The importance of replication in comparative psychology: the lesson of elephant quantity judgments

Quantitative abilities of invertebrates: a methodological review

Quantitative abilities are widely recognized to play important roles in several ecological contexts, such as foraging, mate choice, and social interaction. Indeed, such abilities are widespread among vertebrates, in particular mammals, birds, and fish. Recently, there has been an increasing number of studies on the quantitative abilities of invertebrates. In this review, we present the current knowledge in this field, especially focusing on the ecological relevance of the capacity to process quantitative information, the similarities with vertebrates, and the different methods adopted to investigate this cognitive skill. The literature argues, beyond methodological differences, a substantial similarity between the quantitative abilities of invertebrates and those of vertebrates, supporting the idea that similar ecological pressures may determine the emergence of similar cognitive systems even in distantly related species.

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

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

Numerical abilities in fish: A methodological review

The ability to utilize numerical information can be adaptive in a number of ecological contexts including foraging, mating, parental care, and anti-predator strategies. Numerical abilities of mammals and birds have been studied both in natural conditions and in controlled laboratory conditions using a variety of approaches. During the last decade this ability was also investigated in some fish species. Here we reviewed the main methods used to study this group, highlighting the strengths and weaknesses of each of the methods used. Fish have only been studied under laboratory conditions and among the methods used with other species, only two have been systematically used in fish-spontaneous choice tests and discrimination learning procedures. In the former case, the choice between two options is observed in a biologically relevant situation and the degree of preference for the larger/smaller group is taken as a measure of the capacity to discriminate the two quantities (e.g., two shoals differing in number). In discrimination learning tasks, fish are trained to select the larger or the smaller of two sets of abstract objects, typically two-dimensional geometric figures, using food or social companions as reward. Beyond methodological differences, what emerges from the literature is a substantial similarity of the numerical abilities of fish with those of other vertebrates studied.

Individual differences in cognition among teleost fishes

Individual differences in cognitive abilities have been thoroughly investigated in humans and to a lesser extent in other mammals. Despite the growing interest in studying cognition in other taxonomic groups, data on individual differences are scarce for non-mammalian species. Here, we review the literature on individual differences in cognitive abilities in teleost fishes. Relatively few studies have directly addressed this topic and have provided evidence of consistent and heritable individual variation in cognitive abilities in fish. We found much more evidence of individual cognitive differences in other research areas, namely sex differences, personality differences, cerebral lateralisation and comparison between populations. Altogether, these studies suggest that individual differences in cognition are as common in fish as in warm-blooded vertebrates. Based on the example of research on mammals, we suggest directions for future investigation in fish.

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

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

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

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

Lemurs and macaques show similar numerical sensitivity

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

The "Clever Hans Phenomenon" revisited

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

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.

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.

Activity counts: the effect of swimming activity on quantity discrimination in fish

Human infants and non-human animals can discriminate the larger of two sets of discrete items. This quantity discrimination may be based upon the number of items, or upon non-numerical variables of the sets that co-vary with number. We have demonstrated that angelfish select the larger of two shoals of conspecifics without using inter-fish distance or space occupied by the stimuli as cues. However, density appeared to influence the choice between large shoals. Here, we examine the role of another non-numerical cue, swimming activity of the stimulus fish, in quantity discrimination by angelfish. To control this variable, we varied the water temperature of the stimulus aquaria or restricted the space occupied by each fish in the stimulus shoals. We used the previously successfully discriminated contrasts consisting of large (10 vs. 5) and small (3 vs. 2) shoals. We also studied whether more active or less active shoals are preferred in case of equally sized shoals (10 vs. 10, 5 vs. 5, and 3 vs. 3). When differences in stimulus fish activity were minimized by temperature manipulation we found angelfish to prefer the larger shoal in the 3 vs. 2 comparison, but not in the 10 vs. 5 comparison. When activity was controlled by space restriction, angelfish preferred the larger shoal in both numerical contrasts. These results imply that the overall activity level of the contrasted shoals is not a necessary condition for small shoals discrimination in angelfish. On the other hand, the results obtained for the large shoals, together with results obtained in the control treatments (equal numerical contrasts and differing activity levels), suggest that activity is a sufficient condition for discrimination when large shoals are involved. Further experiments are needed to evaluate the influence of other continuous variables, and to assess whether the mechanisms underlying performance are comparable to those suggested for other animals.

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.