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Messina, A. Numerical Abilities in Fish. Encyclopedia. Available online: (accessed on 06 December 2023).
Messina A. Numerical Abilities in Fish. Encyclopedia. Available at: Accessed December 06, 2023.
Messina, Andrea. "Numerical Abilities in Fish" Encyclopedia, (accessed December 06, 2023).
Messina, A.(2021, November 03). Numerical Abilities in Fish. In Encyclopedia.
Messina, Andrea. "Numerical Abilities in Fish." Encyclopedia. Web. 03 November, 2021.
Numerical Abilities in Fish

Encoding of numerical information has been shown to provide several advantages to animal species, including those which are more evolutionary distant to humans, such as fish. Recently, we combined behavioral tasks with molecular biology assays (e.g c-fos and egr1 and other early genes expression) showing that the thalamus and the caudal region of dorso-central part of the telencephalon seem to be activated upon change in numerousness in visual stimuli. In contrast, the retina and the optic tectum mainly responded to changes in continuous magnitude such as stimulus size. 

fish cognition numerosity cognition

1. Introduction

The concept of numerosity refers to the cardinality and ordinality of a group of items, and it represents a basic characteristic of the stimuli in the environment [1][2][3]. Widespread research has been done to gather evidence of a non-verbal and non-symbolic capacity for the understanding of the number concept in humans [4][5] as well as in other animal species [6][7][8][9]. It has become apparent that the human capacity to accurately count and perform precise arithmetic arose from a much basic mechanism, likely shared with many animal species, such as mammals [10], amphibians [11], reptiles [12], birds [13][14] and fish [15][16][17].
This system, labeled as “number sense” [18] or “Approximate Number System” (ANS) [18][19][20], is capable of accurately representing numerosities obeying to the Weber’s law, which states that the change of a stimulus that is barely noticeable is a constant ratio of the original stimulus [21]. As to numerosity, this means that the distinguishability of two numerosities decreases as the magnitude of the numbers increases [22][23], the so-called “numerical size effect” [24].
It has been shown that the number sense arises very early during development. In humans, newborns and infants are able to discriminate numerosity of small sets [4][8][25][26]. A few hours old chicks (Gallus gallus) are capable of discerning different numerosities [8][13][27][28][29]. Newborns and juvenile fish can be trained to discriminate numerosity [30][31][32].
Since many species display numerical abilities, it has been hypothesized that these abilities guarantee important biological benefits. Numerical skills promote animal’s survival by conferring advantages in food supply [33][34], social interaction [35] and avoiding predation [36][37][38][39].
Given that evolutionarily distant species differ widely in brain organization and complexity, how could they develop similar numerical abilities? This could be either the outcome of common ancestry from which they inherit it, or the outcome of convergent evolutionary processes promoted by similar selective pressures [40][41].
Several techniques have been used to investigate numerical abilities in mammals [42][43][44] and birds [14][27][45][46][47][48]. The most used paradigms were spontaneous choice tests, habituation-dishabituation techniques and operant techniques. Similar methods were used for fish.

2. Spontaneous Choice Tests

This procedure exploits the natural ability of fish to discriminate between two groups of biologically relevant stimuli that differ in numerosity, usually food or social companions. The rationale behind this task is that subjects are motivated to choose the larger (or smaller) group since it offers greater survival advantages (higher energy intake or protection).
Compared to other stimuli, fish are mostly attracted by social companions. Several fish species group together (shoal) so to avoid or protect against predation [49]. When shoals have different numbers of companions, fish prefer joining the larger one [37][50][51]. Exploiting this tendency, many studies have investigated quantitative abilities.
Mosquitofish (Gambusia holbrooki) appear to be able to discriminate between groups of conspecifics that differ by one unit up to four items (1 vs. 2, 2 vs. 3 and 3 vs. 4, but not 4 vs. 5; [52]). Guppies (Poecilia reticulata) show comparable behaviours [15].
Fish are also capable to distinguish between large numerosities (higher than four): swordtails (Xiphophorus elleri, [50]), guppies [15] and mosquitofish [52] discriminate two different quantities with a 0.50 ratio (e.g., 8 vs. 16) but not with a 0.67 ratio (e.g., 8 vs. 12), whereas angelfish (Pterophyllum scalare) discriminate up to a 0.56 ratio (5 vs. 9; [53]). It has also been shown that fish can exploit quantity discrimination to pick up a more profitable shoal depending on the sex of the composing individuals [54].
In all these tests stimuli are fully visible at the moment of the choice, thus fish could use continuous quantities to choose the larger shoal. Experimental strategies have been devoted to control for the role of continuous quantities, such as the total activity of the moving stimuli. Since many fish species live in a range of temperatures and their activity increases as water temperature would rise, by varying the water temperature between a larger and a smaller shoal, it is possible to balance somewhat the total activity of the two groups.
A technique to prevent fish from exploiting continuous quantities consists in first presenting two different numerical shoals at the same time and then at test limiting by occlusion the visibility of some items (i.e., one or more stimuli from the larger group are concealed to the testing fish, leaving the same number of stimuli visible in the two shoals). Using this method, zebrafish proved to choose the larger shoal in numerical comparisons involving both small (1 vs. 2 and 2 vs. 3, but not 3 vs. 4) and large numerosities (4 vs. 6, 4 vs. 8 but not 6 vs. 8), with a discriminative accuracy that depended on the ratio between the sets to be discriminated [17]. Similar results were obtained in 27 days post fertilization (dpf) zebrafish larvae in 1 vs. 8 and 1 vs. 3 comparison [32]. Redtail splitfin fish (Xenotoca eiseni) tested in small numerical comparisons (1 vs. 2 and 2 vs. 3, but not 3 vs. 4) showed similar performance [16]. Of course, one could argue that the use of continuous physical variables was not apparent here at test but it was coded during initial exposure, and thus maintained in memory.
Another method to control continuous quantities in spontaneous choice tests consists of an “item-by-item presentation” procedure. This paradigm has been used in mammals (e.g., chimpanzees; [55]) and in birds (e.g., chicks; [46]) and consists in a sequential (or simultaneous as control) presentation of elements belonging to each group that prevent subjects a global viewing of the whole contents of the groups. Specifically, in order to solve the task, animals need to keep track of each item to form a representation of the contents of the groups and compare the two quantities.
Besides the use of conspecifics as attractive stimuli, spontaneous choice tests can be used for assessing discriminative judgments between different food quantities. Since more food leads to a better chance of survival, animals are expected to select a larger amount. This method is however less commonly used in fish, due to methodological difficulties in delivering and controlling food because of olfactory cues released in the water. A study in guppies investigated the ability to identify the larger number between two sets of food flakes pasted onto plastic cards. Fish picked up the larger food quantity in 1 vs. 4 and 2 vs. 4 (up to a 0.5 ratio) comparisons, while failing in 2 vs. 3 and 3 vs. 4 [56]. Further experiments showed that guppies paid more attention to cumulative surface area of food items rather than number, showing attraction to the larger food item even when belonging to a set with the smaller overall quantity. In spontaneous foraging tasks, angelfish showed to prefer the numerically larger food set as long as the items were sized identically, with an accuracy that depended on the numerical ratio between the two quantities [57]. However, variables such as the size and density of the food items played an important role [58][59], suggesting that numerical and continuous physical cues may not be considered separately but instead are combined by fish to maximize food intake [60].

3. Operant Training Procedures

Spontaneous discrimination takes advantage of ecological and naturalistic setups to investigate quantity discrimination abilities. However, the limitations of this method are apparent, and concern factors such as lack of motivation and difficulty in stimulus control. Discriminative failure may be driven by a lack of motivation, especially when the discrimination involves large numerosities: it is important for animals to maximize the intake strategy when dealing with few items (according to the optimal foraging theory; [33]), but it might not be so relevant when dealing with large numerosities, when both amounts would offer enough energy.
Another issue is related to the difficulty in controlling continuous physical variables that co-vary with numerosity using naturalistic stimuli. Some cues are not easily controllable (e.g., when using social stimuli, the overall movement and the volume of the conspecifics is hard to be taken into account). Besides, the control of some variables does not exclude possible side effects that may influence spontaneous preference, e.g., larger pieces of food may elicit higher attraction [56][58].
Some of these issues may be more easily overwhelmed using artificial and well-controlled stimuli combined with operant procedures. Typically, in training procedures animals are requested to discriminate between different sets of elements with different numerosity by choosing the one associated with a reward (usually food). Differently from spontaneous choice, using discrimination learning procedures it is possible to keep the animal’ motivation high irrespective of the numerosities presented, allowing experimenters to accurately test the actual discriminative limits of the animals’ numerical competence. Agrillo et al. [61] trained mosquitofish (Gambusia holbrooki) to discriminate between sets of visual elements (2 vs. 3) and choose the one associated with a reward (i.e., social reward). Mosquitofish proved able to discriminate between the two sets, showing however a drop of performance when either the cumulative surface area or the overall space occupied by the elements was equalized [61]. Similar results were obtained when mosquitofish were trained with large numerosities (higher than four elements; [62]), suggesting that some physical properties are spontaneously used in the learning discrimination process by fish. However, no discrimination impairment was noticed when non-numerical physical cues were simultaneously controlled for during the training [61].
In order to check whether processing numerosity would be more cognitively demanding than processing of continuous quantities (and thus used as a “last resort” strategy, see [63]), mosquitofish were trained in a 2 vs. 3 discrimination by making available either only continuous variables or only numerical information, or both simultaneously. Fish improved their performance when both numerical and physical information positively correlated than when only one of the two information were differing. However, no difference was found between the two latter conditions, suggesting that numerical information is not more cognitively demanding than other types of information [64].
The influence of non-numerical variables has been recently investigated in archerfish (Toxotes sp.). In a magnitude discrimination task between two groups of dots differing in number, archerfish showed that choice for sets with more/less dots was mainly modulated by non-numerical magnitudes (i.e., overall surface, overall perimeter, density, convex hull, average diameter) that positively correlated with number. Fish tended to select the group containing the larger non-numerical magnitudes and smaller quantities of dots, choosing the larger group of dots only when it was positively correlating with all non-numerical magnitudes [65].
Recent evidence suggests that zebrafish learning performance is strongly influenced by stimulus conspicuosness [66]. Similarly, guppies’ numerical ability is improved when the stimulus saliency is enhanced by the presence of moving targets [67] and is worsened using an automatic conditioning chamber compared to that observed in more naturalistic settings [68]. It is therefore important to take into account that different methods may work well for one species but not for others, and that differences in performance may be related to procedural differences rather than cognitive limitations.
Quantitative abilities have been demonstrated in blind cavefish (Phreatchthys andruzzii) [69] trained to discriminate groups of sticks differing in numerosity in a circular thank subdivided in eight equal sectors. The experiment showed that, using the organs of lateral lines, blind cavefish proved able to discriminate between 2 vs. 4 objects when both numerical information and continuous quantities were simultaneously available, with a drop of performance when presented with stimuli controlled for continuous quantities. However, if trained from the beginning only with stimuli controlled for non-numerical quantities, cavefish proved able to learn the discrimination relying solely on numerical information.

Overall, it appears that fish numerical performances are comparable to those of mammals [70], birds [27][71][72], amphibians [11][73], reptiles [12] and invertebrates such as bees [74][75][76], although discrimination accuracy is often lower than in other species such as primates [77][78] and parrots [79]. In these latter cases, however, animals are usually trained for a massive number of trials (thousands of trials), while fish training is usually limited to less than 100 trials. In fish, extensive training can increase numerical performance accuracy as seen in guppy [80] and goldfish [81]. Goldfish can achieve high accuracy levels (>90% correct) when exposed to extensive training (approximately 1200 trials), with performances similar to those of birds [79] and primates [77][78].

4. Neural Correlates of a Sense of Continuous Magnitude in Zebrafish

The ability of fish to assess quantity (magnitude) in the continuous domain has been widely studied in zebrafish (see Figure 1).
Figure 1. Neural correlates of continuous magnitude estimation in zebrafish. (A) Time line of development of continuous magnitude sense in zebrafish embryo and larva. (B) Scheme of retinotectal pathways involved in object size discrimination in zebrafish larvae using ethological relevant stimuli. (C) The retina and optic tectum are involved in object size classification of visual stimuli in habituation/dishabituation experiments in adult zebrafish brain. See main text and Table 1 for references.
Table 1. Summary of the main findings connected to neural correlates of continuous and discrete quantity discrimination in zebrafish.
  Stage Findings Literature Data
Sense of
72 hpf Retinal Ganglion Cells (RGCs) respond to Large Size Object [82][83]
  84 hpf Retinal Ganglion Cells (RGCs) respond to Small Size Object [84][83]
  5–8 dpf Optic tectum contains different population of neurons involved in large and small size object discrimination [85]
    Retinal Ganglion Cells (RGCs) afferents synapt with Deeper layer of Optic Tectum for Large Size Object  
    Retinal Ganglion Cells (RGCs) afferents synapt with Superficial layer of Optic Tectum for Small Size Object  
  5–8 dpf Size-based categorization of visual targets and involvement of Optic tectum in approach/avoidance behaviors [86][87]
  5–7 dpf Receptive field outputs and visuo-motor response in relation to object size changes [88]
  9 dpf Size-based categorization of visual targets similar to adult life [83]
  Adult Retina responds to change in size of a visual Stimulus [89]
    Optic Tectum responds to change in size of a visual Stimulus  
Sense of
Adult Thalamus responds to change in numerosity of a visual Stimulus [89]
    Telencephalon responds to change in numerosity of a visual Stimulus  
  Adult The caudal region of the central part of area dorsalis telencephali (Dc) responds to change in numerosity of a visual Stimulus [90]
    Numerosity-based categorization of a visual Stimulus and involvement of Dc in approach/avoidance behaviors  
Neill and Smith [83] investigated the ability of large populations of zebrafish larval tectal neurons to respond selectively to the size of visual stimuli. They reported that size selectivity was established earlier during development of zebrafish larvae starting from 72 h post fertilization (hpf) for large stimuli and 78 hpf for the small ones, with a perception of magnitude sensitivity and selectivity that improves with the maturation of retinal and tectal dendrites and connectivity (from 84 hpf to 9 dpf; [83]). Following the evidence that vertebrate retina contains distinct populations of retinal ganglion cells sensitive to object size [91][92], Preuss et al. [86] studied distinct populations of tectal neurons involved in the discrimination between small- and large-size objects. Using calcium imaging of retinal ganglion cells (RGC) afferents to optic tectum and artificial stimuli which were previously shown to evoke different swimming patterns [93][94], they showed that RGC afferents and tectal superficial interneurons arborize in distinct retinorecipient layers of the tectal neuropil playing a critical role in object size classification [85]. It was suggested that small-size-selective retinal inputs would arrive at superficial layers of tectal neuropil while large-size-selective ones to deeper layers connecting the size-based categorization of visual targets to the role played by the tectum in approach/avoidance behaviors [85][87]. Barker and Baier [86], combining optogenetics, imaging and single-cell reconstructions, identify specific interneurons in the optic tectum that are tuned to object size, influenced by prey-selective RGCs inputs and thus guiding behavioral choice (approach or avoidance). Finally, Helmbrecht and colleagues [88] extended this research by identifying how the segregation of the outputs generated by the receptive fields is converted into a visual-motor response processed by premotor nuclei located in the hindbrain of zebrafish larva.
Habituation/dishabituation experiments associated with measurements of early gene (IEGs) expression were performed on adult zebrafish by Messina et al. [89]. Animals were first habituated to a set of stimuli (small dots) and then faced (dishabituation) to a similar stimulus with a change in size (threefold increased or decreased). A selective change in the expression of the immediate early genes c-fos and egr-1 in retinal and optic tectum tissues with respect to a group facing the familiar control stimulus was observed [89]. Overall, these findings indicate a conservative role of retina and optic tectum in the elaboration of continuous quantities in embryonic and adult zebrafish.

5. Neural Correlates of a Sense of Discrete Magnitude (Number) in Zebrafish

Recently, zebrafish studies have expanded our knowledge about the neural correlates of quantity estimation to discrete quantities (numerosity) (see Figure 2).
Figure 2. Neural correlates of numerosity cognition in zebrafish. (A) Possible timeline of development of number sense in zebrafish. (B) Schematic representation of telencephalic and thalamic nuclei activated upon a change in visual numerosity in zebrafish adult brain. (C) Molecular biology analyses revealed that the caudal region of central part of the area dorsalis telencephali (Dc) responds to change in numerosity of visual stimuli in adult zebrafish brain.


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