Teleost fish have been found to be very efficient in the discrimination of numerical quantities, showing abilities comparable to those of many mammals and birds14,33. However it is not known if these similarities extend to other numerical abilities. Rhesus macaques16, rats18, chicks19, pigeons20 and bees23 are able to use ordinal information. Our results show that guppies too can use ordinal information to identify a specific position in a series of otherwise identical objects.

In this study, guppies learned to identify the 3rd feeder in a row of 8 identical alternative feeders in a relatively small number of trials, both when they encountered feeders one after the other in their direction of swimming and when feeders were perpendicularly aligned with respect to the starting point of the fish. However, the performance was much more accurate in the latter condition. With sequentially encountered feeders while swimming along the sequence of feeders, a subject progressively loose the capacity to glance the entire series of objects and it is possible that the need to keep in mind the number of non-visible objects made the task more difficult for guppies. The higher number of errors on the second position also suggests that guppies might be unable to completely inhibit the tendency to dislodge the disc when they encounter the feeder preceding the correct one. Control tests using a larger inter-feeder distance presented in their direction of swimming are necessary to test this hypothesis.

The position of an object in a series can be learned using a non-numerical strategy. For instance an animal can learn to stop at a given distance from the first object of the row or swimming from the starting point in a precise direction. Fish are also able to use specific landmarks and the geometry of the environment to precisely locate a point in space34,35. To prevent this possibility, during the training phase the absolute position of the rewarded feeder was varied across trials. In the second experiment guppies proved able to choose the 3rd position more often than the adjacent ones, indicating that they could rely on solely the ordinal position to identify the location of the reinforced feeder. However, fish are known to possess sophisticated learning skills and can discriminate complex patterns36,37. Blind Mexican cavefish (Astyanax fasciatus) for example can precisely learn the relative position of four landmarks placed in their environment and they change their exploratory behavior when the position of two adjacent landmarks is switched38. Our subjects could have solved the task by learning all the spatial arrangements or, at least, some of them. To test for this hypothesis, we did a control test presenting 12 novel spatial arrangements. Even in this case guppies selected the 3rd feeder thus excluding that pattern recognition played a key role in solving the task.

Several fish species, especially those active at night or living in turbid water, are known to use the olfactory system to search for food29,30. This has never been demonstrated in guppies, but these fish have been shown to respond to chemical cues from conspecifics and predators39. One may argue that olfactory cues may have guided the subjects’ decisions during our experiments. However, the finding that subjects trained to find food on the 3rd position still chose the correct feeder in the absence of a food reward excludes this possibility. This also aligns with previous studies on guppies using similar feeders, in which no influence of olfactory cues was found14,40. That said, it is worth noting that we made every effort to avoid the possibility of fish using olfaction to locate the food in our experiments, but we cannot exclude that guppies in nature might integrate olfactory and visual information to locate a hidden food source.

Some authors have suggested that animals are not naturally attuned to number, as numerical information would be less salient in natural contexts than physical attributes; as a consequence, animals would be expected to use number only as a last-resort strategy, when no other cues are available to discriminate between quantities41,42. This hypothesis is supported by evidence showing that mosquitofish, Gambusia holbrooki, could easily select the larger group of social companions, but their performance dropped to chance level when the cumulative surface area between shoals was controlled for43. However, when prevented from using non numerical attributes, mosquitofish proved able to select the larger shoal relying exclusively on numerical information, in agreement with the last-resort hypothesis26. This does not occur in all cases. Agrillo et al. (2011)44 found that mosquitofish trained to discriminate bi-dimensional figures showed no difference in learning rates when allowed to use continuous quantities only or numbers only. However, they learned more quickly when these two kinds of information were simultaneously available, in accordance with previous literature showing how redundancy of information facilitates learning both in humans and in non-human animals45,46. The same problem exists for discrimination of ordinal position. To address this issue, we repeated the procedure used in the second experiment but maintained constant spacing among the feeders and their absolute spatial position during the whole training period, so that the guppies were free to use ordinal or spatial information (or both) to learn the task. In the test phase, when the ordinal position was contrasted with the spatial position, fish chose the 3rd feeder (the correct ordinal position) significantly more often than the feeder occupying the spatial position held by the feeder reinforced during training. However, 3 out of the 4 subjects also chose the spatially correct position above chance, indicating that, to some extent, guppies were also encoding spatial position during the learning phase. Our data therefore suggest that, for a guppy in an ordinal-position task, numerical information may be easier to be processed than other types of information (i.e., spatial positioning or the spatial relationships among different objects); thus, the argument that fish use number only as a last-resort is not supported in the context of ordinal abilities. In addition, the fact that spatial cues seem to be more salient than numerical information in relative numerosity judgments of fish43,47,48 while the opposite result was found in this ordinal task reinforces the idea – previously advanced in the literature – that the relative salience of numerical information over spatial cues is context-dependent49.

The tendency to rely more on ordinal information than on other cues might have a potential adaptive value in nature for a species living in shallow waters, where the relative position of stable elements of the landscape could be used as cues for orienting in space as observed in other fish, including species of the same family50. For example, guppies could learn that there is a food patch after three consecutive rocks or use a specific position in a row of similar trees on the bank for orientation while escaping from predators. The shape and the details of these objects are more likely to change over seasons than their relative position.

From the results of this experiment it is also clear that, although guppies privileged ordinal information, at least some individuals were in fact making use of multiple types of information (spatial and ordinal) to solve the task. In nature, numerical and continuous information are often simultaneously available: more pieces of food have a greater cumulative surface, larger social groups occupy a larger volume and more calls require more time to be produced43,51,52. Not surprisingly, guppies and other vertebrates have evolved mechanisms that use redundant information to estimate quantities44,53.

Several authors agree with the existence of an approximate number system (ANS) able to support the representations of numerosities over the whole numerical range. Numerical discriminations produced through this mechanism are subject to Weber’s law: errors generally increase in proportion with increasing numerosity and accuracy is determined by the magnitude of the set to be enumerated31,32. The possibility exists that performance in ordinal tasks is similarly affected by the number of items, such that the ability to locate the correct target decreases as the ordinal position increases. For instance, bees can identify up to 4 positions in a series of different alternatives but beyond the 4th position they are no longer able to identify the correct landmark23. Conversely, studies on rats and chicks did not find a similar decrease in discriminability as a function of the ordinal position18,19. We addressed this issue by comparing the training on the 3rd and 5th positions in a row of 12 identical feeders. Fish trained on the 5th feeder still located the correct target but were less accurate than fish trained on the 3rd feeder, as they made more attempts at adjacent feeders compared to the other group. This finding might suggest that 5 units could be the upper limit of guppies’ ability to use ordinal information, the same numerical threshold recently reported in cardinal tasks14. Although future studies in which guppies are trained to select ordinal positions higher than 5 are required to confirm this hypothesis, it seems clear that the performance of guppies does not attain that of other vertebrates (e.g., rats are able to learn up to the 12th position). The most obvious explanation for this difference resides in the enormous brain development of mammals and birds, which are both superior to fish in many other functions54. However, we cannot exclude that different findings may be ascribed to the different methodologies used across the studies (e.g., learning criteria, number of trials, etc.). It has been shown that numerical acuity within the same species can greatly vary as a function of the methodology adopted55. Another possibility is that inter-species differences reflect distinct selective pressures that acted on each species due to adaptation to their respective ecological niches. For instance, rats are known to dig extensive burrow systems consisting of food storage chambers and feeding sites56. It is possible that the foraging behaviour of this species has favoured the development of sophisticated abilities to locate food in different chambers on the basis of their position in the burrow network.

In summary, our experiments provide the first evidence that guppies can use ordinal numerical information, even when alternative non-numerical cues are available. Our findings, together with results in other distantly related species, point to the existence of numerical ordinal competencies widespread among non-human animals. Future studies are now needed to shed more light on ordinal abilities of guppies. For instance, a recent study suggests that birds exhibit a spontaneous leftward bias when required to locate an object by using ordinal information, indirectly evoking the idea of a mental number line similar to that described in humans57. In our study we did not attempt to assess whether also fish preferentially enumerate from left to right or vice versa, a hypothesis that should be tested in the near future. Also, further research is welcome to assess whether this ability is unique to guppies or instead is shared by other fish species living in different ecological contexts—for instance, in pelagic fish that do not normally experience stable sequences of objects in their environment.