Numerical abilities in fish: A methodological review

Behavioural Processes 141 (2017) 161–171

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Review

Numerical abilities in fish: A methodological review Christian Agrillo ∗ , Maria Elena Miletto Petrazzini, Angelo Bisazza Department of General Psychology, University of Padova, Italy

a r t i c l e

i n f o

Article history: Received 24 July 2016 Received in revised form 30 January 2017 Accepted 1 February 2017 Available online 3 February 2017 Keywords: Numerical cognition Fish Shoal choices Operant conditioning Continuous quantities Training procedure

a b s t r a c t The ability to utilize numerical information can be adaptive in a number of ecological contexts including foraging, mating, parental care, and anti-predator strategies. Numerical abilities of mammals and birds have been studied both in natural conditions and in controlled laboratory conditions using a variety of approaches. During the last decade this ability was also investigated in some fish species. Here we reviewed the main methods used to study this group, highlighting the strengths and weaknesses of each of the methods used. Fish have only been studied under laboratory conditions and among the methods used with other species, only two have been systematically used in fish—spontaneous choice tests and discrimination learning procedures. In the former case, the choice between two options is observed in a biologically relevant situation and the degree of preference for the larger/smaller group is taken as a measure of the capacity to discriminate the two quantities (e.g., two shoals differing in number). In discrimination learning tasks, fish are trained to select the larger or the smaller of two sets of abstract objects, typically two-dimensional geometric figures, using food or social companions as reward. Beyond methodological differences, what emerges from the literature is a substantial similarity of the numerical abilities of fish with those of other vertebrates studied. © 2017 Elsevier B.V. All rights reserved.

Contents 1. 2.

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Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 Methodology for the study of quantity discrimination in fish . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 2.1. Spontaneous choice tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 2.1.1.1. Shoal quantity discrimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 2.1.1.2. Shoal quantity discrimination: sequential control of continuous quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 2.1.1.3. Shoal choice discrimination: preventing access to continuous quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164 2.1.2.1. Food quantity discrimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 2.1.2.2. Food quantity discrimination: control for continuous quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 2.2. Discrimination learning procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 2.2.1. Training studies with social reward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 2.2.2. Training studies with food reward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170

1. Introduction Several field studies suggested that numerical abilities are useful for mammals and birds to solve different problems in their natural environment. For instance, chimpanzees (Pan troglodytes, Wilson

∗ Corresponding author at: Department of General Psychology, Via Venezia 8, 35131, Padova, Italy. E-mail address: [email protected] (C. Agrillo). http://dx.doi.org/10.1016/j.beproc.2017.02.001 0376-6357/© 2017 Elsevier B.V. All rights reserved.

et al., 2002), lions (Panthera leo, McComb et al., 1994) and feral dogs (Canis lupus familiaris, Bonanni et al., 2011) are more willing to engage in fights when their group outnumbers that of opponents. Number judgments are important for anti-predator strategies as the probability of being captured by predators diminishes when individuals join a larger group of social companions (e.g., redshanks, Tringa totanus, Cresswell, 1994); for this reason, several species prefer to join a larger group of social companions when exposed to predators (e.g., Cresswell and Quinn, 2011). Numerical abilities

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can provide benefits in mate choice too (Wedell et al., 2002); for instance, the ability to count the number of conspecifics enables bank voles (Myodes glareolus) to adjust their reproductive strategy to the level of sperm competition, with males producing more sperm in the presence of multiple competitors (Lemaitre et al., 2011). Foraging decisions represent another ecological context in which animals can take advantage of numerical abilities; it has been shown that New Zealand robins (Petroica australis, Hunt et al., 2008) and rhesus monkeys (Macaca mulatta, Hauser et al., 2000) can select the larger amount of food in order to optimize food intake. It is likely that similar selective pressures in favour of the ability to select the larger/smaller group of objects are present in other organisms; and indeed, the quantificational abilities in other taxonomic groups, particularly bony fish, have been recently investigated. Several fish species are known to join the larger shoal when exploring a potentially dangerous environment in order to reduce the risks of being predated (Hager and Helfman, 1991; Pritchard et al., 2001; Svensson et al., 2000). The risk of an individual fish being caught diminishes as the quantity of individuals in the group increases, a phenomenon typically called the ‘dilution effect’ (Foster and Treherne, 1981). Also, living in larger shoals makes it more difficult for a predator to single out an individual prey (‘confusion effect’, see Landeau and Terborgh, 1986) and increases the possibility of detecting predators (‘many eyes effect’, Pulliam, 1973). Many piscine predators suffer a low capture success rate when attacking groups of prey (e.g., Krause and Godin, 1995). Indeed some studies have found a preference for attacking individual prey or smaller groups (Milinski, 1977a, 1977b; Morgan and Godin, 1985; but see Botham et al., 2005 for the reverse preference) showing that the capacity to discriminate the larger/smaller shoal is present in both prey and predators. Numerical abilities may also provide benefits in resource competition as it was found that banded killifish (Fundulus diaphanus) form smaller shoals when food is available, probably to reduce the competition for food resources (Hoare et al., 2004). In species with parental care, a further advantage of estimating quantities is the possibility to adjust parental behaviour as a function of the number of the progeny, and it has been recently demonstrated that female convict cichlids (Amatitlania nigrofasciata) in the presence of fry groups differing in number attempt to recover preferentially the fry from the larger group in order to increase their fitness (Forsatkar et al., 2016). Lastly, the capacity to discriminate the sex ratio of social groups in mosquitofish (Gambusia holbrooki) and guppies (Poecilia reticulata) is thought to allow males to adjust their reproductive strategies to the existing level of sperm competition ¨ and Ranta, 1993; Smith and Sargent, 2006). (Lindstrom These kinds of studies give us little information about the exact mechanisms used by animals to solve numerical problems. For instance, in the above examples animals could have used non-numerical mechanisms to discriminate the larger or smaller quantity. They could for example have compared continuous quantities that co-vary with numbers, such as cumulative area occupied by the objects, their density, or the convex hull (that is, the overall space occupied by the most lateral objects of the groups). To understand whether animals really use numerical information and to shed light on the cognitive mechanisms that underlie these abilities it is therefore necessary to conduct controlled experiments in the laboratory. A wide range of techniques has been developed to investigate these issues in mammals and birds. For example, laboratory studies strictly controlling for continuous quantities (e.g., cumulative surface area or density) demonstrated that several mammals (e.g., chimpanzees Pan troglodytes: Garland et al., 2014; dogs: West and Young, 2002) and birds (New Zealand robins, Garland et al., 2012; parrots Psittacus erithacus, Pepperberg, 2006) can solve most quantitative tasks by using numerical information only. The strengths

and limitations in the use of these different methods have been the subject of a recent review (Agrillo and Bisazza, 2014). Because of their morphology, the type of locomotion, the size of the species commonly used and the fact that they live in an aquatic medium, fish cannot be easily investigated with some of the techniques developed for studying warm-blooded vertebrates and in recent years specific methods have been developed to study the numerical ability of fish. In this paper, we review the methods that have been used to investigate numerical abilities in teleost fish and summarize the results that have been obtained. In particular, we focus on the comparison between the two main methods that have been adopted in studying fish, spontaneous choice tests and discrimination learning procedures, highlighting the strengths and weaknesses of each approach and comparing the results obtained using these two different methodologies. 2. Methodology for the study of quantity discrimination in fish Although a wider range of methodologies have been used in mammals and birds (Hauser et al., 2002; West and Young, 2002), without exceptions we can split the literature on numerical abilities in fish into two main methodological approaches: spontaneous choice tests and discrimination learning procedures. 2.1. Spontaneous choice tests Spontaneous choice tests typically take advantage of the natural tendency of an animal to prefer more or less of something. The subject is presented with two sets containing different numbers of biologically-relevant stimuli. In mammal and bird studies, pieces of food represent the most common type of stimuli presented in these tests. For instance, one study tested the spontaneous ability of rhesus monkeys to choose the larger quantity of plums presented on two separate plates (Sulkowski and Hauser, 2001). The assumption underlying these tests is that, if animals are able to discriminate between the two quantities, they are expected to select the most advantageous option in terms of food intake (in this case the larger quantity). In fish research, two types of stimuli have been used: social companions (shoal quantity discrimination) and food items (food quantity discrimination). 2.1.1.1. Shoal quantity discrimination Social companions are by far the most common type of stimuli used in these tests with fish. This is due to the fact that sociality is the main anti-predatory strategy for many fish and the advantages of living in a group tend to increase as the number of individuals in the group increases. As a consequence, individual fish that are inserted in an unfamiliar and potentially dangerous environment tend to join other conspecifics and, if two shoals are present, they show a strong tendency to join the larger shoal (Buckingham et al., 2007; Hager and Helfman, 1991; Mehlis et al., 2015). Several studies have taken advantage of this anti-predator behaviour to assess the limits of quantity discrimination. Typically, a single subject is inserted into an unfamiliar empty tank where two groups of social companions are visible. The visual contact of a potential predator is not necessary as the unfamiliar environment is sufficient to increase subjects’ motivation to join the larger group. The proportion of time spent near the larger shoal is recorded as a measure of quantity discrimination (Fig. 1a). Using this procedure, it was found that mosquitofish (Gambusia holbrooki) can discriminate groups differing by one unit up to 4 items (1 vs. 2, 2 vs. 3, and 3 vs. 4, but not 4 vs. 5; Agrillo et al., 2008a). A closely-related species, the guppy (Poecilia reticulata), exhibits the same limit when tested in similar conditions

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Fig. 1. Schematic representation of the experimental apparatuses used in spontaneous choice tests. A) In shoal quantity discrimination tasks, a single subject is inserted into an unfamiliar tank where two groups of conspecifics differing in number are visible at the two opposite ends. Two lines on the bottom of the tank delimit the choice areas. The proportion of time spent near the larger shoal is used as measure of quantity discrimination. B) In this alternative version of shoal quantity discrimination, subjects are inserted in a central hourglass-shaped sector; stimulus fish are singly confined in separate sectors at the two short sides of the tank; in each choice area, artificial vertical plastic screens are aligned in a grid of 3 by 3, so that the subject can only see one stimulus fish at a time from any position of its sector, thus preventing the possibility of using area or density to select the larger shoal. C) In food quantity discrimination tasks, two groups of food items are simultaneously presented to the subject and remain visible until the time of choice. Live plants are available in the middle of the tank in two opposite transparent containers. The proportion of choices for the larger food quantity is recorded as measure of accuracy.

(Agrillo et al., 2012a) while angelfish (Pterophillum scalare) discriminated 1 vs. 2 and 2 vs. 3, but not 3 vs. 4 fish (Gómez-Laplaza and Gerlai, 2011b). Larger quantities can also be discriminated by increasing the ratio between the smaller and the larger quantity: guppies (Agrillo et al., 2012a), mosquitofish (Agrillo et al., 2008a) and swordtails (Xiphophorus elleri, Buckingham et al., 2007) could discriminate up to a 0.50 ratio (e.g., 8 vs. 16) but not 0.67 ratio (e.g., 8 vs. 12). Angelfish displayed a similar limit of large quantity discrimination, at a 0.56 ratio (5 vs. 9, Gómez-Laplaza and Gerlai, 2011a). In all these species, accuracy of discrimination of numbers greater than 4 appears to decrease with an increasing ratio between

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the smaller and the larger shoal, in agreement with Weber’s law, according to which the least noticeable difference is proportional to the magnitude of the stimulus and is a function of the ratio between the two quantities (see Dehaene et al., 1998). Recently, Lucon-Xiccato et al. (2016) developed an alternative protocol to investigate shoal preference in guppies. The shoalchoice test mentioned above typically requires a long observation time, approximately 15–20 min for each subject (e.g., Agrillo et al., 2008a; Gómez-Laplaza and Gerlai, 2011a), mainly because subjects switch between the two shoals with low frequency. In order to set up a more suitable procedure for large-scale screenings of quantitative abilities in fish, the authors modified the shoal-choice test so that the subject was confined in a large transparent cylinder in the middle of the tank for the whole test. Specifically, the cross-section of the cylinder was divided into three zones with equal longitudinal extension, two choice sectors facing the stimulus shoals and one central, neutral sector. Time spent in the two choice sectors was taken as a dependent variable. Results showed that this procedure permits assessment of shoaling preference in a shorter amount of time, with guppies selecting the larger shoal in a 4 vs. 6 discrimination after only 5 min. Also, subjects proved able to discriminate 4 vs. 5 social companions, a fact that was not reported in poeciliid fish with the traditional shoal-choice test (Agrillo et al., 2007, 2008a). The authors hypothesized that the greater efficiency of this method might be due to the fact that, in this test, guppies switched often between the two shoals, approximately five times more frequently than with the previous shoal-choice methods (e.g., Agrillo et al., 2012a). The increased frequency of switching may hence favour the comparison between the two shoals and lead to a more accurate assessment of the two quantities. Quantitative abilities have been studied also in the context of sexual choices. Agrillo et al. (2008b) found that male mosquitofish prefer larger groups of females. Males selected the larger group in 1 vs. 3 and 2 vs. 4 comparisons. When the same number of females was visible, males preferred a shoal without males. However, no preference for the more favourable sex ratio was observed when the number of males in each shoal was varied (3 females + 2 males vs. 3 females + 4 males), suggesting that males cannot assess simultaneously the quantity of males and females within a group. These types of tests have undoubtedly helped us to assess the limits of quantity discrimination in several fish species. However, in all these studies, stimulus fish were visible at the time of choice and subjects could have used continuous quantities, such as total activity within the shoals, their density, or cumulative surface area of the shoals. This methodological limitation prevents us from establishing the exact mechanism used by subjects to select the larger quantity. 2.1.1.2. Shoal quantity discrimination: sequential control of continuous quantities One experimental strategy to limit the use of continuous quantities consists in controlling one continuous quantity at a time. The total activity of stimulus fish is a continuous quantity that might reveal the numerical size of a shoal. The role of this cue was investigated by varying the temperature of water of the stimulus aquaria in a study done in zebrafish. Like many other fish, zebrafish live in a range of temperatures and their activity increases as water temperature increases. Pritchard et al. (2001) found that subjects generally preferred the larger shoal (the discrimination was 2 vs. 4) when the two stimulus shoals were at the same temperature. This preference was abolished when the water temperature of the larger shoal was reduced, hence reducing fish activity. Recently, Agrillo et al. (2008a) showed that water temperature affects total quantity of movements of mosquitofish too. When subjects were presented with 2 vs. 3 social companions in a condition in which total quantity of movements were paired, mosquitofish did not select either

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group, suggesting the importance of this information in small quantity discrimination. Quantity of movement, however, did not play an important role in large quantity discrimination (4 vs. 8). An alternative way to equate the quantity of movement consists in confining each stimulus fish in a single sector in order to restrict its movement. Using this procedure, Gómez-Laplaza and Gerlai (2012) found that angelfish continue to discriminate 5 vs. 10 conspecifics after the total movement of the two shoals was equated. This study also replicated with angelfish the procedure used with zebrafish and mosquitofish, in which water temperature of stimulus fish was experimentally manipulated. Manipulating water temperature in the stimulus tanks affected angelfish ability to discriminate groups of 5 vs. 10, as subjects did not select the larger shoal. The different outcome of the two experiments on angelfish as a function of the type of control for total quantity of movements (stimulus fish confined in separate compartments/water temperature control) highlights one critical aspect in numerical cognition studies, namely the importance of using multiple experimental strategies before drawing conclusions about the mechanisms used in quantity discrimination of animals (Agrillo and Miletto Petrazzini, 2012). Concerning the control of area, Agrillo et al. (2008a) studied shoal choice preferences in mosquitofish in 2 vs. 3 and 4 vs. 8 discriminations in which the total area of the stimuli was equated within each numerical contrast. To achieve this goal, the authors placed larger individuals in the numerically smaller stimulus-shoal and smaller individuals in the larger stimulus-shoal. When the overall area of the stimulus fish was equated, subjects showed no significant choice preference in either numerical contrast showing that overall area plays a key role in this type of discrimination. Similarly, Gómez-Laplaza and Gerlai (2012) found that overall area is a critical continuous quantity used by angelfish in shoal choice preferences. Subjects were presented with small (2 vs. 3) and large (5 vs. 10) numerical contrasts. When total area of the contrasted shoals was equated, their performance dropped to chance level. The salience of this variable in angelfish was further supported by the fact that subjects selected the shoal with the larger total area when numerical information was made irrelevant (e.g., 3 vs. 3). The role of density (inter-individual distance) was also investigated in angelfish (Gómez-Laplaza and Gerlai, 2013). In order to control for this variable in a 5 vs. 10 discrimination, the volume of the stimulus compartment was reduced by 50% for the smaller of the two stimulus shoals: angelfish were unable to select the larger shoal, indicating the spontaneous use of density information. This continuous quantity did not play a significant role in a 2 vs. 3 discrimination. The above-mentioned procedures are useful to assess the contribution of different continuous quantities, but they can potentially introduce other confounding factors. For instance, when researchers control for the quantity of movement of the stimuli, the behaviour of stimulus fish may be affected thus influencing subjects’ choice. As several fish species often remain immobile to minimize the risk of being detected by predators (an antipredatory strategy called ‘freezing’, see Chivers and Smith, 1994, 1995), experimentally reducing movement of fish included in the larger stimulus group might function as an alarm cue on that side of the tank. As a consequence, the larger shoal might appear less attractive for the subjects. When controlling for the overall area of the stimuli, one must consider that fish often prefer to shoal with similar-sized individuals to minimize their conspicuousness in case of predatory attack (Landeau and Terborgh, 1986). An alternative strategy to reduce the use of continuous variables involves again the simultaneous presentation of two groups of conspecifics (e.g., 2 vs. 3); however, at the time of choice the perception of the two groups is experimentally limited. For instance, Stancher et al. (2013) tested spontaneous quantity discrimination

in male redtail splitfin (Xenotoca eiseni). After having shown both stimulus-groups, in the test phase the authors limited the perception of the two groups by using an opaque barrier so that exactly the same number of females (two) was visible to the test male in both sectors. Subjects were able to select the larger number of females in 1 vs. 2, 2 vs. 3 and 3 vs. 4 comparisons (Stancher et al., 2013). No ability for discrimination was reported with larger numbers. A similar result was recently observed in two other species. Zebrafish (Danio rerio) were initially left free to see two groups of social companions differing in number. At the end of this phase, one or more stimulus fish were hidden by an opaque barrier so that they were no longer visible to the male zebrafish, leaving exactly the same number of stimulus females visible in the transparent parts of each of the two sectors (e.g., 1 vs. 1). Results showed that male zebrafish were able to select the size associated with the larger shoal in 1 vs. 2 and 2 vs. 3. Unlike redtail splitfin, however, they failed in the 3 vs. 4 comparison. Larger quantity discrimination was also found (e.g., 4 vs. 6, but not 6 vs. 8; Potrich et al., 2015). This performance resembles that of angelfish tested in similar conditions: fine numerical discrimination was found in angelfish up to 3 units (1 vs. 2, 2 vs. 3 but not 3 vs. 4; Gómez-Laplaza and Gerlai, 2015); large quantity discrimination is also possible up to a 0.50 ratio (e.g., 4 vs. 8), thus suggesting that angelfish may be less accurate than zebrafish in this task (Gómez-Laplaza and Gerlai, 2016). This procedure, although useful in reducing access to continuous quantities, does not entirely exclude the possibility that animals can use non-numerical information, as subjects could compare the different areas occupied by stimuli when they are visible and then remember the position occupied by the larger amount prior to its disappearance. 2.1.1.3. Shoal choice discrimination: preventing access to continuous quantities Some of the limitations to controlling for continuous quantities in spontaneous choice tests can be overcome using the ‘item-byitem presentation’. This procedure has been repeatedly adopted with mammals (i.e., chimpanzees: Beran et al., 2013; rhesus monkeys: Hauser et al., 2000; dogs: Ward and Smuts, 2007) and birds (chicks: Rugani et al., 2009; New Zealand robins: Garland et al., 2012) and is based on the sequential presentation of items within each set. For example, in one study New Zealand robins could see that experimenters placed mealworms, one at a time, into each of two opaque containers before they were allowed to choose one of the two alternatives. Birds were hence supposed to use working memory and build a representation of the contents of the two boxes only on the basis of the items that came into view sequentially. They were prevented from having a global view of the contents of the groups and could not use continuous quantities such as the cumulative surface area occupied by stimuli or their density (Hunt et al., 2008). The item-by-item procedure was adapted to fish research using social companions as stimuli (Dadda et al., 2009). This study used a modified version of the shoal choice test in which stimulus fish were singly confined in separate compartments at the two bottoms of the tank. Inside the subject tank in correspondence to the two stimulus shoals, several opaque screens were inserted to prevent the possibility that subjects (mosquitofish) could see more than one conspecific at a time (Fig. 1b). Mosquitofish were required to enumerate stimuli on both sides, comparing them before selecting their preferred shoal. Subjects were tested in two numerical contrasts, 2 vs. 3 and 4 vs. 8, and in both they spent more time near the larger shoal. The convex hull and density of individuals were controlled in two further tests. As subjects were able to select the larger shoal also in those control tests, it suggests that mosquitofish had a spontaneous number representation of the two groups of social companions.

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A subsequent study using the same procedure in a closely related species, guppies, showed that newborn guppies can discriminate 2 vs. 3 social companions and juvenile individuals (40-day-old guppies) can discriminate 4 vs. 8 companions (Bisazza et al., 2010), suggesting that numerical abilities might be already present in the first period of life, as previously reported in the domestic chick (Rugani et al., 2007). 2.1.2.1. Food quantity discrimination In mammals and birds, numerical cognition studies using spontaneous choice tests typically present food items as stimuli (Bogale et al., 2014; Hauser et al., 2000). As described above, one of the simplest procedures to test whether animals can discriminate between quantities consists of presenting two groups of food items that remain visible until the time of choice. The assumption is that subjects should select the larger quantity of food in order to maximize food intake. This methodological approach was initially applied to basal vertebrates by Uller et al. (2003) using salamanders (Plethodon cinereus). Salamanders presented with two transparent boxes containing fruit flies differing in number proved able to select the larger group in 1 vs. 2 and 2 vs. 3 but not 3 vs. 4. More recently Stancher et al. (2015) reported a similar result in another amphibian, bombinas (Bombina orientalis). In fish, the use of food items as stimuli is quite recent. In 2015 adult guppies were shown two plastic cards to which small pieces of food flakes were glued (Fig. 1c). Subjects were able to select the larger quantity in 1 vs. 4 and 2 vs. 4, but no discrimination was found in 2 vs. 3 and 3 vs. 4 (Lucon-Xiccato et al., 2015). However, as stated in section 2.1.1.1, the nature of quantitative abilities is unclear when biologically relevant stimuli are simultaneously presented. Subjects could have assessed the larger group by using the cumulative surface area or density (an issue discussed in section 2.1.2.2). 2.1.2.2. Food quantity discrimination: control for continuous quantities As with shoal choice tests, controlling one continuous quantity at a time represents the easiest experimental strategy. For instance, Krusche et al. (2010) investigated the role of the total activity of prey in the quantity discrimination of salamanders. As stimuli, researchers used live crickets, videos of live crickets or images animated by a computer program. When no control was made, subjects discriminated the larger group in an 8 vs. 16 contrast, while they chose randomly when the total movement of the stimuli was controlled for, thus suggesting that the total activity of prey is a dominant feature in their foraging behaviour. Regarding fish, Lucon-Xiccato et al. (2015) conducted a second experiment in which they controlled for the overall quantity of food. The authors presented a 2 vs. 4 comparison (a comparison that guppies proved able to discriminate when number and volume were congruent) and equated the cumulative surface area in the two groups. Subjects no longer selected the group containing the larger number of food items, a result that might appear surprising at first, as it would seem that, when continuous quantities are controlled for, the guppies failed to choose the largest quantity of food items even in a numerical discrimination, such as 2 vs. 4, that they easily discriminated in other contexts using numerical information only. Nonetheless, this outcome can be explained if we take into account the evolutionary pressures that are likely to have shaped the decisional mechanisms in the foraging behaviour of most vertebrates. Natural selection is expected to favour mechanisms that maximize the amount of food (i.e., calories) gained and thus the total volume rather than the number of items of food. In the above-mentioned example (2 vs. 4 with equated volume), both alternatives ensure identical caloric content, so there is no reason

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for the animal to select one more than the other. Hence the control of continuous quantities in numerical experiments with arrays of food items simultaneously available at the time of choice is difficult as the predicted outcome of these experiments is that preference will not based on number of items, regardless of whether animals are able to discriminate number or not. Interestingly, in the experiment we just described, LuconXiccato et al. (2015) observed that guppies selected the smaller set composed by larger items even if the two options contained the same total amount of food, a result that was not predicted assuming that natural selection brought individuals to optimize the choice of the largest total quantity of food. One explanation for this result is that guppies were attracted by the largest available food item. The largest item was indeed more often present in the set containing the smaller number of items, as a consequence of controlling for total surface area. It is worth noting that food items often showed subtle differences in area, thus raising the intriguing possibility that guppies were much better at discriminating the size of food items than their number. To test this hypothesis, in a subsequent experiment, subjects were given the choice between two food items differing in area (1 larger vs. 1 smaller food item) using the same ratios adopted in the numerical experiment (0.25, 0.50, 0.67, 0.75). In this task, guppies’ performance was ratio-dependent as if they were following Weber’s law. Hence, a higher accuracy was shown in the presence of a 0.25 ratio (fourfold difference in area) than a 0.75 ratio. Perhaps the most intriguing finding of this study is that guppies were much more accurate if they had to discriminate between the areas of two items (they can discriminate at least up to a 0.75 ratio) compared to when, in the numerical experiment, they had to discriminate the same two areas fragmented into more units (they could discriminate only up to a 0.5 ratio, 1 vs. 4 and 2 vs. 4). According to Lucon-Xiccato et al. (2015), the different results in the two experiments could be related to the foraging strategy of the species. Guppies in the wild forage in groups and compete for prey items (Magurran and Seghers, 1994). In this context, natural selection might have favoured cognitive mechanisms that allow a rapid and efficient choice of the most profitable piece of food because, while an individual is processing one food item in the patch, shoal mates will probably consume the residual items. The authors hypothesized that there may be a strong advantage for the individual that detects and consumes the larger item of food immediately when the shoal encounters a new patch, as previously hypothesized in non-human primates (Beran et al., 2008). However, the preference for the larger food item can also be explained by optimal foraging models (Krebs, 1978; Pyke et al., 1977). These predict that selecting large prey should be advantageous when handling is relatively costly compared to search (i.e., encounter rate is high). Although this pattern is commonly found in nature, no data are currently available on foraging costs in guppies to substantiate this hypothesis. Indirect evidence of food quantity discrimination may be provided by experiments on ‘ideal free searching’ in fish. Optimal foraging theory predicts that when resources are distributed in patches and these differ in profitability (e.g. the number of prey), in order to maximize their payoff, competing individuals should distribute themselves among patches in a way that is proportional to the amount of resources available (ideal free distribution; Fretwell and Lucas, 1970). For example, Milinski (1979) observed the distribution of six sticklebacks between two feeders at the opposite ends of an aquarium which introduced water fleas at different rates (30 prey per min at one side and 6 at the other). More sticklebacks were observed to gather around the more profitable feeder and the distribution only slightly deviates from that predicted from the theory. According to ideal free distribution theory, to make optimal decisions about which patch to visit, an animal needs to assess not only the instantaneous availability of the resource in a

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patch (number of prey in this example) but also the number of other individuals foraging in the different patches. In fact, one can imagine simple heuristic decision-making rules that do not imply precisely counting the number of competitors and preys at each patch. For example, sticklebacks may measure and compare their rate of prey capture in the two patches. Krause (1992) has investigated the role of different information that determines patch choice in this task and concluded that likely sticklebacks use excitement of conspecifics as a proxy for food availability at the two patches. 2.2. Discrimination learning procedures Spontaneous choice tests present two main limits. First, although several experimental procedures have been devised to prevent the use of continuous quantities, such attempts remain complicated when dealing with living organisms (such as social companions or prey) as stimuli. Also, as explained above, when animals have to maximize food intake, non-numerical continuous quantities may become more salient, thus making an investigation of true numerical abilities of the subjects difficult. Second, motivation may strongly affect the result, and null results do not necessarily imply a lack of discrimination. If a monkey does not show a significant preference in 15 vs. 20 apples, this might occur simply because monkeys are not motivated to select the larger group as both patches provide more food than the animal can handle. To overcome the potential limitation of spontaneous choice tests, training procedures using classical and operant conditioning have often been adopted (Cantlon and Brannon, 2007; Davis, 1984). In a training procedure study, animals are required to learn a numerical rule to receive a reward. Neutral stimuli, such as twodimensional dots presented on the screen, are often associated with a food reward on the basis of some rules such as choosing the larger number of items. In this way, researchers can dissociate how large the stimulus arrays are from how much food is ingested by the subjects. As soon as the subject becomes familiar with the experimental apparatus, a sequence of numerical discrimination is typically presented until the subject reaches the learning criterion (Biro and Matsuzawa, 2001; Vonk and Beran, 2012). In recent years, discrimination learning procedures have been used to investigate numerical abilities in fish too. Both social and food rewards have been used.

Fig. 2. Different training procedures used to study numerical abilities in fish. A) Discrimination learning using social reward. A subject is inserted into an unfamiliar environment provided with two doors at the opposite corners. One door is associated with two figures and the other is associated with three figures. The subject is required to discriminate between the two numbers and select the door associated with the reinforced number to rejoin social companions. B) Discrimination learning using food reward. Two sets of two-dimensional figures differing in number are presented at the two ends of the tank using two PC monitors and a food reward is delivered only near the number to be reinforced. A fluorescent lamp is placed on the top of the tank in the central position C). Alternative discrimination learning apparatus using food reward. Two groups of yellow discs differing in number are placed

2.2.1. Training studies with social reward In the first study that used this methodology, mosquitofish were trained to discriminate between different numbers of twodimensional figures using access to conspecifics as a reward (Agrillo et al., 2009). Fish were removed from their social group and placed in an unfamiliar square environment. They could re-join companions by passing through one of two identical tunnels at opposite corners. Tunnels were associated with different numbers using images of 2 or 3 two-dimensional geometric figures. Only the door associated with the reinforced number allowed the subject to rejoin its companions (Fig. 2a). The shape and spatial arrangement of figures was changed across trials to avoid the possibility that fish could learn to recognize specific patterns. In the first experiment, mosquitofish were trained to discriminate between 2 and 3 figures with no control for continuous quantity. Subjects were then retested while controlling for one continuous quantity at a time: their performance dropped to chance level when stimuli were matched for the cumulative surface area or for the convex hull, showing that these cues had been primarily used during the learning pro-

on a green panel and a food reward is hidden only under the discs of the larger set. The subject is required to dislodge the discs of the larger set in order to obtain the food reward. Two fluorescent lamps are placed on the top of the two sectors.

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Table 1 Summary of the fish species in which some capacity to discriminate quantities was found (without experimental control of all continuous quantities) and species in which the use of numerical information was demonstrated (with control of continuous quantities). Species (alphabetic order)

Angelfish

Banded killifish Blue acara Central mudminnow Climbing perch Fathead minnow Goldbelly topminnow Golden shiner Goldfish Guppies

Mosquitofish

Quantity Discrimination (Number + Continuous Quantities)

Numerical Discrimination

Methodology and References

Methodology and References

Shoal quantity discrimination (Gómez-Laplaza and Gerlai, 2011a, 2011b) Shoal quantity discrimination with sequential control of continuous quantities (Gómez-Laplaza and Gerlai, 2012, 2013) Shoal quantity discrimination (Krause and Godin, 1994) Shoal quantity discrimination (Krause and Godin, 1995) Shoal quantity discrimination (Jenkins and Miller, 2007) Shoal quantity discrimination (Binoy and Thomas, 2004) Shoal quantity discrimination (Hager and Helfman, 1991) Shoal quantity discrimination (Agrillo and Dadda, 2007) Shoal quantity discrimination (Reebs and Sauliner, 1997) – Shoal quantity discrimination (Agrillo et al., 2012a; Ledesma and McRobert, 2008; Lucon-Xiccato et al., 2016; Miletto Petrazzini and Agrillo, 2016; Piffer et al., 2012) Food quantity discrimination with sequential control of continuous quantities (Lucon-Xiccato et al., 2015)

Training study with food reward (Agrillo et al. 2012c; Miletto Petrazzini et al., 2016) Shoal quantity discrimination with stimuli not-visible at the time of choice (Gómez-Laplaza and Gerlai, 2015, 2016) – – – – – – – Training study with food reward (DeLong et al., 2017) Shoal choice discrimination with item by item procedure (Bisazza et al., 2010)

Shoal quantity discrimination (Agrillo et al., 2007) Shoal quantity discrimination with sequential control of continuous quantities (Agrillo et al., 2008a)

Red-bellied piranha Redtail splitfin

Shoal quantity discrimination (Queiroz and Magurran, 2005) –

Sailfin molly Siamese fighting fish Somalian cavefish Swordtail Three-spined sticklebacks

Shoal quantity discrimination (Bradner and McRobert, 2001) Shoal quantity discrimination (Snekser et al., 2006) – Shoal quantity discrimination (Buckingham et al., 2007) Shoal quantity discrimination (Barber et al., 1998; Tegeder and Krause 1995; Mehlis et al. 2015) Shoal quantity discrimination (Svensson et al., 2000) Shoal quantity discrimination (Botham and Krause, 2005) Shoal quantity discrimination with sequential control of continuous quantities (Pritchard et al., 2001)

Two-spotted goby Wolf fish Zebrafish

Training studies with food reward (Agrillo et al., 2012c; Agrillo et al., 2014; Bisazza et al., 2014b; Dadda et al., 2015; Miletto Petrazzini et al., 2015a, 2015b; Piffer et al., 2013) Shoal choice discrimination with item by item procedure (Dadda et al., 2009) Training studies with social reward (Agrillo et al., 2009, 2010, 2011) Training study with food reward (Agrillo et al., 2012b) – Training study with food reward (Agrillo et al., 2012c) Shoal quantity discrimination with stimuli not visible at the time of choice (Stancher et al., 2013) – Training study with food reward (Agrillo et al., 2012c) Training study with food reward (Bisazza et al., 2014a) – – – – Training study with food reward (Agrillo et al., 2012c) Shoal quantity discrimination with stimuli not visible at the time of choice (Potrich et al., 2015)

cess. On the contrary, equalizing the sum of perimeters (that is, the sum of the contours of the figures included in the two arrays) and total brightness did not affect mosquitofish performance. No difference was found between fish trained with the larger or the smaller quantity as positive. In a second experiment, subjects were required to discriminate between 2 and 3 figures in a condition in which only numerical information could be used (cumulative surface area, density, and convex hull were simultaneously controlled for during training). Mosquitofish proved able to solve the task, showing for the very first time that fish can process discrete numerical information. In a subsequent study, Agrillo et al. (2010) used the same discrimination learning procedure to investigate whether continuous quantities are preferentially used when discriminating larger numbers, such as 4 vs. 8. Again, cumulative surface area was primarily used by fish. However, mosquitofish learned the task when trained in a condition that prevented the use of continuous quantities, showing that they are able to use numerical information for quantities larger than 3.

2.2.2. Training studies with food reward Agrillo et al. (2012b) placed mosquitofish individually in rectangular tanks. Two sets of two-dimensional figures of different quantities were repeatedly presented at the opposite ends and food was provided only near the stimulus to be reinforced (Fig. 2b). Stimuli were controlled for continuous quantities (cumulative sur-

face area, convex hull, and density). Food reward was provided by using a syringe submerged in the water. To assess whether fish had learned to discriminate between the two numbers, researchers recorded the proportion of time spent near the positive stimulus in probe trials without food reward. Using this procedure, it was found that mosquitofish can make use of numerical information not only to discriminate small quantities (e.g., 2 vs. 4 items) but also to discriminate very large quantities provided that there is at least a 0.50 ratio between the two numbers (e.g., 100 vs. 200 items). No difference in performance was observed between fish trained with the larger or the smaller quantity as positive. Recently this procedure has been rearranged to investigate quantitative abilities in blind cavefish (Bisazza et al., 2014a). Phreatichthys andruzzii is a cave-dwelling species that evolved for approximately 2 million years in the phreatic layer of the Somalia desert. Subjects were trained to discriminate between 2 groups of three-dimensional sticks placed in opposite sides of the experimental tank in order to receive a food reward. In one experiment, fish were required to discriminate between different quantities (2 vs. 4 sticks); in half of the trials, stimuli were not controlled for continuous quantities (‘number + continuous quantities’ condition) while in the other half they were controlled (‘number’ condition). Cavefish discriminated only in the former condition, showing that they were making spontaneous use of continuous quantities when left free to use both number and continuous quantities, a result that aligns with those previously reported in trained mosquitofish

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(Agrillo et al., 2009, 2010). In another experiment, researchers investigated whether cavefish could learn to use numerical information if prevented from using continuous quantities from the beginning of the training. Subjects proved able to make the discrimination, suggesting that the availability of multiple cues in the first part of the learning process is fundamental in determining which type of information (numerical or continuous) will be adopted as a discriminative cue. The exact sensory mechanism used by P. andruzzii for discriminating objects was not determined. The most likely candidate is the lateral line system which is much better developed in cavefish compared with sighted surface forms and which allows detection of obstacles at a distance by determining the change of water flow along the body while swimming (Münz, 1989; Sguanci et al., 2010; Yoshizawa et al., 2010). Interspecific comparisons are typically difficult with spontaneous choice tests, as biologically relevant stimuli differ across species and different results might be at least partially affected by the nature of the stimuli. By contrast, discrimination learning procedures permit a fine interspecific comparison because of the use of the same stimuli (e.g., two-dimensional figures). When compared to other species tested with discrimination learning procedures, the performance of trained fish appears to be similar to that observed in domestic chicks (Rugani et al., 2008), crows (Bogale et al., 2011), and bees (Gross et al., 2009) but is less accurate than that observed in many other species, such as apes (Biro and Matsuzawa, 2001), monkeys (Cantlon and Brannon, 2007), rats (Suzuki and Kobayashi, 2000), parrots (Pepperberg, 1987), and pigeons (Brannon et al., 2001). Such differences might be related to the relative brain size or the complexity of nervous system. However, Bisazza et al. (2014b) noted that a critical methodological difference exists between fish studies and the majority of training studies done with other species: with mammals and birds, thousands of reinforced trials are often presented (for instance, macaques, approx. 2000 trials, Cantlon and Brannon, 2007; dolphins, approx. 2800 trials, Jaakkola et al., 2005; pigeons, approx. 1000 trials, Roberts and Mitchell, 1994). Conversely, fish studies normally involve a few dozen trials, both because fish are easily stressed by training procedures and, as with the other heterotherms, they rapidly become satiated. It was suggested that part of the interspecific differences might be due to this methodological difference. To test this hypothesis, Bisazza et al. (2014b) set up a novel training procedure that allowed for extended training in guppies (120 trials for each numerical discrimination). Making use of the natural behavioural response of this fish, guppies were presented with two groups of yellow objects (e.g., 3 vs. 4) placed on the tank floor. Only the plates included in the larger amount hid a food reward (Fig. 2c). As in the other experiments, plate size and spatial arrangement was varied to ensure that fish could have used numerical information only. With this procedure guppies could discriminate up to 4 vs. 5 objects, higher than the previous limit observed in this species (Bisazza et al., 2014b) but still considerably far from the limit of 9 vs. 10 items shown by humans and apes. A higher number of trials was recently successfully presented to goldfish (Carassius auratus). DeLong et al. (2017) trained two subjects to discriminate between two arrays of dots with a 0.50 ratio (2 vs. 4, 6 vs. 12) in approximately 1200 trials. Subsequently, novel numerical ratios (e.g., 0.67) were presented to both subjects. Results showed that goldfish performance was higher in the presence of 0.50 ratio, around 90% accuracy, a performance close to that reported in primates, and was not affected by continuous quantities such as cumulative surface area, density, or convex hull. Which kind of cognitive rule do fish adopt when solving these tasks? Indeed, when animals learn to select the larger array between two arrays (e.g., 5 vs. 10) differing in number, they may use two alternative strategies. One strategy consists in learning to select always 10 items (hereafter called “absolute rule”). Alternatively, they might use a “relative rule”, such as “select the larger

number in each pair”. In both cases, the behavioural output is the same. To identify which rule is being used, Miletto Petrazzini et al. (2015a) trained guppies to discriminate between two arrays of twodimensional figures differing in number (e.g., selecting 12 in a 6 vs. 12 discrimination) in order to obtain a food reward. After reaching the learning criterion, they were shown 12 vs. 24 figures in nonreinforced trials. Guppies spontaneously selected the novel (larger) number (24), and not the specific number (12) that was previously reinforced. Hence it seems that they had previously solved the training task using a relative (instead of an absolute) number rule. Since the majority of studies in fish, using both spontaneous choice tests and discrimination learning procedures, involve the simultaneous presentation of two quantities, we might be tempted to conclude that when fish are required to solve relative number judgments, they might be unable to represent absolute numbers. To answer this question, in another experiment guppies were trained to always select a set of 4 items against both smaller (e.g., 2) or larger numbers (e.g., 8). For instance, in one trial they could obtain a food reward by selecting 4 in a 2 vs. 4 discrimination and in the subsequent trial by selecting 4 in a 4 vs. 8 comparison (4 is the larger number in the first case, the smaller in the second). Guppies quickly learned this task and were able to generalize choosing the number four even in novel comparisons, such as 3 vs. 4 and 4 vs. 6. A recent study (Miletto Petrazzini et al., 2016) showed that the preferential use of a relative number rule is not confined to guppies. Angelfish and adult humans tested in the absence of verbal instructions were initially trained to select arrays containing 10 dots (in 5 vs. 10 or 10 vs. 20 comparisons). Subsequently they were presented with the previously trained number (10) and a novel number (20 vs. 10 for the group trained in the 5 vs. 10 contrast; 5 vs. 10 for the group trained in the 10 vs. 20 contrast). Both species favoured a relative number rule, suggesting that distantly related species may share a similar cognitive system for determining quantities. Another type of numerical ability that can be investigated using training procedures is the capacity to use ordinal information, namely the ability to locate an object on the basis of its position in a sequence of identical objects. This ability has been reported in mammals (Judge et al., 2005) and birds (Rugani et al., 2007). For instance, rats were trained to enter one box in an array of identical boxes. Subjects were able to select the correct target even when it occupied the 11th or the 12th position in a sequence of 18 (Suzuki and Kobayashi, 2000). Recently, Miletto Petrazzini et al. (2015b) adapted this procedure to investigate ordinal abilities in guppies. In one experiment, guppies were trained to select the 3rd feeder in a row of 8 alternative feeders placed perpendicularly in front of them (Fig. 3). To avoid the use of continuous quantities (e.g., the overall distance necessary to reach the correct feeder), the inter-feeder distance was experimentally manipulated between trials. Subjects proved able to solve the task, providing the first evidence of ordinal abilities in a fish species. In a further experiment, researchers tried to assess which information (ordinal or spatial) is preferentially used by fish. Guppies were initially trained in a condition in which both ordinal and spatial information were simultaneously available; in the test phase, the two types of information were contrasted to assess which strategy they had spontaneously used in the previous training phase. Guppies appear to use both types of information, although they relied more on ordinal information. Another experiment showed that guppies could be trained to select the 5th feeder in a row of 12 but were less accurate than subjects trained to learn the 3rd position, a result that aligns with previous literature on human and non-human species showing that estimation becomes less precise as the numerical quantity to estimate increases (Revkin et al., 2008; Tomonaga and Matsuzawa, 2002).

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Fig. 3. Experimental set up for the study of ordinal abilities. Eight identical feeders are displaced in a row perpendicularly in front of the subject but only the 3rd feeder from the left is reinforced with food (left, lateral view; right, aerial view). The interfeeder distance and the relative position of the 3rd feeder vary across trials to avoid the possibility of the subject using non-numerical spatial cues (e.g., overall distance necessary to swim) to locate the correct feeder.

3. Conclusions Numerical abilities in fish have begun to be investigated only recently. At least eight species seem to display the ability to use numerical information when continuous quantities are strictly controlled for (see Table 1): guppies (Poecilia reticulata), mosquitofish (Gambusia holbrooki), zebrafish (Danio rerio), angelfish (Pterophyllum scalare), redtail splitfin (Xenotoca eiseni), goldfish (Carassius auratus), Siamese fighting fish (Betta splendens) and Somalian cavefish (Phreatichthys andruzzii). Among these species, only three have been extensively investigated, Poecilia reticulata (e.g., Agrillo et al., 2012a, b, c, 2014; Bisazza et al., 2014a; Miletto Petrazzini et al., 2015a, b; Piffer et al., 2012, 2013), Gambusia holbrooki (e.g., Agrillo et al., 2008a, 2010, 2012a, b, c; Dadda et al., 2009) and Pterophyllum scalare (Agrillo et al., 2012a, b, c; Gómez-Laplaza and Gerlai, 2011a, b, 2012, 2013, 2015, 2016; Miletto Petrazzini et al., 2016). As fish represent approximately 50% of living vertebrates, a greater effort is required to understand numerical abilities in this large vertebrate group. For instance, all these species are freshwater teleost fish and we have no information on numerical abilities in saltwater or pelagic teleosts or in cartilagineous fish, a gap that must be filled in the future. As illustrated above, fish have only been studied in the laboratory. In particular, two main methodological approaches, adapted from studies in mammals and birds, have been used. Spontaneous choice tests and training procedures differ in many respects. In spontaneous choice tests, animals are thought to exhibit their natural behaviour in the presence of biologically relevant stimuli, such as food or social companions. For instance, the natural tendency of angelfish to select the larger shoal in a 2 vs. 3 discrimination (Gómez-Laplaza and Gerlai, 2011b) not only provides information about their quantitative abilities but also suggests that angelfish use this quantitative ability in their natural context when exploring an unfamiliar environment. Some have suggested instead that extensive training procedures may lead to recruitment of neurocognitive systems that may normally have different functions and use cues that are not involved in quantity estimation in the natural habitat of the species. When a mosquitofish learns to discriminate between sets of 2 and 3 two-dimensional figures using numerical information only (Agrillo et al., 2009), researchers can claim that this species is equipped with the neurocognitive abilities necessary to process numerical information; however, it is not guaranteed that the abilities assessed in this way will actually be used in a natural context. Training procedures, however, offer unquestionable advantages. Motivation is a critical aspect in spontaneous choice tests and a

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lack of preference for two large quantities of food does not necessarily mean a lack of discrimination. Also, with biological stimuli it is difficult to separate the contributions of the different sensorial modalities, for example conspecifics have a shape, produce smells, move in space and change orientation repeatedly. Above all, with spontaneous choice tests the fine control of continuous quantity is often critical. For instance, to control for the total area of stimulus fish in shoal choice tests (e.g., 3 vs. 4), researchers often manipulate the individual size of stimulus (3 larger fish vs. 4 smaller fish). However, as a result of this control, subject fish may not be motivated to join either shoal, as fish often prefer to shoal with individuals of similar body size to avoid being spotted by predators (a phenomenon known as ‘oddity effect’). These problems could be solved by using training procedures with two-dimensional, static figures drawn or presented on a monitor. For these reasons, the two methodological approaches appear to be complementary and both necessary to provide a clear picture of numerical abilities in fish. However, other methodologies are often used with mammals and birds, such as expectancy violation (e.g., Hunt et al., 2008) and habituation-dishabituation paradigms (e.g., Hauser et al., 2002). The former paradigm permits investigation of the spontaneous cognitive processes that occur during numerical estimation. It works on the principle that animals should look longer at an event that contradicts their knowledge. For instance, West and Young (2002) inserted two food treats behind an opaque barrier (1 + 1); the screen was then lowered to allow domestic dogs to see three possible outputs: 1 + 1 = 1, 1 + 1 = 2, and 1 + 1 = 3. Dogs looked longer when the outcome of the calculation was unexpected, such as 1 + 1 = 1, suggesting they have the ability to use numerical information. In a habituation-dishabituation paradigm, a single stimulus is initially repeated several times and the change in time spent fixating on the stimulus is used as a measure of habituation. A lower fixation time is expected after the habituation phase. Then a novel stimulus is presented: if animals are able to detect the difference between previous the stimulus and the novel one, this latter stimulus should re-excite the orienting response of the subjects, leading to an increased reaction fixation time. For instance, Hauser et al. (2002) habituated cotton-top tamarins with two pulses; subsequently they were presented with three sounds and had an increased fixation time, supporting the idea of numerical abilities in tamarins. Both expectancy violation and habituationdishabituation paradigm should be used in fish research. Unlike studies on mammals (Sulkowski and Hauser, 2001) and birds (Hunt et al., 2008), no fish study has used the item-by-item procedure with food items as stimuli. In addition, with the exception of the study on blind cavefish (Bisazza et al., 2014a), all fish studies have been restricted to the visual modality while other vertebrates have been also studied with auditory (Hauser et al., 2002) and tactile (Davis et al., 1989) stimuli. In humans, Tokita et al. (2013) reported a different performance in number estimation in the presence of visual and auditory stimuli, suggesting the existence of multiple numerical systems that may be modalitydependent. As far as we know, it is possible that the numerical acuity of fish is modality-dependent too. Partially related to this topic, studies investigating cross-modal interaction of numerical information are also needed, like the ones performed on primates (Jordan et al., 2005, 2008). In sum, current research on fish used a limited set of methodological tools compared to other vertebrates. At present, the choice between two shoals of different numbers is by far the most common paradigm used in fish; however, studies of this type in other organisms are lacking, which strongly limits the comparison of fish with other taxa. Only after having collected further data with the same methodological approaches used in mammals and birds, may we draw a firm picture of the similarities and differences between numerical abilities in fish and those in land vertebrates.

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Methodological differences aside, existing literature summarized here suggests a substantial similarity in numerical abilities of fish and other vertebrate groups.

Acknowledgments The authors would like to thank the two anonymous reviewers for their useful comments. Financial support was provided by FIRB grant “Futuro in Ricerca 2013” (prot.: RBFR13KHFS) from ‘Ministero dell’Istruzione, Università e Ricerca’ (MIUR, Italy) to Christian Agrillo.

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