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

Individual differences in non-symbolic numerical abilities predict mathematical achievements but contradict ATOM

BACKGROUND

A significant debate surrounds the nature of the cognitive mechanisms involved in non-symbolic number estimation. Several studies have suggested the existence of the same cognitive system for estimation of time, space, and number, called "a theory of magnitude" (ATOM). In addition, researchers have proposed the theory that non-symbolic number abilities might support our mathematical skills. Despite the large number of studies carried out, no firm conclusions can be drawn on either topic.

METHODS

In the present study, we correlated the performance of adults on non-symbolic magnitude estimations and symbolic numerical tasks. Non-symbolic magnitude abilities were assessed by asking participants to estimate which auditory tone lasted longer (time), which line was longer (space), and which group of dots was more numerous (number). To assess symbolic numerical abilities, participants were required to perform mental calculations and mathematical reasoning.

RESULTS

We found a positive correlation between non-symbolic and symbolic numerical abilities. On the other hand, no correlation was found among non-symbolic estimations of time, space, and number.

CONCLUSIONS

Our study supports the idea that mathematical abilities rely on rudimentary numerical skills that predate verbal language. By contrast, the lack of correlation among non-symbolic estimations of time, space, and number is incompatible with the idea that these magnitudes are entirely processed by the same cognitive system.

Chimpanzees (Pan troglodytes) can wait, when they choose to: a study with the hybrid delay task

Self-control has been studied in nonhuman animals using a variety of tasks. The inter-temporal choice (ITC) task presents choices between smaller-sooner (SS) and larger-later (LL) options. Using food amounts as rewards, this presents two problems: (a) choices of the LL option could either reflect self-control or instead result from animals' difficulty with pointing to smaller amounts of food; (b) there is no way to verify whether the subjects would not revert their choice for the LL option, if given the opportunity to do so during the ensuing delay. To address these problems, we have recently introduced a new protocol, the hybrid delay task, which combines an initial ITC with a subsequent accumulation phase in which selection of the SS option leads to its immediate delivery, but choice of the LL option then leads to one-by-one presentation of those items that continues only as long as the subject does not eat any of the accumulated items. The choice of the LL option therefore only reflects self-control when the number of items obtained from LL choices during the accumulation phase is higher than what could be received in the SS option. Previous research with capuchin monkeys demonstrated that their apparent self-control responses in the ITC task may have overestimated their general self-control abilities, given their poor performance in the hybrid delay task. Here, chimpanzees instead demonstrated that their choices for the LL option in the ITC phase of the hybrid delay task were confirmed by their ability to sustain long delays during accumulation of LL rewards.

What counts for 'counting'? Chimpanzees, Pan troglodytes, respond appropriately to relevant and irrelevant information in a quantity judgment task

Nonhuman animals quantify all manner of things, and the way in which this is done is fairly well understood. However, little research has been conducted to determine how they know what is or is not relevant in the instances in which they quantify stimuli. We assessed how four chimpanzees chose between two sets of food items when the items were distributed across separate spatial arrays. Each item was covered by a container, and then was revealed in sequence so that neither whole set was visible at one time. After all containers were revealed, some were revealed again. The chimpanzees should have ignored items that were seen a second time and instead enumerated each item only once. In another test, some of the items were transposed in location and then uncovered again. Here, the chimpanzees needed to recognize that the newly shown food items were ones they already had seen. Overall, the chimpanzees were successful in selecting the truly larger array of items despite these potential distracting re-presentations of items. Discrimination performance also reflected analogue magnitude estimation because comparisons of sets that differed by larger amounts were easier than comparisons that differed by smaller amounts. Thus, chimpanzee quantity judgments for nonvisible sets of items are inexact, but they include an aspect of control for determining when items are uniquely presented versus re-presented.

Large number discrimination in newborn fish

Quantitative abilities have been reported in a wide range of species, including fish. Recent studies have shown that adult guppies (Poecilia reticulata) can spontaneously select the larger number of conspecifics. In particular the evidence collected in literature suggest the existence of two distinct systems of number representation: a precise system up to 4 units, and an approximate system for larger numbers. Spontaneous numerical abilities, however, seem to be limited to 4 units at birth and it is currently unclear whether or not the large number system is absent during the first days of life. In the present study, we investigated whether newborn guppies can be trained to discriminate between large quantities. Subjects were required to discriminate between groups of dots with a 0.50 ratio (e.g., 7 vs. 14) in order to obtain a food reward. To dissociate the roles of number and continuous quantities that co-vary with numerical information (such as cumulative surface area, space and density), three different experiments were set up: in Exp. 1 number and continuous quantities were simultaneously available. In Exp. 2 we controlled for continuous quantities and only numerical information was available; in Exp. 3 numerical information was made irrelevant and only continuous quantities were available. Subjects successfully solved the tasks in Exp. 1 and 2, providing the first evidence of large number discrimination in newborn fish. No discrimination was found in experiment 3, meaning that number acuity is better than spatial acuity. A comparison with the onset of numerical abilities observed in shoal-choice tests suggests that training procedures can promote the development of numerical abilities in guppies.

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

We simulated the situation of risky hunting in the striped field mouse Apodemus agrarius in order to examine whether these animals are able to make a choice between small and large quantities of live prey (ants). In the first (preliminary) experiment we investigated to what extent mice were interested in ants as a live prey and how their hunting activity depended on the quantity of these edible but rather aggressive insects. We placed mice one by one into arenas together with ant groups of different quantities, from 10 to 60. Surprisingly, animals, both wild-caught and laboratory-reared, displayed rather skilled predatory attacks: mice killed and ate from 0.37 ± 003 to 4 ± 0.5 ants per minute. However, there was a threshold number of ants in the arenas when rodents expressed signs of discomfort and started to panic, likely because ants bit them. This threshold corresponds to the dynamic density (about 400 individuals per m² per min) in the vicinity of anthills and ants' routes in natural environment. In the second experiment mice had to choose between different quantities of ants placed in two transparent tunnels. Ants here served both as food items and as a source of danger. As far as we know, this is the first experimental paradigm based on evaluation of quantity judgments in the context of risk/reward decision making where the animals face a trade-off between the hedonistic value of the prey and the danger it presents. We found that when mice have to choose between 5 vs. 15, 5 vs. 30, and 10 vs. 30 ants, they always tend to prefer the smaller quantity, thus displaying the capacity for distinguishing more from less in order to ensure comfortable hunting. The results of this study are ecologically relevant as they reflect situations and challenges faced by free-living small rodents.

1 < 2 and 2 < 3: non-linguistic appreciations of numerical order

Ordinal understanding is involved in understanding social hierarchies, series of actions, and everyday events. Moreover, an appreciation of numerical order is critical to understanding number at a highly abstract, conceptual level. In this paper, we review findings concerning the development and expression of ordinal numerical knowledge in preverbal human infants in light of literature about the same cognitive abilities in non-human animals. We attempt to reconcile seemingly contradictory evidence, provide new directions for prospective research, and evaluate the shared basis of ordinal knowledge among non-verbal organisms. Our review of the research leads us to conclude that both infants and non-human animals are adapted to respond to monotonic progressions in numerical order, consonant with mathematical definitions of numerical order. Further, we suggest that patterns in the way that infants and non-human animals process numerical order can be accounted for by changes across development, the conditions under which representations are generated, or both.

Do Social Conditions Affect Capuchin Monkeys' (Cebus apella) Choices in a Quantity Judgment Task?

Beran et al. (2012) reported that capuchin monkeys closely matched the performance of humans in a quantity judgment test in which information was incomplete but a judgment still had to be made. In each test session, subjects first made quantity judgments between two known options. Then, they made choices where only one option was visible. Both humans and capuchin monkeys were guided by past outcomes, as they shifted from selecting a known option to selecting an unknown option at the point at which the known option went from being more than the average rate of return to less than the average rate of return from earlier choices in the test session. Here, we expanded this assessment of what guides quantity judgment choice behavior in the face of incomplete information to include manipulations to the unselected quantity. We manipulated the unchosen set in two ways: first, we showed the monkeys what they did not get (the unchosen set), anticipating that "losses" would weigh heavily on subsequent trials in which the same known quantity was presented. Second, we sometimes gave the unchosen set to another monkey, anticipating that this social manipulation might influence the risk-taking responses of the focal monkey when faced with incomplete information. However, neither manipulation caused difficulty for the monkeys who instead continued to use the rational strategy of choosing known sets when they were as large as or larger than the average rate of return in the session, and choosing the unknown (riskier) set when the known set was not sufficiently large. As in past experiments, this was true across a variety of daily ranges of quantities, indicating that monkeys were not using some absolute quantity as a threshold for selecting (or not) the known set, but instead continued to use the daily average rate of return to determine when to choose the known versus the unknown quantity.

Does the stimulus type influence horses' performance in a quantity discrimination task?

The ability to understand the relation between quantities has been documented in a wide range of species. Such quantity discrimination competences are commonly demonstrated by a choice of the larger quantity or numerosity in a two-choice task. However, despite their overall success, many subjects commit a surprisingly large number of errors even in simple discriminations such as 1 vs. 3. Recently, it had been suggested that this is a result of the testing procedure. When monkeys could choose between different quantities of edible rewards, they showed low-level success. If, however, they chose between inedible items and were rewarded with edible items, their performance increased. The same held true if they chose between edible items but were rewarded with other edible items (Schmitt and Fischer, 2011). This led to the suggestion that the monkeys may not have been able to mentally separate between choice- and reward-stimuli in the initial test situation. To investigate if this response pattern can also be found in non-primate species, we replicated the experiment with 12 Icelandic horses kept at a private horse-riding school. Horses are known to discriminate between quantities up to three, but are very distantly related to primates. Unexpectedly, we found only weak evidence for quantity discrimination skills and no effect of the type of stimuli. Only some subjects reliably selected the larger quantity in some, but not all quantity pairs. These findings are not only in contrast to the previously conducted study on monkeys, but also to other studies on horses. From this, we conclude that quantity discrimination competence may only be of minor importance for horses and highlight the influence of experimental conditions on the outcome of cognitive tests.

Inter-specific differences in numerical abilities among teleost fish

Adults, infants and non-human primates are thought to possess similar non-verbal numerical systems, but there is considerable debate regarding whether all vertebrates share the same numerical abilities. Despite an abundance of studies, cross-species comparison remains difficult because the methodology employed and the context of species examination vary considerably across studies. To fill this gap, we used the same procedure, stimuli, and numerical contrasts to compare quantity abilities of five teleost fish: redtail splitfin, guppies, zebrafish, Siamese fighting fish, and angelfish. Subjects were trained to discriminate between two sets of geometrical figures using a food reward. Fish initially were trained on an easy numerical ratio (5 vs. 10 and 6 vs. 12). Once they reached the learning criterion, they were subjected to non-reinforced probe trials in which the set size was constant but numerical ratios varied (8 vs. 12 and 9 vs. 12). They also were subjected to probe trials in which the ratio was constant, but the total set size was increased (25 vs. 50) or decreased (2 vs. 4). Overall, fish generalized to numerosities with a 0.67 ratio, but failed with a 0.75 ratio; they generalized to a smaller set size, but not to a larger one. Only minor differences were observed among the five species. However, in one species, zebrafish, the proportion of individuals reaching the learning criterion was much smaller than in the others. In a control experiment, zebrafish showed a similar lower performance in shape discrimination, suggesting that the observed difference resulted from the zebrafish's difficulty in learning this procedure rather than from a cross-species variation in the numerical domain.

A shared system of representation governing quantity discrimination in canids

One way to investigate the evolution of cognition is to compare the abilities of phylogenetically related species. The domestic dog (Canis lupus familiaris), for example, still shares cognitive abilities with the coyote (Canis latrans). Both of these canids possess the ability to make psychophysical "less/more" discriminations of food based on quantity. Like many other species including humans, this ability is mediated by Weber's Law: discrimination of continuous quantities is dependent on the ratio between the two quantities. As two simultaneously presented quantities of food become more similar, choice of the large or small option becomes random in both dogs and coyotes. It remains unknown, however, whether these closely related species within the same family - one domesticated, and one wild - make such quantitative comparisons with comparable accuracy. Has domestication honed or diminished this quantitative ability? Might different selective and ecological pressures facing coyotes drive them to be more or less able to accurately represent and discriminate food quantity than domesticated dogs? This study is an effort to elucidate this question concerning the evolution of non-verbal quantitative cognition. Here, we tested the quantitative discrimination ability of 16 domesticated dogs. Each animal was given nine trials in which two different quantities of food were simultaneously displayed to them. The domesticated dogs' performance on this task was then compared directly to the data from 16 coyotes' performance on this same task reported by Baker et al. (2011). The quantitative discrimination abilities between the two species were strikingly similar. Domesticated dogs demonstrated similar quantitative sensitivity as coyotes, suggesting that domestication may not have significantly altered the psychophysical discrimination abilities of canids. Instead, this study provides further evidence for similar non-verbal quantitative abilities across multiple species.

Bears "Count" Too: Quantity Estimation and Comparison in Black Bears (Ursus Americanus)

Studies of bear cognition are notably missing from the comparative record despite bears' large relative brain size and interesting status as generalist carnivores facing complex foraging challenges, but lacking complex social structures. We investigated the numerical abilities of three American black bears (Ursus Americanus) by presenting discrimination tasks on a touch-screen computer. One bear chose the larger of two arrays of dot stimuli, while two bears chose the smaller array of dots. On some trials the relative number of dots was congruent with the relative total area of the two arrays. On other trials number of dots was incongruent with area. All of the bears were above chance on trials of both types with static dots. Despite encountering greater difficulty with dots that moved within the arrays, one bear was able to discriminate numerically larger arrays of moving dots, and a subset of moving dots from within the larger array, even when area and number were incongruent. Thus, although the bears used area as a cue to guide responding, they were also able to use number as a cue. The pattern of performance was similar to that found previously with monkeys, and suggests that bears may also show other forms of sophisticated quantitative abilities.