Fig 1.
Experimental apparatus and task structure.
Each participant made planar reaching movements while grasping the KINARM handle. A mirror system occluded vision of the hand and created the impression that the hand and visual targets were in the same plane. Red start target, green reach target, and white cursor feedback are shown.
Fig 2.
Experimental protocols: Example adaptation phase trial conditions.
(A) Experiment 1: Midpoint-only feedback (large uncertainty). (B) Experiment 2: Matched midpoint and endpoint feedback (low uncertainty). (C) Experiment 3: Unmatched midpoint (moderate uncertainty) and endpoint (low uncertainty) feedback. Bottom, middle and top slides represent start, middle and end of reach respectively. coloured panels represent the possible uncertainty conditions (blue: σL, orange: σM, green: σH, red: σ∞). The example condition applied is outlined in black. In all experiments, a no-feedback washout phase followed the adaptation phase.
Fig 3.
Experiment 1 mean initial movement vector across participants per trial.
(a) Dot colour for trial t represents the level of sensory uncertainty applied at midpoint on the previous trial t − 1. Performance during the washout phase is shown by purple x’s. The inset bar graph shows the mean difference between the last 10 trials of adaptation and the first 10 trials of washout plotted separately for each uncertainty level. Error bars are 95% confidence intervals. (b) Dot colour for trial t represents the error at reach midpoint on the same trial. (c) Dot colour for trial t represents the error at the reach endpoint on the previous trial t − 1.
Table 1.
Experiment 1 pairwise comparisons examining differences between uncertainty trial types in adaptation—washout difference scores.
A and B indicate the uncertainty trial types being compared; T is the observed t-statistic; dof is the degrees of freedom of the test; p-corr is the Bonferroni-corrected p-value; hedges is the Hedges G measure of effect size.
Fig 4.
Experiment 1 linear regression fit to initial movement vector.
(a) Initial movement vector predictions from the regression model superimposed over the behavioural data. (b) Point and 95% confidence interval estimates from best fitting regression models. Coefficients of the regression for predicting initial movement vector are shown in blue and coefficients for predicting change in initial movement vector are shown in orange.
Table 2.
Experiment 1 regression results for predicting initial movement vector from error and sensory uncertainty terms.
These results correspond to the blue confidence intervals displayed in Fig 3. The coef column contains β coefficients, the se column contains standard errors of these coefficients, the T column contains corresponding t-statistic, the pval column contains corresponding p-values, the CI[2.5%] and CI[97.5%] columns give the 95% confidence interval, and the relimp column gives the corresponding relative importance.
Fig 5.
Experiment 1 change in initial movement vector and linear regression fits.
(a) Violin plot depicting in the distribution of mean changes in initial movement vector across all adaptation phase trials of the experiment separately for each uncertainty level. The inset of each violin shows a box plot in which the white dot indicates the median data value, the black box spans the 25% to 75% percentiles, and the whiskers extend to the most extreme data points. (b) Scatter plot showing the mean change in initial movement vector as a function of error experienced at midpoint. Lines indicate fitted simple linear regression lines. These regression lines do not correspond to the coefficients included in Table 3, rows 6–8) and are included only as a visual aid. colours indicate uncertainty level.
Table 3.
Experiment 1 regression results for predicting change in initial movement vector from error and sensory uncertainty terms. These results correspond to the orange confidence intervals displayed in Fig 3.
The coef column contains β coefficients, the se column contains standard errors of these coefficients, the T column contains corresponding t-statistic, the pval column contains corresponding p-values, the CI[2.5%] and CI[97.5%] columns give the 95% confidence interval, and the relimp column gives the corresponding relative importance.
Fig 6.
Experiment 1 feedback integration (endpoint hand angle—initial movement vector).
(a) Violin plot depicting the distribution of mean feedback integration across all adaptation phase trials of the experiment separately for each uncertainty level. The inset of each violin shows a box plot in which the white dot indicates the median data value, the black box spans the 25% to 75% percentiles, and the whiskers extend to the most extreme data points. (b) Scatter plot showing the mean feedback integration as a function of error experienced at midpoint. Lines indicate fitted linear regression lines, corresponding to the coefficients included in Table 4, rows 6–8). Point and line colour indicates uncertainty level.
Table 4.
Experiment 1 regression results for predicting feedback integration (endpoint hand angle—initial movement vector) from error and sensory uncertainty terms.
The coef column contains β coefficients, the se column contains standard errors of these coefficients, the T column contains corresponding t-statistic, the pval column contains corresponding p-values, the CI[2.5%] and CI[97.5%] columns give the 95% confidence interval, and the relimp column gives the corresponding relative importance.
Fig 7.
Experiment 2 mean initial movement vector across participants per trial.
(a) The colour of the dot on trial t represents the level of sensory uncertainty applied at midpoint on the previous trial t − 1. Performance during the washout phase is shown by purple x’s. The inset bar graph shows the mean difference between the last 10 trials of adaptation and the first 10 trials of washout plotted separately for each uncertainty level. Error bars are 95% confidence intervals. (b) The colour of the dots on trial t represents the error at the reach midpoint on the same trial. (c) The colour of the dots on trial t represents the error at the reach endpoint on the previous trial t − 1.
Table 5.
Experiment 2 pairwise comparisons examining differences between uncertainty trial types in adaptation—washout difference scores.
A and B indicate the uncertainty trial types being compared; T is the observed t-statistic; dof is the degrees of freedom of the test; p-corr is the Bonferroni-corrected p-value; hedges is the Hedges G measure of effect size.
Fig 8.
Experiment 2 linear regression fit to initial movement vector.
(a) Initial movement vector predictions from the regression model superimposed over the behavioural data. (b) Point and 95% confidence interval estimates from best fitting regression models. Coefficients of the regression for predicting initial movement vector are shown in blue and coefficients for predicting change in initial movement vector are shown in orange.
Table 6.
Experiment 2 regression results for predicting initial movement vector from error and sensory uncertainty terms.
These results correspond to the blue confidence intervals displayed in Fig 8. The coef column contains β coefficients, the se column contains standard errors of these coefficients, the T column contains corresponding t-statistic, the pval column contains corresponding p-values, the CI[2.5%] and CI[97.5%] columns give the 95% confidence interval, and the relimp column gives the corresponding relative importance.
Fig 9.
Experiment 2 change in initial movement vector and linear regression fits.
(a) Violin plot depicting the distribution of mean changes in initial movement vector across all adaptation phase trials of the experiment separately for each midpoint/endpoint uncertainty combination, colour coded as per Fig 6a. The inset of each violin shows a box plot in which the white dot indicates the median data value, the black box spans the 25% to 75% percentiles, and the whiskers extend to the most extreme data points. (b) Scatter plot showing the mean change in initial movement vector as a function of error experienced at midpoint. Point and line colour indicates uncertainty level. (c) Scatter plot showing the mean change in initial movement vector as a function of error experienced at endpoint on the previous trial. Point and line colour indicates uncertainty level. The lines in panel B and C indicate fitted simple linear regression lines. These regression lines do not correspond to the coefficients included in Table 7) and are included only as a visual aid.
Table 7.
Experiment 2 regression results for predicting change in initial movement vector from error and sensory uncertainty terms.
These results correspond to the orange confidence intervals displayed in Fig 8. The coef column contains β coefficients, the se column contains standard errors of these coefficients, the T column contains corresponding t-statistic, the pval column contains corresponding p-values, the CI[2.5%] and CI[97.5%] columns give the 95% confidence interval, and the relimp column gives the corresponding relative importance.
Fig 10.
Experiment 2 feedback integration (endpoint hand angle—initial movement vector).
(a) Violin plot depicting the distribution of mean feedback integration across all adaptation phase trials of the experiment separately for each uncertainty level. The inset of each violin shows a box plot in which the white dot indicates the median data value, the black box spans the 25% to 75% percentiles, and the whiskers extend to the most extreme data points. (b) Scatter plot showing the mean feedback integration as a function of error experienced at midpoint. Lines indicate fitted linear regression lines, corresponding to the coefficients included in Table 8, rows 6–8). Point and line colour indicates uncertainty level.
Table 8.
Experiment 2 regression results for predicting feedback integration (endpoint hand angle—initial movement vector) from error and sensory uncertainty terms.
The coef column contains β coefficients, the se column contains standard errors of these coefficients, the T column contains corresponding t-statistic, the pval column contains corresponding p-values, the CI[2.5%] and CI[97.5%] columns give the 95% confidence interval, and the relimp column gives the corresponding relative importance.
Fig 11.
Experiment 3 mean initial movement vector across participants per trial.
(a) The colour of the dot on trial t represents the combination of sensory uncertainty applied at midpoint and endpoint on the previous trial t − 1. Specifically, σLL in blue, σLH in orange, σHL in green, and σHH in red. Performance during the washout phase is shown by purple x’s. The inset bar graph shows the mean difference between the last 10 trials of adaptation and the first 10 trials of washout plotted separately for each trial type. Error bars are 95% confidence intervals. (b) The colour of the dots on trial t represents the error at the reach midpoint on the previous trial t − 1. (c) The colour of the dots on trial t represents the error at the reach endpoint on the previous trial t − 1.
Table 9.
Experiment 3 pairwise comparisons examining differences between uncertainty trial types in adaptation—washout difference scores.
A and B indicate the uncertainty trial types being compared; T is the observed t-statistic; dof is the degrees of freedom of the test; p-corr is the Bonferroni-corrected p-value; hedges is the Hedges G measure of effect size.
Fig 12.
Experiment 3 linear regression fit to initial movement vector.
(a) Initial movement vector predictions from the regression model superimposed over the behavioural data. (b) Point and 95% confidence interval estimates from best fitting regression models. Coefficients of the regression for predicting initial movement vector are shown in blue and coefficients for predicting change in initial movement vector are shown in orange.
Table 10.
Experiment 3 regression results for predicting initial movement vector from error and sensory uncertainty terms.
These results correspond to the blue confidence intervals displayed in Fig 12. The coef column contains β coefficients, the se column contains standard errors of these coefficients, the T column contains corresponding t-statistic, the pval column contains corresponding p-values, the CI[2.5%] and CI[97.5%] columns give the 95% confidence interval, and the relimp column gives the corresponding relative importance.
Fig 13.
Experiment 3 change in initial movement vector and linear regression fits.
(a) Violin plot depicting the distribution of mean changes in initial movement vector across all adaptation phase trials of the experiment separately for each midpoint/endpoint uncertainty combination, colour coded as per Fig 11a. The inset of each violin shows a box plot in which the white dot indicates the median data value, the black box spans the 25% to 75% percentiles, and the whiskers extend to the most extreme data points. (b) Scatter plot showing the mean change in initial movement vector as a function of error experienced at midpoint. Point and line colour indicates uncertainty level. (c) Scatter plot showing the mean change in initial movement vector as a function of error experienced at endpoint on the previous trial. The lines in panel B and C indicate fitted simple linear regression lines. These regression lines do not correspond to the coefficients included in Table 11) and are included only as a visual aid.
Table 11.
Experiment 3 regression results for predicting change in initial movement vector from error and sensory uncertainty terms.
These results correspond to the orange confidence intervals displayed in Fig 12. The coef column contains β coefficients, the se column contains standard errors of these coefficients, the T column contains corresponding t-statistic, the pval column contains corresponding p-values, the CI[2.5%] and CI[97.5%] columns give the 95% confidence interval, and the relimp column gives the corresponding relative importance.
Fig 14.
Experiment 3 feedback integration (endpoint hand angle—initial movement vector).
(a) Violin plot depicting the distribution of mean feedback integration across all adaptation phase trials of the experiment separately for each midpoint uncertainty level. The inset of each violin shows a box plot in which the white dot indicates the median data value, the black box spans the 25% to 75% percentiles, and the whiskers extend to the most extreme data points. (b) Scatter plot showing the mean feedback integration as a function of error experienced at midpoint. Lines indicate fitted linear regression lines, corresponding to the coefficients included in Table 12, row 4). Point and line colour indicates uncertainty level.
Table 12.
Experiment 3 regression results for predicting feedback integration (endpoint hand angle—initial movement vector) from error and midpoint sensory uncertainty terms.
The coef column contains β coefficients, the se column contains standard errors of these coefficients, the T column contains corresponding t-statistic, the pval column contains corresponding p-values, the CI[2.5%] and CI[97.5%] columns give the 95% confidence interval, and the relimp column gives the corresponding relative importance.
Fig 15.
Bar graph depicting model BIC values for Experiments 1,2 and 3.
Error-scaling model variants in blue. Retention-scaling variants in orange. Bias-scaling variants in green. State-aim variants in red. Output-aim variants in purple. Opacity indicate model sub-type: Non-negative two-state models have 100% opacity. Two-state models have 50% opacity and one-state models have 25% opacity. Error-bars represent 95% confidence intervals.
Fig 16.
Model rank analysis showing the number of particpants that were best fit (rank 1), second best fit (rank 2), third best fit (rank 3) etc.
by a model of each type. Results for Experiment 1 are shown on the left using shades of blue, results for Experiment 2 are shown in the middle using shades of green, and results for Experiment 3 are shown on the right using shades of red. Deeper colours indicate a greater count.
Fig 17.
Left column shows initial movement vectors averaged across participants overlaid with the average full model prediction of the (A) Two-state error-scaling model. (C) Two-state retention-scaling model. (E) Two-state bias-scaling model. (G) Two-state state-aim-scaling model (I) Two-state output-aim-scaling model. Right column shows corresponding model fits to endpoint hand-angles. Here, human performance averaged across participants is shown in blue. Model predictions in orange. Fit lines and R2 values represent average of models fit to individual subjects.
Fig 18.
Left column shows initial movement vectors averaged across participants overlaid with the average full model prediction of the (A) Two-state error-scaling model. (C) Two-state retention-scaling model. (E) Two-state bias-scaling model. (G) Two-state state-aim-scaling model (I) Two-state output-aim-scaling model. Right column shows corresponding model fits to endpoint hand-angles. Here, human performance averaged across participants is shown in blue. Model predictions in orange. Fit lines and R2 values represent average of models fit to individual subjects.
Fig 19.
Left column shows initial movement vectors averaged across participants overlaid with the average full model prediction of the (A) Two-state error-scaling model. (C) Two-state retention-scaling model. (E) Two-state bias-scaling model. (G) Two-state state-aim-scaling model (I) Two-state output-aim-scaling model. Right column shows the corresponding model fits to endpoint hand-angles. Here, human performance averaged across participants is shown in blue. Model predictions in orange. Fit lines and R2 values represent average of models fit to individual subjects.
Table 13.
State-space model parameter bounds.
Lower and upper values are indicated by (lb, ub), respectively. The nomenclature (-,-) indicates that this parameter was not present in the corresponding model. Blank entries indicate that the bounds were inhereted from the one-state model.