Apes are intuitive statisticians

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.

Probabilistic inference and Bayesian-like estimation in animals: Empirical evidence

Animals often make decisions without perfect knowledge of environmental parameters like the quality of an encountered food patch or a potential mate. Theoreticians often assume animals make such decisions using a Bayesian updating process that combines prior information about the frequency distribution of resources in the environment with sample information from an encountered resource; such a process leads to decisions that maximize fitness, given the available information. I examine three aspects of empirical work that shed light on the idea that animals can make such decisions in a Bayesian-like manner. First, many animals are sensitive to variance differences in behavioral options, one metric used to characterize frequency distributions. Second, several species use information about the relative frequency of preferred versus nonpreferred items in different populations to make probabilistic inferences about samples taken from populations in a manner that results in maximizing the likelihood of obtaining a preferred reward. Third, the predictions of Bayesian models often match the behavior of individuals in two main approaches. One approach compares behavior to models that make different assumptions about how individuals estimate the quality of an environmental parameter. The patch exploitation behavior of nine species of birds and mammals has matched the predictions of Bayesian models. The other approach compares the behavior of individuals who learn, through experience, different frequency distributions of resources in their environment. The behavior of three bird species and bumblebees exploiting food patches and fruit flies selecting mates is influenced by their experience learning different frequency distributions of food and mates, respectively, in ways consistent with Bayesian models. These studies lend support to the idea that animals may combine prior and sample information in a Bayesian-like manner to make decisions under uncertainty, but additional work on a greater diversity of species is required to better understand the generality of this ability.

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.

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.

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.

Cognition: Crows are natural statisticians

A new study shows that carrion crows use memorized reward associations in a combinatorial way to apply relative probabilistic information to optimize reward outcome. This for the first time shows that a corvid species can flexibly apply statistical inference during decision making.

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.

Recent developments in parrot cognition: a quadrennial update

Psittacines, along with corvids, are commonly referred to as 'feathered apes' due to their advanced cognitive abilities. Until rather recently, the research effort on parrot cognition was lagging behind that on corvids, however current developments show that the number of parrot studies is steadily increasing. In 2018, M. L. Lambert et al. provided a comprehensive review on the status of the most important work done so far in parrot and corvid cognition. Nevertheless, only a little more than 4 years after this publication, more than 50 new parrot studies have been published, some of them chartering completely new territory. On the 25th anniversary of Animal Cognition we think this warrants a detailed review of parrot cognition research over the last 4 years. We aim to capture recent developments and current trends in this rapidly expanding and diversifying field.

The importance of thinking about the future in culture and cumulative cultural evolution

Thinking about possibilities plays a critical role in the choices humans make throughout their lives. Despite this, the influence of individuals' ability to consider what is possible on culture has been largely overlooked. We propose that the ability to reason about future possibilities or prospective cognition, has consequences for cultural change, possibly facilitating the process of cumulative cultural evolution. In particular, by considering potential future costs and benefits of specific behaviours, prospective cognition may lead to a more flexible use of cultural behaviours. In species with limited planning abilities, this may lead to the development of cultures that promote behaviours with future benefits, circumventing this limitation. Here, we examine these ideas from a comparative perspective, considering the relationship between human and nonhuman assessments of future possibilities and their cultural capacity to invent new solutions and improve them over time. Given the methodological difficulties of assessing prospective cognition across species, we focus on planning, for which we have the most data in other species. Elucidating the role of prospective cognition in culture will help us understand the variability in when and how we see culture expressed, informing ongoing debates, such as that surrounding which social learning mechanisms underlie culture. This article is part of the theme issue 'Thinking about possibilities: mechanisms, ontogeny, functions and phylogeny'.

Rationality and cognitive bias in captive gorillas' and orang-utans' economic decision-making

Human economic decision-making sometimes appears to be irrational. Partly, this is due to cognitive biases that can lead to suboptimal economic choices and context-dependent risk-preferences. A pertinent question is whether such biases are part of our evolutionary heritage or whether they are culturally acquired. To address this, we tested gorillas (Gorilla gorilla gorilla) and orang-utans (Pongo abelii) with two risk-assessment experiments that differed in how risk was presented. For both experiments, we found that subjects increased their preferences for the risky options as their expected gains increased, showing basic understanding of reward contingencies and rational decision-making. However, we also found consistent differences in risk proneness between the two experiments, as subjects were risk-neutral in one experiment and risk-prone in the other. We concluded that gorillas and orang-utans are economically rational but that their decisions can interact with pre-existing cognitive biases which modulates their risk-preference in context-dependent ways, explaining the variability of their risk-preference in previous literature.

The signature-testing approach to mapping biological and artificial intelligences

Making inferences from behaviour to cognition is problematic due to a many-to-one mapping problem, in which any one behaviour can be generated by multiple possible cognitive processes. Attempts to cross this inferential gap when comparing human intelligence to that of animals or machines can generate great debate. Here, we discuss the challenges of making comparisons using 'success-testing' approaches and call attention to an alternate experimental framework, the 'signature-testing' approach. Signature testing places the search for information-processing errors, biases, and other patterns centre stage, rather than focussing predominantly on problem-solving success. We highlight current research on both biological and artificial intelligence that fits within this framework and is creating proactive research programs that make strong inferences about the similarities and differences between the content of human, animal, and machine minds.

Experiencing statistical information improves children's and adults' inferences

How good are people's statistical intuitions? Recent research has highlighted that sequential experience of statistical information improves adults' statistical intuitions relative to situations where this information is described. Yet little is known about whether this is also the case for children's statistical intuitions. In a study with 100 children (8-11 years old) and 100 adults (19-35 years old), we found that sequentially experiencing statistical information improved both adults' and children's inferences in two paradigmatic reasoning problems: conjunction and Bayesian reasoning problems. Moreover, adults' statistical competencies when they learned statistical information through description were surpassed by children's inferences when they learned through experience. We conclude that experience of statistical information plays a key role in shaping children's reasoning under uncertainty-a conclusion that has important implications for education policy.

Young children’s use of probabilistic reliability and base-rates in decision-making

Children are skilled reasoners who readily use causal, reliability, and base-rate (i.e., prior probability) information in their decisions. Though these abilities are typically studied in isolation, children often must consider multiple pieces of information to make an informed decision. Four experiments (N = 320) explored the development of children’s ability to use reliability and base-rate information when making decisions about draw outcomes. Experiment 1 examined the age at which children can first compare and choose between probabilistically reliable machines. Three- and 4-year-old children saw machines that were probabilistically reliable at obtaining objects while sampling from uniform distributions (i.e., all target or non-target objects). Although 4-year-old children correctly used reliability in their decisions, 3-year-olds did not. In Experiment 2a, 4- to 6-year-olds were presented with the same probabilistically reliable machines, although they sampled from a mixture of target and non-target items. Here, children tended to choose the machine with the better proportion of targets, regardless of reliability. This was replicated in Experiment 2b. In Experiment 3, children were presented with one perfectly reliable machine and one probabilistically unreliable machine. Here, children continued to mostly choose the machine with the better proportion of targets. These results raise questions about base-rate overuse early in development and highlight the need for additional work on children’s ability to use multiple pieces of information in decision-making.

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.

The numerator bias exists in millions of real-world comparisons

Fractions are crucial, from math and science education to daily activities, but they are hard. A puzzling aspect of fractions is that people over-rely on the numerator when comparing a pair of fractions. Previous work has considered this numerator bias mostly as a reasoning mishap. Still, in a vast amount of pairwise comparisons, across many real-world domains, not just education textbooks, we report a high prior probability that the larger fraction has the larger numerator, and, for a relevant case, we provide formal arguments why. The existence of such a regularity suggests that the numerator bias may reflect a rational adaptation that detects and exploits likely events. In a pair of visual-proportion tasks (discrete and continuous fractions), we confirm that the numerator bias in participants adapts to experimented regularities. Even though weak education and math abilities play a role, adaptation to informative priors outside the classroom poses a challenge to educators, learners, and decision-makers.

Non-human primates use combined rules when deciding under ambiguity

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

Variation in primate decision-making under uncertainty and the roots of human economic behaviour

Uncertainty is a ubiquitous component of human economic behaviour, yet people can vary in their preferences for risk across populations, individuals and different points in time. As uncertainty also characterizes many aspects of animal decision-making, comparative research can help evaluate different potential mechanisms that generate this variation, including the role of biological differences or maturational change versus cultural learning, as well as identify human-unique components of economic decision-making. Here, we examine decision-making under risk across non-human primates, our closest relatives. We first review theoretical approaches and current methods for understanding decision-making in animals. We then assess the current evidence for variation in animal preferences between species and populations, between individuals based on personality, sex and age, and finally, between different contexts and individual states. We then use these primate data to evaluate the processes that can shape human decision-making strategies and identify the primate foundations of human economic behaviour. This article is part of the theme issue 'Existence and prevalence of economic behaviours among non-human primates'.

Animal models of human mood

Humans' everyday experience of the world is influenced by our moods. Moods are consciously accessible affective states that extend over time that are characterized by their valence and arousal. They also likely have a long evolutionary heritage and serve as an important adaptive affective mechanism. When they become maladaptive or overly biased, pathological affective states such as depression can emerge. Despite the importance of moods for human experience, little is known about their causal neurobiological mechanisms. In humans, limitations related to methods and interpretations of the data prevent causal investigations into the origins of mood, highlighting the importance of animal models. Nonhuman primates that share key neuroanatomical, affective, and social features with humans will be essential to uncovering their foundation. Identifying and validating mood-like states in animals is, however, challenging not least because mood is a human construct requiring verbal communication. Here we outline a theoretical framework for animal models of human mood, drawing upon established psychological literature where it exists before reviewing the extant studies of non-human primate models of mood-like states.

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.

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.

Understanding Language Evolution: Beyond Pan-Centrism

Language does not fossilize but this does not mean that the language's evolutionary timeline is lost forever. Great apes provide a window back in time on our last prelinguistic ancestor's communication and cognition. Phylogeny and cladistics implicitly conjure Pan (chimpanzees, bonobos) as a superior (often the only) model for language evolution compared with earlier diverging lineages, Gorilla and Pongo (orangutans). Here, in reviewing the literature, it is shown that Pan do not surpass other great apes along genetic, cognitive, ecologic, or vocal traits that are putatively paramount for language onset and evolution. Instead, revived herein is the idea that only by abandoning single-species models and learning about the variation among great apes, there might be a chance to retrieve lost fragments of the evolutionary timeline of language.

What animals do not do or fail to find: A novel observational approach for studying cognition in the wild

To understand how our brain evolved and what it is for, we are in urgent need of knowledge about the cognitive skills of a large variety of animal species and individuals, and their relationships to rapidly disappearing social and ecological conditions. But how do we obtain this knowledge? Studying cognition in the wild is a challenge. Field researchers (and their study subjects) face many factors that can easily interfere with their variables of interest. Although field studies of cognition present unique challenges, they are still invaluable for understanding the evolutionary drivers of cognition. In this review, I discuss the advantages and urgency of field-based studies on animal cognition and introduce a novel observational approach for field research that is guided by three questions: (a) what do animals fail to find?, (b) what do they not do?, and (c) what do they only do when certain conditions are met? My goal is to provide guidance to future field researchers examining primate cognition.

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.

The Development of Nonsymbolic Probability Judgments in Children

Two experiments were designed to investigate the developmental trajectory of children's probability approximation abilities. In Experiment 1, results revealed 6- and 7-year-old children's (N = 48) probability judgments improve with age and become more accurate as the distance between two ratios increases. Experiment 2 replicated these findings with 7- to 12-year-old children (N = 130) while also accounting for the effect of the size and the perceived numerosity of target objects. Older children's performance suggested the correct use of proportions for estimating probability; but in some cases, children relied on heuristic shortcuts. These results suggest that children's nonsymbolic probability judgments show a clear distance effect and that the acuity of probability estimations increases with age.

Aligning Developmental and Processing Accounts of Implicit and Statistical Learning

A long‐standing question in child language research concerns how children achieve mature syntactic knowledge in the face of a complex linguistic environment. A widely accepted view is that this process involves extracting distributional regularities from the environment in a manner that is incidental and happens, for the most part, without the learner's awareness. In this way, the debate speaks to two associated but separate literatures in language acquisition: statistical learning and implicit learning. Both fields have explored this issue in some depth but, at present, neither the results from the infant studies used by the statistical learning literature nor the artificial grammar learning tasks studies from the implicit learning literature can be used to fully explain how children's syntax becomes adult‐like. In this work, we consider an alternative explanation—that children use error‐based learning to become mature syntax users. We discuss this proposal in the light of the behavioral findings from structural priming studies and the computational findings from Chang, Dell, and Bock's (2006) dual‐path model, which incorporates properties from both statistical and implicit learning, and offers an explanation for syntax learning and structural priming using a common error‐based learning mechanism. We then turn our attention to future directions for the field, here suggesting how structural priming might inform the statistical learning and implicit learning literature on the nature of the learning mechanism.

In this article, Peter and Rowland explore the role of implicit statistical learning in syntactic development. It is often accepted that the processes observed in classic implicit learning or statistical learning experiments play an important role in the acquisition of natural language syntax. As Peter and Rowland point out, however, the results from neither research strand can be used to fully explain how children's syntax becomes adult‐like. They propose to address this shortcoming by using the structural priming paradigm.

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).

How children come to understand false beliefs: A shared intentionality account

To predict and explain the behavior of others, one must understand that their actions are determined not by reality but by their beliefs about reality. Classically, children come to understand beliefs, including false beliefs, at about 4-5 y of age, but recent studies using different response measures suggest that even infants (and apes!) have some skills as well. Resolving this discrepancy is not possible with current theories based on individual cognition. Instead, what is needed is an account recognizing that the key processes in constructing an understanding of belief are social and mental coordination with other persons and their (sometimes conflicting) perspectives. Engaging in such social and mental coordination involves species-unique skills and motivations of shared intentionality, especially as they are manifest in joint attention and linguistic communication, as well as sophisticated skills of executive function to coordinate the different perspectives involved. This shared intentionality account accords well with documented differences in the cognitive capacities of great apes and human children, and it explains why infants and apes pass some versions of false-belief tasks whereas only older children pass others.

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

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

The development of the representativeness heuristic in young children

In classic examinations of the representativeness heuristic, Kahneman and Tversky (1973) presented adult participants with a description of an individual who fit their stereotype of a typical engineer. Importantly, even when participants were told that the individual was drawn from a sample of 70 lawyers and 30 engineers, they estimated that the individual was an engineer at very high levels, showing that they relied almost exclusively on the personality description. Relying on the representativeness heuristic can lead to base-rate neglect and, thus, biased judgments. Two experiments provide insight into the development of the representativeness heuristic in young children using an adaptation of the classic lawyer-engineer problem. Experiment 1 (N = 96) established that 3- to 5-year-olds can use base-rate information on its own, and 4- and 5-year-olds can use individuating information on its own, to make inferences. Experiment 2 (N = 192) varied the relevance of the individuating information across conditions to assess the pervasiveness of this bias early in development. Here 5- and 6-year-olds, much like adults, continue to attempt to rely on individuating information when making classifications even if that information is irrelevant. Together, these experiments reveal how the representativeness heuristic develops across the preschool years and suggest that the bias may strengthen between 4 and 6 years of age.

Chimpanzees Consider Humans' Psychological States when Drawing Statistical Inferences

Great apes have been shown to be intuitive statisticians: they can use proportional information within a population to make intuitive probability judgments about randomly drawn samples [1, J.E., J.C., J.H., E.H., and H.R., unpublished data]. Humans, from early infancy onward, functionally integrate intuitive statistics with other cognitive domains to judge the randomness of an event [2-6]. To date, nothing is known about such cross-domain integration in any nonhuman animal, leaving uncertainty about the origins of human statistical abilities. We investigated whether chimpanzees take into account information about psychological states of experimenters (their biases and visual access) when drawing statistical inferences. We tested 21 sanctuary-living chimpanzees in a previously established paradigm that required subjects to infer which of two mixed populations of preferred and non-preferred food items was more likely to lead to a desired outcome for the subject. In a series of three experiments, we found that chimpanzees chose based on proportional information alone when they had no information about experimenters' preferences and (to a lesser extent) when experimenters had biases for certain food types but drew blindly. By contrast, when biased experimenters had visual access, subjects ignored statistical information and instead chose based on experimenters' biases. Lastly, chimpanzees intuitively used a violation of statistical likelihoods as indication for biased sampling. Our results suggest that chimpanzees have a random sampling assumption that can be overridden under the appropriate circumstances and that they are able to use mental state information to judge whether this is necessary. This provides further evidence for a shared statistical inference mechanism in apes and humans.

Pigeons play the percentages: computation of probability in a bird

The ability to compute probability, previously shown in nonverbal infants, apes, and monkeys, was examined in three experiments with pigeons. After responding to individually presented keys in an operant chamber that delivered reinforcement with varying probabilities, pigeons chose between these keys on probe trials. Pigeons strongly preferred a 75% reinforced key over a 25% reinforced key, even when the total number of reinforcers obtained on each key was equated. When both keys delivered 50% reinforcement, pigeons showed indifference between them, even though three times more reinforcers were obtained on one key than on the other. It is suggested that computation of probability may be common to many classes of animals and may be driven by the need to forage successfully for nutritional food items, mates, and areas with a low density of predators.

Chimpanzees prioritise social information over pre-existing behaviours in a group context but not in dyads

How animal communities arrive at homogeneous behavioural preferences is a central question for studies of cultural evolution. Here, we investigated whether chimpanzees (Pan troglodytes) would relinquish a pre-existing behaviour to adopt an alternative demonstrated by an overwhelming majority of group mates; in other words, whether chimpanzees behave in a conformist manner. In each of five groups of chimpanzees (N = 37), one individual was trained on one method of opening a two-action puzzle box to obtain food, while the remaining individuals learned the alternative method. Over 5 h of open access to the apparatus in a group context, it was found that 4/5 ‘minority’ individuals explored the majority method and three of these used this new method in the majority of trials. Those that switched did so after observing only a small subset of their group, thereby not matching conventional definitions of conformity. In a further ‘Dyad’ condition, six pairs of chimpanzees were trained on alternative methods and then given access to the task together. Only one of these individuals ever switched method. The number of observations that individuals in the minority and Dyad individuals made of their untrained method was not found to influence whether or not they themselves switched to use it. In a final ‘Asocial’ condition, individuals (N = 10) did not receive social information and did not deviate from their first-learned method. We argue that these results demonstrate an important influence of social context upon prioritisation of social information over pre-existing methods, which can result in group homogeneity of behaviour.

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.

Intuitive probabilistic inference in capuchin monkeys

The ability to reason about probabilities has ecological relevance for many species. Recent research has shown that both preverbal infants and non-human great apes can make predictions about single-item samples randomly drawn from populations by reasoning about proportions. To further explore the evolutionary origins of this ability, we conducted the first investigation of probabilistic inference in a monkey species (capuchins; Sapajus spp.). Across four experiments, capuchins (N = 19) were presented with two populations of food items that differed in their relative distribution of preferred and non-preferred items, such that one population was more likely to yield a preferred item. In each trial, capuchins had to select between hidden single-item samples randomly drawn from each population. In Experiment 1 each population was homogeneous so reasoning about proportions was not required; Experiments 2-3 replicated previous probabilistic reasoning research with infants and apes; and Experiment 4 was a novel condition untested in other species, providing an important extension to previous work. Results revealed that at least some capuchins were able to make probabilistic inferences via reasoning about proportions as opposed to simpler quantity heuristics. Performance was relatively poor in Experiment 4, so the possibility remains that capuchins may use quantity-based heuristics in some situations, though further work is required to confirm this. Interestingly, performance was not at ceiling in Experiment 1, which did not involve reasoning about proportions, but did involve sampling. This suggests that the sampling task posed demands in addition to reasoning about proportions, possibly related to inhibitory control, working memory, and/or knowledge of object permanence.

Non-symbolic division in childhood

The approximate number system (ANS) underlies representations of large numbers of objects as well as the additive, subtractive, and multiplicative relationships between them. In this set of studies, 5- and 6-year-old children were shown a series of video-based events that conveyed a transformation of a large number of objects into one-half or one-quarter of the original number. Children were able to estimate correctly the outcomes to these halving and quartering problems, and they based their responses on scaling by number, not on continuous quantities or guessing strategies. Children's performance exhibited the ratio signature of the ANS. Moreover, children performed above chance on relatively early trials, suggesting that this scaling operation is easily conveyed and readily performed. The results support the existence of a flexible and substantially untrained capacity to scale numerical amounts.

Comparison of discrete ratios by rhesus macaques (Macaca mulatta)

Perceiving and comparing ratios are crucial skills for humans. Little is known about whether other animals can compare ratios. We trained two rhesus macaques (Macaca mulatta) to choose arrays that contained the greater ratio of positive to negative stimuli, regardless of the absolute number of stimuli in each of the two choice arrays. Subjects learned this task, and their performance generalized to novel ratios. Moreover, performance was modulated by the ratio between ratios; subjects responded more quickly and accurately when the ratio between ratios was higher. Control conditions ruled out the possibility that subjects were relying on surface area, although the ratio between ratios of surface area did seem to influence their choices. Our results demonstrate that rhesus monkeys can compare discrete ratios, demonstrating not only proportional reasoning ability but also the ability to reason about relations between relations.