Contribution of visuospatial attention, short-term memory and executive functions to performance in number interval bisection

Author’s Accepted Manuscript Contribution of visuospatial attention, short-term memory and executive functions to performance in number interval bisection Mariagrazia Ranzini, Katia Carbè, Wim Gevers www.elsevier.com/locate/neuropsychologia

PII: DOI: Reference:

S0028-3932(17)30089-1 http://dx.doi.org/10.1016/j.neuropsychologia.2017.03.009 NSY6290

To appear in: Neuropsychologia Received date: 12 May 2016 Revised date: 26 December 2016 Accepted date: 5 March 2017 Cite this article as: Mariagrazia Ranzini, Katia Carbè and Wim Gevers, Contribution of visuospatial attention, short-term memory and executive functions to performance in number interval bisection, Neuropsychologia, http://dx.doi.org/10.1016/j.neuropsychologia.2017.03.009 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting galley proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Contribution of visuospatial attention, short-term memory and executive functions to performance in number interval bisection Mariagrazia Ranzini*, Katia Carbè, Wim Gevers

Université Libre de Bruxelles (ULB). [email protected] [email protected]

*

Corresponding author.

Abstract (264 words) Number interval bisection consists of estimating the mid-number within a pair (1-9=>5). Healthy adults and right-brain damage patients can show biased performance in this task, underestimating and overestimating the mid-number, respectively. The role of visuospatial attention during this task, and its interplay with other cognitive abilities (e.g., working memory) is still object of debate. In this study we explored the relation between visuospatial attention and individual differences in working memory and executive functions during number interval bisection. To manipulate the deployment of visuospatial attention, healthy participants tracked a dot moving to the left or moving to the right while bisecting numerical intervals. We also collected information concerning verbal and visuospatial short-term memory span, and concerning verbal and visuospatial fluency scores. Beside replicating what is typically observed in this task (e.g., underestimation bias), a correlation was observed between verbal short-term memory and bisection bias, and an interesting relation between performance in the number interval bisection, verbal short-term memory, and visuospatial attention. Specifically, performance of those participants with low verbal span was affected by the direction of the moving dot, underestimating at a larger extent when the dot moved leftward than rightward. Finally, it was also observed that participants’ verbal fluency ability contributed in the generation of biases in the numerical task. The finding of the involvement of abilities belonging to the verbal domain contributes to unveil the multi-componential nature of number interval bisection. Considering the debate on the nature of number interval bisection and its use in the clinical assessment of deficits following brain damage, this finding may be interesting also from a clinical perspective.

Keywords: visuospatial attention; number processing; number interval bisection; number-space interactions; short-term memory; working memory; fluency; executive functions.

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Introduction A current view in the domain of numerical cognition is that the mental representation of numbers resembles a spatial continuum, i.e. a mental number line (Dehaene, Bossini, & Giraux, 1993; Dehaene, Dupoux, & Mehler, 1990; Restle, 1970), and visuospatial attention is required to operate along this representation (e.g., Hubbard, Piazza, Pinel, & Dehaene, 2005). Number-space interactions follow the direction of reading/writing habits, oriented from left to right in Western societies (for a review, see: Göbel, Shaki, & Fischer, 2011). A large amount of evidence exists demonstrating number-space interactions (for reviews, see: Fias & Fischer, 2005; de Hevia, Vallar, & Girelli, 2008; Hubbard et al., 2005). At the same time, a number of studies calls the key role of visuospatial attention mechanisms into question. These studies suggest that the contribution of visuospatial attention on number-space interactions might be task-dependent (van Dijck, Gevers, & Fias, 2009; van Dijck, Gevers, Lafosse, & Fias, 2012; van Dijck, Ginsburg, Girelli, & Gevers, 2013) and/or mediated by other cognitive processes, such as verbal mechanisms (Gevers, et al., 2010; Ginsburg, van Dijck, Previtali, Fias, & Gevers 2014), working memory mechanisms (Fias, van Dijck, & Gevers, 2011; van Dijck, Abrahamse, Acar, Ketels, & Fias, 2014; van Dijck & Fias, 2011), or executive functions (Bachmann, Fischer, Landolt, & Brugger, 2010). In the present study we investigate the contribution of both visuospatial attention and individual differences in short-term memory and executive functions to the performance in a classic numerical task (Doricchi, Guariglia, Gasparini, & Tomaiuolo, 2005; Zorzi, Priftis, & Umiltà, 2002): number interval bisection. Number interval bisection consists of estimating – without permission to calculate - the mid-number within a pair (1-9=>5). A number of studies on both healthy populations and brain-damaged patients can be taken to support the idea that this task taps on visuospatial attentional mechanisms (e.g., Goebel, Calabria, Farnè, & Rossetti, 2006; Loftus, Nicholls, Mattingley, Chapman, & Bradshaw, 2009; Longo & Lourenco, 2007; Zorzi et al., 2002). Evidence for the role of attentional orienting in number interval bisection comes from the observation of a pathological performance of right brain-damaged patients suffering from attentional deficits, i.e. neglect. Neglect is characterised by the inability to orient attention and attend to stimuli toward the contralesional side of space (for a review, see: Halligan, Fink, Marshall, & Vallar, 2003). When required to perform number interval bisection, right brain-damaged patients suffering from neglect can pathologically overestimate the mid-number (19=>8; e.g., Zorzi et al., 2002; for a review, see: Umiltà, Priftis, & Zorzi, 2009). It has been shown that this patients’ bias can be improved by manipulating visuospatial attention through prismatic adaptation (Rossetti et al., 2004) or optokinetic stimulation (Priftis, Pitteri, Meneghello, Umiltà, & Zorzi, 2012). The overestimation bias has been considered evidence for the involvement of visuospatial attention mechanisms lying at the basis of number-space interactions because it mirrors the patients’ rightward bias in the bisection of physical horizontal lines (Marshall & Halligan, 1989). Indeed, following the idea of a mental number line, patients’ overestimation in number interval bisection might reflect their difficulty in orienting attention toward the left part of the mental numerical continuum (Zorzi et al., 2002). However, only few neglect studies showed correspondence between biases in line and number interval bisections (Cappelletti, Freeman, & Cipolotti, 2007; Loftus et al., 2009, experiment 5, patients S.K. and G.C.), while a growing body of studies described dissociations between these tasks (e.g., Aiello et al., 2012; Doricchi et al., 2005; Loetscher, Nicholls, Towse, Bradshaw, & Brugger, 2010; Pia et al., 2012; Rossetti et al., 2011; van Dijck et al., 2012). Some authors proposed that short-term memory might be responsible for the pathological performance of patients on number interval bisection (Doricchi et al., 2005; van Dijck, Gevers, Lafosse, Doricchi, & Fias, 2011). In favour of this view, Aiello, Merola, and Doricchi (2013) observed correlations between the performance in number

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interval bisection and the scores on verbal and visuospatial short-term memory tests (digit span and Corsi test) in right-brain damaged patients (see also: Doricchi, et al., 2009), while Storer and Demeyere (2014) failed to observe such correlations in a group of unselected patients with respect to the lesion site. In sum, evidence from neglect studies is mixed, leaving room for arguments favouring both visuospatial attention or working memory as the core cognitive function underlying the observed bisection deficit. Healthy adults usually show a higher degree of accuracy in number interval bisection as compared to neglect patients. However, when presented with large intervals and large magnitudes, healthy adults also show a bias, consisting of a systematic tendency to underestimate the mid-number (e.g., 1298=>51 instead of 55). This bias is independent of the modality of presentation and of task requirements. Indeed, it is similarly observed when number intervals are presented auditorily (Goebel Calabria, Farnè, & Rossetti, 2006) or visually (Longo & Lourenco, 2007). Furthermore, it is observed when the task requires to estimate the mid-number (e.g., Goebel et al., 2006; Longo & Lourenco, 2007), to judge whether a number is the correct mid-number of a given interval (Loftus et al., 2009, Experiment 4), or when judging whether a given mid-number is numerically further away from a smaller or from a larger given number (Loftus et al., 2009, Experiment 1). Finally, underestimation is observed regardless of whether numbers are presented in an increasing (e.g., 1298) or a decreasing order (e.g., 98-12), with participants tending to underestimate to a greater extent in the decreasing than in the increasing condition. In analogy to the typical leftward bias of healthy adults in line bisection (i.e., pseudoneglect; for a review, see: Jewell & McCourt, 2000), several authors argued that the underestimation bias observed in number interval bisection tasks might reflect a leftward bias on a mental number line. Longo and Lourenco (2007) found support for this view by showing that the performance in number interval bisection was positively correlated to the performance in line bisection in a group of healthy adults (see also: Cattaneo, Fantino, Silvanto, Tinti, & Vecchi, 2011a; Goebel et al., 2006; Oliveri et al., 2004). However, Rotondaro, Merola, Aiello, Pinto, and Doricchi (2015) failed to replicate this correlation between numerical and physical bisection tasks when the numbers were presented auditorily. These authors argued that the previously observed correlation between line bisection and interval bisection (Longo & Lourenco, 2007) was induced by the visual presentation of numerical stimuli, and not reflecting the contribution of visuospatial attention on the mental representation of numbers. Altogether, there is no consensus concerning to which extent number interval bisection lies on visuospatial attentional mechanisms (e.g., see: van Dijck et al., 2012). The finding of dissociations between performance on numerical and line bisection tasks both in neglect patients (e.g., Storer & Demeyere, 2014) and in healthy adults (Rotondaro et al., 2015) calls for the idea that a plurality of cognitive mechanisms might contribute to performance in number interval bisection, as well as in other numerical tasks (van Dijck et al., 2012). It is therefore relevant to further investigate the contribution of visuospatial attention as well as its interplay with other cognitive mechanisms during number interval bisection. In this study the role of visuospatial attention in number interval bisection and its link to individual differences in short-term memory and executive functions are investigated in a healthy population. So far, only few studies investigated the effects of manipulation of attention on this task in healthy participants (Cattaneo, Fantino, Silvanto, Vallar, & Vecchi, 2011b; Loftus, Nicholls, Mattingley, & Bradshaw, 2008; Nicholls & Mcllroy, 2010). To the best of our knowledge, there are no studies on healthy populations investigating the interplay between spatial attention and individual differences in other cognitive abilities during number interval bisection. It is therefore relevant to clarify the role of visuospatial attention and its interplay with individual differences in other related cognitive abilities. Therefore, our aim was twofold.

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Our first aim was to directly manipulate the orientation of visuospatial attention to investigate its role in the number interval bisection task in healthy adults. Orienting of attention was manipulated through the execution of leftward or rightward eye movements (for a similar procedure, see: Ranzini, Lisi, & Zorzi, 2016). Indeed, evidence exists suggesting that eye movements and orienting of attention share the same mechanisms (e.g., Casarotti, Lisi, Umiltà, & Zorzi, 2012; Rizzolatti, Riggio, Dascola, & Umiltà, 1987). Importantly, the choice of using eye movements to orient attention in space is also supported by a study by Loetscher, Bockisch, and Brugger (2008) showing that spontaneous gaze shifts were generated while performing number interval bisection, and more in general by an increasing number of studies showing interactions between eye movements and number processing (for a review see, Hartmann, 2015). Using a similar approach, previous studies were able to establish the link between visuospatial attention and number processing in numerical tasks such as parity judgment or number comparison, showing that orienting of attention in physical space induced biases at the cognitive numerical level (e.g., Kramer, Stoianov, Umiltà, & Zorzi, 2011; Stoianov, Kramer, Umiltà, & Zorzi, 2008; Ranzini et al., 2015; Ranzini et al., 2016). We expected first of all to replicate the underestimation bias, reduced or increased as a function of the order of presentation of numbers (e.g., Longo & Lourenco, 2007). Furthermore, because smaller numbers are associated with the left and larger numbers are associated with the right, based on the idea of visuospatial attentional movements along a spatial representation of numbers, we expected the underestimation bias to be reduced or increased by the tracking of a leftward or a rightward dot, respectively. The second aim was to disclose whether individual differences in short-term memory and executive functions contribute to performance in number interval bisection, and whether they interact with the effects of visuospatial attention on bisection. Short-term memory was considered because in leftneglect patients it contributed in determining the performance in number interval bisection (Aiello et al., 2013). More in general, several studies have underlined the contribution of working memory in number-space interactions (e.g., Herrera, Macizo, & Semenza, 2008; van Dijck, Gevers, & Fias, 2009; van Dijck et al., 2013). Executive functions were also taken into account because previous studies found that these functions contributed in the generation of numerical biases (Bachmann et al., 2010; Loetscher & Brugger, 2007). For instance, Bachmann and colleagues (2010) observed that participants relied more or less on a spatial representation of numbers in function of their degree of verbal and visuospatial abilities. In this study, they explored the role of executive functions in another task commonly considered as reflecting number-space interactions, i.e. random digit generation. Here it was found that the group of participants with relatively better visuospatial fluency ability generated smaller digits more frequently than the group with better performance at the verbal fluency task. They concluded that the ones who rely to a larger extent on visuospatial abilities are facilitated in using a spatial strategy during number tasks. Similar to previous studies, individual differences were measured in verbal and visuospatial short-term memory tasks (Aiello et al., 2013) as well as in executive function tasks (Bachmann et al., 2010). By clarifying the involvement of abilities belonging to the verbal and the visuospatial domain, and their interplay between visuospatial attention, this study may contribute to the clarification of the multi-componential nature of number interval bisection performance. Considering the debate concerning the nature of number interval bisection and its use in the clinical assessment of deficits following brain damage, this study may be interesting also from a clinical perspective.

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Methods Participants A hundred and two students from the Université Libre de Bruxelles (76 females; 14 left-handers; mean age: 21, range 18-35) participated to this study in one session. Sixty-two of them received credit grants for their participation. Prior to participation, participants were naive with respect to the aims of the study. They were informed of the rationale and aims at the end of the experimental session. All participants had normal or corrected to normal vision.

Materials and procedure Each participant performed the following three tasks within a single session lasting about 30 minutes: - Number interval bisection with moving dot: at each trial, participants were required to estimate without mental calculation the mid-number of the interval between a pair of orally presented numbers while following with their gaze a dot moving horizontally on the screen (screen resolution: 1280px x 1024px). The dot was a black dot (radius=4px) presented against a silver background, and it moved continuously 1px each 1000/60sec (since the screen resolution was set at 60Hz). The dot could move leftward (two possible starting locations: at 480px or 1040px, on the left or right of the screen center, respectively) or rightward (two possible starting locations: at 240px or 800px, on the left or right of the screen center, respectively). Similar to Ranzini et al. (2016), different starting locations were used to counterbalance the starting position of the eye movement, while controlling for the gaze position with respect to the body midline. The order of presentation of trials with respect to the starting position and direction of the movement was randomized. The timeline of a single trial is illustrated in Figure 1. While tracking the dot with the gaze, the participant listened to a pair of numbers. Each numerical pair could be presented in increasing (e.g., 39-65) or decreasing order (e.g., 65-39). Typically, studies on neglect patients have used blocked designs, where trials belonging to the increasing and decreasing order conditions are presented in separated blocks, while studies on healthy populations have used designs where trials with increasing and decreasing orders are intermixed and randomly presented. To assure that any possible effects of presenting numbers in an increasing or a decreasing order were not due to the choice of a blocked or mixed design, increasing and decreasing trials were presented in separate counterbalanced blocks to 26 participants (Blocked group) and in intermixed random order to 76 participants (Mixed group). The experiment consisted of 96 trials. The 96 number pairs, their overall magnitude and interval length are listed in appendix A. Number pairs were within the range 11-99, and they could belong to three different numerical magnitudes (small, medium, large) and four different interval lengths (16, 26, 36, or 46 units). Number magnitude of each pair was defined by the mid-number, so that small midnumbers felt within 34 and 41, medium mid-numbers felt within 51 and 58, and large mid-numbers felt within 69 and 76 (see Appendix A, for details). There were 8 trials for each numerical magnitude x interval size condition, and the script controlled for the fact that for each other experimental condition (starting position, movement direction, number order of presentation) a number pair was chosen the same number of times from each magnitude x size pool. In this way number pairs were never repeated twice while assuring the same number of trials for each condition, and permitting to analyse the effects of the attentional displacement and order of presentation while controlling for

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magnitude and interval size. Specifically, there were 12 trials for each condition with respect to the attentional variables of interest: side of presentation of the dot (on the left or on the right of the screen centre); dot direction (leftward, rightward); numbers order condition (increasing, decreasing). Each of these 12 trials belonged to a different magnitude (small, medium, large) x interval condition (16, 26, 36, or 46 units). Participants gave their response (the estimated mid-number) orally. Soon after the response (the estimated mid-number) was given, the experimenter discretely encoded it out of sight of the participant. For each trial, the dot disappeared when the response was detected by a microphone connected to a PST serial response box. Instructions emphasized to accurately track the dot as well as to estimate without calculation the mid-number within the numerical interval. There was no time limit to answer. For each trial the experimenter checked whether the participant was correctly and continuously tracking the dot by means of a video camera showing the participants eyes on an additional screen. This additional screen was visible to the experimenter only. In this way, the experimenter could online encode information concerning tracking errors or microphone errors (e.g., detection of sound not related to the response). The checking procedure lead to the exclusion of those trials where the participant was not following the dot with his/her gaze, where the microphone did not work correctly as online detected by the experimenter, where the response felt before the offset of the second number (anticipations), and where the dot was out of the screen halves bounds (corresponding to a tracking duration of approximately 7900ms). This procedure led to the exclusion of 3% of trials. The experimental session was preceded by 8 practice trials. Three questions were presented at the end of the bisection task: 1) whether the participant had the feeling to have attentively followed the dot, 2) whether he/she used to calculate and not to estimate the midnumber and 3) whether he/she perceived the task as difficult. For each question, participants were presented with a Likert scale from 1 (“I was not following the dot/I did not calculate/I did not perceive the task as difficult”) to 9 (“I attentively followed the dot/I calculated/I perceived the task as difficult”).

Figure 1. Timeline of a trial from number interval bisection. Each trial started with a central fixation (font and size: Arial Rounded MT Bold 34) lasting for 1s. The fixation cross was followed by the dot, appearing in one of the four possible starting locations (see the “Materials and procedure” session for details). The dot stayed, without moving, for 500ms, and then it started to move. As soon as the dot started moving, the first number was presented through headphones. The second number was presented after a variable delay (inter-number-interval): this delay was variable in order to keep constant the time occurring between the onset of the first number and the offset of the second number (2s). As soon as the response was detected by the microphone the dot disappeared. A variable inter-trial-interval (lasting the time the

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experimenter took to encode the response plus 1s) preceded the next trial. In the figure the arrow just illustrates the dot movement direction (rightward, in this example) and it was not presented during the experiment.

- Verbal short-term memory span: this task consisted in a computerized variant of the forward digit span. At each trial participants are presented with a sequence of digits, and they have to reproduce aloud the sequence soon after the end of its presentation. The digits were visually presented in sequential order. Each digit was presented at a rhythm of one dot each 1s (800ms followed by 200ms of inter-digit-interval). At each trial, the experimenter discretely encoded accuracy on a keyboard. The digit sequences were taken from the standardized version of Mondini, Mapelli, Vestri, & Bisiacchi (2003). The tasks started with two training trials where the participant was required to recall sequences of two items. Then the experimental trials were presented, from shortest (3 items) to longest sequences (8 items). There were 2 sequences for each sequence length, for a total of 12 sequences. Each sequence could be presented only once, and the total number of sequences presented varied from participant to participant depending on participant’s accuracy: each time a sequence was reproduced correctly, a sequence of increasing length was presented; however, when a sequence was not reproduced correctly another sequence of the same length was presented. The task ended when the participant reproduced incorrectly two consecutive sequences of the same length. The number of items of the longest length for which a sequence was correctly recalled was taken as the span level. Overall, the procedure was close to the one of the classic digit span tests, except that stimuli were visually presented on the screen. - Visuospatial short-term memory span: this task consisted in a computerized visuospatial version of the forward digit span. At each trial a set of nine empty dots was horizontally presented on the screen. Soon after, a sequence of spatial locations was sequentially presented, with one among the nine dots becoming filled at a rhythm of one dot each second (800ms followed by 200ms of interlocation-interval). Soon after the end of the presentation of the spatial sequence, the participant had to reproduce the sequence in the same order by clicking sequentially within each presented dot with the help of the mouse device. The tasks started with two training trials where the participant was required to recall sequences of two items. Then the experimental trials were presented, from shortest (3 items) to longest sequences (8 items). There were 2 sequences for each other sequence length, for a total of 12 sequences. Each sequence could be presented only once, and the total number of sequences presented varied from participant to participant depending on participant’s accuracy: each time a sequence was reproduced correctly, a sequence of increasing length was presented; however, when a sequence was not reproduced correctly another sequence of the same length was presented. The task ended when the participant reproduces incorrectly two consecutive sequences of the same length. The number of items of the longest length for which a sequence was correctly recalled was taken as the span level. Overall, the procedure was similar to the Corsi test, except for the fact that spatial locations were horizontally organized. We opted for a horizontal organization to be more coherent with the theoretical background on number processing which assumes numbers to be preferentially organized horizontally from left to right (e.g., Hubbard et al., 2005). The location sequences were taken from the standardized version of the forward digit span by Mondini et al. (2003) (the computerized program was built in a way that each dot was associated to one digit, e.g., the most leftward dot was associated to “1”, the following rightward to “2”, and so on). For each task, the participant sat comfortably in front of the screen at a distance of approximately 50 cm. The central and fixed position of the microphone constrained the participant to maintain the 7

head at central position with respect to the screen. EPrime 2.0 software was used (Psychology Software Tools, Pittsburgh, PA) to run these three computerized tasks. Additionally, sixty-two participants also performed the following tasks: - Verbal fluency test: The procedure was exactly the same as described in Bachmann et al. (2010). Each participant was required to say during three minutes as many words as possible from the category of words beginning with letter ‘‘S”, without producing proper names, variations or repetitions. This task is a phonological variant of a more general set of verbal fluency tests, it is used in neuropsychological screening of executive dysfunctions, and it has been shown to be specifically related to function of the left frontal lobe (e.g., Baldo, Shimamura, Delis, Kramer, & Kaplan, 2001). The total number of correct words produced was taken as measure of performance. - Design fluency test: The procedure was exactly the same as described in Bachmann et al. (2010). Each participant was required to draw during three minutes as many new designs as possible by connecting each time with straight-line dots, among a set of five dots. Each design could contain a minimum of one line, to a maximum of four lines. Lines within a design should be continuous. For each design, dots were presented on a dice arrangement, on a sheet containing 40 dot matrices. As for the verbal fluency test, the participant had to avoid to produce repetitions of the same design. This task is a version of the non-verbal fluency tests commonly used to assess executive dysfunctions, and it has been shown to be related to functions of the frontal lobes bilaterally (Baldo et al., 2001). The total number of correct designs produced was taken as measure of performance. All participants started with the numerical interval bisection task. The number interval bisection task lasted about 15 minutes. Then, the other tasks (span and fluency tasks) were administered. All participants performed the verbal and the visuospatial span tasks, while a subset of participants (N=62) performed also the verbal and the visuospatial fluency tasks. For those participants performing both the span and the fluency tasks, the order of presentation of span and fluency tasks (verbal and visuospatial) was counterbalanced, so that 28 participants performed the span tasks before the fluency tasks, while 34 participants performed the fluency tasks before the span tasks. For all participants, the order of presentation of verbal and visuospatial tasks (span or fluency) was also counterbalanced: 51 participants performed the verbal task before the visuospatial one, and 51 participants performed the visuospatial task before the verbal one. Span tasks and fluency tasks together took approximately 15 minutes. Since the span and fluency tasks were always presented after the number interval bisection task, they could not affect the numerical task. However, span and fluency tasks were counterbalanced and the order of presentation of these tasks could have had an impact on fluency and span scores. Therefore we performed a series of preliminary analyses (one-way ANOVAs) to check for the absence of counterbalancing effects. Firstly, we compared the group of participants who performed the fluency tasks before the span tasks to the other participants (no fluency task or fluency after span). This counterbalancing procedure had effect neither on the verbal span (p>0.2), nor on the visuospatial span (p>0.5). This means that performing the fluency tasks did not affect the performance on the span tasks. We also compared the scores of the fluency tasks between the group of participants who performed the span tasks before the fluency tasks to the group of participants who performed the span tasks after the fluency tasks. This counterbalancing procedure had effect neither on the verbal fluency (p>0.4), nor on the visuospatial fluency (p>0.8). This means that performing the span tasks did not affect the performance on the fluency tasks. Furthermore, we tested whether performing verbal/visuospatial span first had an effect on the other span task. We compared the verbal and visuospatial span scores between group of participants who performed the

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verbal span before the visuospatial span to the other participants. This counterbalancing procedure had effect neither on the verbal span (p>0.3), nor on the visuospatial span (p>0.3). Finally, we compared on the verbal and visuospatial fluency scores the group of participants who performed the verbal fluency task before the visuospatial one to the other participants. This counterbalancing procedure had effect neither on the verbal fluency (p>0.7), nor on the visuospatial fluency (p>0.4).

Analyses and results Analyses were performed with the R software (version: 3.3.1, R Core Team, 2016). The following packages for R were mainly used: lme4 for mixed effects models (Bates, Maechler, Bolker, & Walker, 2015); ggplot2 for graphics (Wickham, 2009); dplyr (Wickham & Francois, 2016) and tidyr (Wickham, 2016) for data manipulation.

Preliminary analyses Overall participants performed number interval bisection following the instructions correctly, as revealed by the answers to the question concerning subjective judgment on accuracy in tracking the dot (M=6.06, SEM=0.14, t-test vs. 5: t(101)=7.35, p<0.001) and to the question concerning whether they tended to calculate or not the result (M=4.00 SEM=0.22, t-test vs. 5: t(101)=-4.66, p<0.001). Overall, the task was perceived as relatively difficult (M=5.88, SEM=0.19, t-test vs. 5: t(101)=4.70, p<0.001). The dependent variable in the number interval bisection was the mean deviation (difference between the objective minus subjective midpoint) for each relevant condition. A negative deviation corresponds to an underestimation of the mid-number, while a positive deviation corresponds to an overestimation. Prior to the analyses, we calculated the overall mean deviation for each participant and we removed from subsequent analyses the data of those participants whose mean deviation fell outside the 2.5 standard deviations (SD) cut-off from the group average (N=5). The same cleaning procedure was applied for the span and the fluency scores. The data of one additional participant were excluded whose visuospatial span score fell outside the cut-off. The following analyses were therefore conducted on the data from 96 participants. We first verified the presence of an underestimation bias in the number interval bisection task. Participants’ deviations were compared against 0 to evaluate the presence of a systematic underestimation bias, that is the tendency to estimate the mid-number as smaller than its real value. Participants showed, as expected, a significant underestimation bias (M=-2.60, SEM=0.22; t(95)=12.13, p<0.001). The bias was not correlated with the answers to the questions concerning how much the participant followed the dot, how much he/she calculated, and how much he/she found that the task was difficult (all p>0.5). Importantly, the underestimation bias was positively correlated with the verbal span (r=0.43, p<0.001), and uncorrelated to the visuospatial span (r=0.05, p>0.6). To increase the number of observation for condition for subsequent analyses, we performed a median split of participants with respect to span and fluency scores. Median split was chosen to have approximately the same number of participants within each group. The median visuospatial span was 4.5. Dividing participants based on median resulted into two groups: below the median (low visuospatial span: span<5, N=53), and above the median (high visuospatial span: span>4, N=43). The median verbal span of the group was 6. Dividing participants into two groups with respect to the median verbal span would have resulted in highly unbalanced groups, so participants were divided

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into 3 groups: below the median (low verbal span: span<6, N=33), with median span (average verbal span: span=6, N=34), and above the median (high verbal span: span>6, N=29). The verbal fluency median score was 22. A median split of participants with respect to verbal fluency resulted in the following two groups: below or equal to the median (low verbal fluency: N=30), and above the median (high verbal fluency: N=27). The visuospatial fluency median score was 30.00. A median split of the group with respect to visuospatial fluency resulted the following two groups: below or equal to the median (low visuospatial fluency: N=29), and above the median (high visuospatial fluency: N=28). We included these new variables (Verbal Span Group, Visuospatial Span Group, Verbal Fluency Group, Visuospatial Fluency Group) in the analyses on performance at the number interval bisection.

The underestimation bias and the effects of visuospatial attention, short-term memory, numerical magnitude, interval length, and numbers order Mixed effects models were performed so that all variables of interest could be analysed together. The number interval bisection bias was analysed using a linear mixed-effects model procedure (e.g., Pinheiro & Bates, 2000). To select the best model, we first adopted a forward selection modelling procedure consisting in adding to the model a new predictor (either as main effect or in interaction with other variables), and in comparing the fit for this model with the one for the previous reduced model by evaluating the improvement in the goodness of fit (likelihood ratio test). A predictor was first added as fixed effect, and then in interaction with each other variable or with interactions already in the model. When a predictor induced a significant improvement to the model as both main effect and in interaction with other variables we evaluated the improvement in the goodness of the fit by dropping the main effect of that predictor. The factors Subject and Item were included in the model as random effects. The effect of random slopes, i.e. variable effects of predictor among participants, was tested for non-ordered categorical predictors. Interactions of those factors for which we did not have a priori hypotheses (e.g. Order Group; questions scores) were not tested. Also, interactions including three or more factors were not systematically tested, except when we had a priori hypotheses. We first included in the model those variables having a strong influence on interval bisection task performance, i.e., Interval Length, Magnitude, and Number Order (e.g., Longo & Lourenco, 2007; Rotondaro et al., 2015). Subsequently, experimental variables were added for which we had predictions: Dot Direction, Starting Position, Verbal Span Group, and Visuospatial Span Group. Last, those variables were included for which no a priori predictions existed: Order Group and questions scores. Note that none of the models considered for comparison had convergence failures resulting in warning messages (with the default settings for the lmer functions). Once the best final model was selected, the relevance of the observed fixed effects was verified by gradually removing from the model a single term (main effect or interaction) at a time, fitting again the relative reduced model, and tested it against the final model (backward selection procedure). Specifically, the Verbal and Visuospatial Span Group were included as ordered factors. Numerical Magnitude was also considered as ordered factor (levels: small, medium, large). The forward selection procedure resulted overall in the comparison of 77 models. The final model had random intercepts, thus allowing for different mean deviations for each participant and item, and a random slope, allowing for variability in the effect of Number Order among participants. Fixed effects of the final model are here below reported, as well as their statistical results from the backward selection procedure, and planned comparisons.

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- Main effect of Verbal Span Group: excluding this factor gave convergence failures. Local comparisons indicated that the low verbal span group (M=-3.84, SEM=0.46) underestimated more than the average (M=-2.05, SEM=0.25; t(65)=-3.39, p<0.001), or the high group (M=-1.83,SEM=0.24; t(60)=-3.87, p<0.001), while no difference was observed between the average and the high span groups (p<0.5). - Interaction between Verbal Span Group and Magnitude: excluding this interaction induced to a significant worsening of the model fit (Df=6; Chisq=18.46; p<0.01). Separate repeated measures ANOVA for each group with Magnitude as within subject factor revealed that the Magnitude effect was present in all groups (all p<0.001). As can be observed in Figure 2a, the magnitude effect was steeper for the low span group. - Interaction between Verbal Span Groups and Dot Direction: excluding this interaction induced a significant worsening of the model fit (Df=3; Chisq=10.46; p<0.02). As can be seen in Figure 2b, only the low verbal span group was influenced by the direction of the moving dot, underestimating more while following the leftward than the rightward dot (leftward: M=-4.20, SEM=0.47; rightward: M=3.48, SEM=0.49; t(32)=-2.45; p<0.05). There was no difference between leftward and rightward conditions for the average (leftward: M=-2.01, SEM=0.30; rightward: M=-2.10, SEM=0.24; p<0.6) and the high (leftward: M=-1.77, SEM=0.27; rightward: M=-1.90, SEM=0.27; p>0.5) span groups.

Figure 2. Illustration of the effects of interaction between verbal span and numerical magnitude (panel a, on the left), and verbal span and numbers order (panel b, on the right) in number interval bisection. Error bars represent SEM.

- Interaction between Interval Length and Magnitude: excluding this interaction induced a significant worsening of the model fit (Df=2; Chisq=22.10; p<0.001). One-way ANOVA with Interval Length as between-subject variable for each Magnitude level revealed that the interval effect was present for medium magnitudes (F(1,95)=21.46,p<0.001) and for large magnitudes (F(1,95)=26.22,p<0.001), but not for small ones (p>0.1; Figure 3a). - Interaction between Interval Length and Number Order: excluding this interaction induced a significant worsening of the model fit (Df=1; Chisq=48.91; p<0.001). As shown in Figure 3b, in the decreasing condition the underestimation bias was larger for short than for long intervals, while this pattern was somehow opposite in the increasing condition. To further investigate this effect, for each participant we computed the linear regression on the mean deviation with interval length as predictor, and then we compared the group slopes against 0: in this way a significant positive slope

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indicates that the underestimation decreased as a function of increasing interval length, and a significant negative slope indicates that the underestimation increased as a function of increasing interval length. We found that in the decreasing order condition underestimation increased at increasing numerical interval (mean slope = -0.08; SEM=0.01, t(95)=-6.34, p<0.001), while underestimation did not vary as a function of interval length in the increasing order condition (mean slope = 0.01; SEM=0.01, p>0.4).

Figure 3. Illustration of the effects of interaction between interval length and numerical magnitude (panel a, on the left), and interval length and numbers order (panel b, on the right) in number interval bisection. Error bars represent SEM.

Note that the interaction between Interval Length, Magnitude, and Number Order did not improve the model (p>0.05).

The underestimation bias and the effect of executive functions A subgroup of participants also performed the fluency tasks (N=57). Starting from the best model found from the previously described mixed models analysis, we tested the effects of Verbal Fluency Group and Visuospatial Fluency Group on this subgroup of participants, following the same forward selection model procedure. All the fixed effects of the final model replicated the earlier findings (all p<0.05), except for the interaction between Interval Length and Number Order which appeared to be modulated by Verbal Fluency Group: excluding this interaction between Verbal Fluency, Interval Length and Number Order induced a significant worsening of the model fit (Df=2; Chisq=42.22; p<0.001). Note that excluding Verbal Fluency Group only from this interaction, also induced a significant worsening of the model fit (Df=1; Chisq=4.93; p<0.05). As can be seen in Figure 4, this interaction revealed that the effect of numbers order (larger underestimation in the decreasing order condition) was larger in the group with high verbal fluency (Figure 4b) than in the group with low verbal fluency (Figure 4a), and this was particularly true at shorter interval lengths. Indeed, when subtracting the deviation for decreasing trials from the one for increasing trials, this difference was larger in the high verbal span group than in the low one at shorter interval lengths (16 and 26; t(112)=-2.98,p<0.005) as well as at longer interval lengths (36 and 46; t(112)=-2.21,p<0.05).

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Figure 4. Illustration of the effects of interaction between interval length and number order in number interval bisection, in participants with lower verbal fluency (panel a, on the left), and in participants with higher verbal fluency (panel b, on the right). Error bars represent SEM.

General discussion In this study we aimed to explore the relation between visuospatial attention on the one hand, and individual differences in working memory and executive functions on the other hand. To do so we used the interval bisection task, a task which has previously been used to investigate the contribution of visuospatial attention in number processing in both healthy and in brain-damaged populations (e.g., Longo & Lourenco, 2007; Zorzi et al., 2002). Visuospatial attention was manipulated during number interval bisection: participants tracked a dot moving to the left or moving to the right while bisecting numerical intervals. We also collected information concerning verbal and visuospatial shortterm memory span, and verbal or visuospatial fluency scores. First, we replicated what is typically observed in this task (underestimation bias, and its sensitivity to numerical magnitude, number order and interval length). Second, we found a relation between bisection performance, verbal short-term memory, and visuospatial attention. Third and finally, we also found a relation between executive functions and number order. We will now discuss in detail each of these findings. First, the results were in line with previous findings (e.g., Longo & Lourenco, 2007) as participants overall underestimated the mid-number. Moreover, we observed an effect of order of presentation of numbers, again replicating previous findings: participants’ underestimation bias was larger when numbers were presented in decreasing rather than in increasing order (e.g., Longo & Lourenco, 2007), and this effect was modulated by the interval length: underestimation increased at increasing interval length, in the decreasing order condition only. We also found effects of magnitude interacting with interval length: underestimation increased at increasing interval length, except for smaller magnitudes. These effects are similar to those reported in previous studies (e.g., Cattaneo et al., 2011a; Longo & Lourenco, 2007). By replicating these findings we are confident of the reliability of our paradigm. The second main finding of this study was that the underestimation bias was correlated with verbal short-term memory. Overall, underestimation decreased as a function of increasing verbal shortterm memory span. Furthermore, when dividing participants into different groups with respect to their verbal span, only those participants with low verbal spans were influenced by the concurrent eye pursuit task. Specifically, they underestimated more when the dot moved leftward than when it moved rightward. This finding can be related to the very large literature indicating associations between leftward space and small numbers and rightward space and large numbers (e.g., Hubbard et al., 2005): indeed, the larger underestimation means that smaller mid-numbers were given as

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response when the dot moved leftward than when it moved rightward. This finding is also in line with studies investigating the role of visuospatial attention in the emergence of number-space interactions and indicating that directing attention in space can affect number processing (e.g., Cattaneo et al., 2011b; Ranzini et al., 2015; Ranzini et al., 2016; Stoianov et al., 2008). Some studies already reported in healthy adults that the underestimation bias in number interval bisection was modulated by the manipulation of visuospatial attention, such as after prismatic adaptation (Loftus, Nicholls, Mattingley, & Bradshaw, 2008), peripheral spatial cueing (Nicholls & Mcllroy, 2010), or finger tapping (Cattaneo et al., 2011b). However, the paradigms adopted in those studies involved either visual numerical stimuli (Loftus et al., 2008; Nicholls, and Mcllroy, 2010), or hand movements in the absence of vision (Cattaneo et al., 2011b): such manipulations are quite different from the common paradigm used with neglect patients where stimuli are verbally presented, vision is not prevented, and no hand movement is required (e.g., Zorzi et al., 2002). To optimize the generalization of results between healthy and clinical populations, in this study hand movements were not required and numbers were verbally presented. The eye pursuit task influenced the performance to number interval bisection of those participants with low verbal spans. Based on the main existing literature on number-space interactions, we could have predicted that visuospatial abilities may preferentially be related to number interval bisection (e.g., Bachmann et al., 2010). On the contrary, the present finding suggests that under specific task circumstances – for instance, when the numerical task involves verbal material - number-space interactions might depend on verbal mechanisms (Rotondaro et al., 2015), and specifically on verbal short-term memory (Herrera et al., 2008; van Dijck et al., 2011). In fact, the involvement of verbal short-term memory in the underestimation bias and its interaction with attentional shifts might not be surprising results. While the role of verbal cognition on number processing and the specific numerical impairments following damage at language-related brain areas are well known (Dehaene & Cohen, 1995; for evidence of language-related mechanisms on a visual variant of the number interval bisection see: Nuerk, Geppert, van Herten, & Willmes, 2002), the contribution of verbal mechanisms in the manifestations of number-space interactions is still object of debate (e.g., Gevers et al., 2010). Recent accounts on the spatial representation of numbers have proposed that the nature of number-space interactions is related to the ordered organisation of numbers (e.g., Previtali, de Hevia, & Girelli, 2010). For instance, recent studies have shown that ordered numerical sequences in verbal working memory induce spatial biases in healthy participants (e.g., van Dijck, Abrahamse, Majerus, & Fias, 2013b; Antoine, Ranzini, van Dijck, Gebuis, & Gevers, in press). Furthermore, sequences in verbal working memory induce difficulties in processing order information in right-brain damaged patients suffering from neglect (Antoine et al., under review). In line with this evidence, the verbal short-term memory involvement in number interval bisection as shown here establishes a bridge between verbal working memory and visuospatial attentional mechanisms, reducing the traditional gap between verbal and visuospatial domains. The third finding of this study is also in line with the idea that verbal abilities play a role in the emergence of number-related biases. Indeed, we found that the order effect (larger underestimation for the decreasing than for the increasing order of presentation of numbers) was modulated by individual differences in verbal fluency. Specifically, the participants with the higher scores in verbal fluency were those who were affected most by the order of presentation of numbers, underestimating more in the decreasing than in the increasing order condition. This effect appeared larger at shorter interval lengths, but it was fould also at longer interval lengths. This result might seem opposite to the finding on short-term memory, if we assume that “more” is “better”, and so a better performance at a cognitive task (in this case: short-term memory and fluency tasks) should predict a better performance in another related task (in this case: number interval bisection). Here

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we observed that a higher short-term memory span predicted a better performance in number interval bisection, while a higher verbal fluency score was associated to a larger bias. To reconcile these findings, we propose to put a different perspective to them, and to reason in terms of interplay between cognitive mechanisms that modulate performance, rather than reasoning in terms of abilities that can predict performance. In this sense, the present findings on the role of both verbal short-term memory and verbal fluency during number interval bisection converge in indicating that verbal abilities may contribute in the generation of number-related biases, these biases being potentially informative on the nature of the underlying numerical representation. Concerning the nature of the order effect, it was suggested that this effect could reflect the cost paid to mentally rotate numbers when presented in decreasing order, in order to put smaller numbers on the left and larger numbers on the right side of the mental number line (e.g., Longo and Lourenco, 2007). However, the results of the present study could not find clear-cut evidence for this hypothesis, since we find that the order effect was not modulated by dot direction, and not modulated by visuospatial abilities (short-term memory or fluency) either. An alternative interpretation that might account for the results shown here suggests that the order effect originates from the fact that attention is located to the last listened number when the participant starts to solve the task. This focus of attention might bias the estimation of the mid-number: underestimation might be larger(smaller) in the decreasing(increasing) order condition because the subjective mid-number is closer to the last listened number, which is the smallest(largest) within the pair. Some authors (e.g., Cattaneo et al., 2011) referred to this hypothesis - that the focus of attention to the last number might cause the order effect - as an instance of the recency effect. The recency effect consists in the typical facilitation in remembering the last items in a sequence (e.g., Deese & Kaufman, 1957). Indeed, since the recency effect reflects attentional processes (Cowan, 1995; Oberauer, 2002), it may be possible that underlying mechanisms are shared between the order effect as observed in number interval bisection and the recency effect as typically found in memory tasks. Interestingly, the recency hypothesis might also account for the finding of a higher sensitivity to order in those participants presenting a better verbal fluency profile. Indirect evidence arose from a recent study by Consonni et al. (2015) showing that in a group of healthy older adults phonological fluency was correlated with the recency effect as observed in a standard memory task with verbal material (word list recall task). Specifically, a higher fluency score was associated with a better performance for the recall of last items in the sequence. This finding indicates common underlining processes between the recency effect on memory tasks and verbal fluency. Even though these issues should be investigated in future studies, these common processes between recency and fluency might be responsible for the order effect in number interval bisection. The lack of overall effect of dot direction diverges from previous findings showing effects of attentional orienting on number processing (e.g., Stoianov et al., 2008; Ranzini et al., 2015; Ranzini et al., 2016). However, previous studies used different numerical tasks, such as number comparison and parity judgments. A number of recent studies indicates that the way numbers are represented spatially depends on task requirements (van Dijck et al., 2012), and that numerical tasks might differ in their sensitivity to orient visuospatial attention (e.g., Zorzi, Bonato et al, 2012; Ranzini et al., 2014). In line with this, previous studies (Herrera et al., 2008; van Dijck et al., 2009) have investigated the effects of verbal or visuospatial working memory load in numerical tasks and found that verbal working memory load abolished number-space interactions in a verbal-related task (parity judgment), while visuospatial working memory load abolished number-space interactions in a visuospatial-related task (magnitude comparison). Even though our study was not set up to investigate the effects of working memory load in number processing, it should be acknowledged that the low verbal span group rated the number interval bisection task as less difficult (M=5.30)

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compared to the rest of participants (M=6.63; t(94)=-2.314, p<0.05), while there was no difference between the average (M=6.47) and the high (M=5.97) span groups (p>0.2). To interpret this finding in light of the results from the above mentioned studies (Herrera et al., 2008; van Dijck et al., 2009), we might speculate that participants with low verbal span adopted visuospatial strategies, resulting in an effect of the visuospatial attentional manipulation and to a reduced feeling of difficulty, while participants with a higher verbal span might have adopted preferentially verbal strategies, resulting in an absence of effect for the attentional manipulation and to an increased feeling of task difficulty. However, this interpretation remains speculative given that load was not manipulated in this study, and information regarding participants’ strategies in the number interval bisection task was not collected. Also, previous studies showing effects of attentional orienting on number processing typically used one-digit numbers. It is possible that digits, more than multi-digit numbers, are preferentially manipulated through spatial strategies involving visuospatial attention (see also Zamarian, Egger, & Delazer, 2007). In line with this view, it is also possible that the extent of visuospatial involvement might differ between brain-damaged patients and healthy adults because of differences in the numerical set of stimuli: indeed, the typical number interval bisection task used with patients (Zorzi et al., 2002) includes smaller number pairs (within 0-30) and shorter number intervals (interval lengths of 3,5,7, or 9 units), , stimuli which are more indicated to detect pathological performance following brain damage. The fact that in this study number pairs were auditory presented might also have facilitated the use of verbal more than visuospatial strategies (see also Rotondaro et al., 2015) – however this could not solely explain the null main effect of attentional manipulation since previous studies have already shown the role of attentional orienting during number processing with verbal material (e.g., Ranzini et al., 2016; Zorzi et al., 2002). Ultimately, previous neuropsychological studies do not have systematically assessed the contribution of verbal abilities in performance at the number interval bisection, since they were mainly interested in investigating visuospatial aspects of number processing. We suggest that considering the role of verbal abilities in number interval bisection might contribute to the understanding of the heterogeneous performance in the number interval bisection of right-brain damaged patients. Rightbrain damaged patients are likely to show a variety of cognitive impairments (Bartolomeo, 2014), including typical visuospatial attentional disorders (neglect), but also non-spatially lateralised deficits (Husain & Rorden, 2003), as well as impairment in specific verbal memory tasks (Welte, 1993; Gillespie, Bowen, Foster, 2007; see also Antoine et al., under review) and non-aphasic language disorders related to frontal lobes injury (McDonald, 1993). In neglect patients the concurrent deficits might not be characteristic of neglect: however, it is possible that they interact with neglect symptoms (Parton, Malhotra, & Husain, 2004). Although the verbal-related impairment following right-brain damage is however subtle and variable (McDonald, 2000), it might be possible that unexplored deficits related to the verbal domain contribute to variability in performance at number interval bisection, by interacting with attentional deficits. This idea might also hold for patients without apparent neglect and biases at number interval bisection if we consider that subclinical attentional deficits might go undetected at standard neuropsychological screening (Bonato et al., 2013). In this regard, a multiple-case study approach might be complementary to groups studies (see also Bonato, Sella, Berteletti, & Umiltà,2012) to unveil links between different aspects of number processing and visuospatial attentional mechanisms, and how these links are modulated by abilities related to the verbal domain. To conclude, this study provide evidence for the multi-componential nature of the numerical representation, by pointing out the interplay between attention, short-term memory and executive

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functions in number interval bisection. We suggest that investigating the verbal mediation to the pathological performance of right brain-damaged patients in the number interval bisection might lead to reconcile the diverging accounts which have been proposed, and might contribute to explain discrepant findings from neuropsychological studies.

Acknowledgements This study was supported by the Belgian Fonds National de la Recherche Scientifique (F.R.S.-FNRS, F.4512.12). We thank an anonymous reviewer for suggesting us to perform mixed-effects models. MR is grateful to Matteo Lisi (Université de Paris Descartes), Michaël Vande Velde (Université Libre de Bruxelles), and Alain Content (Université Libre de Bruxelles), for occasional insightful discussions on linear mixed-effects models.

References 1. Aiello, M., Jacquin-Courtois, S., Merola, S., Ottaviani, T., Tomaiuolo, F., Bueti, D., Rossetti, Y., & Doricchi, F. (2012). No inherent left and right side in human ‘mental number line’: evidence from right brain damage. Brain, 135(8), 2492-2505. 2. Aiello, M., Merola, S., Doricchi, F., (2013). Small numbers in the right brain: evidence from patients without and with spatial neglect. Cortex 49 (1), 348–351. 3. Antoine, S., Ranzini, M., van Dijck, J., Gebuis, T., & Gevers, W. (in press). Order information in verbal working memory shifts the subjective midpoint in both the line bisection and the landmark tasks. The Quartery Journal of Experimental Psychology. 4. Antoine, S., Ranzini, M., van Dijck, J., Slama, H., Bonato, M., Dewulf, M., Bier, J.-C., & Gevers, W. (under review). Hemispatial neglect and serial order in verbal working memory. Journal of Cognitive Neuroscience. 5. Bachmann, V., Fischer, M.H., Landolt, H.-P., Brugger, P. (2010). Asymmetric prefrontal cortex functions predict asymmetries in number space. Brain and Cognition, 74, 306-311. 6. Baldo, J. V., Shimamura, A. P., Delis, D. C., Kramer, J., & Kaplan, E. (2001). Verbal and design fluency in patients with frontal lobe lesions. Journal of the International Neuropsychological Society, 7(5), 586–596. 7. Bartolomeo, P. (2014). Attention disorders after right brain damage. Springer, New York. 8. Bates, D., Maechler, M., Bolker, B., & Walker, S. (2015). Fitting Linear Mixed-Effects Models Using lme4. Journal of Statistical Software, 67(1), 1-48. 9. Bonato, M., Priftis, K., Umiltà, C., & Zorzi, M. (2013). Computer-based attention-demanding testing unveils severe neglect in apparently intact patients. Behavioural Neurology, 26(3), 179-181. 10. Bonato, M., Sella, F., Berteletti, I., Umiltà, C. (2012). Neuropsychology is nothing without control: A potential fallacy hidden in clinical studies. Cortex, 48, 353-355. 11. Cappelletti, M., Freeman, E. D., & Cipolotti, L. (2007). The middle house or the middle floor: Bisecting horizontal and vertical number lines in neglect. Neuropsychologia, 45, 2989-3000. 12. Casarotti, M., Lisi, M., Umiltà, C., & Zorzi, M. (2012). Paying attention through eye movements: A computational investigation of the premotor theory of spatial attention. Journal of Cognitive Neuroscience, 24, 1519-–1531. 13. Cattaneo, Z., Fantino, M., Silvanto, J., Tinti, C., Vecchi, T. (2011a). Blind individuals show pseudoneglect in bisecting numerical intervals. Attention, Perception and Psychophysics, 73, 1021-1028.

17

14. Cattaneo, Z., Fantino, M., Silvanto, J., Vallar, G., & Vecchi, T. (2011b). Tapping effects on numerical bisection. Experimental Brain Research, 208, 21–28. 15. Consonni, M., Rossi, S., Cerami, C., Marcone, A., Iannaccone, S., Francesco Cappa, S., & Perani, D. (2015). Executive dysfunction affects word list recall performance: Evidence from amyotrophic lateral sclerosis and other neurodegenerative diseases. Journal of neuropsychology. 16. de Hevia, M.D., Vallar, G., & Girelli, L. (2008). Visualizing numbers in the mind’s eye: The role of visuo-spatial processing in numerical abilities. Neuroscience & Biobehavioral Reviews, 32, 1361-1372. 17. Dehaene, S. (2003). The neural basis of the Weber–Fechner law: a logarithmic mental number line. Trends in cognitive sciences, 7(4), 145-147. 18. Dehaene, S., & Cohen, L. (1995). Towards an anatomical and functional model of number processing. Mathematical cognition, 1(1), 83-120. 19. Dehaene, S., Bossini, S., & Giraux, P. (1993). The mental representation of parity and number magnitude. Journal of Experimental Psychology: General, 122, 371-396. 20. Dehaene, S., Dupoux, E., & Mehler, J. (1990). Is numerical comparison digital? Analogical and symbolic effects in two-digit number comparison. Journal of Experimental Psychology: Human Perception and Performance, 16, 626-641. 21. Doricchi, F., Guariglia, P., Gasparini, M., Tomaiuolo, F., (2005). Dissociation between physical and mental number line bisection in right hemisphere brain damage. Nat. Neurosci. 8 (12), 1663–1665. 22. Doricchi, F., Merola, S., Aiello, M., Guariglia, P., Bruschini, M., Gevers, W., Tomaiuolo, F., (2009). Spatial orienting biases in the decimal numeral system. Curr. Biol. 19 (8), 682–687. 23. Fias, W., & Fischer, M. H. (2005). Spatial representation of numbers. In J. Campbell (Ed.), Handbook of mathematical cognition (pp. 43–54). London: Routledge. 24. Fias, W., van Dijck, J. P., & Gevers, W. (2011). How is Number associated with space? The role of short-term memory. In S. Dehaene, & E. Brannon (Eds.), Space, time and number in the brain : Searching for the foundations of mathematical thought (pp. 133-148). Amsterdam, Netherlands : Elsevier 25. Gevers, W., Santens, S., Dhooge, E., Chen, Q., Fias, W., and Verguts, T. (2010). Verbal-spatial and visuospatial coding of number-space interactions. J. Exp. Psychol. Gen. 139, 180–190. 26. Gillespie, D. C., Bowen, A., & Foster, J. K. (2006). Memory impairment following right hemisphere stroke: a comparative meta-analytic and narrative review. The Clinical Neuropsychologist, 20(1), 59-75. 27. Ginsburg, V., van Dijck, J. P., Previtali, P., Fias, W., & Gevers., W. (2014). The impact of verbal short-term memory on number–space associations. Journal of Experimental Psychology: Learning, Memory, and Cognition, 40, 976-986. 28. Goebel, S.M., Calabria, M., Farnè, A., Rossetti, Y. (2006). Parietal rTMS distorts the mental number line: Simulating ‘spatial’ neglect in healthy subjects. Neuropsychologia, 44, 860-868. 29. Goebel, S.M., Shaki, S., & Fischer, M.H. (2011). The cultural number line: A review of cultural and linguistic influences on the development of number processing. Journal of Cross-Cultural Psychology, 42, 543-565. 30. Halligan, P.W., Fink, G.R., Marshall, J.C., & Vallar, G. (2003). Spatial cognition: evidence from visual neglect. Trends in Cognitive Sciences, 7, 125-133. 31. Hartmann, M. (2015). Numbers in the eye of the beholder: What do eye movements reveal about numerical cognition? Cognitive Processing, 1, 245–248. 32. Herrera, A., Macizo, P., & Semenza, C. (2008). The role of short-term memory in the association between number magnitude and space. Acta Psychologica, 128, 225–237 33. Hubbard, E.M., Piazza, M., Pinel, P., & Dehaene, S. (2005). Interactions between number and space in parietal cortex. Nature Reviews Neuroscience, 6, 435-448. 34. Husain, M., & Rorden, C. (2003). Non-spatially lateralized mechanisms in hemispatial neglect. Nature Reviews Neuroscience, 4(1), 26-36. 18

35. Jewell, G., & McCourt, M. E. (2000). Pseudoneglect: A review and meta-analysis of performance factors in line bisection tasks. Neuropsychologia, 38, 93-110. 36. Kramer, P., Stoianov, I., Umiltà, C., & Zorzi, M. (2011). Interactions between perceptual and numerical space. Psychonomic Bulletin Review, 18, 722-728. 37. Loetscher T, Brugger P. (2007) Exploring number space by random digit generation. Experimental Brain Research, 180, 655-665. 38. Loetscher, T., Bockisch, C. J., & Brugger, P. (2008). Looking for the answer: The mind’s eye in number space. Neuroscience, 151, 725–729. 39. Loetscher, T., Nicholls, M.E.R., Towse, J.N., Bradshaw, J.L., & Brugger, P. (2010). Lucky numbers: spatial neglect affects physical, but not representational, choices in a Lotto task. Cortex, 46, 685-90. 40. Loftus, A. M., Nicholls, M. E. R., Mattingley, J. B., & Bradshaw, J. L. (2008). Left to right: Representational biases for numbers and the effect of visuomotor adaptation. Cognition, 107, 1048-1058. 41. Loftus, A.M., Nicholls, M.E.R., Mattingley, J.B., Chapman, H.L., & Bradshaw, J.L. (2009). Pseudoneglect for the bisection of mental number lines. The Quarterly Journal of Experimental Psychology, 62, 925-945. 42. Longo, M.R., & Lourenco, S.F. (2007). Spatial attention and the mental number line: Evidence for characteristic biases and compression. Neuropsychologia, 45, 1400-1407. 43. Marshall, J. C., & Halligan, P. W. (1989). When right goes left: an investigation of line bisection in a case of visual neglect. Cortex, 25(3), 503-515. 44. McDonald, S. (1993). Viewing the brain sideways? Frontal versus right hemisphere explanations of non-aphasic language disorders. Aphasiology, 7(6), 535-549. 45. McDonald, S. (2000). Exploring the cognitive basis of right-hemisphere pragmatic language disorders. Brain and Language, 75(1), 82-107. 46. Mondini, S., Mapelli, D., Vestri A. & Bisiacchi PS. (2003). Esame neuropsicologico breve: una batteria di test per lo screening neuropsicologico. Milano: Raffaello Cortina Editore. 47. Nicholls, M.E.R., & Mcllroy, A.M. (2010). Spatial cues affect mental number line bisections. Experimental Psychology, 57, 315-319. 48. Nuerk, H. C., Geppert, B. E., van Herten, M., & Willmes, K. (2002). On the impact of different number representations in the number bisection task. Cortex, 38(5), 691-715. 49. Oliveri, M., Rausei, V., Koch, G., Torriero, S., Turriziani, P., Caltagirone, C. (2004). Overestimation of numerical distances in the left side of space. Neurology, 63, 2139-2141. 50. Parton, A., Malhotra, P., & Husain, M. (2004). Hemispatial neglect. Journal of Neurology, Neurosurgery & Psychiatry, 75(1), 13-21. 51. Pia, L., Neppi-Mòdona, M., Cremasco, L., Gindri, P., Dal Monte, O., Folegatti, A., 2012. Functional independence between numerical and visual space: evidence from right braindamaged patients. Cortex 48 (10), 1351–1358. 52. Pinheiro, J. C., & Bates, D. M. (2000). Linear mixed-effects models: basic concepts and examples. Mixed-effects models in S and S-Plus, 3-56. 53. Previtali, P., de Hevia, M. D., & Girelli, L. (2010). Placing order in space: the SNARC effect in serial learning. Experimental Brain Research, 201(3), 599-605. 54. Prifts, K., Pitteri, M., Meneghello, F., Umiltà, C., & Zorzi, M. (2012). Optokinetic stimulation modulates neglect for the number space: evidence from mental number interval bisection. Frontiers in Human Neuroscience, 6, 23. 55. R Core Team (2015). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/. 56. R Core Team (2016). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/. 57. Ranzini, M., Lisi, M., & Zorzi, M. (2016). Voluntary eye movements direct attention on the mental number space. Psychological research, 1-10.

19

58. Ranzini, M., Lisi, M., Blini, E., Pitteri, M., Treccani, B., Priftis, K., & Zorzi, M. (2015). Larger, smaller, odd or even? Task-specific effects of optokinetic stimulation on the mental number space. Journal of Cognitive Psychology, 27, 459-470. 59. Restle, F. (1970). Speed of adding and comparing numbers. Journal of Experimental Psychology, 83, 274-278. 60. Rizzolatti, G., Riggio, L., Dascola, I., & Umiltà, C. (1987). Reorienting attention across the horizontal and vertical meridians: Evidence in favor of a premotor theory of attention. Neuropsychologia, 25(1), 31–40. 61. Rossetti, Y., Jacquin-Courtois, S., Aiello, M., Ishihara, M., Brozzoli, C., Doricchi, F., 2011. Neglect “around the clock”: dissociating number and spatial neglect in right brain damage. In: Dehaene, S., Brannon, E.M. (Eds.), Space, Time and Number in the Brain: Searching for the Foundations of Mathematical Thought. Elsevier, Amsterdam, pp. 149–173. 62. Rossetti, Y., Jacquin-Courtois, S., Rode, G., Ota, H., Michel, C., & Boisson, D. (2004). Does action make the link between number and space representation? Visuo-manual adaptation improves number bisection in unilateral neglect. Psychological Science, 15, 426-430. 63. Rotondaro, F., Merola, S., Aiello, M., Pinto, M., Doricchi, F. (2015). Dissociation between line bisection and mental-number-line bisection in healthy adults. Neuropsychologia, 75, 565576. 64. Stoianov, I., Kramer, P., Umiltà, C., & Zorzi, M. (2008). Visuospatial priming of the mental number line. Cognition, 106, 770-779. 65. Storer, L., Demeyere, N. (2014). Disruptions to number bisection after brain injury: neglecting parts of the Mental Number Line or short-term memory impairments? Brain Cogn. 86, 116– 123. 66. Umiltà, C., Priftis, K., & Zorzi, M. (2009). The spatial representation of numbers: evidence from neglect and pseudoneglect. Experimental Brain Research, 192, 561-569. 67. van Dijck J.-P., Abrahamse E. L., Acar F., Ketels B., Fias W. (2014). A short-term memory account of the interaction between numbers and spatial attention. Q. J. Exp. Psychol. (Hove) 67, 1500-1513. 68. van Dijck, J. P., Abrahamse, E. L., Majerus, S., & Fias, W. (2013b). Spatial attention interacts with serial-order retrieval from verbal working memory. Psychological Science, 24(9), 18541859. 69. van Dijck, J. P., Gevers, W., Lafosse, C., Doricchi, F., & Fias, W. (2011). Non-spatial neglect for the mental number line. Neuropsychologia, 49(9), 2570-2583. 70. van Dijck, J.-P., & Fias, W. (2011). A short-term memory account for spatial numerical associations. Cognition, 119, 114-119. 71. van Dijck, J.-P., Gevers, W., & Fias, W. (2009). Numbers are associated with different types of spatial information depending on the task. Cognition, 113(2), 248–253. 72. van Dijck, J.-P., Gevers, W., Lafosse, C., & Fias, W. (2012). The heterogeneous nature of number-space interactions. Front Hum Neurosci. 5:182. 73. van Dijck, J., Ginsburg, V., Girelli L., & Gevers, W. (2013). Linking Numbers to Space: From the Mental Number Line towards a Hybrid Account. In R. Cohen Kadosh & A. Dowker (Eds.), The Oxford Handbook of Numerical Cognition. Oxford, United Kingdom: Oxford University Press. 74. Welte, P. O. (1993). Indices of verbal learning and memory deficits after right hemisphere stroke. Archives of physical medicine and rehabilitation, 74(6), 631-636. 75. Wickham, H. (2009). ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York. 76. Wickham, H. (2016). tidyr: Easily Tidy Data with `spread()` and `gather()` Functions. R package version 0.6.0. https://CRAN.R-project.org/package=tidyr. 77. Wickham, H., & Francois, R. (2016). dplyr: A Grammar of Data Manipulation. R package version 0.5.0. https://CRAN.R-project.org/package=dplyr. 78. Zorzi, M., Priftis, K., & Umiltà, C. (2002). Brain damage: Neglect disrupts the mental number line. Nature, 417, 138-139.

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Appendix A: table containing the pairs of number used as stimuli for the number interval bisection.

Interval Length (units) 16

26

36

46

Small Pair

Medium Pair

Large Pair

Smaller Number

Larger Number

Midnumber

Smaller Number

Larger Number

Midnumber

Smaller Number

Larger Number

Midnumber

26 27 28 29 30 31 32 33 21 22 23 24 25 26 27 28 16 17 18 19 20 21 22 23 11 12 13 14 15 16 17 18

42 43 44 45 46 47 48 49 47 48 49 50 51 52 53 54 52 53 54 55 56 57 58 59 57 58 59 60 61 62 63 64

34 35 36 37 38 39 40 41 34 35 36 37 38 39 40 41 34 35 36 37 38 39 40 41 34 35 36 37 38 39 40 41

43 44 45 46 47 48 49 50 38 39 40 41 42 43 44 45 33 34 35 36 37 38 39 40 28 29 30 31 32 33 34 35

59 60 61 62 63 64 65 66 64 65 66 67 68 69 70 71 69 70 71 72 73 74 75 76 74 75 76 77 78 79 80 81

51 52 53 54 55 56 57 58 51 52 53 54 55 56 57 58 51 52 53 54 55 56 57 58 51 52 53 54 55 56 57 58

61 62 63 64 65 66 67 68 56 57 58 59 60 61 62 63 51 52 53 54 55 56 57 58 46 47 48 49 50 51 52 53

77 78 79 80 81 82 83 84 82 83 84 85 86 87 88 89 87 88 89 90 91 92 93 94 92 93 94 95 96 97 98 99

69 70 71 72 73 74 75 76 69 70 71 72 73 74 75 76 69 70 71 72 73 74 75 76 69 70 71 72 73 74 75 76

Highlights   

Visuospatial attentional orienting was manipulated during number interval bisection The interplay between attention, memory span and fluency was investigated Performance relied on both attention, verbal span and verbal fluency

21



The role of verbal abilities in this task might help to interpret clinical results

22