bioRxiv preprint doi: https://doi.org/10.1101/2021.03.03.433737; this version posted March 4, 2021. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license. 1 1 Towards a standardization of non-symbolic numerical experiments: GeNEsIS, 2 a flexible and user-friendly tool to generate controlled stimuli 3 4 Mirko Zanon1, Davide Potrich1, Maria Bortot1, Giorgio Vallortigara1 5 6 1 Center for Mind/Brain Sciences, University of Trento, Rovereto, Italy 7 8 Corresponding author: 9 Mirko Zanon 10 Piazza Manifattura,1 38068 Rovereto 11 +39 3473009313 [email protected] bioRxiv preprint doi: https://doi.org/10.1101/2021.03.03.433737; this version posted March 4, 2021. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license. 2 12 Abstract 13 Several studies have suggested that vertebrate and invertebrate species may 14 possess a number sense, i.e. an ability to process in a non-symbolic and non-verbal 15 way the numerousness of a set of items. However, this hypothesis has been 16 challenged by the presence of other non-numerical continuous physical variables, 17 that vary along with numerosity (e.g. any change in the number of visual physical 18 elements in a set naturally involves a related change in visual features such as area, 19 density, contour length and convex hull of the stimulus). It is therefore necessary to 20 control and manipulate the continuous physical information when investigating the 21 ability of humans and other animals to perceive numerousness. During decades of 22 research, different methods have been implemented in order to address this issue, 23 which has implications for experiments replicability and inter-species comparisons, 24 since no general standardized procedure is currently being used. Here we present 25 the “Generation of Numerical Elements Images Software” (GeNEsIS) for the creation 26 of non-symbolic numerical arrays in a standardized and user-friendly environment. 27 The main aim of this tool would be to provide researchers in the field of numerical 28 cognition with a manageable and precise instrument to produce visual numerical 29 arrays controlled for all the continuous variables; additionally, we implemented the 30 possibility to actively guide stimuli presentation during habituation/dishabituation and 31 dual-choice comparison tasks used in human and comparative research. 32 Keywords 33 Number sense; numerical abilities; number comparison; quantity discrimination; 34 Approximate Number System (ANS); continuous physical variables; standardized 35 method; numerical stimuli generator; MatLab GUI; bioRxiv preprint doi: https://doi.org/10.1101/2021.03.03.433737; this version posted March 4, 2021. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license. 3 36 Introduction 37 The ability to operate with numerical information is an essential skill to deal with our 38 everyday life. However, the symbolic numerical system and the formal arithmetic 39 developed by humans are believed to be rooted in a more ancient and possibly 40 innate numerical ability, the so-called “number sense” (Dehaene, 1997). This sense 41 of number is a non-symbolic, language-independent and evolutionary conserved 42 ability that allows humans and other animals to represent numerical sets of physical 43 items in the surrounding environment (Ferrigno & Cantlon, 2017; Vallortigara, 2014, 44 2017). Animals, both vertebrates and invertebrates, can take advantage of this ability 45 in order to optimize foraging decision (vertebrates: Garland et al., 2012; Gazzola et 46 al., 2018; Hanus & Call, 2007; Stancher et al., 2015; invertebrates: Bar-Shai et al., 47 2011; Hemptinne et al., 1992; Nelson & Jackson, 2012), conflicts between groups, 48 defensive strategies (vertebrates: McComb et al., 1994; Potrich et al., 2015; Wilson 49 et al., 2002; invertebrates: (Tanner, 2006), mating competition (vertebrates: Flay et 50 al., 2009; invertebrates: Carazo et al., 2009) and parental care (Lyon, 2003). 51 It has been hypothesized that the number sense is actually instantiated in an 52 “Approximate Number System” (ANS), a non-verbal mechanism that allows to 53 estimate and represent numerosity of sets of physical elements, which obeys the 54 Weber’s Law (Gallistel, 1990), i.e. as the ratio between the numbers to be 55 discriminated increases, response times increases and accuracy decreased (e.g., 56 discriminate 5 vs. 15, with a 0.33 ratio, is easier than discriminate 10 vs. 20, with a 57 0.5 ratio; Gallistel & Gelman, 1992; for general reviews see e.g. Butterworth, 1999; 58 Hyde, 2011; Nieder & Dehaene, 2009). Evidence for a dedicated neural network for 59 processing numerical information involving parietal and prefrontal cortical regions 60 has been reported in humans (Arsalidou & Taylor, 2011; Piazza & Eger, 2016) and bioRxiv preprint doi: https://doi.org/10.1101/2021.03.03.433737; this version posted March 4, 2021. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license. 4 61 non-human primates (Wang et al., 2015). Furthermore, neurons that show tuned 62 selectivity to specific numerousness have been described in both humans (see 63 Nieder, 2016 for review) and non-human species, e.g. primates (Viswanathan & 64 Nieder, 2013) and corvids (Ditz & Nieder, 2015; Wagener et al., 2018). Recently, 65 evidence for neurons sensitive to numerousness has been reported in the dorso- 66 central pallium of zebrafish (Messina et al., 2020a, 2020b). 67 The evidence supporting non-symbolic numerical estimation in a variety of 68 species is robust; however, specifying the precise nature of what is actually 69 estimated is challenging, since it has been argued that estimation may be guided by 70 non-numerical continuous physical variables, such as the amount of stimulus 71 extension in space (Leibovich et al., 2017). The debate regarding the existence of a 72 number sense is rooted in a methodological issue for which it is empirically 73 impossible to take apart numerical information from all other continuous properties at 74 once, making it difficult to study the non-symbolic numerosity processed in isolation 75 from continuous magnitudes. In a natural environment, a change in numerosity of a 76 set of items usually involves a change in the overall items’ properties (such as 77 volume, area and perimeter) that co-varies with numbers: five objects normally 78 occupy a larger space than three objects. At the same time, if the elements are 79 displaced at the same distance one from the others, the global occupied field (known 80 also as convex-hull) will be different, and inversely, by pairing the global field, the 81 larger group will present a higher density. 82 As an alternative to the number sense theory, some authors have suggested 83 that numbers are estimated and compared by combining the different sensory cues 84 comprising the numerical value, using a sensory-integration-system (Gebuis et al., 85 2016). According to another hypothesis numerosities and magnitudes would be bioRxiv preprint doi: https://doi.org/10.1101/2021.03.03.433737; this version posted March 4, 2021. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under aCC-BY-NC 4.0 International license. 5 86 processed holistically, thus arguing that it would be more appropriate to refer to a 87 sense of magnitude than to a sense of number (Leibovich et al., 2017). Evidence 88 supporting a broader processing of numerosity and continuous magnitudes have 89 been reported by several studies. Using an algorithm capable to generate dot arrays 90 in which continuous variables might be congruent or incongruent with the number of 91 elements in the set, Gebuis and Reynvoet (2011, 2012) showed that participants’ 92 judgement was influenced by the visual properties of the elements’ arrays. 93 Continuous magnitude appears to influence performance even with numerosities in 94 the subitizing range (Leibovich et al., 2015; Salti et al., 2017). Studies carried out in 95 humans and different animal species have shown that numerical tasks might be 96 influenced by non-numerical cues such as the overall surface area (Feigenson et al., 97 2002; Stevens et al., 2007; Tokita & Ishiguchi, 2010), the individual size (Beran et 98 al., 2008; Henik et al., 2017), the spatial frequency (Felisatti et al., 2020), and the 99 density of the elements array (Dakin et al., 2011; Gómez-Laplaza & Gerlai, 2013). 100 This debate between sense of number and sense of magnitude is leading 101 researchers to pay particular attention to the control of continuous physical variables. 102 The simultaneous balancing of all these variables at the same time, however, is not 103 viable: for instance, when the convex hull of the stimuli increases, the density 104 decreases and vice versa; similarly, when the overall area of two sets of elements 105 with different numerousness is balanced, their overall contour length would differ 106 (Gebuis et al., 2014; Leibovich & Henik, 2014; Mix et al., 2002). It is therefore 107 important to set up control conditions in which the different continuous physical 108 variables are randomized and contrasted with numerousness as such to rule out 109 their possible use as non-numerical cues that may guide the discrimination.