Motion perception is essential for visual guidance of behavior and is known to be limited by both internal additive noise (i.e., a constant level of random fluctuations in neural activity independent of the stimulus) and motion pooling (global integration of local motion signals across space). People with autism spectrum disorder (ASD) display abnormalities in motion processing, which have been linked to both elevated noise and abnormal pooling. However, to date, the impact of a third limit—induced internal noise (internal noise that scales up with increases in external stimulus noise)—has not been investigated in motion perception of any group. Here, we describe an extension on the double-pass paradigm to quantify additive noise and induced noise in a motion paradigm. We also introduce a new way to experimentally estimate motion pooling. We measured the impact of induced noise on direction discrimination, which we ascribe to fluctuations in decision-related variables. Our results are suggestive of higher internal noise in individuals with high ASD traits only on coarse but not fine motion direction discrimination tasks. However, we report no significant correlations between autism traits and additive noise, induced noise, or motion pooling in either task. We conclude that, under some conditions, the internal noise may be higher in individuals with pronounced ASD traits and that the assessment of induced internal noise is a useful way of exploring decision-related limits on motion perception, irrespective of ASD traits.

^{1}Importantly, when external noise is low (and thus induced noise is low), the main source of internal noise is additive noise. As external noise increases, induced noise increases also and becomes the main source of internal noise. Figure 1a shows the impact of different types of noise and pooling on thresholds (as measured, for example, using equivalent noise paradigms). As is clear from this figure, it is difficult to distinguish between the different types of noise. To a large degree (but not completely), the changes in different types of noise are interchangeable; for example, additive noise and induced noise together may look like a change in motion pooling. It is thus possible that previous studies of motion perception using equivalent noise paradigms, for example, failed to identify changes in induced noise because they were interpreted as a change in motion pooling and additive noise.

*descriptive*, setting out to determine the relative contributions of different types of noise to performance. The model assumes three independent normally distributed types of noise that contribute to the overall noise (i.e., their variances add). These types are additive noise (σ

_{add}), external stimulus noise (σ

_{ext}), and induced noise (σ

_{ind}). Their combined impact is determined by adding their variances:

_{total}is the total noise that determines the sensitivity of the system (e.g., detection threshold). Both additive noise and induced noise are internal to the brain. Additive noise describes the combination of all noises that together are independent of the level of external noise. The induced noise describes all noise components that together are proportional to the external noise (Burgess & Colborne, 1988). There are no assumptions about the order in which these sources are added

^{2}.

_{ind}is a proportion (

*m*) of external noise (σ

_{ind}=

*m*σ

_{ext}), this can be rewritten as

*n*is interpreted as motion pooling (Dakin, Mareschal, & Bex, 2005a; van Boxtel, 2019):

*n*describing the number of samples that are taken to calculate the mean. The model assumes independence of noise, linear addition of their variances, and a linear and optimal detection process. In our model, we do not include an assumption of noisy motion pooling. This is because simulations showed that assuming noisy motion pooling (i.e., pooling over different numbers of moving dots on different trials) does not materially affect internal noise estimates (see Simulations in https://osf.io/4gdkt/). Increasing noise in the motion pooling increases estimates of average motion pooling, suggesting that it is not possible to separate average motion pooling from variation in motion pooling.

*M*

_{age}= 22.07,

*SD*

_{age}= 4.96)—were recruited from the Monash University Clayton campus. All participants were proficient in English and had normal or corrected-to-normal vision, fulfilling our inclusion criteria. Participants received monetary compensation for their participation. Participants were excluded if the internal noise model (explained below; Equation 5 fitted with an

*R*

^{2}< 0.5). One participant was excluded based on this exclusion criterion.

_{int}/σ

_{ext}), there exists a fixed (nonlinear) relationship between accuracy and consistency at different levels of σ

_{int}/σ

_{ext}(Burgess & Colborne, 1988). These relationships are shown in Figure 3a for different ratios of σ

_{int}/σ

_{ext}(gray dashed lines). Internal noise values can be calculated by fitting such a curve to experimental data and finding the ratio σ

_{int}/σ

_{ext}that best captures the data. Then, because σ

_{ext}is known, σ

_{int}can be calculated. Because this approach will not work for circular variables, we calculated the curves numerically for wrapped circular distributions. Figure 3a shows a comparison of the noncircular (colored lines) and circular (gray dashed lines) approaches, using identical parameters. When noise is large (toward the lower side in the plot), circular data deviate from the noncircular data. The curving toward the point where accuracy and consistency are both 50% occurs because, when external noise levels are large, dots at the extreme end of the distribution will be wrapped around the circle (or more than once). Some information remains as long as internal noise is not heavily wrapped around, but because it is a proportion of external noise it will also wrap around at large values of external noise. The distribution will approach a uniform distribution on a circle. At that point, the stimulus is largely uninformative, and both accuracy and consistency are random. An additional unfortunate consequence of the circular nature of the data is that the exact shape of the curves is dependent on the signal strength. When the mean angle (i.e., signal) is small, the data are well approximated by an approach using Gaussian distributions (only showing deviations at very large noise values).

_{int}/σ

_{ext}. We used an ad hoc function to achieve a reasonable coverage of ratios: (1.12

*–1)/25, with*

^{q}*q*ranging from 1 to 59 in steps of 0.5. Individual data points were compared with these curves, and the curve to which the data point showed the smallest squared Euclidian distance was taken as the best fit (Figure 3b). The squared distance was calculated taking into account deviations in terms of both accuracy and consistency. When the participant's data showed an accuracy below 50% it was adjusted to (1-accuracy). This happened six times (out of 45 × 8 = 360 data points, or 1.67% of all data points). Note that this correction does not materially change the data, because the consistency–accuracy curves are mirror symmetric along the line accuracy = 50%. However, keeping all points above 50% accuracy simplifies the fitting.

_{int}/σ

_{ext}, as well as σ

_{int}(as σ

_{ext}is known). In some cases, data points fell above the curve σ

_{int}/σ

_{ext}= ∞ (e.g., square in Figure 3b). As can be seen from Figure 3b, the data cannot be fit with a theoretical curve. Because we have a limited amount of trials per participant, some points in our dataset fell in this region. The fact that the data lie in that region indicates that the data was dominated by internal noise. Therefore, for those points, internal noise was estimated by fitting the σ

_{int}/σ

_{ext}= ∞ curve to the data; that is, we found the point on this curve that was closest to the data point (square in Figure 3b), where the squared error (in both consistency and accuracy directions) was smallest. The internal noise value that was associated with that point on the curve was taken as the internal noise estimate for our data point. Simulations showed that this resulted in correct approximations of internal noise levels (see Simulations in https://osf.io/4gdkt/).

_{ind}is directly proportional to the external noise; thus, σ

_{ind}=

*m*σ

_{ext}. The total internal noise is σ

_{int}= sqrt(σ

_{add}

^{2}+ σ

_{ind}

^{2}) = sqrt(σ

_{add}

^{2}+

*m*

^{2}σ

_{ext}

^{2}).

*m*can be derived in various ways, and, because we had no a priori reason to assume which one worked best, we performed a simulation study (see the Appendix). This simulation study showed that the best way to determine additive and induced noise was to fit the following function to the collective internal noise data per participant:

*n*is the number of motion samples that are taken to estimate motion direction (i.e., motion pooling). We fitted Equation 5 to individual participant data after first independently estimating

*n*from the data (see below).

*observed*external noise. The data generally fall on a curve that has a lower level of observed external noise than the amount of external noise that was actually present in the stimulus, indicating that information from multiple dots is pooled (see, for example, the data points from σ

_{ext}= 80, which falls on the line of observed external noise = 30) (Figure 4).

_{obs}is the observed standard deviation of the response, and

*n*

_{samp}is the effective number of samples that are combined to give a motion direction estimate (i.e., motion pooling). In our case,

_{int}and σ

_{ext}are the real internal and external noise values, and

*s*

_{int}and

*s*

_{ext}are observed values. The observed values have the motion sampling already taken into account, which is why

*n*

_{samp}does not appear on the right-hand side of the equation. Because we know the ratio (α) between internal and external noise and thus σ

_{int}= α * σ

_{ext}, this equation can be rewritten as

_{ext}(the external noise, or standard deviation of directional noise) and

*s*

_{ext}(the observed external noise), we can calculate the motion pooling,

*n*

_{samp}. Simulations showed that this method of estimation works but only for the lower noise levels (we used 35°, 45°, and 60°) for our coarse discrimination task and for the higher noise levels for the fine discrimination task (3.71–51.19). These simulations can be found in Simulations at https://osf.io/4gdkt/.

_{int}/σ

_{ext}= ∞ curve, observed external noise could not be determined, and these data points were consequently not used to estimate motion pooling.

^{2}(1) = 0.07,

*p*= 0.78; consistency: χ

^{2}(1) = 0.68,

*p*= 0.41] or between unrestricted models and those excluding both AQ and the interaction [accuracy: χ

^{2}(2) = 3.51,

*p*= 0.17; consistency: χ

^{2}(2) = 4.08,

*p*= 0.13]. However, comparing the models with AQ (but without interaction) and those with only external noise showed near significant results [accuracy: χ

^{2}(1) = 3.44,

*p*= 0.065; consistency: χ

^{2}(1) = 3.40,

*p*= 0.065], suggesting that AQ may have a small influence, but our current experiment was not powerful enough to reveal it. Overall, there appears to be no statistically significant influence of AQ on the accuracy or consistency of participants’ reports.

_{int}+1),

*F*(2.27, 97.48) = 218.63,

*p*< 0.0001, η

_{p}^{2}= 0.84, Greenhouse–Geisser corrected]. When performing median split on the AQ scores (median = 18), we obtained a group of

*n*= 20 that scored AQ < 18 and a group of

*n*= 20 that scored AQ > 18 (we discarded the subjects with a median score for this analysis). The mixed-design ANOVA with the factors external noise and group (low vs. high AQ) showed a significant effect of external noise [

*F*(2.21, 83.78) = 202.81,

*p*< 0.0001, η

_{p}^{2}= 0.84, Greenhouse–Geisser corrected], and AQ group [

*F*(1, 266) = 4.29,

*p*= 0.045, η

_{p}^{2}= 0.10], with internal noise increasing as external noise increased, and higher internal noise for the high AQ group. The interaction was not significant [

*F*(7, 266) = 0.21,

*p*= 0.98, η

_{p}^{2}= 0.005] (Figures 6b and 6c). A simple correlation over all participants between AQ and internal noise (averaged over external noise conditions) was also significant (Kendall's τ

_{b}= 0.21,

*p*= 0.048).

*n*to 1 to reduce free parameters. This model was then compared with a model without the impact of external noise (i.e., an intercept-only model). The likelihood ratio tests whether or not the model that incorporated a dependence on external noise was better [χ

^{2}(1) = 190.66,

*p*< 0.0001]. This emphasizes the importance of induced noise within the model.

_{b}= 0.09,

*p*= 0.39; Bayesian correlation Kendall's τ = 0.094,

*BF*

_{10}= 0.29).

*p*< 0.0001, Wilcoxon signed-rank test) indicating that participants were responding using direction information from multiple dots. We also note that 13.73 is rather close to the square root of the number of samples present (\(\sqrt {200} = 14.14\)), which has previously been proposed as a simple rule of thumb for estimating effective sample size in averaging tasks (Dakin, 2001). There was no correlation between the extent of motion pooling and AQ (Kendall's τ = –0.08,

*p*= 0.45) (Figure 7c); one multivariate outlier was removed based on its Mahalanobis distance being >13.8155; that is, the data point deviated from the multivariate mean at a

*p*< 0.001. A Bayesian correlation suggested moderate evidence for the null hypothesis (Kendall's τ = –0.083,

*BF*

_{10}= 0.27).

*R*

^{2}< 0.5. Ten participants were excluded on this basis, leaving 27 participants in the final sample (20 females, seven males; age range, 18–32 years;

*M*

_{age}= 24.8;

*SD*

_{age}= 5.33).

^{2}(1) = 0.068,

*p*= 0.79; consistency; χ

^{2}(1) = 0.13,

*p*= 0.72] and unrestricted models and those excluding AQ and the interaction [accuracy: χ

^{2}(2) = 0.07,

*p*= 0.96; consistency: χ

^{2}(2) = 1.15,

*p*= 0.56]. Comparing the models with AQ (but without the interaction) to those with only external noise showed no significant effects, either [accuracy: χ

^{2}(1) = 0.007,

*p*= 0.93; consistency: χ

^{2}(1) = 1.02,

*p*= 0.31]. Overall, there appears to be no influence of AQ on the accuracy or consistency in our fine motion discrimination task.

_{int}+1),

*F*(2.92, 75.99) = 152.04,

*p*< 0.0001, η

_{p}^{2}= 0.85, Greenhouse–Geisser corrected]. When performing median split on the AQ scores (median = 17), we obtained a group of

*n*= 13 that scored AQ < 17 and a group of

*n*= 12 that scored AQ > 17, discarding the subjects with a median score for this analysis. The mixed-design ANOVA with the factors external noise and group (low vs. high AQ) showed a significant effect of external noise [

*F*(7, 161) = 131.40,

*p*< 0.0001, η

_{p}^{2}= 0.85] but not AQ group [

*F*(1, 161) = 0.34,

*p*= 0.56, η

_{p}^{2}= 0.01]. The interaction was not significant [

*F*(7, 161) = 0.21,

*p*= 0.57, η

_{p}^{2}= 0.03] (Figures 9b and 9c). A simple correlation over all participants between AQ and internal noise (averaged over external noise conditions) was not significant (Kendall's τ

_{b}= 0.035,

*p*= 0.82).

*p*= 0.63;

*BF*

_{10}= 0.28) (Figure 10a).

*n*to 1 to reduce free parameters. This model was then compared to a model that did not incorporate this influence of external noise (i.e., an intercept-only model). The likelihood ratio tests determined whether the model with dependence on external noise was better [χ

^{2}(1) = 105.89;

*p*< 0.0001] and showed a significant impact of induced noise.

*m*, over participants was 1.72 (median, 1.49). These values were not correlated with the AQ measure (Kendall's τ

_{b}= 0.019;

*p*= 0.911;

*BF*

_{10}= 0.25; one multivariate outlier was removed) (Figure 10b).

*p*< 0.0001). There was no significant correlation with AQ (Kendall's τ = –0.13,

*p*= 0.35; one multivariate outlier was removed) (Figure 10c). A Bayesian correlation suggested that there was not sufficient data to support the absence of a correlation (

*BF*

_{10}= 0.39).

_{ext}= 0,

*Z*= 2.06 and

*p*= 0.039; at fine σ

_{ext}= 30.5 and coarse σ

_{ext}= 35,

*Z*= 1.11 and

*p*= 0.27; at fine σ

_{ext}= 51.2 and coarse σ

_{ext}= 45,

*Z*= 5.80 and

*p*< 0.0001).

*Z*= 1.04;

*p*= 0.30, Wilcoxon rank-sum test). Comparing the motion pooling data between coarse and fine discrimination tasks showed no significant difference (

*Z*= 0.05;

*p*= 0.96, Wilcoxon rank-sum test).

_{ext}>> σ

_{int}). This relationship can be derived as follows: variability in the decision variable (σ

_{dec}) adds to the variability in the response (and thus increases threshold), just like additive noise does. Thus, total noise would be \(\sqrt {{{\rm{\sigma }}}_{{\rm{add}}}^2 + {{\rm{\sigma }}}_{{\rm{dec}}}^2} \). Now, if we assume that σ

_{dec}is proportional to the external noise, then total noise is \(\sqrt {{{\rm{\sigma }}}_{{\rm{add}}}^2 + {{(m{\rm{\ }}{{\rm{\sigma }}}_{{\rm{ext}}})}}^2} \), which includes the definition of induced noise.

*d*′) is equated (Spence, Dux, & Arnold, 2016).

*Archiv für Psychiatrie und Nervenkrankheiten*, 117(1), 76–136. [CrossRef]

*Journal of Neuroscience*, 17(20), 7954–7966. [CrossRef] [PubMed]

*Journal of Autism and Developmental Disorders*, 31(1), 5–17. [CrossRef] [PubMed]

*Journal of Cognitive Neuroscience*, 15(2), 218–225, https://doi.org/10.1162/089892903321208150. [CrossRef] [PubMed]

*Brain*, 128(10), 2430–2441. [CrossRef] [PubMed]

*Psychological Science*, 14(2), 151–157. [CrossRef] [PubMed]

*Spatial Vision*, 10(4), 433–436. [CrossRef] [PubMed]

*Neuropsychologia*, 48(6), 1644–1651, https://doi.org/10.1016/j.neuropsychologia.2010.02.007. [CrossRef] [PubMed]

*Journal of the Optical Society of America A: Optics and Image Science*, 5(4), 617–627. [CrossRef]

*Cerebral Cortex*, 27(1), 185–200, https://doi.org/10.1093/cercor/bhw375. [CrossRef] [PubMed]

*Autism*, 18(8), 943–952, https://doi.org/10.1177/1362361313499455. [CrossRef] [PubMed]

*NeuroReport*, 20(17), 1543–1548, https://doi.org/10.1097/WNR.0b013e32833246b5. [CrossRef] [PubMed]

*Journal of Neuroscience*, 35(5), 1849–1857, https://doi.org/10.1523/JNEUROSCI.4133-13.2015. [CrossRef] [PubMed]

*Journal of the Optical Society of America A: Optics, Image Science, and Vision*, 18(5), 1016–1026, https://doi.org/10.1364/josaa.18.001016. [CrossRef]

*Vision Research*, 45(24), 3027–3049, https://doi.org/10.1016/j.visres.2005.07.037. [CrossRef]

*Neuron*, 75(6), 981–991, https://doi.org/10.1016/j.neuron.2012.07.026. [CrossRef] [PubMed]

*PLoS One*, 8(4), e61493. [CrossRef] [PubMed]

*Journal of Neuroscience*, 33(19), 8243–8249. [CrossRef] [PubMed]

*Neuropsychologia*, 46(5), 1480–1494, https://doi.org/10.1016/j.neuropsychologia.2007.12.025. [CrossRef] [PubMed]

*High-functioning individuals with autism*(pp. 105–126). Boston: Springer.

*Psychological Review*, 80(3), 203. [CrossRef] [PubMed]

*Psychological Review*, 71, 392–407. [CrossRef] [PubMed]

*Brain Research Bulletin*, 82(3–4), 147–160. [PubMed]

*Journal of Autism and Developmental Disorders*, 45(5), 1176–1190, https://doi.org/10.1007/s10803-014-2276-6. [CrossRef] [PubMed]

*Journal of Autism and Developmental Disorders*, 36(1), 5–25, https://doi.org/10.1007/s10803-005-0039-0. [CrossRef] [PubMed]

*Research in Autism Spectrum Disorders*, 1(1), 14–27. [CrossRef]

*Vision Research*, 46(13), 2130–2138. [CrossRef] [PubMed]

*Nature*, 446(7138), 912–915, https://doi.org/10.1038/nature05739. [CrossRef] [PubMed]

*Autism Research*, 4(5), 347–357, https://doi.org/10.1002/aur.209. [CrossRef] [PubMed]

*Proceedings of the National Academy of Sciences, USA*, 107(49), 21223–21228, https://doi.org/10.1073/pnas.1010412107. [CrossRef]

*Nervous Child*, 2(3), 217–250.

*KBIT-2: Kaufman Brief Intelligence Test Second Edition*. London: Pearson.

*Autism*, 10(5), 480–494, https://doi.org/10.1177/1362361306066564. [PubMed]

*Brain*, 133(Pt. 2), 599–610, https://doi.org/10.1093/brain/awp272. [PubMed]

*Psychological Review*, 115(1), 44–82, https://doi.org/10.1037/0033-295X.115.1.44. [PubMed]

*Journal of Neuroscience*, 35(18), 6979–6986, https://doi.org/10.1523/JNEUROSCI.4645-14.2015. [PubMed]

*Autism & Developmental Language Impairments*, 2, 1–16.

*Pediatric Research*, 69(5, Pt. 2), 48R–54R. [PubMed]

*NeuroImage*, 59(2), 1524–1533, https://doi.org/10.1016/j.neuroimage.2011.08.033. [PubMed]

*Frontiers in Psychology*, 2, 51, https://doi.org/10.3389/fpsyg.2011.00051. [PubMed]

*Journal of Child Psychology and Psychiatry and Allied Disciplines*, 43(2), 255–263. [PubMed]

*Journal of Autism and Developmental Disorders*, 36(2), 225–237. [PubMed]

*Journal of Autism and Developmental Disorders*, 36(1), 27–43, https://doi.org/10.1007/s10803-005-0040-7. [PubMed]

*Journal of Autism and Developmental Disorders*, 27(3), 283–293. [PubMed]

*Scientific Reports*, 7(1), 17584, https://doi.org/10.1038/s41598-017-17676-5. [PubMed]

*PLoS One*, 10(7), e0132531. [PubMed]

*Spatial Vision*, 10, 437–442. [PubMed]

*Neuropsychologia*, 43(7), 1044–1053, https://doi.org/10.1016/j.neuropsychologia.2004.10.003. [PubMed]

*Nature Human Behaviour*, 4(3), 317–325, https://doi.org/10.1038/s41562-019-0813-1. [PubMed]

*PLoS One*, 5(10), e13491, https://doi.org/10.1371/journal.pone.0013491. [PubMed]

*Vision Research*, 49(22), 2705–2739, https://doi.org/10.1016/j.visres.2009.08.005. [PubMed]

*Journal of Experimental Psychology: Human Perception and Performance*, 42(5), 671. [PubMed]

*NeuroReport*, 11(12), 2765–2767. [PubMed]

*Perception*, 35(8), 1047–1055, https://doi.org/10.1068/p5328. [PubMed]

*Brain*, 133(Pt. 7), 2089–2097, https://doi.org/10.1093/brain/awq122. [PubMed]

*Journal of Vision*, 19(13), 19, https://doi.org/10.1167/19.13.19. [PubMed]

*Autism Research*, 9(10), 1103–1113, https://doi.org/10.1002/aur.1595. [PubMed]

*Journal of Vision*, 15(1):20, 1–17, https://doi.org/10.1167/15.1.20. [PubMed]

*Vision Research*, 141, 136–144. [PubMed]

*Autism Research*, 10(8), 1384–1391, https://doi.org/10.1002/aur.1781. [PubMed]

*Neuropsychologia*, 63, 10–18. [PubMed]

*Inter-observer agreement and models of monaural auditory processing in detection tasks*. Ann Arbor, MI: University of Michigan.

*Proceedings of the National Academy of Sciences, USA*, 112(20), 6461–6466.

*International Journal of Developmental Neuroscience*, 23(2–3), 143–152, https://doi.org/10.1016/j.ijdevneu.2004.05.001. [PubMed]

_{add},

*m*, and

*n*) vary freely. Second, we estimated

*n*from our data using Equation 11 and estimated only σ

_{add}and

*m*. The third and fourth approaches were based on the following approximation: as σ

_{ext}becomes large, σ

_{int}approaches

*m*σ

_{ext}, which means that

*m*= σ

_{int}/σ

_{ext}, or the σ

_{int}/σ

_{ext}ratio that we measure with the double-pass paradigm. This method ignores the influence of motion pooling, which can be included and would lead to the following estimate: \(m = \ \sqrt n *\ {{\rm{\sigma }}}_{{\rm{int}}}/{{\rm{\sigma }}}_{{\rm{ext}}}\). We found, however, that this latter estimate severely overestimates

*m*, and we do not discuss it here. The third method derived σ

_{int}/σ

_{ext}by fitting σ

_{int}/σ

_{ext}curves through each of the data points from the largest five external noise values and taking the median value of these fits. The fourth method derived σ

_{int}/σ

_{ext}, fitting one σ

_{int}/σ

_{ext}curve (Figure 4) through the data from the largest five external noise values only, and this ratio was taken as the induced noise factor

*m*.