Animal Cognition

, Volume 11, Issue 3, pp 495–503

Do fish count? Spontaneous discrimination of quantity in female mosquitofish


    • Department of General PsychologyUniversity of Padova
  • Marco Dadda
    • Department of General PsychologyUniversity of Padova
  • Giovanna Serena
    • Department of General PsychologyUniversity of Padova
  • Angelo Bisazza
    • Department of General PsychologyUniversity of Padova
Original Paper

DOI: 10.1007/s10071-008-0140-9

Cite this article as:
Agrillo, C., Dadda, M., Serena, G. et al. Anim Cogn (2008) 11: 495. doi:10.1007/s10071-008-0140-9


The spontaneous tendency to join the largest social group was used to investigate quantity discrimination in fish. Fish discriminated between shoals that differed by one element when the paired numbers were 1vs2, 2vs3 and 3vs4, but not when 4vs5 or larger. Using large numerosities (>4), the ability to discriminate between two numbers improved as the numerical distance between them increased and a significant discrimination was found only with ratios of 1:2 or smaller (4vs8, 8vs16 and 4vs10). Experiments to control for non-numerical variables evidenced the role played by the total area of stimuli with both large and small numerosities; the total quantity of movement of the fish within a shoal appeared also important but only when large numerosities were involved. Even though the pattern of discrimination exhibited by female mosquitofish is not fully consistent with any of the existing models of quantity representation, our results seem to suggest two distinct mechanisms in fish, one used to compare small numbers of objects and one used when larger numerosities are involved.


Fish cognitionQuantity discriminationContinuous variableNumber


It has long been recognized that the ability to make numerical judgments predates the evolution of human language. Studies on this subject have traditionally focused on human babies and non-human primates with only a handful of other mammal and bird species being investigated (Hauser and Spelke 2004; Pepperberg 2006). Comparative research suggests that there are basically two non-verbal systems for representing numerosity in animals, adults and human infants. Different species are thought to share an analog magnitude system of numerical representations that obeys Weber’s Law, which contains that as numerical magnitude increases, a larger disparity is needed to obtain the same level of discrimination (Xu and Spelke 2000; Jordan and Brannon 2006). Animals can usually discriminate among quantities larger than three or four provided there is some minimal numerosity ratio, usually 1:2 or 2:3 (Hauser et al. 2003; Lewis et al. 2005). The representations are imprecise and the discrimination is determined by the ratio between two numbers rather than the absolute difference. The second mechanism proposed is an object-tracking system (Trick and Pylyshyn 1994; Uller et al. 1999; Feigenson et al. 2002a). This system operates on a small number of items by keeping track of individual objects. It is precise but, due to the limited storage capacity of working memory resources, it is supposed to allow for the parallel representation of up to 3–4 elements only (Pylyshyn and Storm 1988). Feigenson and Carey (2005) found that infants failed to discriminate 1vs4 despite the highly discriminatory ratio, providing the strongest evidence for another mechanism involved in presence of small numerosity.

Organisms can provide quantity judgments without necessarily discriminating on the only basis of the numerosity of the items. Numerosity normally co-varies with several other physical attributes and animals can use the relative magnitude of continuous variables to estimate which group is larger. For example in an experiment involving a discrimination between two sets of objects differing in numerosity, individuals may compare the total area of objects, the sum of their contours, the density of objects in the array or total duration when stimuli are presented in succession (Clearfield and Mix 1999). Quantity discrimination based on non-numerical variables can be very precise and careful control experiments are necessary to determine the exact mechanism involved (Stevens et al. 2007).

The list of organisms whose numerical abilities were investigated has recently broadened to include two cold-blooded vertebrates. Uller et al. (2003) gave salamanders a choice between two glass tubes containing small numbers of live fruitflies. Salamanders selected the tube containing the larger numerosity when the paired numbers were 1vs2 and 2vs3 but not 3vs4 and 4vs6. In mosquitofish, females harassed by a male tend to join the larger of two available shoals and we recently showed (Agrillo et al. 2007) that they were able to discriminate between two shoals that differed by one element when paired numbers were 2vs3 or 3vs4 fish, but not when quantities were larger than 4 (i.e. 4vs5 or 5vs6).

No evidence was, however, provided by these two studies that numerical abilities in fish and amphibians are based on the same cognitive mechanisms that have been hypothesized for birds and mammals. No demonstration in particular was provided that they are really able to represent numbers since discrimination in both studies could be based on continuous variables that correlate with numerosity.

The present research aims to fill this gap. As the procedure previously used to investigate fish quantity discrimination (Agrillo et al. 2007) does not easily permit the manipulation of stimuli and to control the continuous variables that correlate with number, here we used a different experimental procedure, based on a well known social response of fishes, namely spontaneous choice of the larger shoal when placed in a novel environment (Hager and Helfman 1991; Pritchard et al. 2001; Hoare et al. 2004). The first part of the study aimed to determine the limit of numerical discrimination in female mosquitofish. We then used two control situations to examine whether their ability to discriminate was based on number or continuous quantities that co-vary with number.


Subjects and experimental protocol

Eastern mosquitofish, originally of North America, were introduced to Europe nearly a century ago. Females are highly social and in nature they form shoals of variable sizes from 2 to more than 20 individuals (Bisazza and Marin 1995). Fish were maintained in small mixed-sex groups (12–15 fish, approx. 1:1 sex ratio) kept in 70-l glass aquaria with abundant vegetation.

A total of 318 females of Gambusia holbrooki were used as subjects for the experiments. They were used only once and had a standard length, with the exception of experiment 4, of 3.21 ± 0.32 cm. Ninety similar sized (3.20 ± 0.40 cm) females were alternated as stimuli. We tested 14 females for each comparison in experiments 1–3 and 20 females for each comparison of experiment 4 and 5. Experiments were executed in temporal sequence (from pilot to experiment five) with the exception of experiments 1 and 2 whose trials were randomly intermingled.

There is a substantial evidence that in social fish single individuals, that happen to be in a unknown environment, tend to join other conspecifics and, if choosing between two shoals, they exhibit a preference for the large one (Pritchard et al. 2001; Agrillo and Dadda 2007). Such behaviour is thought to be an anti-predatory strategy allowing individuals that explore an unfamiliar environment to reduce the chance of being spotted by predators (Hamilton 1971). We used this spontaneous tendency to go to the larger shoal to study the limits of the quantity discrimination in our experimental model.

The experimental apparatus was composed of three adjacent tanks (Fig. 1). The central one, the “subject tank”, housed the test female (36 × 60 × 35 cm). At two ends two smaller “stimulus tanks” (36 × 10 × 10 cm) faced the subject tank. The walls were covered with green plastic to prevent stimulus fish and subjects from seeing outside.
Fig. 1

Schematic representation of the experimental apparatus: a subject tank, b stimulus tanks. Dotted lines show the area of the subject tank considered for calculating social preference

Each tank was lit by one fluorescent lamp with water maintained at a temperature of 25° ± 2°C. A video camera was suspended about 1 m above the test tank and used to record the position of the female during the tests.

Stimulus females were introduced 10 min prior the test; the test female was introduced into the middle of the test tank and her position was then recorded for 20 min. In half of the tests of each experiment the larger group was on the left and in half it was on the right.

We calculated the time spent by the subject female shoaling within a distance of 11 cm from the glass facing the stimulus tank by superimposing a line on the video. The observer of this video was blind with respect to the aim of the experiment. The dependent variable was the proportion of time (calculated in seconds) spent close to the larger shoal. Subjects that spent less than the 40% of time within 11 cm from the stimulus tanks were discarded and replaced by another fish. Fifteen subjects (5%) fell in this category (7 subjects in the first experiment, 5 in the second, 2 in the third, 1 in the forth). Frequencies were arcsine (square root)-transformed (Sokal and Rohlf 1995). Mean ± SD are provided. Statistical test were carried out using SPSS 11.5.1.

Pilot test of preference for larger shoals

Fourteen subjects were used for this experiment to investigate whether fish, placed in a new environment, prefer to join a larger group of conspecifics. Unlike the other experiments, in the pilot test fish were observed for a total of 15 min. In this test females had the opportunity to choose between two and four individuals.

Experiment 1: Discrimination between quantities differing by one element

Ninety-eight subjects were used for this experiment. They could choose between two shoals of females differing by one unit. Comparisons were 1vs2, 2vs3, 3vs4, 4vs5, 5vs6, 6vs7 and 7vs8.

Experiment 2: Discrimination among large quantities with variation in numerosity ratio

Looking for the minimal ratio necessary to distinguish among large shoals, in this series of comparisons the size of the smaller shoal was kept constant (four individuals) while the ratio was increased from 2:5 to 4:5. Seventy subjects were used for this experiment. We evaluated the following numerical comparisons: 4vs6, 4vs7, 4vs8 and 4vs10 (the 4vs5 comparison was presented above in exp. 1). We also investigated the ability to discriminate a 3:4 numerosity ratio (6vs8 comparison).

Experiment 3: Discrimination between very large numerosities

We intended to verify whether mosquitofish are able to distinguish very large groups of conspecifics provided that they differ enough in numerosity. We used comparisons with 1:2 (that was successfully discriminated in previous experiment) and 2:3 numerosity ratios (not significantly discriminated in previous experiment). The comparisons were 8vs16 and 8vs12. The apparatus was modified, enlarging the stimulus tanks (36 × 18 × 10 cm) to hold the larger shoals used for this experiment.

Experiment 4: Surface area control

The subject could choose between shoals differing in size but with the same total surface occupied by stimuli. We studied two numerical comparisons: 2vs3 (small numerosities) and 4vs8 (large numerosities). Several females were photographed using a digital camera and their area estimated by using TpsDig software (Rohlf 2004), a program that allows estimation of the area and the perimeter of objects from digitized images. Fish slightly larger than the subjects were selected to form the smaller shoal and fish slightly smaller than subjects to form the larger shoal so that the two shoals could be matched in total area. Size of subjects and stimulus fish are summarized in Table 1.
Table 1

Total length (cm) of stimuli and subjects and total area (cm2) occupied by shoals in experiment 4


Length (mean ± SD)

Total area (mean ± SD)

Stimulus fish (2 vs 3)

 Two individuals

3.54 ± 0.09

8.75 ± 0.16

 Three individuals

3.02 ± 0.14

8.74 ± 0.09

 Experimental subjects

3.30 ± 0.39


Stimulus fish (4 vs 8)

 Four individuals

3.67 ± 0.20

19.92 ± 0.31

 Eight individuals

2.57 ± 0.11

19.95 ± 0.17

 Experimental subjects

3.28 ± 0.39


To test for a possible size preference, 14 females (3.02 ± 0.10 cm) were observed for their choice between one slightly larger and one slightly smaller fish (3.45 ± 0.20 and 2.55 ± 0.31 cm, respectively).

Experiment 5: Fish movement control

We studied the same numerical comparisons (2vs3 and 4vs8) as the previous experiment.

Most fish can live in a wide range of temperatures and their activity is influenced by water temperature (Krause and Godin 1995; Pritchard et al. 2001). In a preliminary experiment we assessed that in G. holbrooki a 10° increase in temperature nearly doubled the movements in a shoal. To match the total activity, the smaller shoal of this experiment was kept at 29 ± 1°C and the large one at 19 ± 1°C. Two pools of 32 stimulus fish each were kept at these two temperatures for 2 days prior to the experiment. To ensure that activity was matched we video-recorded stimuli in a sub-sample of five tests and measured the total number of movements. The surface of stimulus tank was subdivided in a 38 × 10 (380 squares) grid superimposed on the monitor and we recorded the number of times a fish crossed the border between squares.

To test for a possible preference for slow moving or fast moving fish, 14 females (3.23 ± 0.11 cm) were tested for their choice between one fish kept at 29 ± 1°C and one fish kept at 19 ± 1° using the same procedure described above.


Pilot test of preference for larger shoals

The position of the stimuli (right/left) was not significant [t(12) = −0.087, P = 0.932]. On the whole females spent more time near the larger shoal [0.624 ± 0.167, t(13) = 2.786, P = 0.015, two tailed].

Experiment 1: Discrimination between quantities differing by one element

A significant choice of the larger shoal was found in comparisons 1vs2 [t(13) = 3.154, P = 0.008; Fig. 2], 2vs3 [t(13) = 2.453, P = 0.029], and 3vs4 [t(13) = 2.504, P = 0.026]. No significant choice was observed in 4vs5 [t(13) = 0.370, P = 0.717], 5vs6 [t(13) = 0.799, P = 0.438], 6vs7 [t(13) = −1.600, P = 0.134] and 7vs8 [t(13) = 0.212, P = 0.835].
Fig. 2

Proportion of time near the larger shoal (mean ± SE) in choice test of experiment 1 (* one sample t-test, P < 0.05). A significant choice for the larger shoal is found in comparisons 1vs2, 2vs3 and 3vs4

A significant difference was found [t(96) = 3.041, P = 0.003] when the three comparisons with both numerosities ≤4 (1vs2, 2vs3 and 3vs4) were contrasted with the four comparisons (4vs5, 5vs6, 6vs7 and 7vs8) containing at least one larger group.

Experiment 2: Discrimination among large quantities with variation in numerosity ratio

A significant choice of the larger shoal was found both in comparisons with 2:5 numerosity ratio, 4vs10 [t(13) = 5.156, P < 0.001] and 1:2 numerosity ratio, 4vs8 elements [t(13) = 4.036, P = 0.001; Fig. 3a], whereas no significant choice was found in 4vs6 [t(13) = 1.490, P = 0.160] and 4vs7 [t(13) = 1.975, P = 0.070]. Fish also failed to choose the larger shoal in the comparison with 3:4 numerosity ratio, 6vs8 [t(13) = 0.481, P = 0.639].
Fig. 3

Proportion of time near the larger shoal (mean ± SE) in choice test of experiment 2 (a) and experiment 3 (b) (* one sample t-test, P < 0.05). A significant choice for the larger shoal is found in comparisons with 1:2 or 2:5 numerical ratio

Overall there was a significant increase in preference for the large shoal with decreasing numerosity ratio from 4:5 to 2:5 (Spearman rank correlation test Rho = 0.943, P = 0.005).

Experiment 3: Discrimination between very large numerosities

A significant choice of the larger shoal was found in comparisons 8vs16 [t(13) = 2.372, P = 0.034; Fig. 3b], but not in 8vs12 [t(13) = 1.027, P = 0.323]. When all comparisons involving numerosity ratios of 2:3 or 3:4 (6vs8, 4vs6 and 8vs12) are pooled together to obtain a large sample size a non-significant choice toward the larger shoal was found [t(41) = 1.781, P = 0.082].

Experiment 4: Surface area control

When total area of fishes was matched, we found no significant choice for the larger shoal both in 2vs3 [t(19) = 0.297, P = 0.770; Fig. 4a] and in 4vs8 comparison [t(19) = −0.289, P = 0.775].
Fig. 4

Proportion of time near the larger shoal (mean ± SE) in choice test of experiment 4 and experiment 5. When the total area occupied by the stimuli was paired, no significant choice has been observed in either the comparisons (a). When the overall quantity of movement was paired, a significant preference for the larger shoal was evident when numerosities were smaller than 4, whereas no significant choice was found for the other comparison (b). Open circles experiments with continuous variable paired, black squares tests with same numerosity without control of continuous variable (from experiment 1 and 2). * Denotes significant departure from chance (one sample t-test, P < 0.05)

In the control experiment, when choosing between single stimulus fish, females showed no significant preference for the slightly larger or the slightly smaller fish [t(13) = 0.753; P = 0.465].

Experiment 5: Fish movement control

Small and large shoals did not differ in total movements both in 2vs3 comparison [small shoal: 581 ± 145; large shoal: 555 ± 31; t(8) = 0.383, P = 0.711] and in 4vs8 comparison (small shoal: 1,376 ± 255; large shoal: 1,416 ± 308; t(8) = 0.223, P = 0.829).

Subjects spent significantly more time near the larger shoal in 2vs3 comparison [t(19) = 2.757, P = 0.013; Fig. 4b] whereas no significant choice was found in 4vs8 comparison [t(19) = 1.139, P = 0.269].

In the control experiment, when choosing between single stimulus fish, females showed no significant preference for the slow moving or the fast moving fish [t(13) = 0.103, P = 0.920].


Like most gregarious fishes, female mosquitofish placed in a new, unexplored and potentially dangerous environment choose to stay close to the group containing the larger number of conspecifics (Hager and Helfman 1991; Hoare et al. 2004). The results of the pilot experiment show that fish stay systematically closer to the larger of the two available shoals. This robust spontaneous response can therefore be used to investigate the ability in this species to discriminate between groups containing different numbers of objects.

Limits on discrimination of quantities of mosquitofish

In the first experiment female mosquitofish were given the choice between shoals that differed by one unit. The subjects’ performance revealed a clear set-size effect marked by a significant choice in the comparisons with up to four elements in the larger shoal (1vs2, 2vs3 and 3vs4) but a failure with larger numbers (4vs5, 5vs6, 6vs7 and 7vs8). The overall pattern observed in experiment 1 matches the results previously obtained in the same species using a different method (Agrillo et al. 2007). The limit in the capacity to discriminate between two groups that differ by one unit also parallels that observed in higher vertebrates using a spontaneous preference paradigm. In an experiment with rhesus macaques, for example, monkeys were confronted with two quantities of apple slices and successfully chose the greater number with comparison of 1vs2, 2vs3 and 3vs4, but failed with 4vs5 and 4vs6 (Hauser et al. 2000). In a similar experiment, 12-month-old infants chose the larger quantity of crackers in the comparisons 1vs2 and 2vs3 but failed in the comparisons of 3vs4, 2vs4 and 3vs6 (Feigenson et al. 2002a). Even though we presently lack sufficient knowledge to determine whether the same cognitive processes are involved in all species, our results show that organism as diverse as primates and teleost fishes, whose divergence occurred more than 450 million years ago, share similar capacities in precise discrimination of small quantities.

Since fish discriminated 1vs2 just as well as 3vs4, our experiment seems to suggest that with small numbers, the ratio between quantities may be unimportant. Nonetheless, the results of experiment 1 alone do not support the existence of two distinct mechanisms for quantity discrimination: it is worth noting that subjects’ performance with these comparisons may also be consistent with a potential limit on the ratio discrimination the fish can perform, since the ratio progressively increases with increasing numerosity, so it is not possible to exclude that only one mechanism based on analog magnitude is involved in this task.

In the second experiment we found that mosquitofish were able to distinguish between shoals containing more than 4 elements, provided that numerosity ratio of the two sets was 1:2 or smaller. As shown by experiment 3, with a 1:2 numerosity ratio, discrimination is possible even when shoals contain fairly large numbers of individuals (8vs16). As in previous experiments the fish failed to select the larger group when the numerosity ratio was increased to 2:3 (8vs12). However, there was not an abrupt fall in the ability to discriminate with ratios below 1:2. Rather we observed a steady decrease in preference with ratios increasing from 2:5 to 4:5. When all comparisons involving numerosity ratios of 2:3 or 3:4 are pooled together to obtain a large sample size (N = 42) a marginally non-significant choice of the larger shoal was found, indicating that a difference is also perceived above the 1:2 ratio but that discrimination of the two quantities becomes more and more difficult when the relative distance between numerosities is reduced. The pattern of discrimination shown by female mosquitofish when sets contain more than four elements approaches that observed in infants and in the other non-human species in similar comparisons (Meck and Church 1983; Xu and Spelke 2000; Hauser et al. 2003; Cantlon and Brannon 2006). Six-month-old infants studied using a habituation paradigm were able to discriminate the numerosities 8vs16 but failed with a 2:3 ratio such as in the comparison of 8vs12 (Xu and Spelke 2000). However, in humans the ability to discriminate increases in precision during development: ten-month old infants are able to discriminate 8 from 12 elements (2:3 ratio) but not 8 from 10 (4:5) and adults can discriminate larger ratios (Barth et al. 2003; Xu and Arriaga 2007). Cotton tamarins tested with auditory stimuli showed abilities similar to 10-month old infants; they successfully discriminated 4 from 6, and 8 from 12 syllables (2:3 ratio) but failed to discriminate sequences of 4vs5 and 8vs10 syllables (Hauser et al. 2003). Several authors agree that this evidence implies that adult, child and non-human mammals share a core system for representing large discrete quantities, approximately in accordance with Weber’s law. Here fish showed a clear Weber signature, thus indicating that some capacity to use approximate magnitudes to represent number might be phylogenetically very old; at least predating the divergence of the main vertebrate classes.

Discrete versus continuous quantities

Experiments 4 and 5 tried to determine the contribution of continuous variables on quantitative abilities of mosquitofish. With visual stimuli, features such as total surface area, contour length or density normally co-vary with number and can easily be used to select the larger quantity of the objects in an array (Feigenson et al. 2002b; Feigenson and Carey 2005). When the objects move, the total quantity of movement could also be used to estimate number (Uller et al. 2003).

In experiment 4, once the total area occupied by fish stimuli had been controlled for, our subjects failed to choose the larger shoal both in the 2vs3 and in the 4vs8 comparison. One can argue that in this experiment, results were influenced by preference of subjects for the size of shoal mates. Fish normally prefer shoal mates as close as possible to their own size to avoid oddity (Barber et al. 1998; Peichel 2004). For this reason, to make total areas equivalent, in our experiments we used fish stimuli on average slightly larger or slightly smaller than the subjects so that difference between stimuli and subjects was minimized and approximately the same in the two directions. Indeed in the control experiment, when females were allowed to choose between two single stimulus fish, we found no evidence of a preference for the slightly larger or for the slightly smaller fish.

In experiment 5 we manipulated the total activity of fish within a shoal by keeping the groups at different water temperatures, a method previously used for other species (Reynolds and Casterlin 1979; Pritchard et al. 2001). Equating total activity of the two shoals had no effect on the choice of the larger group in the 2vs3 comparison. In contrast, fish failed to discriminate four from eight fish, suggesting that this additional information may be necessary in large quantity discrimination. The possibility that in this experiment slow and fast swimming fish differed in their attractiveness is unlikely since the result of the control experiment, when females chose between single stimulus fish, showed no significant preference for one or the other type.

When considering large quantity discrimination, experiment 4 indicates that subjects base their decision on the total surface area of the fish while experiment 5 indicates that they base their decision on the amount of movement. Taken together these results lead to a paradox. The two experiments suggest that fish use total surface area as well as total movement when determining shoal size. However, because our experiments only controlled for one variable at a time then the fish should have succeeded in both control conditions. That is, although total movement was controlled in one condition, total surface area was not; thus, why did fish not choose the shoal with the larger number given that they showed the ability to use total surface area in the other experiment? One explanation of this apparent conflict is that perhaps fish need to use multiple cues to differentiate quantity (i.e., they are unable to base shoal decisions on only a single type of non-numerical cue). An alternative hypothesis is that quantity information from multiple non-numerical cues is fed into a single accumulator, which needs to reach a threshold for the subject to perceive one shoal as being larger than the other. A choice mechanism based on multiple cues is certainly not unexpected for this class of stimuli. Fish can sometimes be motionless or occlude each other or differ in their orientation and natural selection may have favored a mechanism that recruits all the available cues in order to increase speed and accuracy of shoal choice. Careful experiments involving variation in the number of cue types and magnitude of differences within each cue type could test the different models and reveal more precisely how fish compute quantity.

Quantity representation in mosquitofish

Although the results of this study are largely preliminary, a first appraisal is possible of the significance of these results with fish relative to the general theoretical framework that is emerging in recent years, primarily on the basis of data deriving from the enormous amount of empirical work on numerical cognition with infants and non-human primates (Dehaene et al. 1998; Hauser and Spelke 2004). Most researchers now agree that more than one non-verbal mechanism is available to represent quantity of objects (Feigenson et al. 2002a). One is a system of analog magnitude that represents items in an array as a single magnitude proportional to their number. This kind of mental magnitude could also be used to represent continuous quantity. The magnitude would be proportional, for example, to the total area of the objects or to the density of objects in an array and it would allow the comparison of two quantities without necessarily representing objects but using such continuous variables (Gallistel and Gelman 2000).

Organisms could also be using an object-file system to represent small numbers of objects. According to this model each object in an array is represented by a distinct symbol and these implicitly contain information about the number of objects in the array (Trick and Pylyshyn 1994; Feigenson and Carey 2005). The signature of this system is a set-size limit. Success in discrimination is not influenced by number ratio but is generally limited to four or fewer objects.

It is not clear which mechanism underlies a fish’s capacity to estimate the number of individuals in a shoal. Experiment 4 and 5 show clearly that fish are sensitive to continuous properties of the stimuli, but the way in which they respond is not consistent with any of the existing accounts of number representation. Previous evidence has found that human infants are sensitive to continuous variables such as total area, but only when presented with small numbers (Feigenson et al. 2002b; Xu 2003; Wood and Spelke 2005). On the other hand in the presence of large numbers they seem not to attend to total area (Xu and Spelke 2000; Lipton and Spelke 2003). We observed a different pattern in female mosquitofish: when total area is made equal, the fish fail to choose systematically in either small or large number comparisons. Furthermore, in the movement control experiment we found a reverse pattern from what would be predicted from the infant data: fish seem to ignore continuous movement in the small number condition and attend to movement in the large number condition. According to these differences, it is reasonable to guess that, even if the limits exhibited by fish to select the larger quantity are very close to that observed in human infants, such ability relies on a different system. Evolutionary convergence may have led to such a similar performance in spontaneous quantity tasks, but the cognitive mechanisms on the basis may not be homologues.

On the other hand, an important factor to take into account when comparing our results with those of other studies, is that here fish are quantifying conspecifics whereas the other species tested have been quantifying food or artefacts. Compelling evidence exists, at least in mammals and birds, that perceptual information related to conspecifics is usually processed by distinct and specialized neural mechanisms (Haxby 2002; Gentner 2004). In the previous section we also pointed out that the properties of living things can greatly differ from those of inanimate objects. The possibility is left open that fish and mammals share homologous systems that access different types of processes in different contexts.

Our results do not unambiguously support the existence of two distinct numerical systems in fish. Yet, many signs indicate that mosquitofish were using two different methods of discrimination when they estimated large and small numerosities. Discrimination using a numerosity of less than four appears insensitive to total fish movement, which instead affects discrimination of large numerosities. In addition here we did not observe a strong influence of numerosity ratio (since they equally discriminated 1vs2, 2vs3 or 3vs4), the typical signature of analog magnitude representation that we observed with large quantity discrimination; instead we observed a set-size signature similar to that typically found in the object-file system hypothesized for mammals. Further confirmation of the possible existence of two separate systems comes from the evidence of dissociation between performance with small and large numbers in experiments with the same numerical ratio: discriminations among quantities with ratios of 2:3 or 3:4 were successful with numerosities of less than four (comparisons 2vs3 and 3vs4, exp. 1) but not with larger numerosities (comparisons 4vs6, 6vs8 and 8vs12, exp. 2–3).

In the hypothetical system of discrimination of small numbers, a set-size signature typical of an object-file system is apparently coexisting with a mechanism of discrimination based on total area occupied rather than the number of elements in the set. This pattern closely resembles that found in 10–12 month infants in a choice task with different quantities of crackers (Feigenson et al. 2002a). To explain these results it was suggested that infants can compare an object-file representation on the basis of non-numerical dimensions bound to those representations, rather than via a one-to-one correspondence (Feigenson et al. 2002a; 2004).

To summarize, we suggest that mosquitofish use two distinct systems for quantity discrimination that are activated in relation to the numerosity to be valued but that they are not necessarily identical to the systems that have been hypothesized for infants and primates. At the same time our study provides persuasive evidence that when choosing between two shoals, fish do not use numerical representation but rather base their choice on non-numerical variables that are correlated with shoal size. Such results do not necessarily imply an incapability to discriminate two groups on only the basis of the numerosity of the items. Perceptual cues of the stimuli may simply be the easiest indicators of the numerosity in this task. In nature, a quick choice of the best option may mean escape from a predatory attack and in the course of evolution speed in choosing the best refuge may have been traded off with accuracy. In adult humans there is compelling evidence that abstract numerosity representations are used for judgments of large numerosities (Whalen et al. 1999; Cordes et al. 2001; Barth et al. 2003). Nonetheless, under some circumstances, large number estimation is based on stimulus properties such as area or density, which are correlated with stimulus numerosity (Durgin 1995; Vos et al. 1988). Further research using different procedures (e.g. training with operant conditioning) and different categories of stimuli (e.g. inanimate artefact) are required in order to clarify if fish have the capacity to discriminate two groups of elements when no other perceptual feature of the stimuli can be used.


The authors would like to thank Brian Butterworth, Elizabeth Spelke, Marco Zorzi for useful comments, Jonathan Daisley and Peter Kramer for their suggestions and Maria Anna Posa for her help conducting the experiments. This study was supported by research grants of the University of Padova to AB. The reported experiments comply with all laws of the country (Italy) in which they were performed.

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© Springer-Verlag 2008