Figure 3. Effect of control dynamics on participants’ responses.

(A) Participant average of radial and angular response gains in each condition, with trials grouped into tertiles of increasing time constant τ. Error bars denote ±1 SEM. (B) Effect of time constant $\tau$ on radial (left) and angular (right) residual error, for an example participant (Figure 3—source data 1). Solid lines represent linear regression fits and ellipses the 68% confidence interval of the distribution for each sensory condition. Dashed lines denote zero residual error (i.e. stopping location matches mean response). (C) Correlations of radial (${\epsilon }_r$) and angular (${\epsilon }_{\theta }$) residual errors with the time constant for all participants. Ellipses indicate the 68% confidence intervals of the distribution of data points for each sensory condition. Solid diagonal line has unit slope. Across participants, radial correlations, which were larger for the vestibular condition, were greater than angular correlations (see also Appendix 2—table 2). (D) Linear regression coefficients for the prediction of participants’ response location (final position:,${\displaystyle \tilde{r},}$ ${\displaystyle \tilde{\theta }}$; left and right, respectively) from initial target location ($r$,$\theta$) and the interaction between initial target location and the time constant (${\displaystyle r\cdot \tau }$,${\displaystyle \theta \cdot \tau }$) (all variables were standardized before regressing, see Materials and methods; Figure 3—source data 2). Asterisks denote statistical significance of the difference in coefficient values of the interaction terms across sensory conditions (paired t-test; *: p<0.05, **: p<0.01, ***: p<0.001; see main text). Error bars denote ±1 SEM. Note a qualitative agreement between the terms that included target location only and the gains calculated with the simple linear regression model (Figure 2B). (E) Comparison of actual and null-case (no adaptation) response gains, for radial (top) and angular (bottom) components, respectively (average across participants). Dashed lines represent unity lines, that is, actual response gain corresponds to no adaptation. Inset: Regression slopes between actual and null-case response gains. A slope of 0 or 1 corresponds to perfect or no adaptation (gray dashed lines), respectively. Error bars denote ±1 SEM.

Figure 3—figure supplement 1. Effect of time constant on residual errors.

(A) Sampling distributions of the time constant for all three sensory conditions across participants.

The sampling distribution both across participants and across conditions is almost identical.

Transparent lines and thick lines represent the individual sampling distributions of participants and their mean, respectively. (B–J) Effect of the time constant on radial (left) and angular (right) residual error, for a large subset of participants.Solid lines represent linear regression fits (see Appendix 2—table 3 for individual regression coefficient values). Dashed lines denote zero residual error (i.e. stopping location matches mean response).

Figure 3—figure supplement 2. Partial correlation analysis.

(A) Partial correlation coefficients for prediction of stopping distance ${\displaystyle \tilde{r}}$ (relative to starting position) from initial target distance ($r$), τ, and the interaction of the two ($r\tau$), for all participants across sensory conditions.

Values at each bar group represent the average coefficient value across participants ±1 standard deviation. The contribution of the τ-only term was considered insignificant across all conditions. The simplified version of this model would be: ${\displaystyle \tilde{r}=r\left(\alpha +\gamma \tau \right)}$ , which implies that the radial gain is τ-dependent. (B) Partial correlation coefficients for prediction of stopping angle ${\displaystyle \tilde{\theta }}$ (relative to starting position) from initial target angle ($\theta$), τ, and the interaction of the two ($\theta \tau$), for all participants across sensory conditions. Values at each bar group represent the average coefficient value across participants ±1 standard deviation. In agreement with the findings for the response distance, the contribution of the τ-only term was considered insignificant across all conditions. The simplified version of this model would be: ${\displaystyle \tilde{\theta }=\theta \left(\alpha +\gamma \tau \right)}$ , which implies that the angular gain is also τ-dependent.