Each panel shows the movement direction errors predicted for different values of α_MV and α_INV , which represent the relative weighting of visual feedback at the first and second stages of reach planning, respectively (see Methods) . Both panels include the model predictions for α_MV = 0.9, α_INV = 0.3 (black lines), corresponding to the values expected for reaches to a visual target with fingertip feedback6. (a) Proprioceptive targets in Experiment 1 are expected to result in a lower value of α_MV. (b) Arm feedback in Experiment 2 is expected to result in a higher value of α_INV.

(a) Raw reach trajectories for a representative subject. Filled symbols, reach targets; corresponding open symbols, reach endpoints. (b) Initial reach direction with respect to target direction, using the color conventions of (a). (c) Reach errors induced by visual feedback shifts, computed by subtracting the baseline directional biases (dotted lines in b) from the initial directions in the shifted conditions (solid lines in b). Model fits, dashed lines. Best-fit weighting parameters: α_MV = 0.96, α_INV = 0.32 for visual-target reaches and α_MV = 0.49, α_INV = 0.19 for proprioceptive-target reaches. Error bars, ±1 s.e.m.

(a,b) Fit values of α_MV and α_INV for reaches to visual and proprioceptive targets, respectively. Ellipses represent 1 s.e.m.. Dotted lines, α_INV = α_MV and α_INV = 0. (c) Differences in model fit between visual- and proprioceptive target reaches. The top left half of the symbol is filled if the task-dependent change in α_MV is significant (permutation test, P < 0.05), and the bottom right half is filled if the change in α_INV is significant. +, average across subjects. In all plots, the gray symbols are for the example subject shown in Figure 4.

(a,b) Fit values of α_MV and α_INV for fingertip-feedback and arm-feedback trials, respectively. (c) Differences in model fit between arm- and fingertip-feedback reaches. In all plots, the gray dot represents the subject whose data is shown in Figure 7a and b. Other plotting conventions as in Figure 6.

(a) Error in planned movement direction resulting from a leftward error in the position estimate used to plan the movement vector (“MV error”). This error is caused by a leftward shift of the visual feedback. The planned movement direction for a reach to the target at 90° (blue dot) differs from the true hand-to-target direction, resulting in a clockwise error (blue arrow). (b, c) Error in initial movement direction resulting from a leftward error in the position estimate used to evaluate the inverse model of the arm and compute the motor command (“INV error”). The wrong joint angle displacement (motor command) is planned for the desired movement vector (b), resulting in a movement error (c). (d) The bimodal MV error pattern resulting from a leftward error in estimated position. The blue arrow represents the MV error shown in (a). (e) A leftward error in estimated position results clockwise errors for all target directions. (f) Measured errors in initial direction are a combined effect of MV and INV errors (black curve). A rightward error in position estimates would produce an error pattern of opposite sign (gray curve). Here and in subsequent figures, 0° refers to a rightward vector and positive angles are counterclockwise.

(a) Virtual visual feedback setup. (b) In Experiment 1 a visual and a proprioceptive target were present on every trial; the “go” signal cued subjects which reach to make. Visual feedback of the fingertip position was either veridical (gray dot) or shifted leftward (white dot) or rightward by 6 cm. (c) In Experiment 2, subjects reached to visual targets with visual feedback that showed either the fingertip or a simple, polygonal rendering of the arm. Visual feedback either reflected the true position of the fingertip or was shifted leftward (white dot, polygon) or rightward by 7 cm.

(a) Average initial direction (±1 s.e.m.), with respect to target direction, for visual- and proprioceptive-target reaches. (b) Average errors in initial direction (±1 s.e.m.). Color conventions as in Figure 4.

(a,b) Data from a representative subject in the fingertip-feedback and arm-feedback conditions, respectively. Gray, rightward visual shift; black, leftward visual shift; dashed lines, mean error across the six target directions. Error bars, ±1 s.e.m.. Arrows indicate ΔE̅, the difference between the mean errors for rightward- and leftward-shifted visual feedback. (c) Differences in mean errors for all subjects. Gray dot, example subject whose data are shown in (a) and (b); dashed line, ΔE̅_Arm = ΔE̅_Fingertip.