Continuous versus discrete quantity discrimination in dune snail (Mollusca: Gastropoda) seeking thermal refuges

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 gastropds^1,2,3. 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 patch^4,5,6.

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 sets^7,8. 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 items^9,10,11. Conversely, some predators, namely lions and striped field mice, use this ability to select the smallest prey groups because they are more vulnerable to predation^12,13. Various group-living mammals, including chimpanzees, lions, and hyenas, gauge the relative number of opponents before deciding whether to attack or withdraw^14,15,16. Gregarious fish use the same ability to select the social group that provides the best protection from predators^17,18,19. Some species, including eastern mosquitofish, brown-headed cowbirds, and American coots, use their quantitative abilities to increase reproductive success^20,21,22.

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 number^23,24. 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 prevented^8,25. 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 honeybee^28,29,30. Honeybees, Apis mellifera, can be trained to discriminate different numbers of dots to obtain a food reward^31,32. 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 terrestris^34,35. 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).

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 risk^42,43.

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).

Results and discussion

In Experiment 1a, 21 subjects of 24 chose the stimulus with three bars (χ²₁ = 13.500, P < 0.001, effect size: φ = 0.530; Fig. 3a). In Experiment 1b, all 24 subjects chose the larger quantity in the 1 versus 4 discrimination (χ²₁ = 24.000, P < 0.001, φ = 0.707), 20/24 subjects in 2 versus 4 (χ²₁ = 7.538, P = 0.006, φ = 0.396), 17/24 in 3 versus 4 (χ²₁ = 4.167, P = 0.041, φ = 0.295), and 17 /24 in 4 versus 5 (χ²₁ = 4.167, P = 0.041, φ = 0.295); but 13 out of 24 subjects chose the larger quantity in 5 versus 6 (χ²₁ = 0.167, P = 0.683, φ = 0.059). The general linear model (GLM) showed a significant difference among the numerical ratios (χ²₄ = 21.790; P < 0.001, R² = 0.215). We found a significant correlation between the numerical ratio and the degree of preference (Kendall non-parametric correlation on the six ratios of Experiments 1a and 1b: τ = 0.966; P = 0.007).

In Experiment 1c, snails significantly discriminated the stimulus with larger surface area in the easiest, 0.25-ratio area (19 out of 24 subjects; χ²₁ = 8.167, P = 0.004, φ = 0.412; Fig. 3b). In the remaining four ratios, the number of subjects who chose the stimulus with larger surface area did not significantly differ from chance: 16/24 in the 0.50 ratio (χ²₁ = 2.667, P = 0.103, φ = 0.236), 16/24 in the 0.75 ratio (χ²₁ = 2.667, P = 0.103, φ = 0.236), 14/24 in the 0.80 ratio (χ²₁ = 0.667, P = 0.414, φ = 0.118), and 13/24 in the 0.83 ratio (χ²₁ = 0.167, P = 0.683, φ = 0.059). The general linear model (GLM) did not show a significant difference among the numerical ratios (χ²₃ = 2.507; P = 0.474, R² = 0.036). To contrast the accuracy in the numerical and the surface area discrimination, we performed an overall GLM analysis comparing the results of these two experiments for the ratios of 0.25–0.80. The 0.83 ratio was not included in the analysis since it was above the discrimination threshold in both experiments and hence non-informative. We found a significant effect of the ratio (χ²₄ = 10.255, P = 0.017), a significant effect of the experiments (χ²₁ = 4.908, P = 0.027), and no interaction (χ²₁ = 6.601, P = 0.158, R² = 0.148).

As predicted from their ecology, the large majority of dune snails preferred to approach a group of stems, instead of a single one. When we investigated their discrimination ability, we found snails to be surprisingly accurate in selecting the larger group. Preference is significant up to 4 versus 5 items, while preference drops to chance level in the comparison 5 versus 6. It is interesting to note that only primates and a few other vertebrates appear similar or more accurate in discriminating discrete quantities (chimpanzees⁴⁴, rhesus monkeys⁵, and pigeons⁴⁵), while many other species show much lower numerical acuity (e.g., red-backed salamander, 2 vs 3⁴⁶; horses, 2 vs. 3⁴⁷; and angelfish, 2 vs. 3¹⁷).

As for other cognitive skills, numerical abilities are commonly believed to correlate with the size and the degree of complexity of the nervous system^48,49,50,51. However, one would expect natural selection to favour the evolution of specialised cognitive abilities, even in species with relatively simple brains, if these functions have high survival value^52,53. Each day during summer, for a snail living along the coastal dunes, the probability of surviving until the next day crucially depends on its capacity to reach an adequate shelter. It is not surprising that this severe selective pressure could have promoted the evolution of elaborate mechanisms for shelter seeking, which include an extraordinary ability to estimate the quantity of available refuges in a cluster and make comparisons among clusters.

Various vertebrates and some invertebrates are able to perform tasks of this kind by using numerical information only. Yet, the result of our experiment does not necessarily imply that snails possess the capacity to process number. As we used the same type of bar for all stimuli, larger groups had a larger cumulative surface area and snail could have used this cue to orient toward the larger set. Among vertebrates the capacity of estimating areas, alone or in combination with other cues, can account for astonishing discrimination abilities. For example fish can discriminate the numerosity of two groups of conspecifics up to a 0.85 ratio relaying on cumulative area of the fish or on the amount of their movements; they do not use numerical information in this social context although they appear able to do so in other conditions⁵³. An even simpler mechanism that snails could have used is scototaxis, i.e. the tendency to orient toward a dark part of the environment. Scototactic responses are widespread among invertebrates, and it was frequently observed that larger dark areas are preferred over small ones^54,55.

This hypothesis seems to be supported by the results of Experiment 1c in which dune snails responded in a comparable way when tested in a discrimination of areas of two single shapes. It should be noticed that, contrarily to the expectancy of the cumulative area hypothesis, snails were significantly less accurate in discriminating two objects than two groups of objects. However, the difference in accuracy is small and might be explained by other factors, for example that snails were less motivated to choose the larger area due to the shape of the stimuli that differed substantially from that of a stem. In addition, subjects could have attended only to the height or to the width of stimuli (see results of Experiment 3b). In this case, the discrimination of two linear dimensions would not be directly comparable with results of Experiment 1b. To unravel this problem, it becomes necessary to carry out an experiment that directly tests the cumulative area hypothesis, by verifying whether the snails discriminate discrete quantities, even when the cumulative area of two stimuli is equalled.

A second continuous quantity that snails could have used as a proxy of number is the convex hull of the group. In our experiment, the space between two adjacent bars was kept constant, and the convex hull increased with the number of elements in the group. Several species, including humans, have been observed to use convex hull as a proxy of number during quantity discrimination^56,57. This issue can be experimentally addressed by testing an animal in a numerical task in which these non-numerical features are made irrelevant⁵⁸.

Two other continuous cues, density and cumulative contour length (i.e. the sum of the perimeters of the items of the set), are potentially relevant for snail shelter choice. If two sets of objects occupy the same space (i.e. have the same convex hull), the more numerous also has a greater density. Density could thus be used in some conditions as a proxy of number^59,60. In our experiment, density was kept constant, but this variable could be relevant whenever the subject is required to discriminate two different quantities with the same convex hull. In numerical experiments, the contour length strictly co-varies with surface area and the relative importance of these two variables has been rarely studied independently^61,62. In the few cases in which this has been done, with the only exception of human infants, it has been found that subjects use the total area rather than the perimeter (Mosquitofish⁵⁷; Chimpanzee⁵; Rhesus macaques⁶³; Human infants⁶⁴; Pigeons⁶⁵). However, snails have a nervous system and a visual system markedly different from those of vertebrates and insects, and the situation may be different.

Experiment 2: the influence of area, convex hull, and density on quantity discrimination

To study the influence of non-numerical variables on a snail’s preference, we presented the discrimination 3 versus 4, controlling the stimuli for convex hull (Experiment 2a; Fig. 4a) and for cumulative surface area (Experiment 2b; Fig. 4b). As side-effect of controlling for convex hull the two stimuli had a different density. To test if dune snails had any preference for dense or sparse clusters, we presented a discrimination between the same number of bars with a different density (Experiment 2c; Fig. 4c).

Results and discussion

In Experiment 2a, 21 out of 30 subjects chose the larger quantity controlled for convex hull, significantly above chance (χ²₁ = 4.800, P = 0.028, φ = 0.283; Fig. 4d). In Experiment 2b, in which cumulative surface area was kept constant, the number of subjects choosing the larger quantity (13 out of 30) was not significantly different from chance (χ²₁ = 0.533, P = 0.465, φ = 0.094). The Bayes Factor was 17 indicating that the hypothesis that snails did not prefer the larger quantity was much more likely than the alternative hypothesis. In Experiment 2c snails did not show a preference for dense or sparse bars (dense bars: 13 out of 30; χ²₁ = 0.533, P = 0.465, φ = 0.094; Fig. 4e). The Bayes Factor was 17 indicating that the hypothesis that snails did not prefer the stimuli with larger density was much more likely than the alternative hypothesis.

The results of this experiment suggest that snails use continuous variables for their estimations of discrete quantities. When tested with stimuli in which the convex hull, i.e. a convex polygon enclosing all bars, was equalled, subjects continued to choose the larger quantity. Density of bars is however a cofounding variable in this experiment because as a by-product of controlling for convex hull, the two stimuli had different density. A preference for denser clusters instead of the discrimination of the larger numerosity could explain the preference for four bars we observed in this experiment. In Experiment 2c, we found no evidence that snails prefer denser to sparser clusters of bars, an indication that the convex hull is likely not a perceptual cue used by dune snail to choose their refuges.

Conversely, when the cumulative area of stimuli was paired, the choice of the larger numerosity disappeared, suggesting that dune snails use this variable to discriminate between quantities of bars. Cumulative surface area is probably the continuous variable most frequently used for numerical discrimination in the animal kingdom. Some species, apparently, do not process numerical information and use cumulative area as a proxy of number^54,66,67. However, even those species that definitely have been shown to possess core numerical systems, including humans, preferentially use the cumulative area information to solve numerical tasks or combine numerical and continuous information to increase accuracy^8,25. The teleost Gambusia holbrooki, for example, can solve numerical tasks using only number or only area, but the performance improves when it is allowed to use both^25,57.

Therefore, it is quite plausible that dune snails too, when orienting towards the largest group of bars, are selecting the largest cumulative area, or even more simply, they are guided by a scototactic response towards the darkest part of the landscape⁴¹. Before accepting the hypothesis that this species uses the cumulative area to choose the larger set of bars, it is necessary to exclude two other hypotheses that are compatible with the above results. The first concerns the fact that, in the above experiments, we used stimuli with widths just above the perception threshold (see Experiment 5b). Even if we showed they can perceive an isolated bar 2-cm wide, it might be difficult for snails to precisely distinguish just-above-threshold bars when grouped together, and hence, they may be prompted to rely on the amount of visible surface. This issue was addressed in Experiment 3.

A second important factor concerns the fact that, to control for surface area in Experiment 3b, we used bars of different widths. If snails have spontaneous preferences for the width of the bars, this could affect the results. For example, larger stems may represent refuges that are more valuable because they hide snails from predators better. Another reason for preferring wider bars is that terrestrial gastropods likely lack efficient mechanisms of depth perception: wider stems are probably perceived as closer and, hence, faster to reach^68,69. Consequently, in Experiment 3b, snails could have been attracted to the cluster containing wider bars, counterbalancing their preference for larger clusters. This issue was addressed in Experiment 4.

It is noteworthy that even if we could dismiss the role of cumulative surface area, there is a fourth important continuous variable, which is cumulative contour length, that in Experiment 1 increases linearly with numerosity ratio and that snails could have used as a cue in quantity discrimination. We will consider this problem in Experiment 3 and 4.

Experiment 3: influence of bar width

To exclude that the use of bars just above-threshold could have determined poor discriminability, in Experiment 3a, we repeated the discrimination 3 versus 4 shown in Experiment 1b and Experiment 2b, but we used stimuli doubled in width (Fig. 5a). To verify if snails have an innate preference for wider stems in Experiment 3b, we gave snails the choice between bars of different widths, while keeping the number of elements and the cumulative surface area in the two clusters identical (Fig. 5b).

Results and discussion

When stimuli were controlled for overall surface area (Experiment 3a), snails continued to manifest no preference for the larger numerosity, even when bars were doubled in width (12 out of 30 subjects, χ²₁ = 1.200, P = 0.273, φ = 0.141; Fig. 5c). The group of snails tested with stimuli non-controlled for area showed a tendency to prefer the larger quantity though the preference did not reach significance (20 out of 30 subjects, χ²₁ = 3.333, P = 0.068, φ = 0.236). The difference between the two groups is significant (χ²₁ = 4.339; P = 0.037, φ = 0.269). We performed an overall analysis comparing the results with 4 cm-wide bars of this Experiment with the same types of experiments done with 2 cm-wide bars (Experiment 1b: 3 vs. 4 non-controlled, Fig. 3a; Experiment 2b: 3 vs. 4 controlled for area, Fig. 4b) using a GLM model. We found a significant effect of experimental condition, controlled versus non-controlled (χ²₁ = 8.497, P = 0.004), no effect of the width of stimuli (χ²₁ = 0.171, P = 0.679), and no interaction (χ²₁ = 0.005, P = 0.943, R² = 0.097). The approximate Bayes factor was 104 indicating that the GLM model without the effect of the factor “width” was much more likely to explain the performance of the subjects than the model with such effect. In Experiment 3b, 21 out of 30 subjects chose the stimulus with wider bars (χ²₁ = 4.800, P = 0.029, φ = 0.283; Fig. 5d).

Replication of the Experiments 1b and 2b using bars doubled in width confirmed the original results, therefore excluding that the outcome the experiment controlling for cumulative surface area (Experiment 2b) was the artefactual consequence of using unsuitable stimuli.

In Experiment 3b, we found a clear preference for wider bars, even if the number of bars and their cumulative areas were the same on the two sides. In the environment in which dune snails live, stems show little variation in diameter. To an animal that lacks independent mechanisms for estimating the distance of an object, a bar twice in width likely appears much closer than the thinner one. The results of this experiment allow an interpretation of the results of Experiment 2b, which does not imply that snails are basing their quantity discrimination on the cumulative surface areas of the stems.

To summarise, there are two main hypotheses to explain the results so far obtained. The first hypothesis suggests that snails are able to discriminate between different amounts of stems based only on the areas occupied stimuli. This hypothesis is plausible because Zanforlin has shown that T. pisana spontaneously orient towards the larger of two dark surfaces and we confirmed this finding⁴¹. At this stage, a second hypothesis is equally plausible, i.e. that snails possess more sophisticated perceptual and cognitive functions, capable of extracting more detailed information about the characteristics of the surrounding environment. These putative functions could even include the possibility of snails to possess a true numerical system, i.e. a system capable of extracting information about the number of objects in a set, regardless of the other cues that co-vary with number.

However, there is no single experiment capable of directly contrasting the two hypotheses. We can only perform experiments to test some of the predictions generated by these hypotheses. First, the hypothesis of snails being guided only by the cumulative area of bars predicts that, in a choice test, the attraction to one stimulus is determined only by the amount of black surfaces and that the degree of attraction should be independent from the shape or orientation of the elements in the set. To verify it, we tested the snails in a choice between the same set of bars but with different orientations (Experiment 4a). Second, if the result of Experiment 2b was due to a preference for larger bars and not to a preference for larger cumulative surface area, snails should still prefer the larger numerosity when the control for cumulative areas is obtained by manipulating the heights instead of the widths of the bars in the sets. We verified this hypothesis in Experiment 4b.

As previously mentioned, cumulative contour length is another continuous variable that varied linearly with numerosity ratio in our stimuli. By, studying the preference between two shapes, Zanforlin found that dune snails were attracted to figures with the longer perimeter⁴¹. He considered this effect to be of secondary importance since he observed that snails oriented themselves towards the figure with the longer perimeter if the two figures had the same area, but preferred a figure with shorter perimeter if this had a larger area. In Experiment 3b the two stimuli had the same area whereas the ratio of the perimeters was 0.82 and the snails significantly preferred the stimulus with the smaller perimeter. This suggests that they do not rely on the perimeter at least when they must, as in this study, compare two groups of figures.

Experiment 4: further tests of the cumulative area hypotheses

In Experiment 4, we checked whether the behaviour of dune snails could simply be explained by a scototactic reaction, i.e. an attraction to the larger amount of “black”. In Experiment 4a, subjects were given the choice between the same number of bars, but with different orientations (horizontal vs. vertical; Fig. 6a). As height, width, and cumulative surface area were identical, an animal using a scototactic response should not discriminate among them. In Experiment 4b, we controlled stimuli for cumulative areas and convex hull but the area control was obtained by manipulating the heights instead of the widths of the bars (Fig. 6b). If dune snails use area as a proxy of number, they should not discriminate between the two stimuli. If the outcome of Experiment 2b was due to spontaneous preference for larger stems, in this experiment they should prefer the larger quantity of bars.

Results and discussion

In Experiment 4a, the number of subjects that chose the stimulus with vertical bars (23 out of 30) was significantly above chance (χ²₁ = 8.533, P = 0.004, φ = 0.377; Fig. 6c). In Experiment 4b, the number of snails that chose the larger quantity (22 out of 30) was significantly above chance (χ²₁ = 6.533, P = 0.011, φ = 0.330; Fig. 6d).

The two stimuli used in Experiment 4a had the same cumulative surface area, heights, and widths. Preference for the stimulus with vertically oriented bars, therefore, is not compatible with a simple response to the amount of “black” (i.e. a scototactic response) and requires that such a mechanism is paired with a detector of orientation. In Experiment 4b, we found that dune snails continued to prefer the larger quantity, even with equaled cumulative surface area, provided this was obtained by manipulating the heights instead of the widths of the bars. With the results of Experiment 3b, this finding supports the hypothesis that, in Experiment 2b, subjects failed to choose the larger quantity, not because the cumulative area was equaled in the two stimuli, but because wider bars attracted them.

Experiment 5: reliability and repeatability

Four additional tests were performed to measure repeatability and reliability and to set the width of stimuli used. In Experiment 5a, we replicated one of the original experiments of the study of Zanforlin (Fig. 7a) to assess the robustness of the procedure when using a different population and after some changes in the setup, particularly to the type of light and the material that we used for building the arena⁴¹. There are no data on visual acuity of T. pisana. Zanforlin tested snails with bars 2 cm versus 3 cm in width (approx. 2.2° and 3.3° respectively), finding a preference for the latter stimulus⁴¹. Experiment 5b was aimed at verifying the minimum width necessary for a stimulus to elicit an approach response in the conditions of our experiment (Fig. 8a). Experiments 6c and 6d were aimed respectively at the reliability and repeatability of our procedure.

Results and discussion

In Experiment 6a (inter-study repeatability), 20 out of 24 subjects chose the stimulus with larger surface area (χ²₁ = 10.667, P < 0.001, φ = 0.471). In previous work, 30 out of 35 subjects chose the stimulus with larger surface area⁴¹. Using a GLM model, we found no difference between the two studies (χ²₁ = 0.062, P = 0.803, R² = 0.002; Fig. 7b).

In Experiment 5b (minimum discriminable width), 12 out of 20 snails chose the bar that corresponded to a 1.58° visual angle (χ²₁ = 0.800, P = 0.371, φ = 0.141), 16 out of 20 the bar with the 2.12° visual angle (χ²₁ = 7.200, P = 0.007, φ = 0.424), and 18 out of 20 the bar with the 2.64° visual angle (χ²₁ = 12.800, P < 0.001, φ = 0.567, Fig. 8b).

In Experiment 5c (inter-rater reliability), the binary measure of the snail’s choice did not differ between the two scorers (98.2% concordance, Cohen’s kappa = 0.96). In Experiment 5d (intra-study repeatability), the preference for the larger quantity in the replicate experiment was 19/24 (χ²₁ = 8.167, P = 0.004, φ = 0.413), whereas in the original experiment it was 17/24; the difference was not significant (χ²₁ = 0.446, P = 0.504, φ = 0.096).

Zanforlin described a tendency to reach for dark shapes and prefer larger stimuli in a T. pisana population from the north Italy coast⁴¹. Our subjects were collected approx. 65 km northeast along the coast in a more anthropised area. Inter-population differences in behaviour have been reported for many species, including snails⁷⁰. With Experiment 6a, we showed that the same behaviour is present in snails from the population we studied. The response thus appears robust to changes in some details of the apparatus and procedure, including the use of a different source of illumination. Experiment 6c and 6d show that the response of dune snails in our discrimination tests is also robust and that its measure is highly reliable and replicable.

Prior to the start of the main experiments, in Experiment 6b, we determined the minimum visual angle to elicit an approach response from snails. With a bar width of 1.10 cm (1.58° visual angle), snails showed a random response, whereas they were attracted by the stimulus with bars of 1.48 and 1.84 cm (2.12° and 2.64°, respectively). For Experiments 1 and 2, we therefore adopted 2 cm wide bars corresponding to an angle of 2.86°.

Source: Ecology - nature.com