Anim Cogn DOI 10.1007/s10071-014-0791-7 ORIGINAL PAPER Numerical discrimination by frogs (Bombina orientalis) G. Stancher • R. Rugani • L. Regolin • G. Vallortigara Received: 24 February 2014 / Revised: 7 July 2014 / Accepted: 30 July 2014  Springer-Verlag Berlin Heidelberg 2014 Abstract Evidence has been reported for quantity dis- Keywords Number cognition
Quantity discrimination
crimination in mammals and birds and, to a lesser extent, Analog magnitude system (AMS)
Object file system fish and amphibians. For the latter species, however, (OFS)
Frogs whether quantity discrimination would reflect sensitivity to number or to the continuous physical variables that covary with number is unclear. Here we reported a series of Introduction experiments with frogs (Bombina orientalis) tested in free- choice experiments for their preferences for different Some forms of numerical abilities, including cardinal and amounts of preys (Tenebrio molitor larvae) with systematic ordinal identifications (e.g., Brannon and Terrace 1998; controls for variables such as surface area, volume, weight, Rugani et al. 2010a, b, 2011; Pepperberg and Carey 2012) and movement. Frogs showed quantity discrimination in and arithmetic calculations (e.g., Beran and Beran 2004; the range of both small (1 vs. 2, 2 vs. 3, but not 3 vs. 4) and Baker et al. 2011; Pepperberg 2012; Rugani et al. 2009, large numerousness (3 vs. 6, 4 vs. 8, but not 4 vs. 6), with 2011, 2013a; Ward and Smuts 2007), have been widely clear evidence of being able to discriminate numerousness demonstrated in non-human animals. even when continuous physical variables were controlled Studies in human infants suggest that nonverbal for in the case of small numerousness (i.e., 1 vs. 2), numerical capacities are based on two separate systems: whereas in the case of large numerousness it remains one that processes small numerousness: the Object File unclear whether the number or surface areas were domi- System (OFS); and the other that estimates larger numer- nant. We suggested that task demands are likely to be ical values: the analogue magnitude system (AMS, e.g., responsible for the activation of different systems for small Feigenson et al. 2002; Coubart et al. 2014; Hyde and and large numerousness and for their relative susceptibility Spelke 2011; for a review see Feigenson et al. 2004; Hyde to quantitative stimulus variables. 2011). The OFS would be based on the capability of individuating each new object entering into a scene, to which a new file (‘‘object file’’) would be assigned and stored in the working memory (thus, numbers would be only implicitly represented in this system). The signature of G. Stancher (&)
G. Vallortigara the OFS is that there is a limit to the number (usually B3) Center for Mind/Brain Sciences, University of Trento, Rovereto, of object files that can be simultaneously tracked and stored Trento, Italy in the working memory (Trick and Pylyshyn 1994). Esti- e-mail: gionata.stancher@unitn.it mations involving larger numerousness ([3) would be G. Stancher dealt by the AMS. According to the Weber’s law, the Fondazione Museo Civico (FMC), Rovereto, Italy functioning of that system would be ratio-dependent. As the ratio between the numbers to be discriminated becomes R. Rugani
L. Regolin Department of General Psychology, University of Padova, larger, response times decrease and accuracy increases Padua, Italy (Gallistel and Gelman 1992). 123  Anim Cogn The existence of an OFS is debated in non-human ani- Pe´russe 1988). Such an ability would conceivably be at the mals. For instance, it has been not revealed in prosimian basis of efficient foraging strategies. The theory of optimal primates tested in conditions similar to those used on foraging (Krebs 1974) states that animals, when faced with human infants (Jones and Brannon 2012). Moreover, evi- two or more food options, would choose the one that pro- dence suggests that the AMS can deal also with discrimi- vides the greatest energetic gain. Proto-numerical discrim- nations involving small sets of numbers in a variety of ination is often found in ecological situations in which an different species (Cordes et al. 2001; De Hevia and Spelke animal has to choose between two sets made of identical 2009; Cordes and Brannon 2009; Cantlon and Brennon food items and differing in their numerosity. Salamanders 2007; Brannon and Terrace 1998; Smith et al. 2003; Judge (Plethodon cinereus), when presented with two different et al. 2005; Beran 2007; Pepperberg 2012; Rugani et al. quantities of live fruit flies (Drosophila virilis), choose the 2013a, b; Stancher et al. 2013). Nonetheless, some evi- larger quantity in the comparisons 1 versus 2 and 2 versus 3. dence for an OFS has been reported. Rugani et al. (2008) The salamanders were allowed to approach either alterna- trained young chicks (Gallus gallus) to peck at arrays of tive, and flies remained visible throughout the duration of dots differing in their numerosity. Chicks successfully the trial. Thus, salamanders were not required to memorize learned to discriminate 2 versus 3, but failed to learn to the two different quantities of food available, but instead discriminate 4 versus 6, which suggests that the chicks were required to make a decision on the basis of what they were using the OFS rather than the AMS (because ratios were actually seeing (Uller et al. 2003). Robins (Petroica were the same). Gross et al. (2009) showed a similar result longipes) have been shown to be capable of selecting the with honeybees (Apis mellifera): Bees successfully learned larger of two quantities when they were presented with two to distinguish between 2 and 3, but not 4 and 6 items. sets of food items such as 6 versus 8, 8 versus 64, and 16 Agrillo et al. (2007) reported a set-size limit (B3) charac- versus 64 (Gerland et al. 2012). Coyotes’ (Canis latrans) teristic of the OFS in the numerical comparisons of mos- could discriminate between quantities of discrete food items quito fish, such that fish (Gambusia hoolbrooki) were more in the comparisons 2 versus 5, 1 versus 3, and 1 versus 4 likely to move toward the larger of two shoals in com- (Baker et al. 2011). Domestic dogs (Canis lupus familiaris) parisons of 1 versus 2, 2 versus 3, and 3 versus 4, but were select the larger amount of hotdog, in the comparisons 1 not more likely to select the larger shoal for comparisons of versus 4, 1 versus 3, 2 versus 4, 3 versus 5, 1 versus 2, 2 4 versus 5, 5 versus 6, 6 versus 7, or 7 versus 8. However, versus 3, 3 versus 4, 4 versus 5, and 5 versus 6 (Ward and other reports in fish (Xenotoca eiseni) seem to suggest the Smuts 2007). Asian Elephants (Elephas maximus) when use of the AMS even with small numerousness (Stancher simultaneously presented with two baskets, each containing et al. 2013). Chicks too appear to use the AMS also with different numbers of fruit pieces, identified divergences of small numbers in certain tasks (e.g., Rugani et al. 2010b, quantities up to 6 (i.e., 4 vs. 1, 3 vs. 1, 4 vs. 2, 5 vs. 3, 2 vs. 1, 2013a, b). New-born chicks were reared with two stimuli, 3 vs. 2, 4 vs. 3, 5 vs. 4, and 6 vs. 5; Irie-Sugimoto et al. each characterized by a different number of heterogeneous 2009). Orangutans (Pongo pygmaeus) compared two sets (for shape, color, and size) elements, and food was found in each containing a different number (within the range 1–6) proximity of one of the two stimuli. At test, on day 3, of cereal bits and chose the larger quantities when these chicks were presented with stimuli depicting novel ele- were presented simultaneously (Call 2000). ments (for shape, color, and size) representing either the It should be noted, however, that whenever different numerousness associated or not associated with food. We numbers of identical items are used at test, changes in found that chicks preferred the number associated with number correlate with changes in quantitative variables— food in the 5 versus 10 and 10 versus 20 comparisons both also called ‘‘continuous physical variables’’ (e.g., volume, when quantitative cues were unavailable (stimuli were of contour length, and surface area) that covary with numer- random sizes) and when the overall area or perimeter was ousness. Unless continuous variables are controlled for, it equated (Rugani et al., 2013b). Using the same experi- is factually impossible to conclude that subjects’ discrim- mental paradigm, we also proved young chicks’ capability inations are based actually on numerical information. to distinguish between two small (2 vs. 3), two large (6 vs. Under which conditions animals would take into 9, 8 vs. 14, 4 vs. 6, and 4 vs. 8), and a small and a large account numerousness versus continuous extent has been number (2 vs. 8), even when the overall area and perimeter poorly considered in the comparative literature, as noted by were equated. These data, and especially the discrimination Cantlon and Brennon (2007). One of the first attempts to between 2 and 8, demonstrated that small and large num- control for the possible use of the quantitative information bers can be processed via AMS (Rugani et al. 2014). has been reported by Hauser et al. (2000). When observing A most basic numerical competence is the ability to an experimenter hiding some pieces of apple, one at a time make judgments of size differences (e.g., ‘‘more than…,’’ into one opaque container and a different number of pieces ‘‘less than…’’) between two or more sets (Davis and of apple into another opaque container, monkeys (Macaca 123 Anim Cogn mulatta) approached the container containing the larger In all the experiments, we exploited the predatory quantity in the comparisons 1 versus 2, 2 versus 3, 3 versus response that frogs manifest selectively toward moving 4, and 3 versus 5. To address the possibility that monkeys prey (such as Tenebrio molitor larvae, used in the present were attending to volume rather than number, in one study). The lack, in some anurans including Bombina ori- control condition the authors compared 1 versus 3 pieces of entalis, of frontal eyes and head movement produces a apple equalizing the overall volume of the two sets. response to the stimuli which is ideal for scoring choice Monkeys again chose the larger number, showing that the behavior. Such straightforward and clear-cut response numerical cues were independent of the quantitative ones consists in an abrupt movement of the frog toward the (Hauser et al. 2000). However, other quantitative cues were chosen prey, closely followed by a single tongue protrusion not taken into consideration. Similarly, horses (Equus ca- (Lettvin et al. 1968). ballus) selected the greater of two quantities when com- paring small numerousness: 1 versus 2 and 2 versus 3, even when the total surface area of the two sets was equalized Experiment 1 (Uller and Lewis 2009). Again, contour length or total surface was not controlled for. The aim of the first experiment was to check whether frogs A few studies, though, experimentally controlled for of the species Bombina orientalis are able to discriminate possible use of quantitative cues, Cantlon and Brannon between small numerousness (B3) by testing the compar- (2006) and Merritt et al. (2009) demonstrated that mon- isons 1 versus 2, 2 versus 3, and 1 versus 3, as it has already keys can order numerical values when all quantitative been shown to occur in mammalian (Ward and Smuts variables are irrelevant in the resolution of the task; 2007; Irie-Sugimoto et al. 2009) and avian species (Rugani Vallortigara et al. (2010a, b), Rugani et al. (2008, 2010b, et al. 2008, 2013a; Pepperberg 2012). 2014) showed that chicks (Gallus gallus) discriminate numbers when volume, area, and contour length are Materials and methods controlled for. Among the so-called lower vertebrates, evidence is less Subjects and rearing conditions clear. In salamanders (Plethodon cinereus), movement- related cues seem to be crucial for quantity discrimination Seven adult frogs (Bombina orientalis) obtained from a of food prey (Krusche et al. 2010), whereas in fish, overall commercial stock (Spagnoli & Casagrande Snc, Via Torre surface area appears to be crucial in discrimination of shoal verde, 62, 38122 Trento) were used in experiments 1 and 2. numerousness (Go´mez-Laplaza and Gerlai 2013). Indeed, Oriental fire-bellied toad (Bombina orientalis, Boulenger, whether fish (Pterophyllum scalare) would show any sen- 1890) is a semi-aquatic, small-sized frog (adult male and sitivity to number per se when continuous physical vari- female are approximately 3–4 cm long) belonging to the ables are accurately controlled for is unclear (Go´mez- Bombinatoridae family. The natural distribution of this Laplaza and Gerlai 2013). species is in Korea, northeastern China, and Russia, but it is Given the paucity of experiments that systematically commonly bred and reproduced in captivity. controlled for the possible role of continuous physical In the 3 years, before the experiments, frogs were variables on quantity discrimination in lower vertebrates, group-housed in an aquarium (50 cm 9 50 cm 9 40 cm) we investigated the ability of a frog species (Bombina with the ground completely covered of gray gravel. Water orientalis) to choose the larger versus smaller number of depth was of 10 cm, and water temperature was of 22 ± 5 food items. We devised a series of original experimental C. An emerging island (15 cm 9 10 cm), in the center of controls for the non-numerical variables in an attempt to the aquarium, was used by frogs for the activities normally disentangle the role of numerical versus quantitative cues. carried out on a dry ground (e.g., feeding). The aquarium Moreover, we also tried to address the issue of the possible was illuminated by one fluorescent lamp (15 W) with a existence of a small number system (OFS) in these animals, photoperiod of 14-h light and 10-h dark. separated from the system for the estimation of approxi- Given that frogs respond only to moving prey (the mate magnitude (AMS). movement itself seems to stimulate the predatory response) The frogs Bombina orientalis belong to a primitive (Lettvin et al. 1968), they were fed every other day with live taxonomic group (suborder) characterized by the presence Alphitobius diaperinus and Tenebrio molitor mealworms. of several ancestral characters (called Archaeobatrachia, Due to the larva’s small dimensions, each frog usually ate Familia: Bombinatoridae) and thus offer a unique chance to about 2–4 larvae in each meal; therefore, the amount of the find archaic cognitive structures, allowing investigation of food eaten varied slightly from meal to meal. In order to the origin of the proto-numerical abilities in vertebrates motivate the animals to the testing stimuli, 2 days before (Ren et al. 2009; Gissi et al. 2006). each testing session, frogs were food-deprived. 123  Anim Cogn Materials and procedure larvae varied from a minimum of about 2 cm to a max- imum of about 5 cm (depending on the numerousness of At the beginning of each testing session, frogs were the group). individually transferred into the apparatus. This con- Each frog underwent three numerical comparisons: 1 sisted of a rectangular plastic box (20 cm 9 24 cm 9 versus 2, 2 versus 3, and 3 versus 4 (in this order). For each 15 cm) lit from above (35 cm from the apparatus floor) comparison, 15 valid testing trials were administered so that by one 40-W fluorescent bulb. At the beginning of each each subject underwent an overall of 45 valid trials. The trial, the subject was placed in the starting position, delay between two consecutive trials was C60 min, and which was at the center of the apparatus, at about three trials were administered within each testing session, 10 cm from the closest wall (and facing it) and equi- so that five testing sessions were necessary to complete each distant (8 cm) from the two lateral walls. Stimuli were numerical comparison. One testing session took place every positioned one to the right and one to the left with other 2 days. Larvae of the same size were employed in all respect to the subject. Each stimulus was composed of testing trials for each comparison. The position (on the left - a group of live Tenebrio molitor larvae immobilized by L- or on the right -R) of the larger group of larvae was an entomological needle at about 0.5 cm from the changed from trial to trial, following a semi-random ground, and each larva was arranged in the position sequence (i.e., L–R–L–R–L–L–R–R–L–R–L–R–L–R–L, shown in Fig. 1. The larvae were free to oscillate Fellows 1967) so that for each subject (and for each dif- (mostly along the vertical plane, because of the larva’s ferent comparison) the larger group was 46.667 % of times morphological structure) without touching each other. on the right side and 53.333 % on the left side. We made sure stimuli were moving during the test to In each testing trial, the subject was allowed a single elicit the frog’s predatory response. choice. We considered the choice as a first attempt to catch In order to make both groups of larvae simultaneously any larva of any group. When the subject approached the visible to the frogs, the larvae were aligned parallel to larva at the distance of 1 cm, the choice was considered each other and at 45 with respect to the frog’s sagittal made, and the frog was placed back in the rearing aquar- axis, and the closest larva was 7 cm away from the frog ium. Only the first approach was scored. In no case, frogs in the starting position (Fig. 1). The minimum distance were allowed to eat the larva, in order to exclude any between the two groups of larvae was of about 6 cm. possible learning effect. In this way, the subject’s response Moreover, within each group, the distance between the was emitted in the context of a spontaneous choice task. If after 5 min the frog had not approached any stimulus, the response was considered non-valid and void and that trial was repeated (on average from 1 to 4 trials had to be repeated for each numerical comparison). Results An index of choice for the larger group was computed for each subject and for each comparison according to the formula: (number of choices of the larger set/15) 9 100. An analysis of variance (ANOVA) was performed con- sidering the three numerical comparisons (1 vs. 2, 2 vs. 3, 3 vs. 4) as repeated measures and, as dependent variable, the index of choice for the larger group. The ANOVA revealed a significant difference in frogs’ responses to the different numerical comparisons (F(2,12) = 3.888; p = 0.049). A nonsignificant value in the Mauchly’s sphericity test (p = 0.240) indicated variance homogeneity across groups. A Fisher’s protected LSD post hoc analysis revealed a significant difference between the numerical comparisons 1 versus 2 and 3 versus 4 (p = 0.017). One-sample t test (two-tailed) was used to estimate sig- nificant departures from random choice (50 %) in the overall Fig. 1 A schematic illustration (top view) of the apparatus used in all sample of animals. The results showed a significant prefer- of the experiments (a comparison 2 vs. 3 is shown) ence for the larger group in the comparisons 1 versus 2 123 Anim Cogn Fig. 2 The index of choice for the larger group (mean ± SEM) for each numerical comparison of Exp. 1 (1 vs. 2, 2 vs. 3, and 3 vs. 4) is shown. The dotted line represents chance level (50 %). Asterisks indicate significant departures from chance level (*p \ 0.05; **p \ 0.01) Fig. 3 Schematic representation of the apparatus and of the posi- tioning of the stimuli in one of the numerical comparisons used in (t(6) = 6.0619; p = 0.0009) and 2 versus 3 (t(6) = 2.4627; Exp. 2 (i.e., 4 vs. 8) p = 0.0489), but not in the comparison 3 versus 4 (t(6) = 0.7499; p = 0.4816) (see Fig. 2). Experiment 2 In the previous experiment, we examined frogs’ responses toward two numerically different groups of moving preys, obtaining a preference for the larger group in the case of the comparisons 1 versus 2 and 2 versus 3, but not in the comparison 3 versus 4. These data suggest a limit at about 3 items for the discrimination of these small quantities. However, the results can be explained by the functioning of the analogue magnitude system (AMS). The discrimination based on the AMS becomes less precise according to the Weber’s fraction: As the ratio between the numerousness to be discriminated becomes larger, response times Fig. 4 The index of choice for the larger group (mean ± SEM) displayed at test by frogs in the three numerical comparisons (3 vs. 6, decrease and accuracy increases (Gallistel and Gelman 4 vs. 8, and 4 vs. 6) of Exp. 2. The dotted line represents chance level 1992). The AMS should therefore support the discrimina- (50 %). Asterisks indicate significant departures from chance level tions when the ratio between the two numbers is small (**p \ 0.01) enough (as in the comparisons 1 vs. 2, ratio 0.5, and 2 vs. 3, ratio 0.67), but not when the ratio becomes closer to 1 (as each testing trial. Preys of the larger group were slightly in the comparison 3 vs. 4: ratio of 0.75). The second misaligned, i.e., they were placed along two parallel lines experiment aimed at extending the study to larger numer- (each 10 cm long) spaced about 6 mm apart (Fig. 3), while ousness, using comparisons with a ratio of 0.5 (3 vs. 6, 4 preys of the smaller group were placed along a single line vs. 8) or 0.67 (4 vs. 6). (10 cm long). All frogs underwent three comparisons: 3 versus 6, 4 versus 8, and 4 versus 6. Materials and procedure Results Subjects, apparatus, and procedure were the same as described in the ‘‘Experiment 1’’ section. The only differ- For each experimental comparison, the index of choice for ence was the spatial arrangement of the stimuli, during the larger group was computed using the formula 123  Anim Cogn previously described, see Fig. 4. A nonsignificant value in stimulus was composed of a single moving mealworm and the Mauchly’s sphericity test (p = 0.432) indicated vari- the two-element stimulus was composed of one moving ance homogeneity across groups. The analysis of variance mealworm and of one that could not move (as it was dead). revealed a nonsignificant difference between the three The size of all of the mealworms was identical, and it was numerical comparisons (F(2,12) = 3.324; p = 0.071). identical to that used in ‘‘Experiment 1’’ section. Data were therefore merged, and the resulting mean Second control (Constrained movement) A control for (mean = 66.031; ES = 3.117) was above chance level: the total amount of movement (‘‘stuff in motion’’) was t(20) = 5.143; p \ 0.0001. performed, using alive mealworms of the same size Overall, the results of experiments 1 and 2 demonstrated (identical to those used in Experiment 1). Using small that frogs can discriminate between small (1 vs. 2 and 2 vs. 3) ‘‘bobby pins,’’ the one-element stimulus was immobilized and large (3 vs. 6 and 4 vs. 8) numerousness when a redun- in a single central position, so that both the anterior and the dancy of cues was available. This may suggest that frogs do posterior parts of the body could oscillate, whereas in the possess a system for evaluating the numerousness other than two-element stimulus, both mealworms were fixed in two the OFS, a system that, in the realm of small numerousness, parts (center and posterior segments), so that they moved operates with a set-size limit of about 3 elements. only the anterior portion of their body. Nevertheless, in all these comparisons, the use of iden- Third control (Partial occlusion of the prey) In this test, tical items (larvae of roughly same size) does not allow us we controlled for both volume and movement at the same to exclude the possibility that non-numerical cues were time. Six (three on each side) opaque, rectangular, and employed. Choice for the larger group could be indeed partially overlapping partitions (3 cm 9 2.5 cm) were driven by quantitative cues. In the next experiments, a introduced in the apparatus located at about 5 cm from the series of controls for some of the quantitative variables that subject’s starting point and spaced one from the other of may have affected the subjects’ choice (volume, surface, 4 cm, see Fig. 5. These partitions could selectively hide and movement of the prey) is performed to check whether some portions of the larvae body from the frog’s visual animals respond to the actual number instead of responding perspective at the starting point. In order to obtain a control to the other quantitative features of the stimuli. for both volume and movement, in the one-element stim- ulus, the live worm was entirely visible to the subject (no partition hid any part of the body of the larva). Conversely, Experiment 3 for what concerns the two-element stimulus, only half body of each worm was visible (being each larva positioned in The most relevant non-numerical cues that frogs may use the space between two adjacent partitions): In particular, in discriminating sets of food items are volume, surface, only the anterior half of a worm and only the posterior half weight, and movement. The aim of the present experiment was to investigate the role played by the movement and volume in quantity discrimination of small numerousness (1 vs. 2). In catching behavior, movement is the most important cue to elicit a response toward a prey (Lettvin et al. 1968). On the other hand, volume also is a relevant cue typically used by frogs in the choice of food (Lettvin et al. 1968). Subjects and procedures A new group of 7 adult frogs were used. Rearing condi- tions, apparatus, and procedures were the same as in the previous experiments, unless otherwise noted. Testing Each subject underwent three separate tests employing the comparison 1 versus 2, each test controlled for the possible use of movement and/or volume. First control (Moving and non-moving prey) To equal- Fig. 5 Schematic representation of the apparatus used in Exp. 3 with ize the movement of the two stimuli, the one-element the three partitions on each side and of the location of mealworms 123 Anim Cogn of the other worm were visible to the frog in the starting comparison 1 versus 2, when the most relevant quantitative point. In this way, possible preferences for attacking a variables (movement and volume) were equalized. The certain side of the prey body were also controlled (usually lack of choice in the First control (Moving and non-moving the anterior side is preferred, as attacks are directed toward prey) was probably due to the fact that the dead prey was the head of a prey). neglected by the frogs, which usually much prefer to catch In order to obtain the best possible control for the (at least partly) moving prey (Lettvin et al. 1968). quantity of movement in the two groups, in all these con- ditions, we made sure that all the living mealworms were moving during each trial. Whenever a mealworm was not Experiment 4 moving, the trial was considered null and it was repeated immediately after. Experiment 3 showed that frogs could discriminate between two groups of food items, when the total amount of volume Results and discussion and movement were controlled for. Nevertheless, in catching response, also the total weight of the preys could A within-subject ANOVA (Fig. 6) revealed a significant play a relevant role (Lettvin et al. 1968). In the present difference between the three control tests (First control experiment, we used as stimuli live worms (Tenebrio mol- ‘‘Moving and non-moving prey,’’ Second control ‘‘Con- itor) of different sizes. The use of worms of different size strained movement,’’ and Third control ‘‘Partial occlusion allowed us to obtain two groups of the same weight that of the prey’’), F(2,12) = 5.576; p = 0.019; a nonsignifi- were tested in the comparisons 1 versus 2 and 4 versus 8. cant value in the Mauchly’s sphericity test (p = 0.763) indicated variance homogeneity across groups. A Fisher’s Subjects and procedures protected LSD post hoc analysis showed significant dif- ferences between the First control and the Second control Subjects, rearing conditions, apparatus, and procedures (p = 0.007), and between the First control and the Third were the same as in the previous experiment. control (p = 0.005). One-sample t tests (two-tailed) revealed a significant Testing preference for the larger numerousness in the Second (‘‘Constrained movement’’: mean = 70.475; ES = 2.857; Frog underwent three tests, each controlling for the possi- t(6) = 7.166; p = 0.0004) and Third (‘‘Partial occlusion ble use of weight in discrimination of small or large of the prey’’: mean = 71.428; ES = 4.979; t(6) = 4.303; numerousness. p = 0.0051) controls, but not in the First control (‘‘Moving Fourth control (1 vs. 2—Weight, volume, and surface and non-moving prey’’: mean = 52.380; ES = 4.467; control) We selected larvae of two sizes (‘‘Large’’ larvae: t(6) = 0.533; p = 0.6132). 0.2 gr.; 32 mm 9 4 mm, and ‘‘Small’’ larvae: 0.1 gr.; The results suggested that frogs were able to discrimi- 21 mm 9 2 mm) from two different molting stages, in nate between small numbers of preys, at least in the order to equalize the overall weight of the two stimuli. Larvae were weighted using a Wunder Mix high precision scale with a 0.01 gr. division. Moreover, we controlled for a possible preference for volume and surface, by creating a conflict between numerousness and quantity. To this pur- pose, the worm’s body was approximated to a cylinder; therefore, volume was calculated using the formula V = pr2h, lateral surface using the formula LS = 2prh (see Table 1). The one-element stimulus was composed of a larva having both the bigger volume and surface with respect to the sum of the volume and surface of the larvae composing the two-element stimulus. In this particular case, a choice for the larger group would indicate a pref- erence for the larger number (i.e., 2), whereas the choice of the smaller group (i.e., 1) would indicate a choice of the bigger quantitative variables. Fig. 6 Index of choice for the larger group (mean ? SEM) displayed at test by frogs in each control of the Exp. 3. The dotted line Fifth control (1 big vs. 1 small-Size control) To control represents chance level (50 %). Asterisks indicate significant depar- for the possible preference of frogs for larvae of either size, tures from chance level (**p \ 0.01) we tested the comparison 1 versus 1 using larvae of the two 123  Anim Cogn sizes (1 ‘‘small’’ and 1 ‘‘big’’): The sizes of larvae were Overall, these results indicated that both quantitative exactly the same of those used in the previous experiment and numerical information could be processed by Bombina (1 vs. 2—Weight, volume, and surface control). orientalis frogs in the discrimination of small sets of food Sixth control (4 vs. 8—Weight, volume, and surface items. Results from the ‘‘1 versus 2—Weight, volume, and control) The use of larvae of two different sizes (the same surface control’’ test showed that the numerical cue was used in the ‘‘1 vs. 2—Weight, volume, and surface con- preferred over the quantitative cues (volume and surface). trol’’) made it possible a further control for the use of Interestingly, we did not notice any preference for the weight, surface, and volume in a comparison 4 versus 8 (4 smaller larvae, because in the 1 ‘‘big’’ versus 1 ‘‘small’’- ‘‘big’’ larvae vs. 8 ‘‘small’’ larvae). Again, the overall Size control frogs showed a preference for the bigger larva. volume and surface were bigger in the group with less This also demonstrated that, when numerical information items, see Table 2. was not available, frogs could operate a discrimination on the basis of quantitative variables alone. Lack of difference Results in the 4 versus 8—Weight, volume, and surface control test suggests that large numerousness can be discriminated The index of choice for the larger (or bigger for the com- solely when numerical and non-numerical cues are both parison 1 ‘‘small’’ vs. 1 ‘‘big’’) group was calculated, for each available (see ‘‘Experiment 2’’). experimental test (Fig. 7). Data were analyzed, separately for each testing session, employing a t test. A significant Discussion preference for the two-element stimulus was observed in the Fourth control (1 vs. 2—Weight, volume, and surface: Although evidence for numerousness discrimination is mean = 60.952; ES = 3.390; t(6) = 3.231; p = 0.017). widespread among non-human animals, both vertebrates Frogs thus chose the numerically larger group, showing to (Vallortigara et al. 2010a, b) and invertebrates (Carazo prefer the numerousness over the volume and the surface. et al. 2009; Pahl et al. 2013), accurate control for the role of A significant preference for the bigger worm was continuous physical variables that covary with numerous- observed in the Fifth control (1 ‘‘big’’ vs. 1 ‘‘small’’—Size; ness is relatively scanty, particularly in the so-called lower mean = 75.237; ES = 3.770; t(6) = 6.695; p = 0.0005). vertebrate species (for adequate controls in primates see (In this case, the index of preference was calculated as however Brannon and Terrace 1998). In the present series number of choices for the ‘‘big’’ worm/number of total of experiments, we systematically checked for the possible choices 9 100). The preference for the bigger worm thus use of some quantitative cues (i.e., movement, volume, confirmed that in the 1 versus 2—Weight, volume, and weight, and surface area) in a numerical discrimination surface control test, the frogs’ choice for the two-element task, and we showed that frogs are capable of discrimi- stimulus could be not due to a general preference for the nating small numerousness, even when the possible use of smaller larvae. such quantitative physical variables is controlled. No statistically significant preference was apparent for the The results of the present experiments provide some Sixth control (4 vs. 8—Weight, volume, and surface control: support to the hypothesis that frogs could respond to mean = 42.856; ES = 5.607; t(6) = 1.273; p = 0.249). Table 1 Weight, volume, and surface of the overall stimuli used in the 1 versus 2—Weight, volume, and surface control test (Exp. 4) 1 ‘‘large’’ 2 ‘‘small’’ Weight (gr) 0.2 0.2 Volume (mm3) 401.9 131.8 Total surface area (mm2) 401.9 263.6 Table 2 Weight, volume, and surface of the overall stimuli used in the 4 versus 8—Weight, volume, and surface control test (Exp. 4) 4 ‘‘large’’ 8 ‘‘small’’ Fig. 7 Index of choice for the larger group (or for the larger larva in Weight (gr) 0.8 0.8 the ‘‘Size control’’ test) (means ? SEM) displayed at test by frogs in Volume (mm3) 1,607.6 527.2 each control of the Exp. 4. The dotted line represents chance level Total surface area (mm2) 1,607.6 1,054.4 (50 %). Asterisks indicate significant departures from chance level (*p \ 0.05; **p \ 0.01) 123 Anim Cogn numerousness as such, at least with small numerousness. In the neurons selective for numerousness in the monkey the case of large numerousness (4 vs. 8), however, frogs parietal cortex also show selectivity to continuous physical appeared unable to discriminate in a condition in which the variables that covary with number, and only a minority overall weight was equalized and when both volume and respond only to number (Nieder and Dehaene 2009). It is surface of the stimuli were larger in the group with less tempting to speculate that this may be even more pro- items (i.e., 4 large larvae vs. 8 small larvae). It is unclear nounced in lower vertebrates (or that perhaps lower ver- whether this depends on the size of the numerousness or tebrates only have selectivity to quantitative variables but the test method used. With small numerousness, partial not to pure numerousness). In the absence of any hint about occlusion was used to equalize continuous physical vari- the neural machinery associated with quantity discrimina- ables, which proved, however, impossible to do (for tion in these animals, this remains an open issue. spacing and distance reasons) using large numerousness. It is more likely, however, that the conditions that Given that in a comparison with only two larvae (1 vs. 1), favor the use of either one of the two systems, and of frogs showed a preference for the larger insect, one pos- their relative susceptibility to continuous physical vari- sible explanation is that using 4 large larvae vs. 8 smaller ables, would depend on task demands. It has been sug- ones the preference for the size of the single larva played gested that small quantities may be represented by both against the preference for larger numerousness. It is true the approximate magnitude (AMS) as well as the object that the same could have occurred with the partly occluded file systems (OFS) and that contextual factors may larvae, but in that case, the ‘‘objective’’ difference in size determine which system is engaged (e.g., Wynn et al. between the visible parts could have been compensated by 2002; Feigenson et al. 2004; Barner et al. 2008; Cordes the non-visible ones through perceptual completion. and Brannon 2008, 2009; Hyde 2011; Rugani et al. Indeed, there is evidence in lower vertebrates for the per- 2013a, b). For instance, Hyde (2011) suggested that when ception of partly occluded objects as complete (e.g., items are presented under conditions that allow selection Sovrano and Bisazza 2008). of individuals, they would be attended to by the OFS These data suggest that frogs can discriminate stimuli on rather than the AMS, while when items are presented numerical basis exclusively via OFS, whereas the dis- outside attentional limits (e.g., too many, too close toge- crimination of larger numerousness, which is usually sup- ther), they would be attended to by the AMS rather than ported by the AMS, is possible solely when a redundancy the OFS. Prey catching in frogs clearly allows selection of of information, quantitative, and numerical is available. individual elements as target of feeding responses, thus An alternative account would be to imagine that there promoting use of OFS for small numerousness. When are two separate systems in frogs for small and large faced with large numerousness, however, tracking and numerousness and that they are differently sensitive to targeting individual moving elements prove impossible, continuous physical variables. Support to this hypothesis and use of surface area may represent the best strategy for comes from the fact that frogs failed a discrimination with selection of the group within which to perform targeting a ratio 2:3 in the range of large ([3) numerousness (dis- and prey catching. (Note that Wynn et al. (2002) and crimination 4 vs. 6), whereas they succeeded with small Barner et al. (2008) suggested that objects that undergo numerousness (discrimination 2 vs. 3, see Fig. 1). This common motion are more likely to be represented as a would agree with the idea of a distinct small number sys- collective entity than objects that move independently). tem based on working memory and thus with an upper set It is interesting to observe, in this regard, that discrim- limit of about 3 items (note that frogs failed the discrimi- ination between two shoals of conspecifics differing in the nation 3 vs. 4). In accord with this interpretation is also the number of members in angelfish shows exactly the opposite fact that frogs did not show a significant difference in pattern: Fish (P. scalare) used the number of shoal mem- performance between the two successful discriminations 1 bers as a cue only in large shoal contrasts but not in small versus 2 and 2 versus 3, which is expected if these small shoal contrasts, where surface area dominated choice numerousness discriminations would be treated by a sep- (Go´mez-Laplaza and Gerlai 2013). Differently than prey arate object file system but not if treated by an approximate catching, in which the attention is focused on a single magnitude system because of their different ratios, 0.50 individual, shoaling does not allow individuation of each and 0.67, respectively). element. Indeed, in the case of shoaling, the most relevant This is not of course to argue that the small numerous- aspect is group size and not the identity of the individual ness system would operate on numerousness independent members. Thus, comparison of numerical abilities associ- of continuous physical variables, whereas the large ated with natural-occurring behavior in simple animals numerousness system would not. This seems to be unlikely. such as amphibians and other lower vertebrates may pro- Research on mammals and birds suggests that the AMS vide crucial information about the characteristics of the may operate on number. 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