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

Rational number representation by the approximate number system

The approximate number system (ANS) enables organisms to represent the approximate number of items in an observed collection, quickly and independently of natural language. Recently, it has been proposed that the ANS goes beyond representing natural numbers by extracting and representing rational numbers (Clarke & Beck, 2021a). Prior work demonstrates that adults and children discriminate ratios in an approximate and ratio-dependent manner, consistent with the hallmarks of the ANS. Here, we use a well-known "connectedness illusion" to provide evidence that these ratio-dependent ratio discriminations are (a) based on the perceived number of items in seen displays (and not just non-numerical confounds), (b) are not dependent on verbal working memory, or explicit counting routines, and (c) involve representations with a part-whole (or subset-superset) format, like a fraction, rather than a part-part format, like a ratio. These results vindicate key predictions of the hypothesis that the ANS represents rational numbers.

Chimpanzees (Pan troglodytes) recognize that their guesses could be wrong and can pass a two-cup disjunctive syllogism task

When chimpanzees search for hidden food, do they realize that their guesses may not be correct? We applied a post-decision wagering paradigm to a simple two-cup search task, varying whether we gave participants visual access to the baiting and then asking after they had chosen one of the cups whether they would prefer a smaller but certain reward instead of their original choice (experiment 1). Results showed that chimpanzees were more likely to accept the smaller reward in occluded than visible conditions. Experiment 2 found the same effect when we blocked visual access but manipulated the number of hiding locations for the food piece, showing that the effect is not owing to representation type. Experiments 3 and 4 showed that when given information about the contents of the unchosen cup, chimpanzees were able to flexibly update their choice behaviour accordingly. These results suggest that language is not a pre-requisite to solving the disjunctive syllogism and provides a valuable contribution to the debate on logical reasoning in non-human animals.

Heuristic strategy of intuitive statistical inferences in 7- to 10-year-old children

Intuitive statistical inferences refer to making inferences about uncertain events based on limited probabilistic information, which is crucial for both human and non-human species' survival and reproduction. Previous research found that 7- and 8-year-old children failed in intuitive statistical inference tasks after heuristic strategies had been controlled. However, few studies systematically explored children's heuristic strategies of intuitive statistical inferences and their potential numerical underpinnings. In the current research, Experiment 1 (N = 81) examined 7- to 10-year-olds' use of different types of heuristic strategies; results revealed that children relied more on focusing on the absolute number strategy. Experiment 2 (N = 99) and Experiment 3 (N = 94) added continuous-format stimuli to examine whether 7- and 8-year-olds could make genuine intuitive statistical inferences instead of heuristics. Results revealed that both 7- and 8-year-olds and 9- and 10-year-olds performed better in intuitive statistical inference tasks with continuous-format stimuli, even after focusing on the absolute number strategy had been controlled. The results across the three experiments preliminarily hinted that the ratio processing system might rely on the approximate number system. Future research could clarify what specific numerical processing mechanism may be used and how it might support children's statistical intuitions.

How can I find what I want? Can children, chimpanzees and capuchin monkeys form abstract representations to guide their behavior in a sampling task?

concepts are a powerful tool for making wide-ranging predictions in new situations based on little experience. Whereas looking-time studies suggest an early emergence of this ability in human infancy, other paradigms like the relational match to sample task often fail to detect abstract concepts until late preschool years. Similarly, non-human animals show difficulties and often succeed only after long training regimes. Given the considerable influence of slight task modifications, the conclusiveness of these findings for the development and phylogenetic distribution of abstract reasoning is debated. Here, we tested the abilities of 3 to 5-year-old children, chimpanzees, and capuchin monkeys in a unified and more ecologically valid task design based on the concept of "overhypotheses" (Goodman, 1955). Participants sampled high- and low-valued items from containers that either each offered items of uniform value or a mix of high- and low-valued items. In a test situation, participants should switch away earlier from a container offering low-valued items when they learned that, in general, items within a container are of the same type, but should stay longer if they formed the overhypothesis that containers bear a mix of types. We compared each species' performance to the predictions of a probabilistic hierarchical Bayesian model forming overhypotheses at a first and second level of abstraction, adapted to each species' reward preferences. Children and, to a more limited extent, chimpanzees demonstrated their sensitivity to abstract patterns in the evidence. In contrast, capuchin monkeys did not exhibit conclusive evidence for the ability of abstract knowledge formation.

Observational approaches to chimpanzee behavior in an African sanctuary: Implications for research, welfare, and capacity-building

Research in African ape sanctuaries has emerged as an important context for our understanding of comparative cognition and behavior. While much of this work has focused on experimental studies of cognition, these animals semi-free-range in forest habitats and therefore can also provide important information about the behavior of primates in socioecologically-relevant naturalistic contexts. In this "New Approaches" article, we describe a project where we implemented a synthetic program of observational data collection at Ngamba Island Chimpanzee Sanctuary in Uganda, directly modeled after long-term data collection protocols at the Kibale Chimpanzee Project in Uganda, a wild chimpanzee field site. The foundation for this project was a strong partnership between sanctuary staff, field site staff, and external researchers. We describe how we developed a data-collection protocol through discussion and collaboration among these groups, and trained sanctuary caregivers to collect novel observational data using these protocols. We use these data as a case study to examine: (1) how behavioral observations in sanctuaries can inform primate welfare and care practices, such as by understanding aggression within the group; (2) how matched observational protocols across sites can inform our understanding of primate behavior across different contexts, including sex differences in social relationships; and (3) how more robust collaborations between foreign researchers and local partners can support capacity-building in primate range countries, along with mentoring and training students more broadly.

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.

Keep numbers in view: red-eared sliders (Trachemys scripta elegans) learn to discriminate relative quantities

The ability to discriminate relative quantities, one of the numerical competences, is considered an adaptive trait in uncertain environments. Besides humans, previous studies have reported this capacity in several non-human primates and birds. Here, we test whether red-eared sliders (Trachemys scripta elegans) can discriminate different relative quantities. Subjects were first trained to distinguish different stimuli with food reward. Then, they were tested with novel stimulus pairs to demonstrate how they distinguished the stimuli. The results show that most subjects can complete the initial training and use relative quantity rather than absolute quantity to make choices during the testing phase. This study provides behavioural evidence of relative quantity discrimination in a reptile species and suggests that such capacity may be widespread among vertebrates.

Giraffes make decisions based on statistical information

The ability to make inferences based on statistical information has so far been tested only in animals having large brains in relation to their body size, like primates and parrots. Here we tested if giraffes (Giraffa camelopardalis), despite having a smaller relative brain size, can rely on relative frequencies to predict sampling outcomes. We presented them with two transparent containers filled with different quantities of highly-liked food and less-preferred food. The experimenter covertly drew one piece of food from each container, and let the giraffe choose between the two options. In the first task, we varied the quantity and relative frequency of highly-liked and less-preferred food pieces. In the second task, we inserted a physical barrier in both containers, so giraffes only had to take into account the upper part of the container when predicting the outcome. In both tasks giraffes successfully selected the container more likely to provide the highly-liked food, integrating physical information to correctly predict sampling information. By ruling out alternative explanations based on simpler quantity heuristics and learning processes, we showed that giraffes can make decisions based on statistical inferences.

Evidence for abstract representations in children but not capuchin monkeys

The use of abstract higher-level knowledge (also called overhypotheses) allows humans to learn quickly from sparse data and make predictions in new situations. Previous research has suggested that humans may be the only species capable of abstract knowledge formation, but this remains controversial. There is also mixed evidence for when this ability emerges over human development. Kemp et al. (2007) proposed a computational model of how overhypotheses could be learned from sparse examples. We provide the first direct test of this model: an ecologically valid paradigm for testing two species, capuchin monkeys (Sapajus spp.) and 4- to 5-year-old human children. We presented participants with sampled evidence from different containers which suggested that all containers held items of uniform type (type condition) or of uniform size (size condition). Subsequently, we presented two new test containers and an example item from each: a small, high-valued item and a large but low-valued item. Participants could then choose from which test container they would like to receive the next sample - the optimal choice was the container that yielded a large item in the size condition or a high-valued item in the type condition. We compared performance to a priori predictions made by models with and without the capacity to learn overhypotheses. Children's choices were consistent with the model predictions and thus suggest an ability for abstract knowledge formation in the preschool years, whereas monkeys performed at chance level.

Are Rational Numbers Spontaneous? Natural Numbers Suffice all Processing by the Number Sense

The presence of preverbal numerical abilities in animals and infants is widely established, but an important discussion remains about which cognitive systems support these abilities. In particular, a great amount of research is dedicated to the approximate number system (ANS) for the elaboration of non-symbolic numbers and their possible types of mental numeric representations. In a recently published article, Clarke and Beck (2021) provide a series of evidence that supports its existence (ANS) and argue that the mental referents of this system are both natural and rational numbers. In the current commentary, we introduce the notion of the "whole-entity bias" that permeates perception and cognition and favors an automatic processing of discrete mental magnitudes while hindering the representations of fractional numbers. Further, we argue that a hierarchical structure of the ANS that represents natural numbers and supports the understanding of proportions through a series of computations is a more ecological theorization. To conclude, we believe that such a view is still compatible with the proposal of a single representational system (the ANS) supporting both number kinds but offers a different perspective on the computational level of explanation.

A Model of Scientific Data Reasoning

Data reasoning is an essential component of scientific reasoning, as a component of evidence evaluation. In this paper, we outline a model of scientific data reasoning that describes how data sensemaking underlies data reasoning. Data sensemaking, a relatively automatic process rooted in perceptual mechanisms that summarize large quantities of information in the environment, begins early in development, and is refined with experience, knowledge, and improved strategy use. Summarizing data highlights set properties such as central tendency and variability, and these properties are used to draw inferences from data. However, both data sensemaking and data reasoning are subject to cognitive biases or heuristics that can lead to flawed conclusions. The tools of scientific reasoning, including external representations, scientific hypothesis testing, and drawing probabilistic conclusions, can help reduce the likelihood of such flaws and help improve data reasoning. Although data sensemaking and data reasoning are not supplanted by scientific data reasoning, scientific reasoning skills can be leveraged to improve learning about science and reasoning with data.

Inferential social learning: cognitive foundations of human social learning and teaching

Social learning is often portrayed as a passive process of copying and trusting others. This view, however, does not fully capture what makes human social learning so powerful: social information is often 'curated' by helpful teachers. I argue that both learning from others (social learning) and helping others learn (teaching) can be characterized as probabilistic inferences guided by an intuitive understanding of how people think, plan, and act. Consistent with this idea, even young children draw rich inferences from evidence provided by others and generate informative evidence that helps others learn. By studying social learning and teaching through a common theoretical lens, inferential social learning provides an integrated account of how human cognition supports acquisition and communication of abstract knowledge.

The Number Sense Represents (Rational) Numbers

On a now orthodox view, humans and many other animals possess a "number sense," or approximate number system (ANS), that represents number. Recently, this orthodox view has been subject to numerous critiques that question whether the ANS genuinely represents number. We distinguish three lines of critique-the arguments from congruency, confounds, and imprecision-and show that none succeed. We then provide positive reasons to think that the ANS genuinely represents numbers, and not just non-numerical confounds or exotic substitutes for number, such as "numerosities" or "quanticals," as critics propose. In so doing, we raise a neglected question: numbers of what kind? Proponents of the orthodox view have been remarkably coy on this issue. But this is unsatisfactory since the predictions of the orthodox view, including the situations in which the ANS is expected to succeed or fail, turn on the kind(s) of number being represented. In response, we propose that the ANS represents not only natural numbers (e.g. 7), but also non-natural rational numbers (e.g. 3.5). It does not represent irrational numbers (e.g. √2), however, and thereby fails to represent the real numbers more generally. This distances our proposal from existing conjectures, refines our understanding of the ANS, and paves the way for future research.

A description-experience gap in statistical intuitions: Of smart babies, risk-savvy chimps, intuitive statisticians, and stupid grown-ups

Comparison of different lines of research on statistical intuitions and probabilistic reasoning reveals several puzzling contradictions. Whereas babies seem to be intuitive statisticians, surprisingly capable of statistical learning and inference, adults' statistical inferences have been found to be inconsistent with the rules of probability theory and statistics. Whereas researchers in the 1960s concluded that people's probability updating is "conservatively" proportional to normative predictions, probability updating research in the 1970s suggested that people are incapable of following Bayes's rule. And whereas animals appear to be strikingly risk savvy, humans often seem "irrational" when dealing with probabilistic information. Drawing on research on the description-experience gap in risky choice, we integrate and systematize these findings from disparate fields of inquiry that have, to date, operated largely in parallel. Our synthesis shows that a key factor in understanding inconsistencies in statistical intuitions research is whether probabilistic inferences are based on symbolic, abstract descriptions or on the direct experience of statistical information. We delineate this view from other conceptual accounts, consider potential mechanisms by which attributes of first-hand experience can facilitate appropriate statistical inference, and identify conditions under which they improve or impair probabilistic reasoning. To capture the full scope of human statistical intuition, we conclude, research on probabilistic reasoning across the lifespan, across species, and across research traditions must bear in mind that experience and symbolic description of the world may engage systematically distinct cognitive processes.

First and Second Graders Successfully Reason About Ratios With Both Dot Arrays and Arabic Numerals

Children struggle with exact, symbolic ratio reasoning, but prior research demonstrates children show surprising intuition when making approximate, nonsymbolic ratio judgments. In the current experiment, eighty-five 6- to 8-year-old children made approximate ratio judgments with dot arrays and numerals. Children were adept at approximate ratio reasoning in both formats and improved with age. Children who engaged in the nonsymbolic task first performed better on the symbolic task compared to children tested in the reverse order, suggesting that nonsymbolic ratio reasoning may function as a scaffold for symbolic ratio reasoning. Nonsymbolic ratio reasoning mediated the relation between children's numerosity comparison performance and symbolic mathematics performance in the domain of probabilities, but numerosity comparison performance explained significant unique variance in general numeration skills.

Reduced risk-seeking in chimpanzees in a zero-outcome game

A key component of economic decisions is the integration of information about reward outcomes and probabilities in selecting between competing options. In many species, risky choice is influenced by the magnitude of available outcomes, probability of success and the possibility of extreme outcomes. Chimpanzees are generally regarded to be risk-seeking. In this study, we examined two aspects of chimpanzees' risk preferences: first, whether setting the value of the non-preferred outcome of a risky option to zero changes chimpanzees’ risk preferences, and second, whether individual risk preferences are stable across two different measures. Across two experiments, we found chimpanzees (Pan troglodytes, n = 23) as a group to be risk-neutral to risk-avoidant with highly stable individual risk preferences. We discuss how the possibility of going empty-handed might reduce chimpanzees' risk-seeking relative to previous studies. This malleability in risk preferences as a function of experimental parameters and individual differences raises interesting questions about whether it is appropriate or helpful to categorize a species as a whole as risk-seeking or risk-avoidant.

This article is part of the theme issue ‘Existence and prevalence of economic behaviours among non-human primates’.

Do infants and preschoolers quantify probabilities based on proportions?

Most statistical problems encountered throughout life require the ability to quantify probabilities based on proportions. Recent findings on the early ontogeny of this ability have been mixed: For example, when presented with jars containing preferred and less preferred items, 12-month-olds, but not 3- and 4-years-olds, seem to rely on the proportions of objects in the jars to predict the content of samples randomly drawn out of them. Given these contrasting findings, it remains unclear what the probabilistic reasoning abilities of young children are and how they develop. In our study, we addressed this question and tested, with identical methods across age groups and similar methods to previous studies, whether 12-month-olds and 3- and 4-years-olds rely on proportions of objects to estimate probabilities of random sampling events. Results revealed that neither infants nor preschoolers do. While preschoolers' performance is in line with previous findings, infants' performance is difficult to interpret given their failure in a control condition in which the outcomes happened with certainty rather than a graded probability. More systematic studies are needed to explain why infants succeeded in a previous study but failed in our study.

Macphail’s Null Hypothesis of Vertebrate Intelligence: Insights From Avian Cognition

Macphail famously criticized two foundational assumptions that underlie the evolutionary approach to comparative psychology: that there are differences in intelligence across species, and that intelligent behavior in animals is based on more than associative learning. Here, we provide evidence from recent work in avian cognition that supports both these assumptions: intelligence across species varies, and animals can perform intelligent behaviors that are not guided solely by associative learning mechanisms. Finally, we reflect on the limitations of comparative psychology that led to Macphail’s claims and suggest strategies researchers can use to make more advances in the field.

A review of research in primate sanctuaries

While non-human primate studies have long been conducted in laboratories, and more recently at zoological parks, sanctuaries are increasingly considered a viable setting for research. Accredited sanctuaries in non-range countries house thousands of primates formerly used as subjects of medical research, trained performers or personal pets. In range countries, however, sanctuaries typically house orphaned primates confiscated from illegal poaching and the bushmeat and pet trafficking trades. Although the primary mission of these sanctuaries is to rescue and rehabilitate residents, many of these organizations are increasingly willing to participate in non-invasive research. Notably, from a scientific standpoint, most sanctuaries provide potential advantages over traditional settings, such as large, naturalistic physical and social environments which may result in more relevant models of primates' free-ranging wild counterparts than other captive settings. As a result, an impressive scope of research in the fields of primate behaviour, cognition, veterinary science, genetics and physiology have been studied in sanctuaries. In this review, we examine the range and form of research that has been conducted at accredited sanctuaries around the world. We also describe the potential challenges of sanctuary-based work and the considerations that external researchers may face when deciding to collaborate with primate sanctuaries on their research projects.

Kea show three signatures of domain-general statistical inference

One key aspect of domain-general thought is the ability to integrate information across different cognitive domains. Here, we tested whether kea (Nestor notabilis) can use relative quantities when predicting sampling outcomes, and then integrate both physical information about the presence of a barrier, and social information about the biased sampling of an experimenter, into their predictions. Our results show that kea exhibit three signatures of statistical inference, and therefore can integrate knowledge across different cognitive domains to flexibly adjust their predictions of sampling events. This result provides evidence that true statistical inference is found outside of the great apes, and that aspects of domain-general thinking can convergently evolve in brains with a highly different structure from primates. This has important implications not only for our understanding of how intelligence evolves, but also for research focused on how to create artificial domain-general thought processes.

Long-tailed macaques extract statistical information from repeated types of events to make rational decisions under uncertainty

Human children and apes seem to be intuitive statisticians when making predictions from populations of objects to randomly drawn samples, whereas monkeys seem not to be. Statistical reasoning can also be investigated in tasks in which the probabilities of different possibilities must be inferred from relative frequencies of events, but little is known about the performance of nonhuman primates in such tasks. In the current study, we investigated whether long-tailed macaques extract statistical information from repeated types of events to make predictions under uncertainty. In each experiment, monkeys first experienced the probability of rewards associated with different factors separately. In a subsequent test trial, monkeys could then choose between the different factors presented simultaneously. In Experiment 1, we tested whether long-tailed macaques relied on probabilities and not on a comparison of absolute quantities to make predictions. In Experiment 2 and 3 we varied the nature of the predictive factors and the complexity of the covariation structure between rewards and factors. Results indicate that long-tailed macaques extract statistical information from repeated types of events to make predictions and rational decisions under uncertainty, in more or less complex scenarios. These findings suggest that the presentation format affects the monkeys’ statistical reasoning abilities.

Infant Statisticians: The Origins of Reasoning Under Uncertainty

Humans frequently make inferences about uncertain future events with limited data. A growing body of work suggests that infants and other primates make surprisingly sophisticated inferences under uncertainty. First, we ask what underlying cognitive mechanisms allow young learners to make such sophisticated inferences under uncertainty. We outline three possibilities, the logic, probabilistic, and heuristics views, and assess the empirical evidence for each. We argue that the weight of the empirical work favors the probabilistic view, in which early reasoning under uncertainty is grounded in inferences about the relationship between samples and populations as opposed to being grounded in simple heuristics. Second, we discuss the apparent contradiction between this early-emerging sensitivity to probabilities with the decades of literature suggesting that adults show limited use of base-rate and sampling principles in their inductive inferences. Third, we ask how these early inductive abilities can be harnessed for improving later mathematics education and inductive inference. We make several suggestions for future empirical work that should go a long way in addressing the many remaining open questions in this growing research area.

Rhesus macaques use probabilities to predict future events

Humans can use an intuitive sense of statistics to make predictions about uncertain future events, a cognitive skill that underpins logical and mathematical reasoning. Recent research shows that some of these abilities for statistical inferences can emerge in preverbal infants and non-human primates such as apes and capuchins. An important question is therefore whether animals share the full complement of intuitive reasoning abilities demonstrated by humans, as well as what evolutionary contexts promote the emergence of such skills. Here, we examined whether free-ranging rhesus macaques (Macaca mulatta) can use probability information to infer the most likely outcome of a random lottery, in the first test of whether primates can make such inferences in the absence of direct prior experience. We developed a novel expectancy-violation looking time task, adapted from prior studies of infants, in order to assess the monkeys' expectations. In Study 1, we confirmed that monkeys (n = 20) looked similarly at different sampled items if they had no prior knowledge about the population they were drawn from. In Study 2, monkeys (n = 80) saw a dynamic 'lottery' machine containing a mix of two types of fruit outcomes, and then saw either the more common fruit (expected trial) or the relatively rare fruit (unexpected trial) fall from the machine. We found that monkeys looked longer when they witnessed the unexpected outcome. In Study 3, we confirmed that this effect depended on the causal relationship between the sample and the population, not visual mismatch: monkeys (n = 80) looked equally at both outcomes if the experimenter pulled the sampled item from her pocket. These results reveal that rhesus monkeys spontaneously use information about probability to reason about likely outcomes, and show how comparative studies of nonhumans can disentangle the evolutionary history of logical reasoning capacities.

Long-tailed macaques (Macaca fascicularis) can use simple heuristics but fail at drawing statistical inferences from populations to samples

Human infants, apes and capuchin monkeys engage in intuitive statistics: they generate predictions from populations of objects to samples based on proportional information. This suggests that statistical reasoning might depend on some core knowledge that humans share with other primate species. To aid the reconstruction of the evolution of this capacity, we investigated whether intuitive statistical reasoning is also present in a species of Old World monkey. In a series of four experiments, 11 long-tailed macaques were offered different pairs of populations containing varying proportions of preferred versus neutral food items. One population always contained a higher proportion of preferred items than the other. An experimenter simultaneously drew one item out of each population, hid them in her fists and presented them to the monkeys to choose. Although some individuals performed well across most experiments, our results imply that long-tailed macaques as a group did not make statistical inferences from populations of food items to samples but rather relied on heuristics. These findings suggest that there may have been convergent evolution of this ability in New World monkeys and apes (including humans).