SHORT COMMUNICATION

Extensive training extends numerical abilities of guppies

Angelo Bisazza • Christian Agrillo •

Tyrone Lucon-Xiccato

Received: 28 January 2014 / Revised: 7 May 2014 / Accepted: 13 May 2014

� Springer-Verlag Berlin Heidelberg 2014

Abstract Recent studies on animal mathematical abilities

suggest that all vertebrates show comparable abilities when

they are given spontaneous preference tests, such as

selecting the larger number of food items, but that mam-

mals and birds generally achieve much better performance

than fish when tested with training procedures. At least part

of these differences might be due to the fact that fish are

usually trained with only one or two dozen trials while

extensive training, sometimes with thousands of trials, is

normally performed in studies of mammals and birds. To

test this hypothesis, female guppies were trained on four

consecutive numerical discriminations of increasing diffi-

culty (from 2 vs. 3 to 5 vs. 6 items), with up to 120 trials

with each discrimination. Five out of eight subjects dis-

criminated all contrasts up to 4 versus 5 objects at levels

significantly better than chance, a much higher limit than

the 2 versus 3 limit previously reported in studies that

provided fish with only short training sequences. Our

findings indicate that the difference in numerical cognition

between teleosts and warm-blooded vertebrates might be

smaller than previously supposed.

Keywords Numerical cognition � Poecilia reticulata �Training procedure � Numerical acuity

Introduction

One of the most significant findings of comparative

research in the past decade is the discovery that mathe-

matical abilities are ubiquitous in vertebrates and are

probably common also in some invertebrate taxa (reviewed

in Agrillo and Bisazza 2014; Pahl et al. 2013). The general

picture that emerges when comparing the results obtained

in different species is that the cognitive systems underlying

these abilities appear quite similar in different vertebrates

(see Feigenson et al. 2004 for discussion) but that species

differ considerably with respect to the upper limit of their

discrimination capacities. Restricting the analysis to the

ability to discriminate quantities that differ by one item,

pigeons can be trained to discriminate 6 from 7 objects,

macaques can learn up to a 7 versus 8 discrimination and

adult humans, and possibly apes, are able to discriminate

even 9 from 10 items (Emmerton and Delius 1993; Beran

2004; Cantlon and Brannon 2007; Hanus and Call 2007;

Halberda and Feigenson 2008). In contrast, salamanders

have been found to discriminate up to 2 from 3 fruit flies;

angelfish and guppies discriminate, respectively, 2 versus 3

and 3 versus 4 social companions (Uller et al. 2003;

Gomez-Laplaza and Gerlai 2011; Agrillo et al. 2012c).

The capacity to discriminate numerosities is already

present at birth and increases in precision during devel-

opment. Newborns are able to discriminate numerosities

with up to a 0.33 ratio between the smaller and the larger

quantity, 6-month-old infants discriminate numerosities

with a 0.5 ratio and 10-month-old infants discriminate

numerosities with a 0.67 ratio but not a 0.8 ratio (reviewed

in Cantrell and Smith 2013). The resolution of numerical

systems continues to increase throughout childhood, with

6 year olds being able to discriminate a 0.83 ratio and

adults a ratio of 0.9 (Halberda and Feigenson 2008).

Electronic supplementary material The online version of thisarticle (doi:10.1007/s10071-014-0759-7) contains supplementarymaterial, which is available to authorized users.

A. Bisazza � C. Agrillo � T. Lucon-Xiccato (&)

Department of General Psychology, University of Padova,

Via Venezia 8, 35131 Padua, Italy

e-mail: tyrone.luconxiccato@gmail.com

123

Anim Cogn

DOI 10.1007/s10071-014-0759-7

In observing the above records, one is tempted to con-

clude that numerical abilities increase in precision with

increasing complexity of the nervous system both intra-

and inter-specifically. However, before accepting this

hypothesis, it is necessary to note that different species

have often been studied in very different contexts and with

methods that also differ greatly. Some studies, for example,

have exploited spontaneous preferences of one species (i.e.,

for the larger group of food items or social companions),

whereas others have adopted an habituation paradigm or an

operant conditioning paradigm to teach an animal a

numerical rule. The conclusions of a recent review that

compares the two main methods—spontaneous choice tests

and training procedures—suggest that better numerical

performances are usually reported using the latter approach

(Agrillo and Bisazza 2014). For example, when assessed in

spontaneous choice tasks, African gray parrots discriminate

2 versus 3 food items, and New Zealand robins discrimi-

nate 3 versus 4 mealworms (Al Aın et al. 2009; Hunt et al.

2008), well below the performance of birds studied with

training procedures (African gray parrot: 5 vs. 6 items,

Pepperberg 2006; pigeon: 6 vs. 7 items, Emmerton and

Delius 1993). Similarly, in spontaneous choice tests,

chimpanzees were observed to discriminate a 0.67 ratio (4

vs. 6 and 6 vs. 9 items; Beran 2001), and free ranging

macaques discriminated a 0.75 ratio (3 vs. 4 items, Hauser

et al. 2000). However, when tested with extensive training

procedures, both species could easily discriminate a 0.80

ratio (i.e., 8 vs. 10 items, Beran 2008a; Tomonaga 2008).

As mammals and birds were investigated more often with

training procedures and amphibians and fish with sponta-

neous choice paradigms, the possibility exists that the

differences among taxa are at least partly due to the dif-

ferent methods used.

Studies on the guppy (Poecilia reticulata) and on the

closely related eastern mosquitofish (Gambusia holbrooki)

have shown that those species discriminate up to 3 versus 4

social companions (Agrillo et al. 2008; Piffer et al. 2012).

In these spontaneous choice experiments, the continuous

quantities that covary with number (such as the density of

items or the sum of areas occupied by stimuli) were not

controlled for, and fish might have used these cues, instead

of number, to discriminate between shoals. The only two

studies in which these factors were controlled for have

tested a 2 versus 3 companion choice, a discrimination that

both species successfully achieved using the sole numerical

information (Bisazza et al. 2010; Dadda et al. 2009).

Using the training procedures, mosquitofish could dis-

criminate 2 versus 3 but not 3 versus 4 items (Agrillo et al.

2012b), and guppies could discriminate 2 versus 4 but not 3

versus 4 items, although the latter discrimination could be

achieved when moving objects were presented (Agrillo

et al. 2014). It should be said, however, that for practical

reasons, the number of trials in fish studies typically ranges

between 10 and 30 (e.g., Agrillo et al. 2012b), while studies

done on mammals and birds sometimes involved thousands

of reinforced trials (e.g., macaques, approx. 2,000 trials,

Cantlon and Brannon 2007; dolphins, approx. 2,800 trials,

Jaakkola et al. 2005; pigeons, approx. 1,000 trials, Roberts

and Mitchell 1994).

Here, we adopted a new training procedure that allows

for extended training in fishes as well. Making use of the

natural behavioral response of this fish (Rodd et al. 2002),

guppies were presented with two groups of yellow objects

placed on the tank floor with only the larger amount hiding

a food reward. Fish were trained with four discriminations

of increasing difficulty from 2 versus 3 to 5 versus 6 in

order to establish the upper limit of their discrimination

capacity.

Methods

Subjects and apparatus

The subjects were eight adult female guppies (Poecilia

reticulata) of a domestic strain, seven to 10 months old at

the start of the experiment.

The apparatus was a 60 9 40 cm glass tank with

gravel bottom, filled with 30 cm of water (Fig. 1a). By

using green plastic material, the apparatus was divided

into a rear ‘‘home compartment’’ with abundant natural

vegetation and a front ‘‘experimental compartment,’’

which were connected by a 10 9 8 cm corridor provided

with a transparent guillotine door. The experimental

compartment (30 9 40 cm) contained a green plastic

plate (30 9 20 cm) provided with 166 holes (Ø 1 cm,

depth 0.5 cm) (Fig. 1b). Two 15 W fluorescent lamps

illuminated the apparatus. In order to avoid social isola-

tion of the subjects, two adult conspecifics (one male and

one female) were kept in the apparatus as social com-

panions. During the experimental trials, the two social

companions were temporarily moved to another tank

where they were fed.

Procedure

Before the test, the subject was allowed to habituate to the

experimental apparatus with the companions for 5 days. In

the last 3 days, each subject was familiarized with the

experimental procedure by closing it in the home com-

partment with the guillotine door and, hence, allowing it to

feed on dry food delivered in the holes of the plate. Three

subjects that did not accustom to this procedure (i.e., they

refused to leave the home compartment) were excluded

from the experiment and replaced with other subjects.

Anim Cogn

123

At the beginning of each trial, the subject was gently

encouraged to swim in the home compartment using a

transparent plastic panel, and the guillotine door was

closed. A green plastic barrier was placed by the experi-

menter in front of the corridor to block the view of the

experimental compartment. The experimenter collocated

two groups of small plastic disks differing by one numer-

ical unit on the plate so that each disk covered one hole.

Using a Pasteur pipette, a small piece of commercial food

flakes was placed in the holes covered by the disks

belonging to the group with larger numerosity. The barrier

was then removed, and after 10 s, the guillotine door was

opened, allowing the subject to enter the compartment and

dislodge the disks. We consider the first disk dislodged by

the subject as an indicator of the choice. In a pilot exper-

iment that used a no-correction procedure, subjects fre-

quently ceased to respond after a few consecutive wrong

choices. For this reason, we adopted a correction proce-

dure, and the trial continued until the subject opened one of

the correct disks and ate the food. The subject was then

accompanied toward the home compartment to start a new

trial. If the subject did not dislodge any disk in 10 min, the

trial was considered null and repeated later. An example of

a trial can be seen in Online Resource 1.

During the first 2 days of the experiment, twenty trials

were administered (1 vs. 2 discrimination) with the aim of

teaching the fish to dislodge the disks to get food. The

procedure was identical to that described above, but the

disks covered only partially the holes. In trials 1–3, the

disks covered 25 % of the hole; in trials 4–6, they covered

50 %; in trials 7–9, they covered 75 %; and in trial 10, the

disks completely covered the holes. All subjects learned to

dislodge the disk in 1 day. This rapid acquisition probably

depends on the strong natural attraction of guppies to small

fruits falling in water and their tendency to peck colored

objects on the bottom (Rodd et al. 2002). During the

second day, the disks covered 75 % of the hole in trials 1–3

while in the remaining 7 trials, the disks covered the holes

entirely. During the third day, twelve trials were adminis-

tered with holes covered and all trials involved a 2 versus 3

discrimination. In all of these trials, all disks had the same

diameter (15 mm) and no control for continuous quantities

was used, meaning that in these trials the fish could use the

overall amount of disks as a cue as well as the number of

disks.

Numerical discrimination

In this phase, subjects performed twelve trials per day, in

two sessions of six trials (one session in the morning and

one in the afternoon). Each subject started with a 2 versus 3

discrimination. The positions (left or right) and the distance

from the corridor (near or far) of the two groups of disks

were varied in each trial, according to a pseudo-random

sequence. If the subject reached the criterion of 75 %

correct responses in two consecutive days (corresponding

to a statistically significant preference with the chi-square

test), it was presented with a more difficult discrimination,

3 versus 4; if it failed to reach the criterion within 120

trials, the experiment ended. In case of success, the same

procedure with the same criterion was presented with the

discrimination of 4 versus 5 and finally 5 versus 6.

Stimuli were controlled for the three most important

continuous quantities that covary with number, cumulative

surface area (summed area of disks), the density of ele-

ments (average inter-disk distance) and the overall space

occupied by the arrays (space encompassed by the most

lateral disks) following the procedure in Agrillo et al.

(2012b). Cumulative surface area was equated using disks

of 5 different diameters (15, 16, 17, 18, 19 mm Ø). When

controlling for area in this way, smaller than average ele-

ments become more frequent in the more numerous groups.

Fig. 1 The experimental

apparatus was composed by a

home compartment connected

to the experimental

compartment by a corridor

provided with a guillotine door

(a). Two groups of yellow disks

differing by one numerical unit

were used as stimuli (b). Food

reward could be obtained by

dislodging disks included in the

larger group (color figure

online)

Anim Cogn

123

To prevent fish from using this cue, in one-third of the

stimuli, the cumulative surface area was equated between

76 and 85 %; in one-third, it was equated between 86 and

95 % and in one-third between 96 and 105 %.

A control test was performed at the end of the exper-

iment to rule out the possibility that the subjects had

solved the task using olfactory cues. Each subject per-

formed fifty more trials with the same procedure in which

we presented two groups of the same numerosity, but

only one of those groups (randomly chosen) had food

hidden under its disks.

Results

Subject N4 did not reach the criterion with the 2 versus 3

discrimination and, thus, was not continued in the experi-

ment. The overall performance of this fish in this test was,

however, above chance overall (Table 1). Two subjects,

N2 and N8, did not reach the criterion in the 3 versus 4

discrimination. With this discrimination, the performance

of subject N2 was above chance, while N8 showed a

marginally significant performance (Table 1). The

remaining five subjects were given the 4 versus 5 dis-

crimination. All of these fish performed above chance

levels in this test, but only one (N6) also reached the cri-

terion of 75 % correct responses in two consecutive days.

This subject, however, failed to reach the criterion in the

subsequent 5 versus 6 discrimination, showing 53 % cor-

rect responses.

The proportion of correct responses were arcsine square-

root transformed to meet the assumptions of ANOVA

(Sokal and Rohlf 1995). A repeated-measure ANOVA

including the subjects that discriminated up to 4 versus 5

items showed that performance was significantly affected

by the numerical contrast (2 vs. 3, 3 vs. 4 and 4 vs. 5,

F(2,8) = 12.9, p = 0.003, Fig. 2). Post hoc analyses (Tu-

key’s HSD test) showed a significant difference between 2

versus 3 and 4 versus 5 (p \ 0.001) and between 3 versus 4

and 4 versus 5 (p \ 0.001) but not between 2 versus 3 and

3 versus 4 (p = 0.784). We found a positive correlation

between the performance in 3 versus 4 and 4 versus 5

discrimination (Spearman q = 0.947, p = 0.014) but not

between 2 versus 3 and 4 versus 5 (q = 0.553, p = 0.334)

and between 2 versus 3 and 3 versus 4 (q = 0.5,

p = 0.391).

Table 1 Column 2–5: number of days of training and percentage of correct choices with statistics for the eight subjects. Column 6: results of

control test for olfactory cues (percentage of choice of the baited stimulus with statistics). All chi-squares have one degree of freedom

Subject 2 versus 3 3 versus 4 4 versus 5 5 versus 6 Control

4 12

60 %

v2 = 4.8, p = 0.029

48 %

v2 = 0.1, p = 0.777

2 5

62 %

v2 = 3.3, p = 0.071

12

63 %

v2 = 7.5, p = 0.006

52 %

v2 = 0.1, p = 0.777

8 8

74 %

v2 = 22.0, p \ 0.001

12

58 %

v2 = 3.3, p = 0.068

44 %

v2 = 0.7, p = 0.396

1 2

79 %

v2 = 8.2, p = 0.004

3

69 %

v2 = 5.4, p = 0.020

12

59 %

v2 = 4.0, p = 0.045

44 %

v2 = 0.7, p = 0.396

3 5

73 %

v2 = 13.1, p \ 0.001

3

78 %

v2 = 11.1, p \ 0.001

12

65 %

v2 = 10.8, p = 0.001

56 %

v2 = 0.7, p = 0.396

5 4

83 %

v2 = 21.3, p \ 0.001

2

83 %

v2 = 10.7, p = 0.001

12

69 %

v2 = 17.6, p \ 0.001

44 %

v2 = 0.7, p = 0.396

7 7

65 %

v2 = 8.0, p = 0.005

4

75 %

v2 = 12.0, p \ 0.001

12

59 %

v2 = 4.0, p = 0.045

56 %

v2 = 0.7, p = 0.396

6 2

79 %

v2 = 8.2, p = 0.004

2

83 %

v2 = 10.7, p = 0.001

2

75 %

v2 = 6.0, p = 0.014

12

53 %

v2 = 0.3, p = 0.584

54 %

v2 = 0.3, p = 0.572

Anim Cogn

123

In 4 versus 5 discrimination, no subject showed differ-

ences in the proportion of correct responses between the

three levels (76–85 %; 86–95 %; and 96–105 %) of control

for cumulative surface area (chi-square, all fish p [ 0.05).

An overall analysis of the five subjects reached the same

conclusion (repeated-measure ANOVA F(2,8) = 3.8,

p = 0.070).

In the control test for olfactory cues, no subject chose

the reinforced group of disks more than chance levels

(Table 1). The overall preference of the eight fish for the

baited group was not significant (mean ± SD:

49.7 ± 5.4 %; one sample t test: t(7) = 0.1, p = 0.9).

Discussion

Previous studies have indicated that many vertebrates show

comparable numerical abilities when given spontaneous

preference tests but that some mammals and birds achieve

a much better performance than fish when training proce-

dures are adopted. Our study investigates the possibility

that at least part of this difference is due to the fact that fish

are usually trained with much fewer trials than are nor-

mally presented when testing rodents, pigeons, parrots,

dolphins or monkeys. Indeed, in our experiment, when

training was extended, five out of the eight fish performed

all discriminations up to 4 versus 5 items, which was a

much better performance than previously reported in fish

with a training procedure (2 vs. 3 items in mosquitofish;

Agrillo et al. 2012b). These results highlight the need to

use procedures that are as similar as possible to compare

numerical abilities in different species. The main differ-

ence between our experiment and previous studies of

numerical discrimination in fish regards the length of the

training. However, we cannot exclude that at least part of

the difference in fish performance could be due to the fact

that here, we used a procedure close to the foraging habits

of the species: Guppies have a natural tendency to search

for small, orange fruits dropped into the river bottom (Rodd

et al. 2002), and this tendency may have acted in synergy

with our training to enable their achievement of finer

numerical discriminations.

We observed similar performances in 2 versus 3 and

in 3 versus 4 comparisons, while the accuracy signifi-

cantly decreased in the 4 versus 5 discrimination. One

might be tempted to suggest that, in the 2–4 numerical

range, a ratio-independent mechanism was operating

(see Feigenson et al. 2004 for discussion). However, this

conclusion is not justified by our data because in our

procedure we presented a sequence of discriminations of

increasing difficulty, and therefore, the fish had a longer

training experience when faced with the more difficult

discriminations.

Individual variation in mathematical achievements is

commonly found in human studies and has been reported in

other species as well (Cantlon and Brannon 2007; Libertus

et al. 2013). In our experiment, one subject could only

discriminate up to 2 versus 3 objects and two others only

up to 3 versus 4 objects. It is not clear at present whether

this lower performance is due to poorer numerical skills or,

rather, to a more general difference in learning ability. In a

recent interspecific comparison, we found in one species,

the zebrafish, much lower performance in a numerical task

than in the other four fish species studied. A control

experiment showed that this result was better explained by

interspecific differences in learning rate, rather than in

numerical abilities per se (Agrillo et al. 2012a).

Previous methods that investigated numerical abilities in

fish were limited in the maximum number of trials that

could be given. One procedure consisted of repeatedly

delivering live food at the two ends of a small rectangular

tank housing a single subject (Agrillo et al. 2012a, b). This

method allows researchers to rapidly train several fish

simultaneously but permits only four reinforced trials per

day and, hence, would require maintaining fish in this

condition for months in order to give hundreds of trials. In

other studies (Agrillo et al. 2010, 2011), a fish was inserted

in an unfamiliar tank and trained to discriminate between

two doors associated with different numerosities in order to

rejoin with shoal-mates. This procedure allows many more

trials per day but, as time passes, the subject becomes

familiar with the process and motivation for social rein-

statement decreases. The method used in the present study

allowed for the first time to surpass these limits, allowing

up to 120 trials for each numerical discrimination. It is

worth noting, however, that we are still far from the effi-

cacy provided by conducting hundreds of trials in a

Fig. 2 Percentage of correct choices for the four numerical contrasts.

The black line indicates the average performance of all subjects, and

the gray line indicates the average performance of the five subjects

that discriminated up to 4 versus 5 items

Anim Cogn

123

computerized setting that can be observed, for example, in

studies on pigeons and macaques (Cantlon and Brannon

2007; Roberts and Mitchell 1994). Future studies will tell

us whether fish can even further enhance their numerical

performance if tested in the latter conditions, as suggested,

for example, by outstanding results obtained in other types

of cognitive tasks by goldfish trained for several weeks in a

modified Skinner box (e.g., Goldman and Shapiro 1979).

This, however, raises an important question. While it is

incontestable that performance in spontaneous choice tests

reflects the capacities that a species would display in its

natural environment, it is possible that performance

observed after extensive training may be the result of the

recruitment of neuro-cognitive systems that are usually not

involved in number processing. In humans, for instance,

there is evidence that expertise may, in some cases,

determine exceptional performance and consistent modifi-

cation of cognitive systems, comprising some cognitive

systems that are not directly involved in the specific

domain of expertise (Gauthier et al. 2000; Cheek and Smith

1999). Regarding numerical competence, a recent meta-

analysis showed that abilities that predate the emergence of

language, such as the capacity to make rapid relative

numerosity judgments, are processed mainly by the intra-

parietal sulcus; conversely, the abilities developed after the

extensive training derived from culture and education (the

so-called symbolic numerical abilities) lead to the recruit-

ment of additional neural circuits and brain areas, such as

the prefrontal cortex, cingulate gyri, the insula and the

cerebellum (Arsalidou and Taylor 2011). Even though we

must acknowledge that there is a lack of studies supporting

similar conclusions in nonhuman animals, the possibility

remains, as suggested by several authors (Barnard et al.

2013; Hauser et al. 2000), that some of the exceptional

mathematical performances exhibited by animals after

extensive training may derive from the recruitment of

neural resources that are not normally involved in numer-

ical cognition and that these capacities would hardly be

displayed under natural conditions.

Previous comparative studies have highlighted the similar

characteristics of the numerical systems of fish and warm-

blooded vertebrates while evidencing a clear superiority of

performance in the latter. The results of the present study

seem to reduce the gap in this latter aspect too. Why would

fish have the same quantitative mechanisms as mammals

and birds, given the enormous differences between species

in morphology, behavior and environmental demands?

Some authors (Beran 2008b; Feigenson et al. 2004) have

proposed that the basic elements for processing quantitative

and numerical information may have appeared early in the

evolutionary history and, inherited in a substantially

unchanged form by all extant vertebrates, they constitute the

building blocks for the sophisticated numerical abilities that

can be observed today in some species, such as in humans. It

is also possible that, regardless of the enormous differences

in natural history and habitat, the types of problems that are

solved through the numerical systems are substantially the

same (e.g., counting social companions, opponents or food

items) in all species, and thus, similarities are the conse-

quence of convergent evolution, rather than common

ancestry.

In any case, it is intriguing that numerical abilities of

fish can compare with those of primates, despite the

enormous differences in the size and complexity of their

neural structures. This accords with the recent disclosure

that bony fish possess several other cognitive abilities that

were previously believed to be uniquely present in mam-

mals and birds. For instance, teleost fish can recognize up

to forty familiar individuals, cooperate to achieve a com-

mon goal, learn new foraging and antipredator habits from

experienced conspecifics, use tools and exhibit cultural

traditions (reviewed in Bisazza 2010; Bshary et al. 2002;

Brown and Laland 2003). This evolutionary success could

partly be due to the whole-genome duplication event that

occurred between 400 and 450 million years ago after the

separation of the teleost fishes from the lineage that led to

the origin of terrestrial vertebrates. Following this event,

many duplicated genes freed up to evolve novel functions,

and many authors have suggested that the increased genetic

complexity of the teleosts might be the reason for their

amazing biological diversity (Volff 2005; Wittbrodt et al.

1998) as well as the evolution of novel and complex cog-

nitive functions (Schartl et al. 2013).

Acknowledgments The authors would like to thank Michael J

Beran for his useful comments and Michela Giovagnoni for her help

in testing the animals. This work was funded by the FIRB grant

(RBFR13KHFS) from Ministero dell’Istruzione, Universita e Ricerca

(MIUR, Italy) to Christian Agrillo. Experiments comply with all laws

of the country (Italy) in which they were performed.

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