multisensory representations are formed in individual animals, including the relative importance of low level feature-related correspondences. Such investigations will generate important insights into how animals perceive and categorise their environment, as well as provide an essential basis for understanding the evolution of multisensory perception in humans.

Quantity Discrimination in Domestic Rats, Rattus norvegicus

Simple Summary

Quantity discrimination involves distinguishing which of two quantities is greater. This discrimination between larger and smaller quantities has only been demonstrated in rats post extensive training. We tested whether domestic rats could perform quantity discrimination without explicit training. We found that rats could distinguish the greater amount in comparisons of 1 vs. 2, 2 vs. 3, 3 vs. 5, 3 vs. 8, 4 vs. 6, and 4 vs. 8. Rats could not distinguish between 3 vs. 4, 4 vs. 5 and 5 vs. 6. We also found that as the ratio between quantities became finer the choice of the larger quantity decreased. We conclude that rats can perform quantity discrimination without extensive training and that their quantity discrimination ability is influenced by the ratio between quantities.

Abstract

Quantity discrimination is a basic form of numerical competence where an animal distinguishes which of two amounts is greater in size. Whilst quantity discrimination in rats has been investigated via training paradigms, rats’ natural quantity discrimination abilities without explicit training for a desired response have not been explored. This study investigated domestic rats’ ability to perform quantity discrimination. Domestic rats (n = 12) were examined for their ability to distinguish the larger amount under nine quantity comparisons. One-sample t-tests identified a significant preference for the larger quantity in comparisons of 1 vs. 2, 2 vs. 3, 3 vs. 5, 3 vs. 8, 4 vs. 6, and 4 vs. 8. No preference between quantities was found for comparisons of 3 vs. 4, 4 vs. 5 and 5 vs. 6. Overall, this study drew two key conclusions. Firstly, that domestic rats are capable of performing quantity discrimination without extensive training. Secondly, as subjects adhered to Weber’s law, it was concluded that the approximate number system underpins domestic rats’ ability to perform spontaneous quantity discrimination.

Abstract numerical discrimination learning in rats

In this study, we examined rats' discrimination learning of the numerical ordering positions of objects. In Experiments 1 and 2, five out of seven rats successfully learned to respond to the third of six identical objects in a row and showed reliable transfer of this discrimination to novel stimuli after being trained with three different training stimuli. In Experiment 3, the three rats from Experiment 2 continued to be trained to respond to the third object in an object array, which included an odd object that needed to be excluded when identifying the target third object. All three rats acquired this selective-counting task of specific stimuli, and two rats showed reliable transfer of this selective-counting performance to test sets of novel stimuli. In Experiment 4, the three rats from Experiment 3 quickly learned to respond to the third stimulus in object rows consisting of either six identical or six different objects. These results offer strong evidence for abstract numerical discrimination learning in rats.

What counts for dogs (Canis lupus familiaris) in a quantity discrimination task?

Numerous studies have reported that animals reliably discriminate quantities of more or less food. However, little attention has been given to the relative salience of numerosity compared to the total amount of food when animals are making their choices. Here we investigated this issue in dogs. Dogs were given choices between two quantities of food items in three different conditions. In the Congruent condition, the total amount of food co-varied with the number of food items; in the Incongruent condition the total amount was pitted against the numerosity; and in the Controlled condition the total amount between the sets was equal. Results show that dogs based their choice on the total amount of edible food rather than on the number of food items, suggesting that, in food choice tasks, amount counts more than number. The presence of the largest individual item in a set did not bias dogs' choices. A control test excluded the possibility that dogs based their choices on olfactory cues alone.

Non-visual numerical discrimination in a blind cavefish (Phreatichthys andruzzii)

Over a decade of comparative studies, researchers have found that rudimentary numerical abilities are widespread among vertebrates. While experiments in mammals and birds have employed a variety of stimuli (visual, auditory and tactile), all fish studies involved visual stimuli and it is unknown whether fish can process numbers in other sensory modalities. To fill this gap, we studied numerical abilities in Phreatichthys andruzzii, a blind cave-dwelling species that evolved in the phreatic layer of the Somalia desert. Fish were trained to receive a food reward to discriminate between two groups of objects placed in opposite positions of their home tank. In Experiment 1, subjects learned to discriminate between two and six objects, with stimuli not controlled for non-numerical continuous variables that co-vary with numbers, such as total area occupied by stimuli or density. In Experiment 2, the discrimination was two versus four, with half of the stimuli controlled for continuous quantities and half not controlled for continuous quantities. The subjects discriminated only the latter condition, indicating that they spontaneously used non-numerical information, as other vertebrates tested in similar experiments. In Experiments 3 and 4, cavefish trained from the beginning only with stimuli controlled for continuous quantities proved able to learn the discrimination of quantities based on the sole numerical information. However, their numerical acuity was lower than that reported in other teleost fish tested with visual stimuli.

Difference in quantity discrimination in dogs and wolves

Certain aspects of social life, such as engaging in intergroup conflicts, as well as challenges posed by the physical environment, may facilitate the evolution of quantity discrimination. In lack of excessive comparative data, one can only hypothesize about its evolutionary origins, but human-raised wolves performed well when they had to choose the larger of two sets of 1-4 food items that had been sequentially placed into two opaque cans. Since in such paradigms, the animals never see the entire content of either can, their decisions are thought to rely on mental representation of the two quantities rather than on some perceptual factors such as the overall volume or surface area of the two amounts. By equaling the time that it takes to enter each quantity into the cans or the number of items entered, one can further rule out the possibility that animals simply choose based on the amount of time needed to present the two quantities. While the wolves performed well even in such a control condition, dogs failed to choose the larger one of two invisible quantities in another study using a similar paradigm. Because this disparity could be explained by procedural differences, in the current study, we set out to test dogs that were raised and kept identically as the previously tested wolves using the same set-up and procedure. Our results confirm the former finding that dogs, in comparison to wolves, have inferior skills to represent quantities mentally. This seems to be in line with Frank's (1980) hypothesis suggesting that domestication altered the information processing of dogs. However, as discussed, also alternative explanations may exist.

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.

Trained Quantity Abilities in Horses (Equus caballus): A Preliminary Investigation

Once believed to be a human prerogative, the capacity to discriminate between quantities now has also been reported in several vertebrates. To date, only two studies investigated numerical abilities in horses (Equus caballus) but reported contrasting data. To assess whether horses can be trained to discriminate between quantities, I have set up a new experimental protocol using operant conditioning. One adult female was trained to discriminate between 1 and 4 (Test 1) in three different conditions: non-controlled continuous variables (numerical and continuous quantities that co-vary with number are simultaneously available), 50% controlled continuous variables (intermediate condition), and 100% controlled continuous variables (only numerical information available). The subject learned the discrimination in all conditions, showing the capacity to process numerical information. When presented with a higher numerical ratio (2 vs. 4, Test 2), the subject still discriminated between the quantities but its performance was statistically significant only in the non-controlled condition, suggesting that the subject used multiple cues in presence of a more difficult discrimination. On the whole, the results here reported encourage the use of this experimental protocol as a valid tool to investigate the capacity to process numerical and continuous quantities in horses in future research.

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.

Lemurs and macaques show similar numerical sensitivity

We investigated the precision of the approximate number system (ANS) in three lemur species (Lemur catta, Eulemur mongoz, and Eulemur macaco flavifrons), one Old World monkey species (Macaca mulatta) and humans (Homo sapiens). In Experiment 1, four individuals of each nonhuman primate species were trained to select the numerically larger of two visual arrays on a touchscreen. We estimated numerical acuity by modeling Weber fractions (w) and found quantitatively equivalent performance among all four nonhuman primate species. In Experiment 2, we tested adult humans in a similar procedure, and they outperformed the four nonhuman species but showed qualitatively similar performance. These results indicate that the ANS is conserved over the primate order.

The role of body surface area in quantity discrimination in angelfish (Pterophyllum scalare)

Although some fish species have been shown to be able to discriminate between two groups (shoals) of conspecifics differing in the number of members, most studies have not controlled for continuous variables that covary with number. Previously, using angelfish (Pterophyllum scalare) we started the systematic analysis of the potential influence of such continuous variables, and found that they play different roles in shoal discrimination depending on whether large (≥ 4 fish) or small (<4 fish) shoals were contrasted. Here, we examine the potential role of the overall body surface area of stimulus fish in shoal preference, a prominent variable not yet examined in angelfish. We report that both when numerically large (5 versus 10 fish) and when small (2 versus 3 fish) shoals were contrasted, angelfish were unable to discriminate the numerically different shoals as long as the surface area of the contrasted shoals was equated. Thus, we conclude that body surface may be an important continuous variable in shoal discrimination. This conclusion was further supported by the analysis of preference when shoals of the same numerical size but different body surface area were contrasted. We found subjects to spend significantly more time close to the shoals with the greater overall surface area. Last, we conducted an experiment in which we simultaneously controlled a set of continuous variables, including overall surface area, and found angelfish to use the number of shoal members as a cue only in large shoal contrasts but not in small shoal contrasts. This result suggests the potential existence of different processing systems for large and small numbers in fish.

Female meadow voles, Microtus pennsylvanicus, respond differently to the scent marks of multiple male conspecifics

Many nonhuman animals are capable of discriminating a group or entity containing more objects from one containing less of the same objects. The capacity for making judgments of numerousness may also allow individuals to discriminate between potential mates. Female meadow voles (Microtus pennsylvanicus) may use judgments of relative numerousness to distinguish between potential suitors by selecting males that signal their interest by depositing more scent marks relative to other males. We used a familiarization-discrimination paradigm in the absence of training to test the hypothesis that female voles will discriminate between the different numerosities of scent marks of two male conspecifics that are similar in features of their phenotype and quality. During the exposure phase, we presented female voles with different ratios of feces scent marks from two males. During the test phase, we presented females with a single, fresh fecal scent mark from each of the two male donors, whose marks they had previously encountered during the exposure phase. In both phases, females spent more time investigating the scent mark(s) of the male that deposited more scent marks than that of the male that deposited fewer scent marks provided the difference in the ratio of scent marks provided by the male donors in the exposure phase was ≥2. Our results are consistent with studies on a variety of taxa, suggesting that numerosity discriminations are evolutionarily ancient and spontaneously available to nonhuman animals and humans.

The "Clever Hans Phenomenon" revisited

In the first decade of the 20th century, a horse named Hans drew worldwide attention in Berlin as the first and most famous "speaking" and thinking animal. Hans solved calculations by tapping numbers or letters with his hoof in order to answer questions. Later on, it turned out that the horse was able to give the correct answer by reading the microscopic signals in the face of the questioning person. This observation caused a revolution and as a consequence, experimenters avoided strictly any face-to-face contact in studies about cognitive abilities of animals-a fundamental lesson that is still not applied rigorously.