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

Quantity discrimination by kittens of the domestic cat (Felis silvestris catus)

Quantitative abilities are well described in many species and in diverse life situations, including in the adult domestic cat. However, such abilities have been much less studied during ontogeny. In the present study we examined spontaneous quantity discrimination by pre-weaning age kittens in two-way food choice experiments. In Experiment 1, 26 kittens performed 12 trials with different ratios between the number of same-size food items. In Experiment 2, 24 other kittens performed eight trials with different ratios between the size of two food items. We found, in general, that the kittens discriminated between the different amounts of food and spontaneously chose the larger one, but that their choice was influenced by the ratio of difference. The kittens in Experiment 1 chose the larger number of same-size food items if the ratio was smaller than 0.4 and in Experiment 2 they chose the larger pieces of food if the ratio between the items was smaller than 0.5. Because the kittens' choice was not influenced by the absolute number of food items or the numerical difference between them in Experiment 1, it suggests that their cognitive performance relied on an analog magnitude system rather than on an object file system during the quantity discrimination tasks. We discuss our results considering the ecological and social background of cats and compare it with the performance of previously studied species.

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.

Are you scared yet? Variations to cue indices elicit differential prey behavioral responses even when gape-limited predators are relatively small

Anti-predator behavior is often evoked based on measurements of risk calculated from sensory cues emanating from predators independent of physical attack. Yet, the exact sensory indices of cues utilized in risk assessment remain largely unknown. To examine how different predatory cue indices of information are used in risk assessment, we presented prey with various cues from sub-lethal gape-limited predators. Rusty crayfish (<i>Faxonius rusticus</i> (Girard, 1852)) were exposed to predatory odors from sub-lethal sized largemouth bass (<i>Micropterus salmoides</i> (Lacepѐde, 1802)) to test effects of changing predator abundance, relative size relationships, and total predator length in flow through mesocosms. Foraging, shelter use, and movement behavior were used to measure cue effects. Foraging time depended jointly upon predator abundance and total predator size (p = 0.030). Specifically, high predator abundance resulted in decreased foraging efforts as gape ratio increased. Similarly, sheltering time depended on the interaction between predator abundance and gape ratio when predator abundance was highest (p = 0.020). Crayfish significantly increased exploration time when gape ratio increased (p = 0.010). Thus, this study shows crayfish can utilize different indices of predatory cues, namely total predator abundance and relative size ratios, in risk assessment but do so in context specific ways.

Flexibility and rigidity in hunting behaviour in rodents: is there room for cognition?

Predatory hunting is a complex species-typical behaviour involving different skills, some of which may include learning. This research aims to distinguish between rigid and flexible parts in live-insect hunting behaviour in nine herbivorous and granivorous rodent species, and to find out whether there is room for cognition in this activity. In laboratory experiments, all species studied manifest skilful attacks towards insects in a manner that is typical for specialised predators chasing a fleeing prey. Voles demonstrate a "core" and somewhat primitive scheme of a hunting pattern: approaching a potential victim, biting it, and then seizing and handling. Hamsters display the tendency to start their attacks by actions with paws, but they can achieve success only using teeth as well. Gerbils can successfully use both paws and teeth to start the attack, which brings their hunting behaviour closer to that of specialised rodent predators. We revealed variability in the display of hunting in different species, methods of seizing the prey, and the number of attempts to attack an insect before catching it. We found specific flexible fragments within the "bite-grasp-handle" bouts that can be precursors for adaptive phenotypic variations and include some cognitive attributes. We hypothesise that the divergence and specialisation of predatory behaviour in rodents can be based on the natural fragmentation of the original hunting patterns, that is, on the loss or recombination of particular behavioural elements. We consider a possible link between the fragmentation of hunting behaviour and social learning in different classes of animals and conjecture an intriguing correlation between predatory activity, cognitive skills and personal traits in rodents.

Innate visual discrimination abilities of zebrafish larvae

The ability to discriminate between objects visually plays a key role in animals' interactions with their environment because it enables them to recognise companions, prey, and predators. In the zebrafish, Danio rerio, hatching occurs early on during development (48-72 h post fertilisation), and the larvae must forage and evade predators despite their immature sensory and cognitive systems. Using a preference paradigm, we investigated whether larval zebrafish are nonetheless capable of discriminating between visual stimuli. We found that larvae discriminated not only between figures with different colours or different shapes, but also between two identical figures with different orientations and between sets of figures with different numerosities. By manipulating larvae's exposure to objects before the test, we demonstrated that their discrimination abilities are innate and do not depend upon experience. This study highlighted that zebrafish possess relatively sophisticated visual discrimination abilities even at the larval stage. These abilities likely improve larval survival via the recognition of biologically relevant stimuli.

Counting on Numbers-Numerical Abilities in Grey Bamboo Sharks and Ocellate River Stingrays

Over the last decade, studies examining the cognitive abilities of fish have increased, using a broad range of approaches. One of the foci has been to test the ability of fish to discriminate quantities of items and to determine whether fish can solve tasks solely on the basis of numerical information. This study is the first to investigate this ability in two elasmobranch species. All animals were trained in two-alternative forced-choice visual experiments and then examined in transfer tests, to determine if previously gained knowledge could be applied to new tasks. Results show that the grey bamboo shark (Chiloscyllium griseum) and the ocellate river stingray (Potamotrygon motoro) can discriminate quantities based on numerical information alone, while continuous variables were controlled for. Furthermore, the data indicates that similar magnitudes and limits for quantity discrimination exist as in other animals. However, the high degree of intraspecific variation that was observed as well as the low rate of animals proving to be successful suggest that the ability to discriminate quantities may not be as important to these species as to some other vertebrate and invertebrate species tested so far.

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.

Comparative cognition in three understudied ungulate species: European bison, forest buffalos and giraffes

Background

Comparative cognition has historically focused on a few taxa such as primates, birds or rodents. However, a broader perspective is essential to understand how different selective pressures affect cognition in different taxa, as more recently shown in several studies. Here we present the same battery of cognitive tasks to two understudied ungulate species with different socio-ecological characteristics, European bison (Bison bonasus) and forest buffalos (Syncerus caffer nanus), and we compare their performance to previous findings in giraffes (Giraffa camelopardalis). We presented subjects with an Object permanence task, Memory tasks with 30 and 60 s delays, two inference tasks based on acoustic cues (i.e. Acoustic inference tasks) and a control task to check for the use of olfactory cues (i.e. Olfactory task).

Results

Overall, giraffes outperformed bison and buffalos, and bison outperformed buffalos (that performed at chance level). All species performed better in the Object permanence task than in the Memory tasks and one of the Acoustic inference tasks (which they likely solved by relying on stimulus enhancement). Giraffes performed better than buffalos in the Shake full Acoustic inference task, but worse than bison and buffalos in the Shake empty Acoustic inference task.

Conclusions

In sum, our results are in line with the hypothesis that specific socio-ecological characteristics played a crucial role in the evolution of cognition, and that higher fission-fusion levels and larger dietary breadth are linked to higher cognitive skills. This study shows that ungulates may be an excellent model to test evolutionary hypotheses on the emergence of cognition.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12983-021-00417-w.

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.

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).

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.

Revisiting more or less: influence of numerosity and size on potential prey choice in the domestic cat

Quantity discrimination is of adaptive relevance in a wide range of contexts and across a wide range of species. Trained domestic cats can discriminate between different numbers of dots, and we have shown that they also spontaneously choose between different numbers and sizes of food balls. In the present study we performed two experiments with 24 adult cats to investigate spontaneous quantity discrimination in the more naturalistic context of potential predation. In Experiment 1 we presented each cat with the simultaneous choice between a different number of live prey (1 white mouse vs. 3 white mice), and in Experiment 2 with the simultaneous choice between live prey of different size (1 white mouse vs. 1 white rat). We repeated each experiment six times across 6 weeks, testing half the cats first in Experiment 1 and then in Experiment 2, and the other half in the reverse order. In Experiment 1 the cats more often chose the larger number of small prey (3 mice), and in Experiment 2, more often the small size prey (a mouse). They also showed repeatable individual differences in the choices which they made and in the performance of associated predation-like behaviours. We conclude that domestic cats spontaneously discriminate between the number and size of potential prey in a way that can be interpreted as adaptive for a lone-hunting, obligate carnivore, and show complex levels of risk-reward analysis.

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

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

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.

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'.

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.

Number sense and state-dependent valuation in cuttlefish

Identifying the amount of prey available is an important part of an animal's foraging behaviour. The risk-sensitive foraging theory predicts that an organism's foraging decisions with regard to food rewards depending upon its satiation level. However, the precise interaction between optimal risk-tolerance and satiation level remains unclear. In this study, we examined, firstly, whether cuttlefish, with one of the most highly evolved nervous system among the invertebrates, have number sense, and secondly, whether their valuation of food reward is satiation state dependent. When food such as live shrimps is present, without training, cuttlefish turn toward the prey and initiate seizure behaviour. Using this visual attack behaviour as a measure, cuttlefish showed a preference for a larger quantity when faced with two-alternative forced choice tasks (1 versus 2, 2 versus 3, 3 versus 4 and 4 versus 5). However, cuttlefish preferred the small quantity when the choice was between one live and two dead shrimps. More importantly, when the choice was between one large live shrimp and two small live shrimps (a prey size and quantity trade-off), the cuttlefish chose the large single shrimp when they felt hunger, but chose the two smaller prey when they were satiated. These results demonstrate that cuttlefish are capable of number discrimination and that their choice of prey number depends on the quality of the prey and on their appetite state. The findings also suggest that cuttlefish integrate both internal and external information when making a foraging decision and that the cost of obtaining food is inversely correlated with their satiation level, a phenomenon similar to the observation that metabolic state alters economic decision making under risk among humans.

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.

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'.

Quantity discrimination in parental fish: female convict cichlid discriminate fry shoals of different sizes

Numerical abilities have been found to be adaptive in different contexts, including mating, foraging, fighting assessment and antipredator strategies. In species with parental care, another potential advantage is the possibility to adjust parental behavior in relation to the numerosity of the progeny. The finding that many fish vary their parental investment in relation to brood size advocates the existence of a mechanism for appraising offspring number, an aspect that has never been directly investigated. Here we tested the ability of parental female convict cichlid (Amatitlania nigrofasciata) to discriminate between two fry groups differing in number by measuring time spent attempting to recover groups of fry experimentally displaced from the next. Females spent more time trying to recover the fry from larger groups when tested with contrasts 6 versus 12 (1:2) and 6 versus 9 fry (2:3); however, they showed no preference in the 6 versus 8 (3:4) contrast, suggesting that this task exceeds their discrimination capacity.

Experimental study of cognitive aspects of ambivalent foraging as exemplified by the great tit

A hypothesis of ambivalent foraging is proposed based on ideas about dual treating of the prey by a consumer: the food value attracts while the danger repulses. The foraging strategy of the great tit was investigated experimentally with the use of artificial "food patches" with variable amounts of dangerous prey (live red wood ants) and non-dangerous prey (fly larvae). With non-dangerous prey, the behavior of the birds corresponded to the known marginal value theorem: they proceeded with foraging until the resources were exhausted. We found the threshold amount of dangerous prey that prevents tits from hunting.

Laterality enhances numerical skills in the guppy, Poecilia reticulata

It has been hypothesized that cerebral lateralization can significantly enhance cognition and that this was one of the primary selective forces shaping its wide-spread evolution amongst vertebrate taxa. Here, we tested this hypothesis by examining the link between cerebral lateralization and numerical discrimination. Guppies, Poecilia reticulata, were sorted into left, right and non-lateralized groups using a standard mirror test and their numerical discrimination abilities tested in both natural shoal choice and abstract contexts. Our results show that strongly lateralized guppies have enhanced numerical abilities compared to non-lateralized guppies irrespective of context. These data provide further credence to the notion that cerebral lateralization can enhance cognitive efficiency.

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.

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.

Why do we differ in number sense? Evidence from a genetically sensitive investigation

Basic intellectual abilities of quantity and numerosity estimation have been detected across animal species. Such abilities are referred to as 'number sense'. For human species, individual differences in number sense are detectable early in life, persist in later development, and relate to general intelligence. The origins of these individual differences are unknown. To address this question, we conducted the first large-scale genetically sensitive investigation of number sense, assessing numerosity discrimination abilities in 837 pairs of monozygotic and 1422 pairs of dizygotic 16-year-old twin pairs. Univariate genetic analysis of the twin data revealed that number sense is modestly heritable (32%), with individual differences being largely explained by non-shared environmental influences (68%) and no contribution from shared environmental factors. Sex-Limitation model fitting revealed no differences between males and females in the etiology of individual differences in number sense abilities. We also carried out Genome-wide Complex Trait Analysis (GCTA) that estimates the population variance explained by additive effects of DNA differences among unrelated individuals. For 1118 unrelated individuals in our sample with genotyping information on 1.7 million DNA markers, GCTA estimated zero heritability for number sense, unlike other cognitive abilities in the same twin study where the GCTA heritability estimates were about 25%. The low heritability of number sense, observed in this study, is consistent with the directional selection explanation whereby additive genetic variance for evolutionary important traits is reduced.