Cichlids and stingrays can add and subtract ‘one’

AbstractThe numerical understanding of cichlids and stingrays was examined regarding addition and subtraction abilities within the number space of one to five. Experiments were conducted as two-alternative forced-choice experiments, using a delayed matching to sample technique. On each trial, fish had to perform either an addition or subtraction, based on the presentation of two-dimensional objects…

Cichlids and stingrays can add and subtract ‘one’

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The numerical conception of cichlids and stingrays used to be examined concerning addition and subtraction skills inner the amount residing of 1 to 5. Experiments had been conducted as two-different compelled-different experiments, the usage of a delayed matching to sample intention. On every trial, fish needed to create either an addition or subtraction, based totally on the presentation of two-dimensional objects in two certain colours, with the coloration signaling a utter arithmetic activity. Six cichlids and four stingrays successfully completed practicing and known utter colours as symbols for addition and subtraction. Cichlids wanted extra lessons than stingrays to reach the finding out criterion. Transfer assessments showed that finding out used to be honest of easy image memorization. Contributors didn’t correct be taught to steal the easiest or lowest quantity presented based totally on the respective coloration; as an different, finding out used to be utter to adding or subtracting ‘one’. Though neighborhood results had been fundamental for both species in all assessments, individual results assorted. Addition used to be realized extra with out problems than subtraction by both species. Whereas cichlids realized quicker than stingrays, and extra cichlids than stingrays realized the duty, individual efficiency of stingrays exceeded that of cichlids. Old analysis dangle equipped substantial proof that fish dangle numerical skills on par with those of different vertebrate and invertebrate species tested, a result that is extra supported by the findings of the recent look.


Quantity discrimination skills had been demonstrated in all vertebrate lessons besides several invertebrate species1,2,3,4. This looks cheap, as quantity discriminations (including numerical discriminations) are fundamental for a range of species in the context of every single day activities corresponding to foraging5,6, predator avoidance7, education and mate different8,9. Quantity discrimination is also based totally on several parameters corresponding to continuous (e.g. size or surface residing lined by items) or discrete variables (different of things). Whereas both suggestions aren’t mutually queer and will, when blended, yield a extra a hit final result1, some species assure easiest continuous variables corresponding to size to sinister their different on and appear unable to make assure of numerical recordsdata by itself10.

Quite a lot of research dangle proposed that there are two assorted methods for numerical differentiation11,12,13,14,15. Alternatively, there’s an ongoing dialogue inner the literature on whether one or two methods exist which would be utilized for numerical discrimination. Most analysis on fish toughen the two-system hypothesis16. The sizzling look didn’t investigate this method back extra and results are talked about in the context of the findings by the aforementioned look16. With the first of the two hypothesized methods, the ‘object file system’ (OFS), little amounts, differing in easiest one merchandise, is also recorded exactly6; on the opposite hand, the upper limit is low and ranges between 3 and 5 items for most folks17,18. For the OFS, the numerical ratio is inappropriate; as an different, the total portray composition or the amount of things kept in the working reminiscence is fundamental19. With the aid of the 2d system for numerical discrimination, the ‘analogue magnitude system’ (AMS), larger numerical values is also roughly estimated and compared12. The precision of the scale distinction is field to Weber’s law and depends on the connection between the two portions to be discriminated17,20,21. Discrimination is extra a hit with an rising ratio between the two numerical samples.

In stutter in confidence to search these two proposed methods and their limitations, analysis had been performed on a range of species, corresponding to primates22, salamander (Plethodon cinereus)6, mockingbird (Mimus polyglottos)23, jungle crows (Corvus macrorhynchos)24, sticklebacks (Gasterosteus aculeatus)25, guppies (Poecilia reticulata)26 or the eastern mosquito fish (Gambusia holbrooki)9. Most of those analysis found upper limits for the OFS spherical 3–5, with a distinction between either 3:4 or 4:5 items no longer being a hit anymore. Alternatively, guppies still successfully discriminated 4:5 and sticklebacks even 6:7 items25,26. In freshwater stingrays (Potamotrygon motoro) and bamboo sharks (Chiloscyllium griseum) the OFS used to be lately confirmed to be 4, with 4:3 and 5:3 being discriminated successfully by stingrays and sharks respectively, whereas 4:5 used to be no longer27. In cichlids, the OFS looks to range from 1 to 5, with 4:5 still being discriminated successfully by most folks28,29. Whereas no longer all analysis toughen the presence of both an OFS and AMS in all species—basically, easiest honeybees, inner the invertebrates tested to this point, had been in a plight to discriminate numerical portions larger than four30,31—analysis on fish largely counsel the co-existence of two such methods16. With the exception of cardinal recordsdata, numerical skills can also consist of ordinal competence, which has been investigated in non-human species32,33,34,35,36, including fish37.

Whether vertebrates rather than folks and primates can solve extra complicated numerical projects or arithmetic considerations corresponding to addition and subtraction is—with out reference to some promising analysis—in the meanwhile still unclear38,39,40. Accordingly, inner the diversity of the OFS, easy mathematical calculations, corresponding to addition and subtraction, dangle easiest been investigated in a pair of species corresponding to primates (chimpanzees41,42,43, orangutans44, rhesus monkeys45 and vervet monkeys46), birds (grey parrot47,48, pigeons49 and chicks50), besides spiders51,52 and honey bees53.

Within the most up-to-date look53, honeybees known colours as symbols for addition and subtraction projects. The bees successfully added and subtracted objects and utilized this knowledge in transfer assessments to an unknown different of objects, indicating acquisition of long-term principles and non permanent working reminiscence. First, the bees had been taught to flee into a Y-fashioned sample room, valid by which they had been at the birth presented with a single visible ‘test’ stimulus (blue or yellow) exhibiting a obvious different of geometric objects. The animals then needed to flee by a gap into the choice chamber and gain one in all two different stimuli (stimuli A and B). These contained one ingredient extra (stimulus A) and one ingredient less (stimulus B) than the test stimulus confirmed beforehand. Reckoning on the coloration of the test stimulus, the bees successfully performed additions and subtractions inner the amount residing of 1 to 5.

In step with the form by Howard et al.53, the numerical skills of cichlids and freshwater stingrays had been tested in the recent look. More total numerical skills of stingrays and bamboo sharks had easiest lately been investigated for the first time in elasmobranchs25 and found to compare those of teleost species. Old analysis dangle demonstrated that both cichlids and stingrays are love minded for cognition experiments, exhibiting a mammoth different of cognitive skills, starting from visible discrimination experiments to spatial orientation54,55,56,57,58,59,60,61,62.

Affords and suggestions


Experimental animals had been eight cichlids (Pseudotropheus zebra), bought from a industrial vendor (Merz, Germany) and eight experimentally naïve freshwater stingrays (Potamotrygon motoro) from Frankfurt Zoo (Germany). Six of the cichlids had beforehand participated in cognition experiments, the opposite two had been experimentally naïve. Animals had been subjected to a pure light–darkish cycle and experiments had been conducted in the morning and early afternoon six days per week. Food used to be easiest equipped valid by the experiments and consisted of cichlid meals pellets (Sera Granugreen) and of earthworm, tiny or mussel for the stingrays.

Space up

For both species, housing tanks also served as experimental tanks. Cichlids had been saved for my piece in 61 cm × 31 cm × 31 cm test tanks with a most quantity of 54 L (Fig. 1). Individual tanks had been halved by a grey, opaque partition wall into a entrance and a rear compartment. The fish could maybe also swim by a 7 cm × 7 cm window (operated manually by a transparent guillotine door) in the partition to make assure of both areas. The floor of the residing residing (initiating compartment) used to be lined with sand, whereas it used to be empty in the entrance compartment (experimental residing). Within the residing residing, a clay pot served as a hiding plight; additionally, it contained a plant, a pump and an aquarium heater (~ 25 °C). The water wonderful used to be maintained by weekly water changes. A Plexiglas divider used to be placed throughout the milky-colored entrance of the tank, and a line used to be equipped 5 cm earlier than the entrance, as to divide the residing into two equally tall compartments (choice areas). Using a projector (Optoma), PowerPoint slides had been presented on the milky-colored entrance, that contains two-dimensional geometric symbols as stimuli. Using pipettes hooked as a lot as long tubing, one meals pellet used to be expelled straight once a appropriate different used to be made. The tubes had been fastened with suction cups to the entrance wall and positioned appropriate above the stimulus projections. All assessments had been seen by a camera (Logitech), placed on a plastic rope above the plight-up.

Figure 1
figure 1

Experimental setup for the cichlids. 1) initiate box, 2) experimental residing, 3) guillotine door, 4) choice areas, 5) stimuli, 6) feeding tubes, 7) projector.

All stingrays had been saved together in 1300 L of water in a single 2.30 m × 2.07 m × 0.40 m maintaining tank that also contained the experimental apparatus (Fig. 2). The experimental plight-up (53.5 cm × 106 cm) consisted of a initiating compartment (SC, including a initiate box (SB)), a transition residing, and a choice residing, separated by two operated by hand guillotine doorways. Stimuli had been confirmed the usage of laminated cards (A4) on the entrance aspect of the tank, which used to be separated by a plastic divider into two choice areas. Following a appropriate different, meals used to be equipped by forceps. When no longer engaged in trials, stingrays could maybe also freely swim valid by the total setup, whereas valid by experiments the experimental arena used to be closed off. Temperature used to be maintained between 27° and 29 °C and conductivity between 390 and 420 μS. Water used to be filtered at a constant charge of 270 L/h and partly exchanged once per week to defend nitrite values under 0 0.05 mg/L. Gentle intensity in the experimental room used to be 320 lx. All assessments had been seen by a Logitec camera, which used to be placed on a plastic rope above the plight-up.

Figure 2
figure 2

Experimental setup for the stingrays. 1) initiate box, 2) experimental residing, 3) guillotine door, 4) door with test stimulus, 5) choice areas, 6) different stimulus cards.

Frequent practicing activity

All experimentally naïve fish had been first unsleeping of the experimental activity by feeding them from a pipette (cichlids) or forceps (stingrays). This used to be followed by practicing them to swim by the guillotine doorways in the direction of the choice residing to hunt meals along the stimulus wall, i.e., at the milky-colored entrance onto which a white PowerPoint scurry used to be projected (cichlids) or in entrance of two blank stimulus cards (stingrays). If the fish swam successfully by the gates to feed from the pipette/forceps with out apprehension, experiments commenced.

Practising consisted of a ‘delayed matching-to-sample experiment’, valid by which a test stimulus used to be confirmed first (then eradicated), followed by the presentation of two different stimuli (stimulus A and B), one in all which used to be linked to a meals reward whereas the opposite used to be no longer. Take a look at and different stimuli assorted in how they had been presented on the slides and cards, e.g. close to surface residing, size and approach to stimuli (entire residing lined), to manipulate for any confounding variables and reduce abet finding out to the usage of numerical variations easiest. As a minimal ten randomly extinct versions existed for every quantity per coloration.

Two every single day lessons (no longer no longer as a lot as five hours apart) had been conducted six days per week, with ten trials per session. Stimuli had been presented in a pseudo-random expose, exhibiting equally most often on either aspect of the divider on the entrance wall but by no manner extra than twice consecutively on the equivalent aspect. There used to be an inter-trial-interval (ITI) of 30 s. If a fish didn’t purchase a stimulus inner one minute, the trial used to be aborted; three aborted trials terminated a session. Practising for every individual used to be regarded as a hit or completed as quickly as a finding out criterion (LC) of ≥ 70% appropriate choices in three consecutive lessons used to be reached (χ2 (1) ≤ 0.05; to repeat statistical significance).

After a hit practicing, fish entered the overtraining half valid by which transfer assessments had been conducted. On this half, a session consisted of ten frequent trials (as valid by practicing) and two to three extra transfer test trials, that had been randomly interspersed with frequent ones valid by a session. To put together the fish for transfer test trials, that had been constantly unrewarded, meals used to be easiest equipped in eight out of ten appropriate (frequent) trials in any lessons following a hit practicing. This can even lead to a tumble in efficiency by the oldsters once the LC used to be completed. Earlier than every session, it used to be randomly obvious which trials remained unrewarded (with out reference to the categorical different made by the fish). The first and final trials inner a session had been constantly rewarded and there had been by no manner two unrewarded trials in a row. No longer rewarding a pair of of the frequent trials used to be supposed to cease fish from realizing that transfer trials had been unrewarded and, therefore, no longer charge taking piece in.


First, whereas still at the birth compartment, cichlids had been presented with the everyday test stimulus for five seconds on the milky-colored entrance of the tank. Cichlids seen this stimulus by the closed but transparent guillotine door. After five seconds, the stimulus presentation modified to the two different stimuli and the door used to be opened. As quickly as the test animal swam by the gate (crossed the highway with its mouth), time (in seconds) used to be taken. The 2d the animal crossed the choice line with its mouth, time used to be stopped and different recorded. If the animal made a appropriate different, it used to be rewarded, if the different used to be wrong, the projection used to be stopped and a black scurry used to be confirmed as an different. The animal used to be then led abet into the initiating compartment, the gate used to be closed and (if fundamental) the tube used to be geared up with a brand recent pellet.


The first guillotine door used to be raised and stingrays had been presented with the everyday test stimulus for five seconds (Fig. 2). Then, the 2d guillotine door used to be raised and stingrays could maybe also enter the experimental residing and the choice residing, where the two different stimuli had been presented on laminated cards on either aspect of a divider. As quickly as the stingray swam by the 2d gate (crossing the highway with its disc), time used to be taken. The 2d the animal crossed the choice line with its disc, time used to be stopped and different recorded. If the animal made a appropriate different, it used to be rewarded, if the different used to be wrong, cards had been eradicated. The animal used to be then guided abet into the initiating compartment and the gates had been closed.


Equivalent to the look by Howard et al.53, it used to be tested whether folks of both species can be taught to acknowledge colours as symbols for addition (blue) and subtraction (yellow) by the part ‘one’ and to title the becoming result of the respective arithmetic scenario. First, fish had been presented with the test stimulus for five seconds, that contains a utter plight of geometric symbols (sq., circle, triangle) in either yellow (two, four or five) or blue (one, two or four). Decision stimuli then depicted numbers of symbols plus or minus one object (Fig. 3). Within the blue addition projects, the fish needed to make a different the stimulus that featured one ingredient extra than the test stimulus. Within the yellow subtraction projects, the fish needed to make a different the stimulus that featured one image less (Fig. 3). The quantity three used to be no longer confirmed as an preliminary stimulus valid by practicing but easiest extinct in subsequent transfer assessments. The total residing of ​​the symbols confirmed inner one ‘stimulus’ used to be 36 cm2. For one image this amounted to 36 cm2, for every of the two symbols to 18 cm2 and so forth. As in other experiments, the test animals needed to entire two lessons of ten trials every single day, valid by which they every needed to solve five addition and five subtraction projects. Stimulus cards (stingrays) had been laminated and measured 21.0 × 29.7 cm in size (A4).

Figure 3
figure 3

Example for a test stimulus and the corresponding two different stimuli valid by addition (blue) and subtraction (yellow).

After a hit practicing, two to three transfer test trials had been randomly interspersed with the ten frequent trials per session. There had been three forms of transfer assessments (A–C), as explained in the following half. A entire of 20 trials per form of transfer test had been conducted per fish. Transfer assessments had been unrewarded; they had been neither conducted in the very initiating set nor at the cease of a session, and by no manner preceded or followed one in all the unrewarded frequent trials. In every session, the tested animals needed to entire five frequent addition and subtraction projects. The 80% reward used to be continued in the transfer half. Each stimulus used to be presented equally most often on the becoming and left aspect in the transfer assessments. There had been no appropriate or immoral choices in any of the transfer assessments, choices had been easy reflecting and indicative of what suggestions had been extinct valid by practicing to solve the duty. Nonetheless, any choices referring to the anticipated choice (having realized so that it’s essential maybe add or subtract one based totally on the coloration presented) are referred to any longer as ‘appropriate’, whereas other choices are regarded as ‘immoral’.

Transfer test form A

(Take a look at stimulus: 3) (Addition (blue): 4 (appropriate different); 2 (immoral different)) (Subtraction (yellow): 2 (appropriate different); 4 (immoral different))

On this transfer test, the beforehand unused different of three symbols used to be presented as test stimulus (to rule out image memorization) and fish needed to then purchase from two and four symbols as different stimuli. This transfer test used to be performed the usage of both colours. When the blue symbols had been presented, it used to be anticipated that fish would gain the larger object quantity, i.e., add ‘one’. For yellow symbols, on the opposite hand, it used to be anticipated that the fish would subtract ‘one’.

Transfer test form B

(Take a look at stimulus: 3) (Addition (blue): 4 (appropriate different); 5 (immoral different)) (Subtraction (yellow): 2 (appropriate different); 1 (immoral different))

This test obvious whether fish had realized to make a different the stimulus that contains the easiest or lowest different of objects accessible based totally on the coloration presented or whether fish had surely realized so that it’s essential maybe add or subtract ‘one’ from the test stimulus. The different stimuli in this transfer test featured either plus one and plus two (blue) or minus one and minus two (yellow).

Transfer test form C

(Take a look at stimulus: 3) (Addition (blue): Adjusted stimuli size; 4 (appropriate different); 2 (immoral different)) (Subtraction (yellow): Adjusted stimuli size; 2 (appropriate different); 4 (immoral different))

This transfer test managed for the impact of the splendid potentially confounding part, i.e., individual image size. Whereas surface shape, method and residing lined of stimuli had been managed for on the many experimental stimulus cards/projections, individual image size used to be to a lesser extent (correct on some cards). This resulted in individual symbols being larger for lower numbers and smaller for larger numbers extra most often than no longer. To manipulate for this bias, the connection used to be reversed, with the person symbols for the lower probability now being smaller and those for the larger probability now being larger.

Records prognosis

We utilized generalized linear blended models (GLMM) in R (4.0.3), the usage of a binomial distribution with success as the response variable (0 = success, 1 = failure), the test stimulus as fastened attain and the person as random attain. Individual used to be incorporated as random attain to memoir for correlations that could maybe come up by efficiency variations between folks. For every neighborhood and transfer test separate models had been extinct, besides for addition and subtraction. P ≤ 0.05 used to be regarded as fundamental for all assessments and p ≤ 0.001 extremely fundamental.

Ethics statement

The analysis reported here used to be performed below the pointers established by the recent German animal safety law. The experimental protocol for behavioral trials on fish used to be popular by the ethics committee of the LANUV (Order Office for Nature, Atmosphere and Consumer Protection North Rhine-Westphalia, Germany; AZ 81-02.04.2020.A432). All relevant world, nationwide, and/or institutional pointers for the care and assure of animals had been followed. The look used to be performed in compliance with the ARRIVE pointers.



Addition/subtraction practicing

All six folks taking piece in the practicing reached the LC on common in 28 ± 18 Sessions and took part in all subsequent transfer assessments. An exemplary graph of the efficiency valid by your total experimental time of 1 cichlid is confirmed in Fig. 4.

Figure 4
figure 4

Exemplary graph of the efficiency of a cichlid valid by the total practicing and attempting out (overtraining) half. The black line reveals the proportion of appropriate choices per ten-trial session. The horizontal red dotted line signifies the time the LC used to be reached, whereas the vertical red line signifies when the LC used to be completed. Within the lessons following the red vertical line, transfer assessments had been added to the frequent ten trial session. The blue line affords the common trial time for every session.

Transfer assessments

At some level of transfer assessments A, B and C, individual choices pooled as a neighborhood showed that the cichlids selected significantly most often the becoming stimulus (+ 1/− 1). Following an experimental restructuring, three folks bought extra than 20 trials for transfer test A (look desk in supplementary field topic). Within the addition job of transfer test A folks had been appropriate in 117 out of 141 trials (n = 6, p p 5a). I 0.01)a> 0.0001)i>

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