At the root of numerical cognition: fish as a model species to study pre - verbal numerical abilities

Although only our species has achieved high level of mathematical reasoning, numerical abilities are not a human prerogative and in last decades comparative research showed that several animal species display rudimentary numerical capacities (Agrillo & Beran, 2013). The ability to discriminate between quantities provide multiple benefits in different ecological contexts. For instance, numerical abilities can be useful to select the larger amount of food (Hunt et al., 2008), to reduce the probability of being spotted by predators by getting protection within the largest group of social companions (Cresswell, 1994) and to decide whether attack another group based on the assessment of the relative number of intruders (Benson-Amram et al., 2011). In particular, the discovery in recent years that even simple organisms, such as fish, possess numerical abilities similar to primates has made possible the use of fish as an animal model to study numerical cognition in the absence of language. To date, different studies have shown that fish are able to select the larger shoal of conspecifics (Agrillo et al., 2008) and can be trained to discriminate between groups of figures differing in numerosity both when allowed to use number and continuous quantities and when only number was available (Agrillo et al., 2009, 2010). Fish can also make a spontaneous use of numerical information with apparently the same effort required to discriminate continuous quantities (Dadda et al., 2009). These abilities seem to be partially inborn as one-day old fish are already able to discriminate between small groups of peers (Bisazza et al., 2010). Nonetheless several questions about numerical abilities in fish are still unanswered. For instance, it is unclear whether numerical systems are the same among different species, whether numerical acuity may be affected by different factors, such as cooperation among individuals and the presence of items in motion or whether newborn fish could be trained to discriminate between sets of items. The aim of the present study was to fill this gap. In particular, the first part of the thesis deals with some of the open questions about numerical cognition in adult fish; the second part is focused on the ontogeny of numerical competence. In the first study (Section 4.1) we set up a novel procedure for training fish to discriminate between sets of stimuli (groups of geometrical figures) differing in numerosity as the previous methodology used to train fish was time-consuming, suitable only for social species and potentially stressful for fish. To validate the method, we replicated two published experiments that used operant conditioning to investigate mosquitofish (Gambusia holbrooki) abilities to discriminate between small sets of items and the influence of numerical ratio and total number of figures on large number discrimination (Agrillo et al., 2009, 2010). In the new procedure a pair of stimuli differing in numerosity was introduced at the opposite ends of the experimental tank and a food reward was released in correspondence of the stimulus to be reinforced. Fish were initially trained on an easy numerical ratio (0.5) and were then tested in non-reinforced probe trials for their ability to generalize to new numerosities. The new procedure designed replicated previous results: fish proved able to discriminate up to 2 vs. 3 figures and their performance in the large number range decreased while increasing the numerical ratio though their numerical acuity seemed to have no upper limit. In addition, the new method proved to be rapid, applicable to different fish species and efficient to study discrimination learning in fish in tasks requiring visual stimuli. As a consequence, the novel protocol was adopted in all the training experiments presented in this thesis. The second study (Section 4.2) focused on a potential limit in numerical cognition research: the lack of cross-species studies using the same methodology. The question of whether all vertebrates share the same numerical systems or rather numerical abilities have appeared multiple times during evolution in response to specific selective pressures imposed by the environment, represents one of the main issues of animal cognition. Despite the large number of published data, results are inconsistent because the methodologies adopted vary across studies, making difficult any inter-specific comparison. To date no study has investigated if different fish species have the same numerical systems. This experiment represents the first inter-specific study using the same methodology in fish. Five fish species as diverse as guppies (Poecilia reticulata), zebrafish (Danio rerio), angelfish (Pterophyllum scalare), redtail splitfin (Xenotoca eiseni) and Siamese fighting fish (Betta splendens) were trained on an easy numerical ratio (0.50) and then were compared in their ability to generalize to more difficult ratios (0.67 and 0.75), or to a larger (25 vs. 50) or a smaller (2 vs. 4) total set size. Results showed interesting similarities among the species, opening the possibility of shared numerical systems among phylogenetically distantly related species, more in accord with the existence of ancient quantification systems inherited from a common ancestor than with an independent evolution of numerical abilities in different species. Another important question in the study of numerical cognition concerns the influence of contextual factors on the numerical capacities of a species. It is possible that the performance observed in a numerical task is limited to the specific context in which such abilities are observed rather than reflecting the full numerical competence of a species. To this purpose, the third (Section 5.1) and fourth (Section 5.2) studies investigated the potential influence on fish numerical acuity of factors that normally occur in nature, namely, the cooperative behavior within group and the perception of figures in motion. In natural environment grouping animals interact with each other and these repeated interactions among individuals can affect adaptive response. Recent studies have provided evidence that, in some contexts, collective actions allow to bypass the cognitive limits of a species and to solve problems that go beyond the capacity of a single individual (Krause et al., 2010, Couzin, 2009). To date, all numerical studies in non-human animals have tested subjects individually and it is not known whether collective behavior can enhance the capacity to solve numerical tasks. The third study (Section 5.1) aimed to verify whether fish in dyads were more accurate than single individuals in two different numerical discrimination tasks. In the first task, guppies were required to join the larger group of conspecifics (4 vs. 6); in the second one fish were trained to discriminate between sets of figures (0.5 ratio) and hence were tested in discriminations of increasing difficulty (0.67 and 0.75 ratios). Results showed that dyads performed better than singletons in selecting the larger group of social companions and also made better numerical discriminations of arrays of dots, showing that collective behavior may yield benefits that go beyond the single ecological context. In addition, in both conditions, the better individual of the dyad spontaneously emerged as the leader. Interestingly, the results here obtained aligned with data collected in adult humans where dyadic performance was superior than individual in a collective enumeration task (Bahrami et al., 2013), thus suggesting that cooperation similarly increases numerical acuity in two distantly related species, such as humans and fish. The motion of items is another factor that might potentially affect numerical abilities. Animals are naturally exposed to moving items (e.g., prey, predators) and hence the movement represents a relevant cue in their life. It is known that fish ability to discriminate between small and large groups of conspecifics is differently affected by the quantity of movement of social companions (Agrillo et al., 2008). However it is still unexplored whether fish can discriminate between two-dimensional figures in motion and whether their accuracy is the same in the small and large number range. For example, it has been reported that adult humans are faster and more accurate in estimating small numerosities (≤ 4) of dynamic items than large numerosities (≥ 4), supporting the hypothesis of two distinct numerical systems (Trick et al., 2003, Alston & Humphreys, 2004). To this aim, in the fourth study (Section 5.2) guppies were trained (0.5 ratio) and tested (0.75 ratio) with either static or moving stimuli. We observed a similar effect of items in motion in fish: while a 0.75 ratio was not discriminated with static stimuli in either numerical range (3 vs. 4 and 9 vs. 12), guppies were able to discriminate this ratio with items in motion but only in the small number range (3 vs. 4). To date, comparative psychologists disagree as to whether in non-human species a single system accounts for discriminations over the whole numerical range (called “Approximate number system”), or a distinct system operates over the small number range (≤4) (called “Object tracking system”). Although the results do not represent a direct evidence for the existence of a separate system in the range 1-4, the differential effect of motion reported in guppies reinforces the idea of separate cognitive systems for small and large numbers, in line with data collected in humans. Despite no direct comparisons have been made between fish and humans in this thesis, the similarities between the two species are worth noting as they raise the intriguing possibility that the foundation of our numerical abilities might be evolutionarily more ancient than previously thought, dating back at least as far as the divergence between fish and land vertebrates. The second part of the thesis focused on the development of numerical abilities using newborn guppies as a model species. Developmental studies can provide useful insights with respect to the existence of a single or multiple systems of numerical representation. For instance, exploring developmental trajectories of numerical skills in different contexts can help us to assess whether the same or distinct numerical systems are used in different tasks. Since an adequate method to study discrimination learning in newborn guppies was not available, in the fifth study (Section 6.1) we designed a procedure by taking into account the social needs of young individuals in order to minimize potential stress due to social deprivation, without interfering with the normal development of their behavioral repertoire. We investigated the development of social behavior in the first two weeks of life by using a spontaneous choice task where newborn guppies could choose between social companions and an empty compartment. Then, newborns were given the choice between their own mirror image and a group of peers to assess whether mirrors could be used as a substitute for social companions during experiments. Based on the findings of these experiments, the protocol for discrimination learning in adult fish was adapted to study shape discrimination in newborn fish. Newborn guppies proved capable to learn a simple shape discrimination after few trials and the training method was then used in the last study (Section 6.2) to investigate their numerical competence using sets of two-dimensional objects, as commonly done with adult fish. At present only Bisazza and colleagues (2010) investigated the ontogeny of numerical abilities in fish. The authors found that, at birth, the capacity of guppies to discriminate between shoals differing by one individual included all numerical contrasts in the range 1-4; young guppies proved also be able to discriminate small numerosities by using numerical information only. In Section 6.2 we investigated whether newborns could be trained to discriminate between small sets of figures. To this purpose, we set up three different experimental conditions to study the influence of continuous quantities that co-vary with numbers (cumulative surface area, density, etc.). In the first one number and continuous quantities were simultaneously available, in the second condition only numerical information was available and in the last one, numerical information was made irrelevant (3 vs. 3) and only continuous quantities were available. The result that fish discriminated only very easy numerical contrasts in the range 1-4 when both number and continuous variables were available was in contrast with the results of shoal discrimination experiments (Bisazza et al., 2010) thus suggesting that newborns’ capacity to use number is specific to social stimuli. On the whole data on guppies, both adult fish and newborns, are suggestive of the existence of multiple quantification mechanisms in fish which are domain-specific and serve to solve a limited set of problems in accordance with the hypothesis proposed by different authors (Feigenson et al., 2004; Spelke, 2000). In sum, the data collected in this thesis indicate that even fish, which are provided with a much smaller brain than warm-blooded vertebrates, can discriminate between quantities and solve complex numerical tasks, in line with evidence in other research fields which suggest that processing numerical information might not require complex neural circuits (Hope et al., 2010). This goes together with recent discovery that bony fish possess several other cognitive abilities that were previously believed to be uniquely present in species provided with large, complex brains (i.e. mammalian and avian species) (Bshary et al., 2002). For all these reasons, fish may become a proper model to study cognitive abilities and in particular numerical competence.Sebbene solamente la nostra specie abbia raggiunto un elevato livello di competenze matematiche, le capacità numeriche non sono una prerogativa umana e negli ultimi decenni la ricerca comparata ha documentato come molte specie animali posseggano rudimentali abilità numeriche (Agrillo & Beran, 2013). La capacità di saper discriminare tra diverse quantità risulta essere vantaggiosa in diversi contesti ecologici. Per esempio, tale abilità può essere utile per scegliere la quantità maggiore di cibo (Hunt et al., 2008), per ridurre la probabilità di essere predati - ottenendo protezione dal gruppo di conspecifici più numeroso (Cresswell, 1994) - e per decidere se intraprendere interazioni aggressive contro un altro gruppo in base al numero di potenziali rivali (Benson-Amram et al., 2011). In particolare, la recente scoperta che persino organismi semplici, come i pesci, posseggono abilità numeriche simili a quelle osservate nei primati ha reso possibile l'utilizzo dei pesci come modello animale per studiare la cognizione numerica in assenza del linguaggio. Ad oggi, diversi studi hanno infatti dimostrato che i pesci sono capaci di selezionare il gruppo di conspecifici più numeroso (Agrillo et al., 2008) e possono essere addestrati a discriminare tra gruppi di figure di diversa numerosità, sia quando possono utilizzare l’informazione numerica e le variabili continue simultaneamente, sia nel caso in cui sia disponibile solamente l’informazione numerica (Agrillo et al., 2009, 2010). È stato inoltre dimostrato che i pesci sono in grado di discriminare tra quantità usando spontaneamente il numero, apparentemente con lo stesso sforzo cognitive richiesto per discriminare le variabili continue (Dadda et al., 2009). Queste capacità sembrano essere in parte innate, dal momento che gli avannotti di un giorno di vita sono già in grado di discriminare tra piccoli gruppi di conspecifici (Bisazza et al., 2010). Tuttavia diverse domande sulle abilità numeriche nei pesci sono ancora senza risposta. Ad esempio, non è chiaro se i sistemi numerici siano gli stessi fra specie differenti, se l'acuità numerica possa essere influenzata da diversi fattori, come la cooperazione tra gli individui e la presenza di oggetti in movimento o se i pesci appena nati possano essere addestrati a discriminare tra gruppi di oggetti bidimensionali. Lo scopo della presente tesi è stato pertanto quello di colmare queste lacune. In particolare, la prima parte della tesi affronta alcune delle questioni aperte sulla cognizione numerica nei pesci adulti, mentre la seconda parte è focalizzata sull’ontogenesi delle abilità numeriche. Nel primo lavoro (Sezione 4.1) è stata messa a punto una nuova procedura per addestrare i pesci a discriminare tra stimoli bidimensionali (gruppi di figure geometriche) di diversa numerosità, dal momento che il metodo precedentemente utilizzato in letteratura richiedeva tempi prolungati, era adatto solo per le specie sociali ed era potenzialmente stressante per i pesci. Per verificare la validità del metodo, sono stati replicati due esperimenti che hanno usato la procedura del condizionamento operante per indagare le capacità della gambusia (Gambusia holbrooki) di discriminare tra piccole numerosità e l’influenza del rapporto numerico e del numero totale di elementi nella discriminazione di grandi quantità (Agrillo et al., 2009, 2010). Nella nuova procedura, veniva introdotta una coppia di stimoli di diversa numerosità alle estremità della vasca sperimentale e successivamente veniva rilasciato del cibo in corrispondenza dello stimolo da rinforzare. I pesci sono stati inizialmente addestrati a distinguere un rapporto numerico relativamente semplice (0.5); successivamente nella fase di test, sono stati sottoposti a delle prove in estinzione (non veniva fornito il rinforzo alimentare) per verificare la loro capacità di generalizzare a nuove numerosità. La nuova procedura messa a punto ha replicato i risultati ottenuti con quella precedentemente utilizzata: i soggetti sono stati in grado di discriminare fino a 2 figure da 3; in presenza di grandi numerosità la prestazione diminuiva all’aumentare del rapporto numerico sebbene la loro capacità di discriminare sembri non avere un limite superiore. Il nuovo metodo si è inoltre rivelato rapido per la raccolta dei dati, applicabile a diverse specie di pesci ed efficacie per studiare l'apprendimento discriminativo in compiti che richiedono stimoli visivi. Di conseguenza, il nuovo protocollo è stato adottato in tutti gli esperimenti presentati in questa tesi che hanno usato la procedura di addestramento. Il secondo lavoro (Sezione 4.2) è incentrato su un potenziale limite della ricerca sulla cognizione numerica: la mancanza di studi inter-specifici che utilizzano la stessa metodologia. La questione se tutti i vertebrati condividano gli stessi sistemi numerici o se piuttosto le abilità numeriche siano apparse più volte durante l'evoluzione in risposta a specifiche pressioni selettive imposte dall'ambiente rappresenta uno dei temi principali della cognizione animale. Nonostante l’elevato numero di dati pubblicati, i risultati non sono coerenti dal momento che sono state utilizzate diverse metodologie di ricerca rendendo così difficile un confronto inter-specifico accurato. Ad oggi, nessuno studio ha indagato se diverse specie di pesci possiedano gli stessi sistemi numerici. Questo lavoro rappresenta il primo studio inter-specifico che utilizza la stessa metodologia nei pesci. Cinque diverse specie, la pecilia (Poecilia reticulata), lo zebrafish (Danio rerio), il pesce scalare (Pterophyllum scalare), la xenotoca (Xenotoca eiseni) ed il pesce combattente (Betta splendens), sono state inizialmente addestrate utilizzando un rapporto numerico semplice (0.50) e successivamente è stata confrontata la loro capacità di generalizzare a rapporti più difficili (0.67 e 0.75) o ad una numerosità maggiore (25 vs. 50) o minore (2 vs. 4). I risultati hanno mostrato interessanti somiglianze tra le specie, suggerendo la possibilità di sistemi numerici condivisi tra specie filogeneticamente distanti tra loro, più in accordo con l’esistenza di antichi sistemi di quantificazione ereditati da un antenato comune piuttosto che con un’evoluzione indipendente delle abilità numeriche in specie diverse. Un'altra questione importante nello studio della cognizione numerica riguarda l'influenza di fattori contestuali sulle capacità numeriche di una specie. È possibile che la prestazione osservata in un compito numerico sia limitata al contesto specifico in cui tali capacità sono state osservate piuttosto che riflettere le reali abilità numeriche della specie. Per questo motivo, il terzo (Sezione 5.1) e il quarto (Sezione 5.2) lavoro hanno studiato la potenziale influenza sull’accuratezza numerica dei pesci di fattori che normalmente si verificano in natura: il comportamento cooperativo all'interno del gruppo e la percezione di figure in movimento. In natura, gli animali che vivono in gruppo interagiscono tra di loro e queste interazioni ripetute tra gli individui possono incidere sulle scelte fatte in diversi contesti. Studi recenti hanno dimostrato che in alcune circostanze le azioni collettive permettono di aggirare i limiti cognitivi di una specie e di risolvere i problemi che vanno al di là delle capacità del singolo individuo (Krause et al., 2010, Couzin, 2009). Fino ad oggi, tutti gli studi di cognizione numerica condotti negli animali hanno preso in considerazione le prestazioni di singoli soggetti e non si sa quindi se il comportamento collettivo possa migliorare la capacità di risolvere compiti di discriminazione numerica. Lo scopo del terzo lavoro (Sezione 5.1) è stato quello di verificare se i pesci sottoposti a test in coppia fossero più accurati rispetto ai soggetti sottoposti a test individualmente in due diversi compiti di discriminazione num