## Results: 10

1.

Joint direction-disparity tuning profile for a non-DDD, disparity-tuned, congruent MSTd cell. For this neuron, direction and disparity tuning are essentially separable, such that disparity tuning is similar for different directions and direction tuning is similar across disparities. Global DSDI = 0.707 (p<0.001, permutation test). Format as in Fig. 2C.

2.

Dependence of DSDI on dot density and stimulus speed. Data are shown for non-DDD cells from area MSTd.

**(A)**DSDI measured at a higher dot density (0.01 dots.deg^{−2}) is plotted against DSDI measured at the standard density (0.002 dots.deg^{−2}, n=21).**(B)**DSDI is measured as a function of stimulus speed for a subset of MSTd neurons (n=38).3.

Viewing geometry and the relationships between depth and retinal velocity.

**(A)**When a subject fixates a world-fixed target while translating upwards, near objects move downward on the display screen whereas far objects move upward.**(B)**When the same self-translation occurs while fixating a head-fixed target, both near and far objects move downward in the display.4.

Population summary of DSDI and speed preferences.

**(A), (B)**Distributions of the global DSDI (computed across all motion directions) for disparity-selective non-DDD neurons from areas MSTd (n=49) and VIP (n=36).**(C), (D)**Distributions of preferred speed for MSTd (n=41) and VIP (n=73) neurons. Data are color coded to represent visual only neurons (red) and multisensory congruent (green) or opposite (blue) cells.5.

Example disparity tuning curves and Gabor fits for MSTd and VIP neurons. For each neuron/row, disparity tuning is shown for the direction of maximum DDI (left) and for the direction 180° opposite to it (right). Data are shown for two DDD cells from MSTd

**(A, B),**one non-DDD cell from MSTd**(C),**and one non-DDD neuron from VIP**(D)**. Smooth curves represent Gabor function fits (see*Materials and Methods*). Gabor fits are shown for both directions of motion for DDD cells, but only for the maximum DDI direction for non-DDD cells.6.

Population summary of response patterns for DDD cells. For each neuron, the scatter plot shows the difference in average response between preferred and null directions at far disparities (ordinate) vs. the corresponding difference in response at near disparities (abscissa). Data are shown only for DDD neurons from MSTd (red) and VIP (blue). Insets a–e show disparity tuning curves for preferred and null directions for 5 different example neurons, corresponding to the labeled data points in the scatter plot.

7.

Examples of two DDD neurons from area MSTd.

**(A)**For this cell, disparity preference reversed for opposite motion directions (left), and direction preference reversed for near versus far disparities (top).**(B)**For this neuron, disparity preference reversed for opposite motion directions (left), but direction preference did not reverse for near versus far disparities (top). Format as in Fig. 2C and 3.**(C)**The depth-sign-discrimination-index (DSDI) of the 3 disparity-selective example neurons (from Figs. 3, 4A, and 4B) is plotted as a function of motion direction. For non-DDD cells like the one from Fig. 3, DSDI changes little with direction of motion (red). For DDD cells (cyan, blue), DSDI shows a strong reversal in sign across different motion directions.8.

Population summary of dependence of DSDI on motion direction. Data are averaged across all disparity-selective neurons from MSTd

**(A, C)**and VIP**(B, D)**, and are shown separately for DDD (A, B) and non-DDD (C, D) cells. Data are color-coded to represent visual-only neurons (red) and multisensory congruent (green) or opposite (blue) cells. Before averages were computed, data for each neuron were horizontally shifted and wrapped such that the peaks of all DSDI curves aligned at a direction of 90°. The necessary shift for each neuron was determined by computing a cross-correlation between the DSDI vs. direction curve and a sinusoid (see*Materials and Methods*). The numbers of neurons contributing to each summary curve are as follows: A) 3 congruent cells, 3 opposite cells, 17 visual-only cells; B) 1 congruent cell, 4 visual-only cells; C) 9 congruent cells, 11 opposite cells, 29 visual-only cells; D) 5 congruent cells, 5 opposite cells, 26 visual-only cells.9.

Comparison of disparity selectivity in areas MSTd, VIP, and MT. The top row shows distributions of the disparity discrimination index (DDI)

**(A)**, preferred disparity**(B),**and disparity frequency**(C)**parameters. Panel A shows data for all neurons tested: 103 MSTd neurons (red), 101 VIP cells (blue), and 501 MT neurons (green). Panels B and C show data for 55 MSTd cells and 29 VIP neurons that had significant disparity tuning (p<0.01, one-way ANOVA) for the max DDI direction and were well-fit by the Gabor function (R^{2}>0.8) (see*Materials and Methods*). The MT data in panels B and C represent 453 MT neurons with significant disparity tuning (p<0.01) (DeAngelis and Uka, 2003). Numbers above arrowheads show the median values for each distribution.**(D)**DDI is plotted as a function of receptive field eccentricity for neurons from MT (n=501), MSTd (n=65), and VIP (n=28).**(E)**Preferred disparity as a function of eccentricity (MT: n=453; MSTd: n=41; VIP: n=15).**(F)**Disparity frequency as a function of eccentricity, for the same samples of neurons as in panel E.10.

3D heading tuning and joint disparity-direction tuning for an ‘opposite’ MSTd neuron. (

**A, B**) 3D heading tuning is shown for the vestibular**(A)**and visual**(B)**stimulus conditions as color contour maps of mean firing rate as a function of azimuth and elevation angles. Each contour map shows the Lambert cylindrical equal-area projection of the spherical data onto Cartesian coordinates (Gu et al., 2006). In this projection, the ordinate is a sinusoidally transformed version of elevation angle. Tuning curves along the margins of each color map illustrate mean firing rates plotted as a function of either elevation or azimuth (averaged across azimuth or elevation, respectively).**(C)**The joint disparity-direction tuning profile of the same MSTd neuron is shown as a color-contour map, where direction of motion is plotted on the abscissa and binocular disparity on the ordinate. Tuning curves along the margins show direction tuning for each disparity (top) and disparity tuning for each direction (left). Dashed lines denote spontaneous activity levels. This neuron was direction-tuned (ANOVA, p<0.001) but not disparity-tuned (ANOVA, p=0.135).