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Continuous and discrete quantity information are important in guiding animal behaviour in virtually all aspects of life. The capacity to evaluate continuous (uncountable) quantities, such as length, area, weight, or duration, is widespread and can be found in organisms with relatively simple nervous systems, such as annelids, crustaceans, or gastropds1,2,3. This quantitative information takes part in decision-making processes in different contexts. For example, animals may gauge body sizes of rivals or prospective mates, assess distances from home, or estimate the extent of a food patch4,5,6.
Several vertebrates, from teleost fishes to primates, can also process discrete (countable) information. For example, many species are capable of accurately estimating the number of elements in a set and comparing the numerosity of different sets7,8. Studies conducted in nature or in the laboratory have shown that numerical abilities serve important adaptive functions. For example, in guppies, New Zealand robins, and macaques, quantity discrimination is used to select the patch containing the larger number of food items9,10,11. Conversely, some predators, namely lions and striped field mice, use this ability to select the smallest prey groups because they are more vulnerable to predation12,13. Various group-living mammals, including chimpanzees, lions, and hyenas, gauge the relative number of opponents before deciding whether to attack or withdraw14,15,16. Gregarious fish use the same ability to select the social group that provides the best protection from predators17,18,19. Some species, including eastern mosquitofish, brown-headed cowbirds, and American coots, use their quantitative abilities to increase reproductive success20,21,22.
Cognitive psychologists have shown that in these cases it is not necessary to assume the existence of a true numerical estimation system because an animal can use continuous cues, such as the amount of movement, the cumulative surface occupied by items, or the convex hull of the set as a proxy for number23,24. Inferring the existence of a numerical system requires a series of careful laboratory control experiments in which the animal is subjected to numerical tasks, while the access to non-numerical information is simultaneously prevented8,25. This process is not always straightforward and studies often fail to reach a firm conclusion even after numerous experiments are performed. In fact, convincing evidence of the presence of a numerical system exists only for a small fraction of the species investigated (e.g., guppy26, chicken27, and rhesus monkeys10).
It is not known whether numerical abilities have similar selective advantages in other phyla and whether numerical systems are widespread outside the vertebrate group. To date, this issue has been investigated only in a handful of species, and there is convincing evidence of a true numerical system for only one of them, the honeybee28,29,30. Honeybees, Apis mellifera, can be trained to discriminate different numbers of dots to obtain a food reward31,32. They are able to accomplish this task even when main continuous cues are controlled, thus it is suggested that they possess a numerical system analogous to that of vertebrates. Honeybees can also use ordinal information and learn the correct position in a sequence of artificial flowers when distance cues are made irrelevant33. Similar evidences have been recently provided for another social bee, the bumblebee, Bombus terrestris34,35. The function of cardinal and ordinal numerical abilities in social bees is unclear, but it has been suggested that they mainly serve to recognise flowers from the number of petals and to learn the location of food around their hives, respectively.
Circumstantial evidence suggests the ability to estimate the quantity of conspecifics in three other arthropod species. The juvenile spiders of Portia africana have been reported to take into account the number of competitors present when choosing between two patches of food36. Males of the coleopteran Tenebrio molitor are able to discriminate different numbers of females based on the odours they emit37. Ants (Formica xerophila) perceiving themselves as part of a large group are more aggressive towards another species than ants perceiving themselves as isolated individuals38. Controls are difficult to perform in these types of experiments, and it is unknown whether these three species are actually estimating the number of individuals or they are using other types of information as a proxy of number.
Recently, a mollusc, the cuttlefish, was observed to prefer the larger quantity of shrimps up to 4 versus 5 items39. Although authors manipulate some continuous cues (i.e., density and total activity of preys), it is unclear whether cuttlefish are really counting prey or are using other cues, such as the cumulative area occupied by shrimps or the convex hull of the groups.
Theba pisana is a small terrestrial snail inhabiting the dunes of the Mediterranean coasts. Similar to most snails, it is active mainly at night. This species has a considerable thermal tolerance, with an upper lethal limit that lies, depending on exposure time, between 46 °C and 50 °C40. However, during sunny days, the sandy ground can reach temperatures that largely exceed this lethal limit (up to 75 °C). To avoid these adverse conditions at sunrise, dune snails climb the stem of tall vegetation, where the temperature rarely exceeds 30 °C, and remain inactive until night. If placed on the ground during the day, these snails rapidly regain an elevated position by orienting towards nearby stems and climbing on them (Fig. 1a; Supplementary Video S1). At our site of capture, snails were collected mainly from vertical, unbranched stems of live or dead inedible plants and herbs (e.g., Puccinellia palustris, P. distans, and Juncus maritimus).
Figure 1

(a) Example of a dune snail T. pisana climbing on the stem of tall vegetation. (b) The circular arena used for investigating quantity discrimination ability in laboratory.

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Zanforlin showed that it is possible to simulate this behaviour in the laboratory41. After placing dune snails on a brightly lit arena, they rapidly orient towards a black cardboard shape on a white background and climb on it. With this setup, it was possible to study shape preference by placing two shapes at 60° angle from the centre and releasing the snail from the centre of the arena. He found that, confronted with similar geometric figures (e.g., two rectangles), snails oriented consistently towards the stimulus with the largest area. When area was kept constant, no particular preference for shape was observed, although there was a tendency to prefer the figure with a longer perimeter or with wider axes.
In all the experiments of the former study, snails were required to choose between two single shapes. In nature, however, stems are frequently arranged in clusters. All things being equal, there are several potential advantages in heading towards a large cluster of stems. In a cluster, there is greater probability of finding the stem with the most suitable features, such as a correct diameter or an optimal orientation to shelter from wind and sun40. In addition, not all the stems are accessible due to the presence of intricate or thorny vegetation at the base. Heading towards a group of stems increases the chances that at least one stem can be reached and climbed. Furthermore, most predators (mainly passerine birds, wall lizards, and rats) are small and catch only one or few preys at a time, and hence, sheltering in clusters could determine a dilution effect on predation risk42,43.
Based on the above considerations, we made the prediction that natural selection in T. pisana should favour the ability to discriminate between a single stem and a cluster and discriminate among clusters, based on the quantity of stems. The aim of the first experiment was to test this hypothesis. In the laboratory, we simulated stems used by dune snails as refuges by using black vertical bars on a white background (Fig. 1b; Supplementary Video S2). As we found that dune snails discriminate rather accurately between quantities of stems, in a series of subsequent experiments, we investigated the mechanism involved. Specifically, we tried to figure out if snails were using a true numerical system or if they used continuous quantitative information that co-varied with numerosity, such as the cumulative area occupied by items, their density or the convex hull they spanned.
Experiment 1: discrimination of the quantity of refuges
A previous study on dune snails investigated the choice between single objects that differed in shape and size41. However, based on their ecology, we predict that snails searching for protection from the heat also should focus on number and should move towards the largest available group of stems. In Experiment 1a, we studied whether dune snails prefer a group of refuges to a single one (Fig. 2a), and in Experiment 1b, we measured their accuracy to discriminate among groups of refuges differing in numerosity (Fig. 2b). To obtain reference data about snails’ general discriminatory abilities, in Experiment 1c, we measured the accuracy of dune snails to discriminate two equally shaped objects that differ in surface area (Fig. 3c).
Figure 2

(a–c) Stimuli used in Experiment 1a, 1b and 1c, respectively.

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Figure 3

(a) Percentage of snails choosing the stimulus with larger quantity of bars in Experiment 1a and 1b. Snails showed a significant preference for larger quantity up to 4 versus 5 bars. There was a significant difference amongst the numerical ratios (P  More