Adaptation Biases the Parallel Perception of Subitized Numerosities

Adaptation Biases the Parallel Perception of Subitized Numerosities | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Adaptation Biases the Parallel Perception of Subitized Numerosities Wei Liu, Xiaoke Zhao, Ying Liu, Yating Li, Jingguang Li This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4746948/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 29 Oct, 2024 Read the published version in Scientific Reports → Version 1 posted 10 You are reading this latest preprint version Abstract Numerosity adaptation, the phenomenon where prolonged exposure to a stimulus of greater numerosity makes the subsequent stimulus appear less numerous, and conversely, has been confined to moderated numerosities. This study investigated whether the estimation of small numerosities ( 1 – 4 ), which is performed rapidly and accurately due to the mechanism of subitizing, is susceptible to adaptation. After adapting to a 50-dot stimulus, participants were presented with stimuli consisting of 1–5 color sets. In some trials, participants were informed of the target color set before the presentation of the stimulus, while in others, they were instructed afterwards. When estimating dots in the single-color set or superset, no adaptation aftereffect was observed. The coefficient of variation (CV) was below 0.05, indicating the effective function of subitizing. However, when enumerating subsets in parallel, adaptation biased the estimation. The CV in estimating subitized numerosities was comparable to and correlated with that of estimating moderate numerosities, suggesting that subitizing was superseded by numerosity estimation. Greater aftereffects occur in the probe-after conditions, accompanied by higher perceptual uncertainty. The function of numerosity adaptation can be demonstrated within a Bayesian framework, where the prior adaptor is more weighted to optimize the detection of deviation under high uncertainty. Biological sciences/Psychology Biological sciences/Neuroscience/Cognitive neuroscience numerosity adaptation subitizing estimation parallel processing gist perception Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction Numerosity, like most primary sensory systems, is susceptible to adaptation 1 . Numerosity adaptation refers to the phenomenon where the perception of numerosity decreases after adapting to a larger number of stimuli, and conversely, it increases after adapting to a smaller number 1–3 . Numerosity adaptation is independent of the processing of visual inputs, such as size, shape, color, or contrast of stimuli, and it occurs across different stimulus modalities and formats 4–6 . However, it is still debatable whether this adaptation acts via a mechanism dedicated to numerosity, or via low-level texture-like mechanisms, as perceived number cannot be isolated from all confounding magnitudes that are related with number 7–9 . We can appraise the number of up to four items rapidly and errorlessly based on a mechanism dubbed subitizing 10,11 . Naming numbers in the subitizing range involves processes distinct from estimation 12–14 . Whilst being fast and accurate, subitizing is highly dependent on attentional resources 15,16 . Visual attention is efficient for selecting and enumerating the number (7–30 dots) of three sets in parallel: two color subsets and the superset, which is compatible with the three-item limits of object-based attention 17 . However, with very few items ( 1 – 4 ), subitizing only occurs in the single-set and superset conditions, and is absent in multiple-subset conditions, where the participants are required to distribute their attention and simultaneously enumerate more than one subset 13 . In other words, subitizing lacks the capability for processing subsets in parallel. In that case, estimation carries out the enumeration with a reasonable precision 13,14 . Most studies of numerosity adaptation have been confined to the moderate numerosity range. Under normal conditions adaptation has little effect in the low subitizing range 8 . A previous study has suggested that susceptibility to numerosity adaptor stimuli emerges at very low numerosities under conditions of attentional deprivation. When attentional load is induced by a dual-task paradigm, perception of the three-dot reference is biased against the adapted numerosity 12 . Given that an asymmetric presentation of adaptor is employed in this study, the adaptation aftereffect can be partly explained by the intrusion of uncontrolled visuo-spatial attentional processes in subsequent comparison tasks 18 . However, as pointed out by this previous study, it is possible that even at low numerosities, the mechanisms of numerosity and subitizing may operate concurrently. Therefore, numerosity adaptation can potentially affect subitized numerosities, particularly when subitizing is disrupted by attentional load 12 . The current study investigated whether the perception of subitized numerosities ( 1 – 4 ) is susceptible to adaptation when attention is distributed across multiple subsets. The estimation paradigm was employed in order to directly describe the perception of subitized numerosities, without resorting to testing series that might exceed the subitizing range. Participants were presented with stimuli comprising multiple subsets (from 1 to 5) defined by different colors, which changed on every trial. In some trials, participants were instructed about the target color before stimulus presentation, while in other trials, they were instructed after stimulus presentation. Once the target was cued, the participants had to estimate its numerosity. Prior to the testing stage, the adaptor stimulus was presented. The estimation of target number under the adapted condition was compared with that under the non-adapted condition, in order to determine the occurrence of adaptation. The coefficient of variation (CV) of estimation was computed in order to derive the processing precision in each condition. Anticipating the results, we found that adaptation biases the perception of subitized numerosities when participants were required to enumerate more than one subset during the testing stage (i.e., when the target was cued after the presentation of multiple subsets). In this condition, CV of estimating subitized numerosities ( 1 – 4 ) was comparable to and correlated with that of estimating moderate numerosities ( 5 – 12 ), indicating that subitizing is superseded by numerosity estimation under attentional load. Moreover, the aftereffects of adaptation were significantly stronger in the probe-after condition compared to the probe-before condition, both for subitized and moderate numerosities. This suggests that numerosity adaptation is modulated by attention. Greater adaptation aftereffects occur in accompaniment with higher CV, which reflects higher perceptual uncertainty induced by attention allocation. These results demonstrate the function of numerosity adaptation: Rather than being a by-product of neural fatigue resulting from processing low-level degradation of inputs, numerosity adaptation reflects perceptual flexibility. In the case of higher uncertainty, the prior adaptor would be more weighted to optimize the detection of deviation in subsequent numerosity perception. Method Statement of ethical approval For both of the experiments, the data were analyzed anonymously. All participants provided their informed consent according to the Declaration of Helsinki prior to the experiment in both verbal and written forms, and they were compensated for their participation. Yunnan Minzu University’s ethics committee approved this study(No.20230913-01). Sample size and participants Participants aged 17 to 32 years with normal or corrected-to-normal vision and normal color perception were recruited. A total of 30 participants (averagely aged 24 years, 10 males) participated in this study. A total of 720 trials were conducted for each participant. Specifically, 57% of the trials with target number ranges of 1–4, and 36% of the trials with target number ranges of 5–12 were analyzed separately in the subitizing and numerosity groups. Compared with previous studies, sufficient participants were enrolled, and sufficient trials were provided in each condition 13,17 . The remaining 6% of the trials, in which the target was not shown or the subset number exceeded three, were excluded from the analyses. In particular, the trials with four or five subsets were excluded due to their insufficiency for statistical analysis. Stimuli and procedure Participants sat approximately 50 cm from an LCD monitor with a viewable area measuring 41 cm by 26 cm (19”, 1920 × 1080, 60 Hz) in a dimly lit quiet room. Stimuli were generated from Matlab (Mathworks, Natwick, MA). The diameter of each dot is 0.5° visual angle (20 pixel). Dots were presented in a circle at the center of the screen with a diameter of 15° (600 pixel) visual angle. Figure 1 illustrates the procedure for the adapted conditions. The adaptation began with a fixation lasting for 500 ms, followed by a probe lasting for 500 ms, which indicated the target color in the probe-before condition, or indicated ‘Probe After’ in the probe-after condition. Then, an adaptor showed up. It was presented for 30 seconds on the first trial and appeared for 3000 ms at the beginning of each subsequent trial. The participants should keep their eyes on the central adaptor. Next, it proceeded to the testing phase. The paradigm of the testing phase followed that of previous studies 13,17 . At the beginning of each trial, a fixation was displayed for 150–1150 ms. Subsequently, participants were presented with a 200-ms stimulus display containing 1–12 dots of one to five colors. The stimulus was followed by a blank slide lasting for 500 ms. If the first probe screen stated ‘Probe After’, it would be followed by a second probe slide displaying the target color for 500 ms, which succeeded the blank slide. Else if the first probe screen stated the target color, no probe would be presented. The participants were required to enumerate the number of dots in the target, which could be one of the color subsets or the superset, and they entered their answers into the computer following the appearance of the second probe. Dots in stimulus patch were randomly distributed with the constraint that they could not overlap with each other. The number of dots in each color subset was randomly determined, and in half (49.6%) of the trials the target subset was smaller than at least one distracting subset, making the strategy of attending only to the largest subset ineffective. For each participant, an average of 360 trials which combined all conditions in a randomized order were run in 3 blocks. Generally, on 22% of the trials, participants were asked to report the overall number of the dots regardless of the colors (superset trials). The proportion of one-, two-, and three-color subset conditions was 19%, 32%, and 21%, respectively. In each of the subset/superset group, the proportion and target number range of the probe-before and probe-after conditions are approximately equal. In 2% of the trials, there were four or five color subsets. In 4% of the trials, there was no target color represented, and the correct respond is ‘0’. Proportion of each condition is slightly different among participants. The procedure in the adapted condition was similar to the baseline condition except that there was an adaptation stage prior to the testing procedure. Adaptor always comprised 50 orange dots, which was different from the color of testing dots (blue, green, Magenta, red, or yellow). The participants were asked to keep their eyes on the middle fixation during the whole trial. The baseline condition was conducted prior to the adapted condition for each participant. Adequate rest was ensured to avoid fatigue. Data analysis As there were various target numbers, the ratio between the estimation and the target number was adopted to assess the enumeration. The mean estimation ratio was calculated to assess the accuracy of estimation in each condition, and the difference in the ratio between baseline and adaptation conditions was calculated to measure adaptation aftereffects. These aftereffects were compared to ‘0’ using a one-sample t -test (one-tailed) to determine whether the adaptation induced significant underestimation. The coefficient of variation (CV) was calculated as the ratio between the standard deviation (SD) and the mean of enumeration. It provides a dimensionless measure of the noise in the judgments, allowing comparison of performance precision across numerosities, as well as comparison between baseline and adapted (biased) conditions. Pearson correlation coefficient r was calculated for CV between related conditions. One sample t -test is one-tailed to test the hypothesis that the aftereffect is significantly larger than ‘0’, and paired samples t -test is two-tailed to test whether the CV is significantly different between two conditions. Cohen’s d was reported to provide a complement to null hypothesis statistical significance testing by estimating the magnitude of the difference (0.2–0.5 for small effect size, 0.5–0.8 for moderate effect size, and > 0.8 for large effect size). Bayes factors ( BF 10 ) were reported to estimate whether the null hypothesis H 0 or the alternative hypothesis H 1 is more likely to be correct. BF 10 3 indicates clear evidence for H 1 .The False Discovery Rate probability (FDR), or Q value, is adopted in this study to correct probability of type-Ⅰerror in multiple comparisons 19 . For example, with four p values in multiple comparisons, we multiply the smallest p -value by four to get its Q value. Then we multiply the second smallest p by 4/2, the third p by 4/3, and the last p (the largest one) by 4/4 to get their Q values. To determine whether a comparison is statistically significant, Q values are used instead of p values, * Q < 0.05, ** Q < 0.01, *** Q < 0.001. Q = 0.05 is a widely accepted threshold for significance. Results Figure 2a displays the adaptation aftereffects in different conditions. As the adaptation aftereffects are assessed by subtracting the mean estimation ratio between the baseline and adapted conditions, a positive value indicates the presence of adaptation aftereffects, i.e., underestimation induced by the adaptor. For target numbers within subitizing range (1–4, three clusters on the left of Fig. 2a), no underestimation was induced by adaptation when there was only one set, either in the probe-after condition, t (29) = 0.595, p = 0.278, Q = 0.371, Cohen’s d = 0.109, BF 10 = 0.327, or in the probe-before conditions, t (29) = 1.583, p = 0.084, Q = 0.126, Cohen’s d = 0.258, BF 10 = 0.867. Importantly, for target numbers within subitizing range ( 1 – 4 ), significant underestimation was induced by adaptation in the probe-after condition with multiple color subsets (2–3 color groups), t (29) = 2.407, p = 0.011, Q = 0.033, Cohen’s d = 0.439, BF 10 = 4.476. It is suggested that numbers within the subitizing range ( 1 – 4 ) are susceptible to adaptation when attention is distributed across different subsets in the probe-after condition. No aftereffects were observed in the probe-before conditions, t (29) = -0.139, p = 0.655, Q = 0.786, Cohen’s d = -0.073, BF 10 = 0.147. It is worth noting that no adaptation aftereffect was observed when the participants were asked to enumerate the number of superset, either in the probe-after condition, t (29) = -1.193, p = 0.879, Q = 0.879, Cohen’s d = -0.218, BF 10 = 0.097, or in the probe-before condition, t (29) = 0.882, p = 0.807, Q = 0.880, Cohen’s d = 0.161, BF 10 = 0.112. Participants always perceived the dot number in the superset in an unbiased manner, even when the target was probed after the testing stimuli, and when the superset comprised up to five color subsets. Three clusters of bars on the right of Fig. 2a demonstrate the results within the numerosity range ( 5 – 12 ). Adaptation aftereffects are significant in the single-set group, t (29) = 3.274, p = 0.001, Q = 0.006, Cohen’s d = 0.598, BF 10 = 27.314 in the probe-after condition, and t (29) = 2.416, p = 0.011, Q = 0.033, Cohen’s d = 0.441, BF 10 = 4.555 in the probe-before condition. The aftereffects are significant in the superset group, t (29) = 2.259, p = 0.016, Q = 0.033, Cohen’s d = 0.412, BF 10 = 3.399 in the probe-after condition, and t (29) = 2.321, p = 0.014, Q = 0.033, Cohen’s d = 0.424, BF 10 = 3.810 in the probe-before condition. Significant aftereffects were also observed when there were multiple subsets in the display, t (29) = 4.070, p < 0.001, Q = 0.001, Cohen’s d = 0.743, BF 10 = 176.998 in the probe-after condition, and t (29) = 2.927, p = 0.003, Q = 0.012, Cohen’s d = 0.534, BF 10 = 12.776 in the probe-before condition. Notably, when multiple-color subsets were simultaneously presented in the display, the adaptation aftereffect in the probe-after condition is greater than that in the probe-before condition, t (29) = 1.902, p = 0.034, Cohen’s d = 0.374, BF 10 = 1.824. Numerosity adaptation is modulated by attention, and greater aftereffects are revealed in the probe-after conditions, both for subitized and moderated numerosities. To better illuminate the adaptation aftereffects in the multiple-subset conditions, the individual data in the probe-before and probe-after conditions are shown in Fig. 2b. As for targets within the subitizing range (1–4, red dots), underestimation primarily occurs in the probe-after condition, rather than the probe-before condition, for most participants. By contrast, adaptation biases numerosity perception both in the probe-after and probe-before conditions for targets within the numerosity range (5–12, blue dots). Figure 2 . Results of adaptation aftereffects. The adaptation aftereffects are assessed by subtracting the mean estimation ratio between the baseline and adaptation conditions. (a) Three clusters on the left demonstrate the results within the subitizing range ( 1 – 4 ). Significant underestimation is induced by adaptation in the probe-after condition with multiple color subsets. No adaptation aftereffects are observed in other conditions. Three clusters on the right show the results within the numerosity range ( 5 – 12 ). Adaptation aftereffects are significant in each condition. When multiple color subsets were simultaneously presented in the display, the adaptation aftereffect in the probe-after condition is significantly greater than in the probe-before condition, both for the subitizing and numerosity groups. Error bars represent one standard error. (b) Individual adaptation aftereffects in probe-before and probe-after conditions with multiple color subsets. Red dots represent for the aftereffect of subitizing targets, and blue dots represent for numerosity targets. Starts denote the mean of each group. In superset condition, notably, CV is below 0.03, both on probe before and after trials. When the target is probed before the stimuli, the CV in the superset is significantly different from that in the multiple-subset condition, t (29) = 4.649, p < 0.001, Q 100, whereas it is not different from those in single-set condition, t (29) = 0.205, p = 0.839, Q = 0.839, Cohen’s d = 0.037, BF 10 = 0.201. When the target is probed after the stimuli, the CV in the superset is significantly different from that in the multiple-subset condition, t (29) = 14.141, p < 0.001, Q 100, whereas it is not different from those in single-set condition, t (29) = 1.191, p = 0.243, Q = 0.324, Cohen’s d = 0.218, BF 10 = 1.791. Thus, participants can subitize if they are asked to enumerate all dots, irrespective of probe conditions and the colors defining each group. As for the numerosities of 5–12, CV range between 0.14 and 0.27 across conditions. In the face of multiple subsets, CV is significantly larger in the probe-after condition, compared with the probe-before condition, t (29) = 5.961, p 100. In superset condition, however, the probe has little effect on CV, t (29) = 1.104, p = 0.279, Cohen’s d = 0.202, BF 10 = 0.338. Previous studies suggested that we can estimate up to three sets in parallel without a tangible cost: two subsets and superset 13,17 . In this study, we have combined the two- and three-subset conditions to get a stable data for analyses, hence CV is larger in the probe-after multiple-subset condition. Nevertheless, in line with previous studies, our data shows that participants can enumerate superset effectively, irrespective of probe conditions and the colors defining each group. A similar CV pattern was revealed in the adaptation conditions (Fig. 3 b). In the face of multiple subsets, CV is significantly larger in the probe-after condition compared with the probe-before condition, t (29) = 2.259, p = 0.032, Cohen’s d = 0.412, BF 10 = 1.731 for subitized numerosities 1–4, and t (29) = 3.939, p 100 for moderate numerosities 5–12. By contrast, CV for enumerating superset does not increase when the target is probed afterwards. It even decreases in those conditions. When target numbers are within the subitizing range, a significant adaptation aftereffect was observed when there were multiple subsets, and the targets were cued after stimuli (Fig. 2a). In addition, CV of this condition was revealed to be comparable with that in the numerosity group. To check if the results in this condition reflect a genuine result of the numerosity system, we investigated the CV correlation of this condition across other conditions. We first calculated the CV correlation across the probe-after conditions within the subitizing group. No significant CV correlation is found between this multiple-subset condition and the single-set condition (Fig. 4 a), r = 0.330, p = 0.075, Q = 0.100, BF 10 = 1.033, and no significant correlation was found between this multiple-subset condition and the superset condition (Fig. 4 b), either, r = -0.058, p = 0.763, Q = 0.763, BF 10 = 0.237. Then we analyzed the CV correlation across the multiple-color conditions between subitizing and numerosity groups. Significant CV correlation was observed between this subitizing and the numerosity conditions: r = 0.526, p = 0.003, Q = 0.012, BF 10 = 16.041 for the numerosity condition in which the target was cued after the stimuli (Fig. 4 c), and r = 0.416, p = 0.022, Q = 0.044, BF 10 = 2.739 for the condition in which the target was cued before the stimuli (Fig. 4 d). To sum up, in the face of multiple subsets, perception of subitized numerosities should be based on numerosity mechanisms. This point of view is supported by two evidences. First, the perception is susceptible to adaptation. Second, the processing precision is comparable to and significantly correlated with that for moderate numerosities. Discussion Under normal condition, numerosity adaptation is confined to moderate numerosities 1,12,18,20 . Debate exists in whether numerosity adaptation is based on a mechanism dedicated to numerosity or via texture-like mechanisms 7–9,21 . The current study investigated whether the perception of subitized numerosities ( 1 – 4 ) is susceptible to adaptation when attention is distributed across multiple subsets. The result that subitized numerosities are also susceptible to numerosity adaptation contributes in elucidating the mentioned debate, as a mechanism based on extensive measures could hardly operate at such low numerosities. A series of studies have suggested that even at subitized numerosities, the mechanisms of numerosity and subitizing may operate concurrently, and numerosity will take over the job of enumeration when subitizing cannot benefit from attention. In that case, similar processing features can be observed both for subitized and moderate numerosities 12–14 . This study went further to investigate whether adaptation biases the perception of subitized numerosities, as it does with moderate numerosities, when attention is distributed across multiple subsets. According to the current results, although the absence of PSE shift in the single-set condition indicates that the perception of subitized numerosities is resistant to adaptation when subitizing persists under normal condition, it is also clear that adaptation biases this perception when participants have to simultaneously enumerate more than one subset in the testing stage. Our previous study 13 have pointed out that subitizing lacks the capability to process subsets in parallel. With multiple subsets, when the target was probed after the stimuli, participants had to simultaneously enumerate the numerosity of each subset. Errorless subitizing disappeared as it cannot benefit from distributed attention. In the current study, compared to the single-set condition, the CV of estimating subitized numerosities in the multiple-subset condition increases from 3–31%, which is comparable with the CV of estimating moderate numerosities ( 5 – 12 ) in the same condition (27%). In addition, the CV of estimating subitized numerosities in this multiple-subset condition is positively correlated with that of estimating moderate numerosities in the same condition, whereas it is not correlated with the CV in the single-set or superset conditions, despite the identical target number range across these conditions. These results are in line with our previous study, indicating that while subitizing functions effectively in processing single set and superset (mean CV is below 3%), it is superseded by numerosity estimation under the attentional load induced by processing multiple subsets 13 . Furthermore, this study offers novel evidence indicating that adaptation occurs in the multiple-subset group with the probe-after-target paradigm, yet it is absent in the single-set or superset groups, regardless of the probe conditions. In other words, adaptation may occur when numerosity takes over the job of enumerating small numerosities 12 . Subitizing performs well in the superset condition, irrespective of whether the target is cued before or after, suggesting that the processing of superset possesses a certain degree of invulnerability to the availability of attentional resources 13 . Consistent with our previous research, the current results indicate that adaptation cannot bias the perception of subitized numerosities when enumerating “all” numbers. Regardless of the probe conditions, both the precision and the accuracy of the perception remains unaffected. The priority of processing superset has also been illuminated in the moderate group: both the adaptation aftereffects and the CV remain constant irrespective of the probe conditions. These results provide further evidence supporting the idea that the superset is processed by an efficient perceptual subsystem 13,17,22 . According to our previous research, the simple request to segregate the visual scene into two groups can drain resources critical for subitizing. When distinct color subsets are presented simultaneously, subitizing can be lost even when the target is cued before the stimuli 13 . In the current study, the CV (13%) indicates that subitizing is affected in the multiple-subset condition even when the target is probed before the stimuli. Given that the CV is substantially lower than that in the probe-after condition (31%), it is possible that subitizing can occasionally benefit from attention in this condition. When the target subset is notified prior to the presentation of the intermingled display, subitizing may be preserved with higher noise 23 , but it can also be superseded by numerosity when the non-target subsets are perceptually competitive enough to distract attention 13,14 . However, the noisy subitizing hypothesis cannot fully explain the absence of adaptation in this probe-before condition. We propose that attention enhancement may account for this lack of adaptation. Previous study suggests that attention can enhance both the precision and the accuracy of numerosity perception, with a greater improvement in the enumeration of subitized numerosities and a weaker improvement for moderate numerosities 24 . Recent studies further point out that numerosity adaptation is also modulated by attention allocation in testing stages. In the testing stage, items in the cued patch can be overestimated compared to the opposite patch, and adaptation amplifies this cue-dependent numerosity bias 18 (the current study). Numerosity adaptation reflects a mixture of both perceptual and attentional processes 18 , which may facilitate the subsequent perception of numerosity. Adaptation had long been considered a by-product of neuronal activation fatigue. However, a series of studies have suggested that adaptation, especially to high-level attributes, may reflect a dynamic adjustment to improve our sensitivity to changes along the adapted dimension 18,25 . There are models linking adaptation effects to Bayesian prediction, suggesting that prior adaptor may serve as a standard for self-calibration 26,27 . Within a Bayesian framework, the distribution of the current stimuli is combined with that of the adaptor to form the posterior distribution. As the effect of the prior depends on the relative reliability, the adaptor would have a greater effect when the width of the current stimuli distribution is wider, namely, when discrimination of the current stimuli is lower 20,28 . On the assumption that the adaptor serves as a prior of this Bayesian model, greater perceptual bias is predicted when numerosity perception in the testing stage is under higher perceptual uncertainty. In other words, greater adaptation aftereffects are expected when the target is probed following the presentation of multiple subsets, during which higher uncertainty is induced by attention allocation. The current results support this prediction: For targets 5–12, similarly to that for targets 1–4, the adaptation aftereffects in the probe-after condition are significantly greater than that in the probe-before condition. In addition, adaptation bars (Fig. 2a) and CV bars (Fig. 3 , a&b) share a similar pattern, suggesting greater adaptation aftereffects in conditions with higher CV: Greatest adaptation aftereffects are revealed in multiple-after conditions in both number groups, along with the highest CV. Conversely, in the one-set and superset conditions of the subitized group, where the close-to-zero CV indicates high reliability in perceiving subitized target numbers, adaptation barely biases perception during the testing phase. These results well elucidate the function of numerosity adaptation: the repulsive bias caused by adaptation 29 enhances the signal-to-noise representation, which therefore optimizes the detection of deviation along the adapted dimension in the subsequent perception, especially when the perception is under high uncertainty. Declarations Competing interests The authors declare no competing interests. Funding This study was supported by funding from the National Natural Science Foundation of China (Grant No. 32060192; 31500879; 31500884). Author Contribution W. L. developed the study concept and contributed to the study design. Testing and data collection were performed by Y. L. (3rd author) and Y. L. (4th author). The data analysis and interpretation was performed by W. L. The figures were drawn by X. Z. The manuscript was drafted by W. L., and J. L. provided critical revisions. All authors approved the final version of the manuscript for submission. Acknowledgement We express our sincere gratitude to Guido Marco Cicchini for conceiving the concept of this study and for providing substantial suggestions during the experiments. Data Availability The data sets generated and analyzed during the current study are available from the corresponding author on reasonable request. References Burr, D. & Ross, J. A visual sense of number. Current biology 18 , 425-428. https://doi.org/10.1016/j.cub.2008.02.052 (2008). Fornaciai, M., Cicchini, G. & Burr, D. C. Adaptation to number operates on perceived rather than physical numerosity. Cognition 151 , 63-67.https://doi.org/10.1016/j.cognition.2016.03.006(2016). Liu, W., Zhang, Z. & Zhao, Y. Numerosity adaptation effect on the basis of perceived numerosity. Acta Psychologica Sinica 44 , 1297.https://doi.org/10.3724/SP.J.1041.2012.01297 (2012). Arrighi, R., Togoli, I. & Burr, D. C. A generalized sense of number. 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Subitizing endures in sequential rather than simultaneous comparison tasks. PsyCh Journal , 1–12 . .https://doi.org/10.1002/pchj.750(2024). Egeth, H. E., Leonard, C. J. & Palomares, M. The role of attention in subitizing: Is the magical number 1? Visual Cognition 16 , 463-473. https://doi.org/10.1080/13506280801937939 (2008). Pomè, A., Anobile, G., Cicchini, G. M., Scabia, A. & Burr, D. C. Higher attentional costs for numerosity estimation at high densities. Attention, Perception, & Psychophysics 81 , 2604-2611. https://doi.org/10.3758/s13414-019-01831-3(2019). Halberda, J., Sires, S. F. & Feigenson, L. Multiple spatially overlapping sets can be enumerated in parallel. Psychological science 17 , 572-576 .https://doi.org/10.1111/j.1467-9280.2006.01746. (2006). Grasso, P. A., Anobile, G. & Arrighi, R. Numerosity adaptation partly depends on the allocation of implicit numerosity-contingent visuo-spatial attention. Journal of Vision 21 , 12-12.https://doi.org/10.1167/jov.21.1.12 (2021). Benjamini, Y. & Hochberg, Y. Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the Royal statistical society: series B (Methodological) 57 , 289-300.https://doi.org/10.1111/j.2517-6161.1995.tb02031.x (1995). Anobile, G., Cicchini, G. M. & Burr, D. C. Number as a primary perceptual attribute: A review. Perception 45 , 5-31.https://doi.org/10.1177/030100661560259 (2016). Durgin, F. H., Doyle, E. & Egan, L. Upper-left gaze bias reveals competing search strategies in a reverse Stroop task. Acta Psychologica 127 , 428-448.https://doi.org/10.1016/j.actpsy.2007.08.007 (2008). Mack, A. & Rock, I. Inattentional blindness: Perception without attention .(MIT Press, Cambridge1998). Trick, L. M. & Pylyshyn, Z. W. What enumeration studies can show us about spatial attention: evidence for limited capacity preattentive processing. Journal of Experimental Psychology: Human perception and performance 19 , 331.http://dx.doi.org/10.1037//0096-1523.19.2.331 (1993). Pomè, A., Thompson, D., Burr, D. C. & Halberda, J. Location-and object-based attention enhance number estimation. Attention, Perception, & Psychophysics 83 , 7-17.https://doi.org/10.3758/s13414-020-02178-w (2021). Aagten-Murphy, D. & Burr, D. Adaptation to numerosity requires only brief exposures, and is determined by number of events, not exposure duration. Journal of vision 16 , 22-22.https://doi.org:https://doi.org/10.1167/16.10.22 (2016). Stocker, A. A. & Simoncelli, E. Sensory adaptation within a Bayesian framework for perception. Advances in neural information processing systems 18 (2005). Turi, M. et al. Children with autism spectrum disorder show reduced adaptation to number. Proceedings of the National Academy of Sciences 112 , 7868-7872.https://doi.org/10.1073/pnas.1504099112 (2015). Cicchini, G. M., Anobile, G., Burr, D. C., Marchesini, P. & Arrighi, R. The role of non-numerical information in the perception of temporal numerosity. Frontiers in Psychology 14 , 1197064.https://doi.org/10.3389/fpsyg.2023.1197064(2023). Aulet, L. S. & Lourenco, S. F. Visual adaptation reveals multichannel coding for numerosity. Frontiers in Psychology 14 , 1125925.https://doi.org/10.3389/fpsyg.2023.1125925(2023). Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 29 Oct, 2024 Read the published version in Scientific Reports → Version 1 posted Editorial decision: Revision requested 16 Aug, 2024 Reviews received at journal 14 Aug, 2024 Reviews received at journal 05 Aug, 2024 Reviewers agreed at journal 05 Aug, 2024 Reviewers agreed at journal 03 Aug, 2024 Reviewers invited by journal 03 Aug, 2024 Editor assigned by journal 03 Aug, 2024 Editor invited by journal 17 Jul, 2024 Submission checks completed at journal 16 Jul, 2024 First submitted to journal 16 Jul, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4746948","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":336472597,"identity":"a69b140d-a597-4f95-856c-4622fed61d8b","order_by":0,"name":"Wei Liu","email":"","orcid":"","institution":"Yunnan Minzu University","correspondingAuthor":false,"prefix":"","firstName":"Wei","middleName":"","lastName":"Liu","suffix":""},{"id":336472598,"identity":"6fe8341d-b240-4bf6-86e3-f08c05dde8ac","order_by":1,"name":"Xiaoke Zhao","email":"","orcid":"","institution":"Dali University","correspondingAuthor":false,"prefix":"","firstName":"Xiaoke","middleName":"","lastName":"Zhao","suffix":""},{"id":336472599,"identity":"26745718-1db4-4cbd-b950-2ba9f651a000","order_by":2,"name":"Ying Liu","email":"","orcid":"","institution":"Yunnan Minzu University","correspondingAuthor":false,"prefix":"","firstName":"Ying","middleName":"","lastName":"Liu","suffix":""},{"id":336472600,"identity":"1c8cbacc-7b57-485f-aee8-e69e0bda2efc","order_by":3,"name":"Yating Li","email":"","orcid":"","institution":"Yunnan Minzu University","correspondingAuthor":false,"prefix":"","firstName":"Yating","middleName":"","lastName":"Li","suffix":""},{"id":336472601,"identity":"4a263185-8741-4ad4-a8eb-db922f633cf4","order_by":4,"name":"Jingguang Li","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+ElEQVRIiWNgGAWjYBACxmY4k7nhAMMBG5BY4wEitTCCtKRBGURa2MDAcOAwmIlXC3M77+GXX9vs8uQdQO45c95ubfthoC01NtG4HcaXZi3bllxseADknhu3k7edSQQyjqXlNuDUwmNmLNnGnLixAaTlw+1kswNALYwNhwlpqYdpOZdsdv4hQS3GDz+2HU6cDw6oGwfszG4QYQszw7njiRuYgVoSziQnmN0A2pKAxy+G/WeMP/4oq06c3958+MOHY3b2ZufTHz74UGODW0sDA5s0D5BhAIqRBAaGRLDKBBzKQUAeGDUff4AYUEPt8SgeBaNgFIyCEQoAFb9q3+XOcD8AAAAASUVORK5CYII=","orcid":"","institution":"Dali University","correspondingAuthor":true,"prefix":"","firstName":"Jingguang","middleName":"","lastName":"Li","suffix":""}],"badges":[],"createdAt":"2024-07-16 04:25:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4746948/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4746948/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1038/s41598-024-76536-1","type":"published","date":"2024-10-29T16:13:11+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":62653628,"identity":"78a33e5f-9beb-4820-97d1-fb617faa39d1","added_by":"auto","created_at":"2024-08-17 01:16:37","extension":"jpeg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":41594,"visible":true,"origin":"","legend":"\u003cp\u003eSchematic illustration describing the procedure of the adaptation conditions. The adaptation started with a fixation lasting for 500 ms, followed by a probe lasting for 500 ms, and an adaptor lasting for 3000 ms. Then, it proceeded to the testing phase. At the beginning of each trial, a fixation was shown for 150-1150 ms. Then, participants saw a 200-ms stimulus display containing 1-12 dots of one to five colors. The stimulus was followed by a blank slide lasting for 500 ms. If the first probe screen stated ‘Probe After’, there would be a second probe slide stating the target for 500 ms, which followed the blank slide. The participants enumerated the number of the target, which could be one of the color subsets or the superset, typing their answers into the computer after the onset of the second probe.\u003c/p\u003e","description":"","filename":"floatimage1.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4746948/v1/fe9713fc80e12e6c7562a761.jpeg"},{"id":62653627,"identity":"60bab6ca-71ae-4090-9a43-fce0fdfb6f23","added_by":"auto","created_at":"2024-08-17 01:16:37","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":18872,"visible":true,"origin":"","legend":"\u003cp\u003eResults of adaptation aftereffects. The adaptation aftereffects are assessed by subtracting the mean estimation ratio between the baseline and adaptation conditions. (a) Three clusters on the left demonstrate the results within the subitizing range (1-4). Significant underestimation is induced by adaptation in the probe-after condition with multiple color subsets. No adaptation aftereffects are observed in other conditions. Three clusters on the right show the results within the numerosity range (5-12). Adaptation aftereffects are significant in each condition. When multiple color subsets were simultaneously presented in the display, the adaptation aftereffect in the probe-after condition is significantly greater than in the probe-before condition, both for the subitizing and numerosity groups. Error bars represent one standard error. (b) Individual adaptation aftereffects in probe-before and probe-after conditions with multiple color subsets. Red dots represent for the aftereffect of subitizing targets, and blue dots represent for numerosity targets. Starts denote the mean of each group.\u003c/p\u003e","description":"","filename":"Onlinefloatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-4746948/v1/908297a685cfeb8efd6cb11d.png"},{"id":62653630,"identity":"98fea040-b512-4835-90f8-c5301f780f6b","added_by":"auto","created_at":"2024-08-17 01:16:37","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":268889,"visible":true,"origin":"","legend":"\u003cp\u003eCoefficient of variation for estimation ratio. CV provides a dimensionless measure of the noise in judgments, which allows comparison of performance precision across numerosities, as well as comparison between baseline and adaptation (biased) conditions. (a) Results in the baseline condition. For numbers within the subitizing range (1-4), CV for enumerating a single set is below 0.05, highlighting the hallmark of errorless subitizing. When multiple color subsets are presented, CV reaches 0.15-0.3, even when the target subset is probed before stimulus onset. The signature of approximate estimation is evident in these conditions. Noticeably, CV falls back to near zero when the superset is asked, regardless of whether the target number is probed before or after the stimulus, suggesting an activation of subitizing. For numbers beyond the subitizing range (5-12), CV is above 0.15, indicating the activity of an approximate numerosity mechanism. Both for subitizing and numerosity groups, CV for enumerating multiple subsets is higher in the probe-after condition, compared to the probe-before condition. By contrast, no such difference is observed in the superset groups. (b) Results in the adaptation condition. The CV pattern is reminiscent of that in the baseline condition. Error bars denote one standard error.\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-4746948/v1/639a7a2347c360ef15c9471a.jpeg"},{"id":62653629,"identity":"dd309c2f-d138-4f79-bee7-db7d0a0f4425","added_by":"auto","created_at":"2024-08-17 01:16:37","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":16342,"visible":true,"origin":"","legend":"\u003cp\u003eScatters for individual CV. When target numbers are within the subitizing range (1-4), a significant adaptation aftereffect was observed when there were multiple subsets, and when the targets were cued after stimuli. To check if this adaptation reflect the activity of the numerosity system, we investigate the CV correlation of this condition across other conditions. Within the subitizing range, no significant CV correlation is found, either between this condition and the single-set condition (a), or between this condition and the superset condition (b), even if the target number range was identical, and the targets were probed in the same way (after the stimuli). By contrast, with multiple subsets, CV in this subitizing condition is significantly correlated with that in the numerosity group (5-12), despite the targets being probed before (c) or after (d) the stimuli. Pink area donates 95% CI.\u003c/p\u003e","description":"","filename":"Onlinefloatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-4746948/v1/01350735c0f4c9ffca1648f5.png"},{"id":68206972,"identity":"ab6e73e7-7bbd-45bb-a75d-51565748dd3b","added_by":"auto","created_at":"2024-11-04 16:34:15","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":802396,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4746948/v1/1c218c2b-da01-42e0-9e92-299a9c512ae3.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Adaptation Biases the Parallel Perception of Subitized Numerosities","fulltext":[{"header":"Introduction","content":"\u003cp\u003eNumerosity, like most primary sensory systems, is susceptible to adaptation\u003csup\u003e1\u003c/sup\u003e. Numerosity adaptation refers to the phenomenon where the perception of numerosity decreases after adapting to a larger number of stimuli, and conversely, it increases after adapting to a smaller number\u003csup\u003e1\u0026ndash;3\u003c/sup\u003e. Numerosity adaptation is independent of the processing of visual inputs, such as size, shape, color, or contrast of stimuli, and it occurs across different stimulus modalities and formats\u003csup\u003e4\u0026ndash;6\u003c/sup\u003e. However, it is still debatable whether this adaptation acts via a mechanism dedicated to numerosity, or via low-level texture-like mechanisms, as perceived number cannot be isolated from all confounding magnitudes that are related with number\u003csup\u003e7\u0026ndash;9\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eWe can appraise the number of up to four items rapidly and errorlessly based on a mechanism dubbed subitizing\u003csup\u003e10,11\u003c/sup\u003e. Naming numbers in the subitizing range involves processes distinct from estimation\u003csup\u003e12\u0026ndash;14\u003c/sup\u003e. Whilst being fast and accurate, subitizing is highly dependent on attentional resources \u003csup\u003e15,16\u003c/sup\u003e. Visual attention is efficient for selecting and enumerating the number (7\u0026ndash;30 dots) of three sets in parallel: two color subsets and the superset, which is compatible with the three-item limits of object-based attention\u003csup\u003e17\u003c/sup\u003e. However, with very few items (\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e), subitizing only occurs in the single-set and superset conditions, and is absent in multiple-subset conditions, where the participants are required to distribute their attention and simultaneously enumerate more than one subset\u003csup\u003e13\u003c/sup\u003e. In other words, subitizing lacks the capability for processing subsets in parallel. In that case, estimation carries out the enumeration with a reasonable precision \u003csup\u003e13,14\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eMost studies of numerosity adaptation have been confined to the moderate numerosity range. Under normal conditions adaptation has little effect in the low subitizing range \u003csup\u003e8\u003c/sup\u003e. A previous study has suggested that susceptibility to numerosity adaptor stimuli emerges at very low numerosities under conditions of attentional deprivation. When attentional load is induced by a dual-task paradigm, perception of the three-dot reference is biased against the adapted numerosity \u003csup\u003e12\u003c/sup\u003e. Given that an asymmetric presentation of adaptor is employed in this study, the adaptation aftereffect can be partly explained by the intrusion of uncontrolled visuo-spatial attentional processes in subsequent comparison tasks\u003csup\u003e18\u003c/sup\u003e. However, as pointed out by this previous study, it is possible that even at low numerosities, the mechanisms of numerosity and subitizing may operate concurrently. Therefore, numerosity adaptation can potentially affect subitized numerosities, particularly when subitizing is disrupted by attentional load\u003csup\u003e12\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eThe current study investigated whether the perception of subitized numerosities (\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e) is susceptible to adaptation when attention is distributed across multiple subsets. The estimation paradigm was employed in order to directly describe the perception of subitized numerosities, without resorting to testing series that might exceed the subitizing range. Participants were presented with stimuli comprising multiple subsets (from 1 to 5) defined by different colors, which changed on every trial. In some trials, participants were instructed about the target color before stimulus presentation, while in other trials, they were instructed after stimulus presentation. Once the target was cued, the participants had to estimate its numerosity. Prior to the testing stage, the adaptor stimulus was presented. The estimation of target number under the adapted condition was compared with that under the non-adapted condition, in order to determine the occurrence of adaptation. The coefficient of variation (CV) of estimation was computed in order to derive the processing precision in each condition.\u003c/p\u003e \u003cp\u003eAnticipating the results, we found that adaptation biases the perception of subitized numerosities when participants were required to enumerate more than one subset during the testing stage (i.e., when the target was cued after the presentation of multiple subsets). In this condition, CV of estimating subitized numerosities (\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e) was comparable to and correlated with that of estimating moderate numerosities (\u003cspan additionalcitationids=\"CR6 CR7 CR8 CR9 CR10 CR11\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e), indicating that subitizing is superseded by numerosity estimation under attentional load. Moreover, the aftereffects of adaptation were significantly stronger in the probe-after condition compared to the probe-before condition, both for subitized and moderate numerosities. This suggests that numerosity adaptation is modulated by attention. Greater adaptation aftereffects occur in accompaniment with higher CV, which reflects higher perceptual uncertainty induced by attention allocation. These results demonstrate the function of numerosity adaptation: Rather than being a by-product of neural fatigue resulting from processing low-level degradation of inputs, numerosity adaptation reflects perceptual flexibility. In the case of higher uncertainty, the prior adaptor would be more weighted to optimize the detection of deviation in subsequent numerosity perception.\u003c/p\u003e"},{"header":"Method","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eStatement of ethical approval\u003c/h2\u003e \u003cp\u003eFor both of the experiments, the data were analyzed anonymously. All participants provided their informed consent according to the Declaration of Helsinki prior to the experiment in both verbal and written forms, and they were compensated for their participation. Yunnan Minzu University\u0026rsquo;s ethics committee approved this study(No.20230913-01).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003eSample size and participants\u003c/h2\u003e \u003cp\u003eParticipants aged 17 to 32 years with normal or corrected-to-normal vision and normal color perception were recruited. A total of 30 participants (averagely aged 24 years, 10 males) participated in this study. A total of 720 trials were conducted for each participant. Specifically, 57% of the trials with target number ranges of 1\u0026ndash;4, and 36% of the trials with target number ranges of 5\u0026ndash;12 were analyzed separately in the subitizing and numerosity groups. Compared with previous studies, sufficient participants were enrolled, and sufficient trials were provided in each condition\u003csup\u003e13,17\u003c/sup\u003e. The remaining 6% of the trials, in which the target was not shown or the subset number exceeded three, were excluded from the analyses. In particular, the trials with four or five subsets were excluded due to their insufficiency for statistical analysis.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003eStimuli and procedure\u003c/h2\u003e \u003cp\u003eParticipants sat approximately 50 cm from an LCD monitor with a viewable area measuring 41 cm by 26 cm (19\u0026rdquo;, 1920 \u0026times; 1080, 60 Hz) in a dimly lit quiet room. Stimuli were generated from Matlab (Mathworks, Natwick, MA). The diameter of each dot is 0.5\u0026deg; visual angle (20 pixel). Dots were presented in a circle at the center of the screen with a diameter of 15\u0026deg; (600 pixel) visual angle. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e illustrates the procedure for the adapted conditions. The adaptation began with a fixation lasting for 500 ms, followed by a probe lasting for 500 ms, which indicated the target color in the probe-before condition, or indicated \u0026lsquo;Probe After\u0026rsquo; in the probe-after condition. Then, an adaptor showed up. It was presented for 30 seconds on the first trial and appeared for 3000 ms at the beginning of each subsequent trial. The participants should keep their eyes on the central adaptor. Next, it proceeded to the testing phase. The paradigm of the testing phase followed that of previous studies\u003csup\u003e13,17\u003c/sup\u003e. At the beginning of each trial, a fixation was displayed for 150\u0026ndash;1150 ms. Subsequently, participants were presented with a 200-ms stimulus display containing 1\u0026ndash;12 dots of one to five colors. The stimulus was followed by a blank slide lasting for 500 ms. If the first probe screen stated \u0026lsquo;Probe After\u0026rsquo;, it would be followed by a second probe slide displaying the target color for 500 ms, which succeeded the blank slide. Else if the first probe screen stated the target color, no probe would be presented. The participants were required to enumerate the number of dots in the target, which could be one of the color subsets or the superset, and they entered their answers into the computer following the appearance of the second probe.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eDots in stimulus patch were randomly distributed with the constraint that they could not overlap with each other. The number of dots in each color subset was randomly determined, and in half (49.6%) of the trials the target subset was smaller than at least one distracting subset, making the strategy of attending only to the largest subset ineffective. For each participant, an average of 360 trials which combined all conditions in a randomized order were run in 3 blocks. Generally, on 22% of the trials, participants were asked to report the overall number of the dots regardless of the colors (superset trials). The proportion of one-, two-, and three-color subset conditions was 19%, 32%, and 21%, respectively. In each of the subset/superset group, the proportion and target number range of the probe-before and probe-after conditions are approximately equal. In 2% of the trials, there were four or five color subsets. In 4% of the trials, there was no target color represented, and the correct respond is \u0026lsquo;0\u0026rsquo;. Proportion of each condition is slightly different among participants.\u003c/p\u003e \u003cp\u003eThe procedure in the adapted condition was similar to the baseline condition except that there was an adaptation stage prior to the testing procedure. Adaptor always comprised 50 orange dots, which was different from the color of testing dots (blue, green, Magenta, red, or yellow).\u003c/p\u003e \u003cp\u003eThe participants were asked to keep their eyes on the middle fixation during the whole trial. The baseline condition was conducted prior to the adapted condition for each participant. Adequate rest was ensured to avoid fatigue.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003eData analysis\u003c/h2\u003e \u003cp\u003eAs there were various target numbers, the ratio between the estimation and the target number was adopted to assess the enumeration. The mean estimation ratio was calculated to assess the accuracy of estimation in each condition, and the difference in the ratio between baseline and adaptation conditions was calculated to measure adaptation aftereffects. These aftereffects were compared to \u0026lsquo;0\u0026rsquo; using a one-sample \u003cem\u003et\u003c/em\u003e-test (one-tailed) to determine whether the adaptation induced significant underestimation. The coefficient of variation (CV) was calculated as the ratio between the standard deviation (SD) and the mean of enumeration. It provides a dimensionless measure of the noise in the judgments, allowing comparison of performance precision across numerosities, as well as comparison between baseline and adapted (biased) conditions. Pearson correlation coefficient \u003cem\u003er\u003c/em\u003e was calculated for CV between related conditions. One sample \u003cem\u003et\u003c/em\u003e-test is one-tailed to test the hypothesis that the aftereffect is significantly larger than \u0026lsquo;0\u0026rsquo;, and paired samples \u003cem\u003et\u003c/em\u003e-test is two-tailed to test whether the CV is significantly different between two conditions. Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e was reported to provide a complement to null hypothesis statistical significance testing by estimating the magnitude of the difference (0.2\u0026ndash;0.5 for small effect size, 0.5\u0026ndash;0.8 for moderate effect size, and \u0026gt;\u0026thinsp;0.8 for large effect size). Bayes factors (\u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e) were reported to estimate whether the null hypothesis H\u003csub\u003e0\u003c/sub\u003e or the alternative hypothesis H\u003csub\u003e1\u003c/sub\u003e is more likely to be correct. \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.3 suggests clear evidence for H\u003csub\u003e0\u003c/sub\u003e, whereas \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;3 indicates clear evidence for H\u003csub\u003e1\u003c/sub\u003e.The False Discovery Rate probability (FDR), or \u003cem\u003eQ\u003c/em\u003e value, is adopted in this study to correct probability of type-Ⅰerror in multiple comparisons\u003csup\u003e19\u003c/sup\u003e. For example, with four \u003cem\u003ep\u003c/em\u003e values in multiple comparisons, we multiply the smallest \u003cem\u003ep\u003c/em\u003e-value by four to get its \u003cem\u003eQ\u003c/em\u003e value. Then we multiply the second smallest \u003cem\u003ep\u003c/em\u003e by 4/2, the third \u003cem\u003ep\u003c/em\u003e by 4/3, and the last \u003cem\u003ep\u003c/em\u003e (the largest one) by 4/4 to get their \u003cem\u003eQ\u003c/em\u003e values. To determine whether a comparison is statistically significant, \u003cem\u003eQ\u003c/em\u003e values are used instead of \u003cem\u003ep\u003c/em\u003e values, *\u003cem\u003eQ\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.05, **\u003cem\u003eQ\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.01, ***\u003cem\u003eQ\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001. \u003cem\u003eQ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.05 is a widely accepted threshold for significance.\u003c/p\u003e \u003c/div\u003e"},{"header":"Results","content":"\u003cp\u003eFigure 2a displays the adaptation aftereffects in different conditions. As the adaptation aftereffects are assessed by subtracting the mean estimation ratio between the baseline and adapted conditions, a positive value indicates the presence of adaptation aftereffects, i.e., underestimation induced by the adaptor. For target numbers within subitizing range (1\u0026ndash;4, three clusters on the left of Fig.\u0026nbsp;2a), no underestimation was induced by adaptation when there was only one set, either in the probe-after condition, \u003cem\u003et\u003c/em\u003e(29)\u0026thinsp;=\u0026thinsp;0.595, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.278, \u003cem\u003eQ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.371, Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.109, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.327, or in the probe-before conditions, \u003cem\u003et\u003c/em\u003e(29)\u0026thinsp;=\u0026thinsp;1.583, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.084, \u003cem\u003eQ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.126, Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.258, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.867.\u003c/p\u003e \u003cp\u003eImportantly, for target numbers within subitizing range (\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e), significant underestimation was induced by adaptation in the probe-after condition with multiple color subsets (2\u0026ndash;3 color groups), \u003cem\u003et\u003c/em\u003e(29)\u0026thinsp;=\u0026thinsp;2.407, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.011, \u003cem\u003eQ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.033, Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.439, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;4.476. It is suggested that numbers within the subitizing range (\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e) are susceptible to adaptation when attention is distributed across different subsets in the probe-after condition. No aftereffects were observed in the probe-before conditions, \u003cem\u003et\u003c/em\u003e(29) = -0.139, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.655, \u003cem\u003eQ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.786, Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e = -0.073, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.147.\u003c/p\u003e \u003cp\u003eIt is worth noting that no adaptation aftereffect was observed when the participants were asked to enumerate the number of superset, either in the probe-after condition, \u003cem\u003et\u003c/em\u003e(29) = -1.193, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.879, \u003cem\u003eQ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.879, Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e = -0.218, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.097, or in the probe-before condition, \u003cem\u003et\u003c/em\u003e(29)\u0026thinsp;=\u0026thinsp;0.882, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.807, \u003cem\u003eQ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.880, Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.161, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.112. Participants always perceived the dot number in the superset in an unbiased manner, even when the target was probed after the testing stimuli, and when the superset comprised up to five color subsets.\u003c/p\u003e \u003cp\u003eThree clusters of bars on the right of Fig.\u0026nbsp;2a demonstrate the results within the numerosity range (\u003cspan additionalcitationids=\"CR6 CR7 CR8 CR9 CR10 CR11\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e). Adaptation aftereffects are significant in the single-set group, \u003cem\u003et\u003c/em\u003e(29)\u0026thinsp;=\u0026thinsp;3.274, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.001, \u003cem\u003eQ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.006, Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.598, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;27.314 in the probe-after condition, and \u003cem\u003et\u003c/em\u003e(29)\u0026thinsp;=\u0026thinsp;2.416, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.011, \u003cem\u003eQ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.033, Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.441, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;4.555 in the probe-before condition. The aftereffects are significant in the superset group, \u003cem\u003et\u003c/em\u003e(29)\u0026thinsp;=\u0026thinsp;2.259, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.016, \u003cem\u003eQ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.033, Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.412, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;3.399 in the probe-after condition, and \u003cem\u003et\u003c/em\u003e(29)\u0026thinsp;=\u0026thinsp;2.321, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.014, \u003cem\u003eQ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.033, Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.424, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;3.810 in the probe-before condition. Significant aftereffects were also observed when there were multiple subsets in the display, \u003cem\u003et\u003c/em\u003e(29)\u0026thinsp;=\u0026thinsp;4.070, \u003cem\u003ep\u0026thinsp;\u0026lt;\u003c/em\u003e\u0026thinsp;0.001, \u003cem\u003eQ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.001, Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.743, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;176.998 in the probe-after condition, and \u003cem\u003et\u003c/em\u003e(29)\u0026thinsp;=\u0026thinsp;2.927, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.003, \u003cem\u003eQ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.012, Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.534, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;12.776 in the probe-before condition.\u003c/p\u003e \u003cp\u003eNotably, when multiple-color subsets were simultaneously presented in the display, the adaptation aftereffect in the probe-after condition is greater than that in the probe-before condition, \u003cem\u003et\u003c/em\u003e(29)\u0026thinsp;=\u0026thinsp;1.902, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.034, Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.374, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.824. Numerosity adaptation is modulated by attention, and greater aftereffects are revealed in the probe-after conditions, both for subitized and moderated numerosities.\u003c/p\u003e \u003cp\u003eTo better illuminate the adaptation aftereffects in the multiple-subset conditions, the individual data in the probe-before and probe-after conditions are shown in Fig.\u0026nbsp;2b. As for targets within the subitizing range (1\u0026ndash;4, red dots), underestimation primarily occurs in the probe-after condition, rather than the probe-before condition, for most participants. By contrast, adaptation biases numerosity perception both in the probe-after and probe-before conditions for targets within the numerosity range (5\u0026ndash;12, blue dots).\u003c/p\u003e \u003cp\u003e \u003cb\u003eFigure 2\u003c/b\u003e. Results of adaptation aftereffects. The adaptation aftereffects are assessed by subtracting the mean estimation ratio between the baseline and adaptation conditions. (a) Three clusters on the left demonstrate the results within the subitizing range (\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e). Significant underestimation is induced by adaptation in the probe-after condition with multiple color subsets. No adaptation aftereffects are observed in other conditions. Three clusters on the right show the results within the numerosity range (\u003cspan additionalcitationids=\"CR6 CR7 CR8 CR9 CR10 CR11\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e). Adaptation aftereffects are significant in each condition. When multiple color subsets were simultaneously presented in the display, the adaptation aftereffect in the probe-after condition is significantly greater than in the probe-before condition, both for the subitizing and numerosity groups. Error bars represent one standard error. (b) Individual adaptation aftereffects in probe-before and probe-after conditions with multiple color subsets. Red dots represent for the aftereffect of subitizing targets, and blue dots represent for numerosity targets. Starts denote the mean of each group.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn superset condition, notably, CV is below 0.03, both on probe before and after trials. When the target is probed before the stimuli, the CV in the superset is significantly different from that in the multiple-subset condition, \u003cem\u003et\u003c/em\u003e(29)\u0026thinsp;=\u0026thinsp;4.649, \u003cem\u003ep\u0026thinsp;\u0026lt;\u003c/em\u003e\u0026thinsp;0.001, \u003cem\u003eQ\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001, Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.849, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;100, whereas it is not different from those in single-set condition, \u003cem\u003et\u003c/em\u003e(29)\u0026thinsp;=\u0026thinsp;0.205, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.839, \u003cem\u003eQ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.839, Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.037, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.201. When the target is probed after the stimuli, the CV in the superset is significantly different from that in the multiple-subset condition, \u003cem\u003et\u003c/em\u003e(29)\u0026thinsp;=\u0026thinsp;14.141, \u003cem\u003ep\u0026thinsp;\u0026lt;\u003c/em\u003e\u0026thinsp;0.001, \u003cem\u003eQ\u003c/em\u003e\u0026thinsp;\u0026lt;\u0026thinsp;0.001, Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.582, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;100, whereas it is not different from those in single-set condition, \u003cem\u003et\u003c/em\u003e(29)\u0026thinsp;=\u0026thinsp;1.191, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.243, \u003cem\u003eQ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.324, Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.218, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.791. Thus, participants can subitize if they are asked to enumerate all dots, irrespective of probe conditions and the colors defining each group.\u003c/p\u003e \u003cp\u003eAs for the numerosities of 5\u0026ndash;12, CV range between 0.14 and 0.27 across conditions. In the face of multiple subsets, CV is significantly larger in the probe-after condition, compared with the probe-before condition, \u003cem\u003et\u003c/em\u003e(29)\u0026thinsp;=\u0026thinsp;5.961, \u003cem\u003ep\u0026thinsp;\u0026lt;\u003c/em\u003e\u0026thinsp;0.001, Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.088, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;100. In superset condition, however, the probe has little effect on CV, \u003cem\u003et\u003c/em\u003e(29)\u0026thinsp;=\u0026thinsp;1.104, \u003cem\u003ep\u0026thinsp;=\u003c/em\u003e\u0026thinsp;0.279, Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.202, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.338. Previous studies suggested that we can estimate up to three sets in parallel without a tangible cost: two subsets and superset\u003csup\u003e13,17\u003c/sup\u003e. In this study, we have combined the two- and three-subset conditions to get a stable data for analyses, hence CV is larger in the probe-after multiple-subset condition. Nevertheless, in line with previous studies, our data shows that participants can enumerate superset effectively, irrespective of probe conditions and the colors defining each group.\u003c/p\u003e \u003cp\u003eA similar CV pattern was revealed in the adaptation conditions (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). In the face of multiple subsets, CV is significantly larger in the probe-after condition compared with the probe-before condition, \u003cem\u003et\u003c/em\u003e(29)\u0026thinsp;=\u0026thinsp;2.259, \u003cem\u003ep\u0026thinsp;=\u003c/em\u003e\u0026thinsp;0.032, Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.412, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.731 for subitized numerosities 1\u0026ndash;4, and \u003cem\u003et\u003c/em\u003e(29)\u0026thinsp;=\u0026thinsp;3.939, \u003cem\u003ep\u0026thinsp;\u0026lt;\u003c/em\u003e\u0026thinsp;0.001, Cohen\u0026rsquo;s \u003cem\u003ed\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.719, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;\u0026gt;\u0026thinsp;100 for moderate numerosities 5\u0026ndash;12. By contrast, CV for enumerating superset does not increase when the target is probed afterwards. It even decreases in those conditions.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWhen target numbers are within the subitizing range, a significant adaptation aftereffect was observed when there were multiple subsets, and the targets were cued after stimuli (Fig.\u0026nbsp;2a). In addition, CV of this condition was revealed to be comparable with that in the numerosity group. To check if the results in this condition reflect a genuine result of the numerosity system, we investigated the CV correlation of this condition across other conditions. We first calculated the CV correlation across the probe-after conditions within the subitizing group. No significant CV correlation is found between this multiple-subset condition and the single-set condition (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea), \u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.330, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.075, \u003cem\u003eQ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.100, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.033, and no significant correlation was found between this multiple-subset condition and the superset condition (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb), either, \u003cem\u003er\u003c/em\u003e = -0.058, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.763, \u003cem\u003eQ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.763, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.237. Then we analyzed the CV correlation across the multiple-color conditions between subitizing and numerosity groups. Significant CV correlation was observed between this subitizing and the numerosity conditions: \u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.526, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.003, \u003cem\u003eQ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.012, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;16.041 for the numerosity condition in which the target was cued after the stimuli (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec), and \u003cem\u003er\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.416, \u003cem\u003ep\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.022, \u003cem\u003eQ\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.044, \u003cem\u003eBF\u003c/em\u003e\u003csub\u003e10\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;2.739 for the condition in which the target was cued before the stimuli (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ed).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo sum up, in the face of multiple subsets, perception of subitized numerosities should be based on numerosity mechanisms. This point of view is supported by two evidences. First, the perception is susceptible to adaptation. Second, the processing precision is comparable to and significantly correlated with that for moderate numerosities.\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eUnder normal condition, numerosity adaptation is confined to moderate numerosities\u003csup\u003e1,12,18,20\u003c/sup\u003e. Debate exists in whether numerosity adaptation is based on a mechanism dedicated to numerosity or via texture-like mechanisms\u003csup\u003e7\u0026ndash;9,21\u003c/sup\u003e. The current study investigated whether the perception of subitized numerosities (\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e) is susceptible to adaptation when attention is distributed across multiple subsets. The result that subitized numerosities are also susceptible to numerosity adaptation contributes in elucidating the mentioned debate, as a mechanism based on extensive measures could hardly operate at such low numerosities.\u003c/p\u003e \u003cp\u003eA series of studies have suggested that even at subitized numerosities, the mechanisms of numerosity and subitizing may operate concurrently, and numerosity will take over the job of enumeration when subitizing cannot benefit from attention. In that case, similar processing features can be observed both for subitized and moderate numerosities\u003csup\u003e12\u0026ndash;14\u003c/sup\u003e. This study went further to investigate whether adaptation biases the perception of subitized numerosities, as it does with moderate numerosities, when attention is distributed across multiple subsets. According to the current results, although the absence of PSE shift in the single-set condition indicates that the perception of subitized numerosities is resistant to adaptation when subitizing persists under normal condition, it is also clear that adaptation biases this perception when participants have to simultaneously enumerate more than one subset in the testing stage.\u003c/p\u003e \u003cp\u003eOur previous study\u003csup\u003e13\u003c/sup\u003ehave pointed out that subitizing lacks the capability to process subsets in parallel. With multiple subsets, when the target was probed after the stimuli, participants had to simultaneously enumerate the numerosity of each subset. Errorless subitizing disappeared as it cannot benefit from distributed attention. In the current study, compared to the single-set condition, the CV of estimating subitized numerosities in the multiple-subset condition increases from 3\u0026ndash;31%, which is comparable with the CV of estimating moderate numerosities (\u003cspan additionalcitationids=\"CR6 CR7 CR8 CR9 CR10 CR11\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e) in the same condition (27%). In addition, the CV of estimating subitized numerosities in this multiple-subset condition is positively correlated with that of estimating moderate numerosities in the same condition, whereas it is not correlated with the CV in the single-set or superset conditions, despite the identical target number range across these conditions. These results are in line with our previous study, indicating that while subitizing functions effectively in processing single set and superset (mean CV is below 3%), it is superseded by numerosity estimation under the attentional load induced by processing multiple subsets\u003csup\u003e13\u003c/sup\u003e. Furthermore, this study offers novel evidence indicating that adaptation occurs in the multiple-subset group with the probe-after-target paradigm, yet it is absent in the single-set or superset groups, regardless of the probe conditions. In other words, adaptation may occur when numerosity takes over the job of enumerating small numerosities\u003csup\u003e12\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eSubitizing performs well in the superset condition, irrespective of whether the target is cued before or after, suggesting that the processing of superset possesses a certain degree of invulnerability to the availability of attentional resources\u003csup\u003e13\u003c/sup\u003e. Consistent with our previous research, the current results indicate that adaptation cannot bias the perception of subitized numerosities when enumerating \u0026ldquo;all\u0026rdquo; numbers. Regardless of the probe conditions, both the precision and the accuracy of the perception remains unaffected. The priority of processing superset has also been illuminated in the moderate group: both the adaptation aftereffects and the CV remain constant irrespective of the probe conditions. These results provide further evidence supporting the idea that the superset is processed by an efficient perceptual subsystem \u003csup\u003e13,17,22\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eAccording to our previous research, the simple request to segregate the visual scene into two groups can drain resources critical for subitizing. When distinct color subsets are presented simultaneously, subitizing can be lost even when the target is cued before the stimuli\u003csup\u003e13\u003c/sup\u003e. In the current study, the CV (13%) indicates that subitizing is affected in the multiple-subset condition even when the target is probed before the stimuli. Given that the CV is substantially lower than that in the probe-after condition (31%), it is possible that subitizing can occasionally benefit from attention in this condition. When the target subset is notified prior to the presentation of the intermingled display, subitizing may be preserved with higher noise\u003csup\u003e23\u003c/sup\u003e, but it can also be superseded by numerosity when the non-target subsets are perceptually competitive enough to distract attention\u003csup\u003e13,14\u003c/sup\u003e. However, the noisy subitizing hypothesis cannot fully explain the absence of adaptation in this probe-before condition. We propose that attention enhancement may account for this lack of adaptation.\u003c/p\u003e \u003cp\u003ePrevious study suggests that attention can enhance both the precision and the accuracy of numerosity perception, with a greater improvement in the enumeration of subitized numerosities and a weaker improvement for moderate numerosities\u003csup\u003e24\u003c/sup\u003e. Recent studies further point out that numerosity adaptation is also modulated by attention allocation in testing stages. In the testing stage, items in the cued patch can be overestimated compared to the opposite patch, and adaptation amplifies this cue-dependent numerosity bias\u003csup\u003e18\u003c/sup\u003e(the current study). Numerosity adaptation reflects a mixture of both perceptual and attentional processes\u003csup\u003e18\u003c/sup\u003e, which may facilitate the subsequent perception of numerosity.\u003c/p\u003e \u003cp\u003eAdaptation had long been considered a by-product of neuronal activation fatigue. However, a series of studies have suggested that adaptation, especially to high-level attributes, may reflect a dynamic adjustment to improve our sensitivity to changes along the adapted dimension\u003csup\u003e18,25\u003c/sup\u003e. There are models linking adaptation effects to Bayesian prediction, suggesting that prior adaptor may serve as a standard for self-calibration\u003csup\u003e26,27\u003c/sup\u003e. Within a Bayesian framework, the distribution of the current stimuli is combined with that of the adaptor to form the posterior distribution. As the effect of the prior depends on the relative reliability, the adaptor would have a greater effect when the width of the current stimuli distribution is wider, namely, when discrimination of the current stimuli is lower\u003csup\u003e20,28\u003c/sup\u003e. On the assumption that the adaptor serves as a prior of this Bayesian model, greater perceptual bias is predicted when numerosity perception in the testing stage is under higher perceptual uncertainty. In other words, greater adaptation aftereffects are expected when the target is probed following the presentation of multiple subsets, during which higher uncertainty is induced by attention allocation.\u003c/p\u003e \u003cp\u003eThe current results support this prediction: For targets 5\u0026ndash;12, similarly to that for targets 1\u0026ndash;4, the adaptation aftereffects in the probe-after condition are significantly greater than that in the probe-before condition. In addition, adaptation bars (Fig.\u0026nbsp;2a) and CV bars (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, a\u0026amp;b) share a similar pattern, suggesting greater adaptation aftereffects in conditions with higher CV: Greatest adaptation aftereffects are revealed in multiple-after conditions in both number groups, along with the highest CV. Conversely, in the one-set and superset conditions of the subitized group, where the close-to-zero CV indicates high reliability in perceiving subitized target numbers, adaptation barely biases perception during the testing phase. These results well elucidate the function of numerosity adaptation: the repulsive bias caused by adaptation\u003csup\u003e29\u003c/sup\u003e enhances the signal-to-noise representation, which therefore optimizes the detection of deviation along the adapted dimension in the subsequent perception, especially when the perception is under high uncertainty.\u003c/p\u003e "},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting interests\u003c/h2\u003e \u003cp\u003eThe authors declare no competing interests.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis study was supported by funding from the National Natural Science Foundation of China (Grant No. 32060192; 31500879; 31500884).\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eW. L. developed the study concept and contributed to the study design. Testing and data collection were performed by Y. L. (3rd author) and Y. L. (4th author). The data analysis and interpretation was performed by W. L. The figures were drawn by X. Z. The manuscript was drafted by W. L., and J. L. provided critical revisions. All authors approved the final version of the manuscript for submission.\u003c/p\u003e\u003ch2\u003eAcknowledgement\u003c/h2\u003e\u003cp\u003eWe express our sincere gratitude to Guido Marco Cicchini for conceiving the concept of this study and for providing substantial suggestions during the experiments.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe data sets generated and analyzed during the current study are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eBurr, D. \u0026amp; Ross, J. 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The role of non-numerical information in the perception of temporal numerosity. \u003cem\u003eFrontiers in Psychology\u003c/em\u003e\u003cstrong\u003e14\u003c/strong\u003e, 1197064.https://doi.org/10.3389/fpsyg.2023.1197064(2023).\u003c/li\u003e\n\u003cli\u003eAulet, L. S. \u0026amp; Lourenco, S. F. Visual adaptation reveals multichannel coding for numerosity. \u003cem\u003eFrontiers in Psychology\u003c/em\u003e\u003cstrong\u003e14\u003c/strong\u003e, 1125925.https://doi.org/10.3389/fpsyg.2023.1125925(2023).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"numerosity adaptation, subitizing, estimation, parallel processing, gist perception","lastPublishedDoi":"10.21203/rs.3.rs-4746948/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4746948/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eNumerosity adaptation, the phenomenon where prolonged exposure to a stimulus of greater numerosity makes the subsequent stimulus appear less numerous, and conversely, has been confined to moderated numerosities. This study investigated whether the estimation of small numerosities (\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e), which is performed rapidly and accurately due to the mechanism of subitizing, is susceptible to adaptation. After adapting to a 50-dot stimulus, participants were presented with stimuli consisting of 1\u0026ndash;5 color sets. In some trials, participants were informed of the target color set before the presentation of the stimulus, while in others, they were instructed afterwards. When estimating dots in the single-color set or superset, no adaptation aftereffect was observed. The coefficient of variation (CV) was below 0.05, indicating the effective function of subitizing. However, when enumerating subsets in parallel, adaptation biased the estimation. The CV in estimating subitized numerosities was comparable to and correlated with that of estimating moderate numerosities, suggesting that subitizing was superseded by numerosity estimation. Greater aftereffects occur in the probe-after conditions, accompanied by higher perceptual uncertainty. The function of numerosity adaptation can be demonstrated within a Bayesian framework, where the prior adaptor is more weighted to optimize the detection of deviation under high uncertainty.\u003c/p\u003e","manuscriptTitle":"Adaptation Biases the Parallel Perception of Subitized Numerosities","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-08-17 01:16:32","doi":"10.21203/rs.3.rs-4746948/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2024-08-16T10:23:22+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-08-14T09:04:27+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2024-08-05T19:31:15+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"292371721297571623206014196188390746700","date":"2024-08-05T09:38:57+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"97401324167853639652750534296686137667","date":"2024-08-03T13:26:20+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2024-08-03T05:38:34+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2024-08-03T05:35:50+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2024-07-17T13:19:22+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2024-07-16T13:25:55+00:00","index":"","fulltext":""},{"type":"submitted","content":"Scientific Reports","date":"2024-07-16T04:23:56+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"scientific-reports","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"scirep","sideBox":"Learn more about [Scientific Reports](http://www.nature.com/srep/)","snPcode":"","submissionUrl":"","title":"Scientific Reports","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Scientific Reports","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"731a89f0-3a64-417c-9c87-667aef438de6","owner":[],"postedDate":"August 17th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[{"id":35636677,"name":"Biological sciences/Psychology"},{"id":35636678,"name":"Biological sciences/Neuroscience/Cognitive neuroscience"}],"tags":[],"updatedAt":"2024-11-04T16:23:57+00:00","versionOfRecord":{"articleIdentity":"rs-4746948","link":"https://doi.org/10.1038/s41598-024-76536-1","journal":{"identity":"scientific-reports","isVorOnly":false,"title":"Scientific Reports"},"publishedOn":"2024-10-29 16:13:11","publishedOnDateReadable":"October 29th, 2024"},"versionCreatedAt":"2024-08-17 01:16:32","video":"","vorDoi":"10.1038/s41598-024-76536-1","vorDoiUrl":"https://doi.org/10.1038/s41598-024-76536-1","workflowStages":[]},"version":"v1","identity":"rs-4746948","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4746948","identity":"rs-4746948","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}