Article Figures & Data
Figures
- Figure 1.
Description of the experimental paradigm. A, Timeline of visual events on the screen in front of the subject. First, two square boxes appeared with a fixation cross (+ sign) in the central one. The location of the eccentric box was randomly assigned to the left or to the right of the central one with the same probability. Afterwards, a noninformative visual stimulus appeared in the central box for 2000 ms (preforeperiod or “pre-FP” interval) followed by another 1100-ms fixation period. Thereafter, the warning stimulus (WS) was briefly presented in the central box (first red square). The appearance of the WS initiated the FP until the imperative stimulus (IS or “go” signal) appeared in the eccentric box (second red square). The arrow illustrates the direction of the correct saccade executed after the IS appearance at the end of the description of the Figure 1A. B, The high uncertainty U distribution was a composite obtained by convolving the anchor duration with a Gaussian kernel. C, Data collection started with either the short or the long anchor duration (counterbalanced between subjects). For a given anchor duration, two blocks of 100 trials each were collected: first, a baseline (B) condition consisting of only one duration; second, a block of trials drawn from the U distribution. Number of trials (‘N TRIALS’) per condition is included in the round brackets at the end of the description of the Figure 1C. D, Distributions of short (left panel) and long (right panel) anchors, grouped in 50-ms bins. Colored traces represent the B and U hazard functions.
- Figure 2.
Analysis of saccade latencies as a function of FP duration. A, Average saccade latency ± SE for different average FP durations. Each dot shows values for the corresponding bin of the distribution together with its SE (whiskers). Gray solid lines represent linear regression fits to the Ushort (left panel) and Ulong (right panel) distributions of the FP together with the 95% SE (gray ribbon). Yellow dotted lines indicate average latency for the B distributions. B, Average saccade latency as a function of reciprocal HR (in a.u. - arbitrary units) for the Ushort (left panel) and Ulong (right panel) distributions.
- Figure 3.
Analysis of the variability of saccadic latencies. A, SD of saccade latency in the different experimental conditions (dots) together with its SE (dark whiskers), and 95% confidence interval (CI, light whiskers). Horizontal gray bars indicate paired analysis between conditions (n.s., not significant). For the equivalence tests related to the magnitude of difference between the SD of the saccade latency, see Extended Data Figure 2-1A. B, Variance of saccadic latencies plotted against different FP lengths. Each dot shows the value for the corresponding bin of the U distributions. The solid line shows a linear regression line together with the standard error of the regression SE (gray ribbon). Yellow dot indicates average variance around anchor durations. C, SD of saccade latencies plotted against HRclassic for different FP lengths. Each dot shows the value for the corresponding bin of the U distributions. Solid lines show linear regression lines together with the standard error of the regression SE (gray ribbon). Yellow dot indicates average SDs around anchor durations.
- Figure 4.
Comparison of dominant hypotheses of temporal preparation and empirical data. Predictions of temporal preparation models (gray dotted curves) versus experimental data (blue lines for the uncertainty U condition and yellow dots for baseline B condition) for average latency (left panels) and SD (right panels). A, Left, Saccadic latency increased as a function of reciprocal of HR (HRrec). Right, The SD of saccadic latency decreased with increasing FP duration, in contradiction with the temporal blurring hypothesis based on HR. B, Left, Saccadic latency decreased with FP duration in contradiction with predictions of the PDF hypothesis. Indeed, where the PDF is maximum, movement latency should be minimum and “go” signal timings infrequently experienced on the sides of the PDF should evoke longer latencies (inverted U-shape). Right, Probabilistic “blurring” hypothesis. Movement timing variability should follow an inverted U-shape distribution. C, Left, As predicted by the fMTP model, a shorter FP duration during trial “n−1” than during the current trial “n” is associated with a relatively shorter movement latency. Right, The fMTP model assumes temporal blurring of the inner representation of FP duration and an increasing saccadic SD for longer FP durations. This is functionally equivalent to the one assumed by the HR hypothesis and was not observed here. D, Hypothetical build up of temporal expectancy of the imperative “go” signal for short and long anchor durations.
Tables
- Table 1
Data preprocessing number and percentage of the trials that entered the final analysis
Number of trials N % of total Total 16,800 100.00 After artifact rejection 15,948 94.93 With visually guided saccades 11,676 69.50 Dataset Model Fixed terms β ± SE 95% CI p-value Random terms σ [ms] Ushort FPn.rs1 Intercept 307.495 ± 14.293 [279.498, 335.467] <2.22 × 10–16 Residual 51.905 FPn −0.054 ± 0.008 [−0.071, −0.038] 1.00 × 10–10 Subject 33.571 Ulong FPn.rs1 Intercept 298.043 ± 20.465 [257.938, 338.114] <2.22 × 10–16 Residual 52.322 FPn −0.027 ± 0.008 [−0.043, −0.011] 9.49 × 10–4 Subject 34.545 Models were fitted using the restricted maximum likelihood method. Fixed and random effect structures were chosen in advance (see Extended Data Tables 1-1 and 1-2). Models were fitted using the Gaussian fit (see Extended Data Fig. 1-1 for the comparison between different distribution choices).
σ, SD of the random terms (subject and residual).
Dataset Model Fixed terms β ± SE 95% CI p-value Random terms σ [ms] Ushort HRrec.rs1 Intercept 217.924 ± 5.306 [207.398, 228.425] <2.22 × 10–16 Residual 51.949 HRrec 0.371 ± 0.060 [0.253, 0.489] 8.86 × 10–10 Subject 33.400 Ulong HRrec.rs1 Intercept 231.100 ± 5.467 [220.272, 241.932] <2.22 × 10–16 Residual 52.329 HRrec 0.190 ± 0.059 [0.074, 0.306] 0.001 Subject 34.503 Models were fitted using the restricted maximum likelihood method.
σ, SD of the random terms (subject and residual).
Dataset Model Fixed terms β ± SE 95% CI p-value Random terms σ [ms] Ushort FPn–1.rs1 Intercept 213.039 ± 14.550 [184.560, 241.535] <2.00 × 10–16 Residual 52.311 FPn–1 0.005 ± 0.008 [−0.011, 0.022] 0.541 Subject 33.102 Ulong FPn–1.rs1 Intercept 205.805 ± 20.649 [165.360, 246.253] <2.00 × 10–16 Residual 52.410 FPn–1 0.011 ± 0.008 [−0.005, 0.027] 0.176 Subject 34.389 Models were fitted using the restricted maximum likelihood method. For the equivalence tests related to the relationship between the saccade latency and FPn– 1 duration, see Extended Data Figure 2-1B.
σ, SD of the random terms (subject and residual).
Dataset Model Fixed terms β ± SE 95% CI p-value Random terms σ [ms] Ushort sequence.rs1 Intercept 220.861 ± 5.287 [210.372, 231.328] <2.22 × 10–16 Residual 52.071 Sequence −0.029 ± 0.006 [−0.041, −0.018] 7.01 × 10–7 Subject 33.453 Ulong sequence.rs1 Intercept 232.557 ± 5.442 [221.764, 243.332] <2.22 × 10–16 Residual 52.321 Sequence −0.020 ± 0.006 [−0.031, −0.008] 8.41 × 10–4 Subject 34.498 Models were fitted using the restricted maximum likelihood method.
σ, SD of the random terms (subject and residual).
- Table 6
Linear models and slope analysis (Ivry and Hazeltine, 1995) results for saccade latency
Dataset Formula β ± SE 95% CI p-value Adj. R2 Ushort Latency −0.051 ± 0.008 [−0.068, −0.033] 3.01 × 10–5 0.73 Latency 0.319 ± 0.074 [0.155, 0.484] 0.001 0.59 σ2 (latency) −18704.922 ± 7683.918 [−35305.020, −2104.826] 0.030 0.26 σ (latency) −23.317 ± 3.831 [−31.748, −14.885] 7.88 × 10–5 0.75 Ulong Latency −0.023 ± 0.005 [−0.035, −0.011] 0.001 0.54 Latency 0.158 ± 0.032 [0.087, 0.228] 5 × 10–4 0.66 σ2 (latency) −42253.758 ± 7100.721 [−57593.93, −26913.580] 4.82 × 10–5 0.71 σ (latency) −22.625 ± 5.603 [−34.957, −10.293] 0.002 0.56 The dataset was averaged across subjects and distinct FPn lengths.
σ2, variance; k, Weber’s fraction; c, time-independent source of response variance; adj., adjusted.
Extended Data Figure 1-1
Diagnostic plots for the FPn.rs1 model refitted using different distributions. A, Gaussian distribution, link: identity. Plots were generated using R package performance (Lüdecke et al, 2021). B, Gaussian distribution, link: log. C, Gaussian distribution, link: identity, fitting the log-transformed data. D, Gamma distribution, link: identity. Plots were generated using R package DHARMa (Hartig, 2020). E, Gamma distribution, link: log. F, Inverse Gaussian distribution, link: identity. G, Inverse Gaussian distribution, link: log. Download Figure 1-1, EPS file.
Table 1-1
Linear mixed models random structure selection for the analysis of FPn, FPn-1 HRrec and sequence effects on saccade latency. Models were fitted using the restricted maximum likelihood method. Download Table 1-1, DOC file.
Table 1-2
Linear mixed models random structure selection for the analysis of FPn, FPn-1 HRrec and sequence effects on saccade latency. Models were fitted using the restricted maximum likelihood method. Download Table 1-2, DOC file.
Extended Data Figure 2-1
Plots of the equivalence test for the short (left panel) and the long anchor (right panel), separately. A, Equivalence test results for the latency SD between different anchors in the U and B distribution. A black square shows mean difference in raw scores between B and U groups with the 98% confidence intervals (black horizontal line). B, Equivalence test results for the FPn–1 effects on the saccade latency. Colored dot shows the mean effect size in standardized scores with the 98% confidence intervals (horizontal colored line). Download Figure 2-1, EPS file.
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