# «Published in final edited form in: European Journal of Neuroscience. (2013) doi: dx.doi.org/10.1111/ejn.12324 Gaze direction affects linear ...»

Ni, J., Tatalovic, M., Straumann, D., Olasagasti, I. (2013) Gaze direction affects linear self-motion heading discrimination in humans. European Journal of Neuroscience. doi: dx.doi.org/10.1111/ejn.12324 were not statistically significant ( 3 = 7.68, n = (10, 7, 7, 14), P = 0.053), but that those for ( s R s L ) / 2 were ( 3 = 9.61, n = (13, 7, 11, 15), P = 0.022). When data from paradigm A and the eccentric position data from paradigm D were pooled (the experimental conditions for eccentric trials in D were the same as in paradigm A), the effect of the paradigm was significant for l o gR L ( 22 = 7.4, n = (24, 7, 7), P =.025) and ( s R s L ) / 2 ( 22 = 9, n = (28, 7, 11), P = 0.011). Tukey’s honestly significant difference test at the 0.05 significance level found differences in the mean rank of l o gR L between alternating fixations ([A,D]) and dark fixations (B), and in the mean rank of ( s R s L ) / 2 between alternating fixations ([A,D]) and sustained fixations (C). Taken together, the group comparisons for the four quantities of interest suggest that the difference in difficulty did not translate into a clear difference in PSEL PSER or BR BL.

Figure 4 Histograms of data pooled across all paradigms with centered head-on-trunk.

Nonparametric measures on the top row (A-C) and parametric measures on the bottom row (D-F).

Panels C and F are the paired comparisons of the same data represented on panels A and D, respectively. Not only the paired differences peak away from zero (C and F), but the population distributions (A and D) have a small overlap.

Figure 4 shows the population distributions pooled across the four paradigms. As expected from symmetry considerations, there was no significant difference between looking right and left (E = 16 and E = -16) for precision (W = 14, n = 32, P = 0.85, Wilcoxon signed-rank test) or sensitivity (W = 14, n = 38, P = 0.14, Wilcoxon signed-rank test) and there was a high degree of overlap between the right and left populations as quantified by the cosine similarity (non-centered Pearson correlation coefficient) of the two histograms (r = 0.94 and r = 0.72 respectively). The effect on PSE Ni, J., Tatalovic, M., Straumann, D., Olasagasti, I. (2013) Gaze direction affects linear self-motion heading discrimination in humans. European Journal of Neuroscience. doi: dx.doi.org/10.1111/ejn.12324 and B on the other hand is substantial. Not only was the distribution of paired differences significantly different from zero (W = 2, n = 32, P = 2.5e-7 and W = 2, n =38, P =5.4e-9 respectively, Wilcoxon signed-rank test) but the two distributions were well separated, with cosine similarity coefficients of r = 0.18 for both PSE and B. Across the four paradigms PSEL PSER varied between

-3.3 and 9 with a median of 5.3 and the 95% confidence derived from bootstrapping with 1000 iterations was between 4.3 and 6.15. BR BL varied between -0.22 and 0.60 with a median of 0.3 and a 95% confidence interval between 0.23 and 0.35.

The average pooled psychometric curves are shown in Figure 5 together with the average difference between the two as a function of trajectory deviation. In principle, the observed change in the proportion of rightward responses could be due to a horizontal shift of perceived direction of motion (or direction of the subjective median plane of the trunk) or by biasing the response towards the direction of eye eccentricity in lapse trials. The first explanation leads to a horizontal shift of the psychometric curves while the second would predict a vertical shift, and the difference in the proportion of rightward responses would not depend on trajectory deviation. Since the effect of trajectory deviation was significant ( 3 = 17.3, n = 32, P = 6e-4, Friedman test), we conclude that, at least at the population level, the result was not simply due to an effect on lapse trials or to a nonspecific increase to report in the direction of eye deviation.

Figure 5 A: The proportion of rightward responses averaged over all 32 subjects in the head centric paradigms. When subjects participated in several paradigms, a within-subjects average was done prior to the average across subjects. B: average of intra-individual differences in rightward reports. The difference in reports when looking right and left is maximal for trajectories close to straight-ahead and decreases for larger trajectory deviations. In both panels error bars represent the 95% confidence interval as estimated from bootstrapping the data with 500 repetitions.

Centered versus deviated eye-in-head The results from the previous paradigms suggested that eye deviation shifts either the point of subjective equivalence or the median plane of the trunk. In this paradigm we asked whether eye eccentricity also affects the uncertainty in the task. A higher uncertainty would be reflected in higher and lower sensitivities when compared with centric eye fixation. A group of subjects performed the task with blocks that had alternating left and right eccentric fixations and blocks in which gaze was always guided towards a center LED. Figure 6A shows the pooled psychometric functions (including the three subjects that showed the reversed eye eccentricity effect) together with the Ni, J., Tatalovic, M., Straumann, D., Olasagasti, I. (2013) Gaze direction affects linear self-motion heading discrimination in humans. European Journal of Neuroscience. doi: dx.doi.org/10.1111/ejn.12324

Figure 6 Paradigm with eccentric and centric eye positions. The goal was to determine whether eye eccentricity also changes sensitivity. A: average psychometric curves across all the subjects in the paradigm.

B: the difference in sensitivity as quantified by log σ and the nonparametric measure s. Individual data is superimposed on the boxplot. The median log σ was lower for the eccentric conditions, but the difference was not statistically significant.

The effect of head-on-trunk deviation We next asked whether head-on-trunk direction would have a similar effect on vestibular direction discrimination. To that end, another group of subjects performed the experiment with headNi, J., Tatalovic, M., Straumann, D., Olasagasti, I. (2013) Gaze direction affects linear self-motion heading discrimination in humans. European Journal of Neuroscience. doi: dx.doi.org/10.1111/ejn.12324 on-trunk displaced to the left 16° (Figure 1). Eccentric head-on-trunk (H = -16°) combined with a centric eye-in-head (E = 0°, gaze aligned with the head) when fixating the left LED, and with an eccentric eye-in-head (E = 16°, gaze aligned with the trunk) when fixating the center LED. As in paradigms A and D one of the two LEDs stayed on during motion (left or center in pseudo-random order in consecutive trials). Only one participant missed a few trials (four). All but one of the 17 subjects showed a significant effect of eye position on the total number of rightward reports. In 13 out of the 17 datasets the proportion of rightward reports was higher for E = 16° than for E = 0°, but 3 out of 17 showed the reversed effect. Since we were interested on the effect of head eccentricity, we excluded the participants with reversed eye effect from further analysis to minimize the impact of such a confounding factor. Therefore, the following analysis excludes the three reversed datasets. This left 13 parametric and 14 non-parametric datasets.

Figure 7 Bias and PSE with different combinations of eye and head directions. Data came from three datasets: (E=0˚,H=0˚) data from paradigm D, (E=16˚, H=0˚) and (E=-16˚, H=0˚) from paradigm A, and (E=0˚, H=-16˚) and (E=16˚, H=-16˚) from the head eccentric paradigm. With centered eye-in-head (E=0˚), there was a significant difference between the head centric and eccentric conditions. The two conditions with gaze to the left (G = -16˚) did not differ substantially providing evidence that gaze (the combination of eye-in-head and head-on-trunk) might be the determining factor. However, when looking at the condition with both eye- and head-deviations the distribution overlapped those with the same eye position (E=16˚, H=0˚) and same gaze (E=0˚, H=0˚) and the median value was not substantially different from the condition with the same eye position, indicating that the combination of eye and head eccentricity was highly variable across subjects.

To determine the effect of head eccentricity we compared the results in this paradigm with those in the two head-centered paradigms with alternating gaze directions (A and D). The datasets in paradigm A (10 parametric, 13 non-parametric) contributed the data for comparison with the H = 0°, E = +/-16° conditions, and the datasets in paradigm D (14 parametric, 15 non-parametric) the data for comparison with H = 0°, E = 0°. In the following n refers to the number of datasets in a given group.

Ni, J., Tatalovic, M., Straumann, D., Olasagasti, I. (2013) Gaze direction affects linear self-motion heading discrimination in humans. European Journal of Neuroscience. doi: dx.doi.org/10.1111/ejn.12324 First, to isolate the effect of head deviation we compared centric eye conditions (E = 0°) with and without head deviation. PSE (H = -16°, E = 0°) was between -0.4° and 4.6° with a median of

2.2°. The median PSE with head eccentric (n = 13) deviated 2.5° to the right with respect to head centric (H = 0°, E = 0°, n = 14) ( 12 = 10, n = (13, 14), P = 0.001, Kruskal-Wallis test). Thus for E = 0°, a deviation of the head to the left shifted the psychometric curve to the right (higher proportion of leftward reports), that is, in the same direction as the shift due to eye deviations for most subjects described in the previous sections. There was a corresponding shift in the bias measure, which varied between 0.38 and 0.69 with a median of 0.5 with centered head (n = 15), and from 0.2 and 0.54 with a median of 0.39 with head eccentric (n = 14). Therefore, with head deviated to the left, the proportion of rightward responses was 20% smaller ( 12 = 8.8, P = 0.003, n = (14,15), KruskalWallis test). We conclude that head eccentricity affected the proportion of rightward reports in the same direction as eye eccentricity did. Indeed, the difference in PSE median values when comparing the same gaze conditions attained with only head deviation (E = 0°, H = -16°, n = 13) or only eye deviation (E = -16°, H = 0°, n = 10), (columns 4 and 5 in Figure 7), was only -0.1° ( 12 = 0.5, n = (13, 10), P = 0.49, Kruskal-Wallis test).

Finally, we compared the condition with simultaneous eye and head deviations (H = -16°, E = 16°) to the head-centric results with the same eye position (H = 0°, E = 16°) or same gaze (H = 0°, E = 0°). If the effects of eye and head were of the same size and independent, we should recover the head effect mentioned above for the first comparison and should find no difference for the second comparison. For the same eye position, the difference in median PSE was -0.15° ( 12 = 0.015, n = (13, 10), P = 0.90, Kruskal-Wallis test), while the difference in bias was -0.03 ( 12 = 1.0, n = (14, 13), P = 0.31, Kruskal-Wallis test). For the comparisons with the same gaze the difference in median PSE was -1.5° ( 12 = 3.1, n = (13, 14), P = 0.081, Kruskal-Wallis test) and the difference in bias 0.11 ( 12 = 4.8, n = (14, 15), P = 0.029, Kruskal-Wallis test).

In summary, we found an effect of head direction that looked like the effect of eye direction but only when head deviation was not simultaneous with eye deviation. In the condition with both head and eye deviations, the effect of eye direction was stronger.

Discussion Summary and relation to results in the literature Both the direction of eye-in-head and the direction of head-on-trunk affected subjective reports about motion direction during passive translations. Although the deviation of the trajectories with respect to the trunk was the same across eye and head directions, most participants were more likely to judge a motion as ‘to the right’ with respect to their trunk when eyes deviated to the right, and more likely to judge motion as ‘to the left’ when eyes deviated to the left. Likewise, we found evidence that with leftward head-on-trunk there were more reports to the left. Only a few subjects showed a significant and opposite effect of eye/head direction. The observed changes in the proportion of rightward reports were consistent with a shift of the perceived direction of motion towards the eye/head (or a shift of the internal representation of the trunk straight ahead in the opposite direction). At the population level there was no bias when eye, head and trunk were aligned;

and the shift, although in opposite directions, was of the same magnitude for right and left eye deviations (Figure 7A). Despite introducing a shift in heading perception, eye deviation had no Ni, J., Tatalovic, M., Straumann, D., Olasagasti, I. (2013) Gaze direction affects linear self-motion heading discrimination in humans. European Journal of Neuroscience. doi: dx.doi.org/10.1111/ejn.12324 measurable effect on the uncertainty of the task; sensitivities and thresholds were not significantly different when comparing centered and deviated eye conditions. Assuming that the point of subjective equivalence can be written as PSE = aE + b, we were able to estimate the weight of eye deviation, a = 0.17 (0.06) (median and median absolute deviation).

This is the first time that shifts evoked by eye- and head- direction are reported in a task involving the perception of linear motion direction based on vestibular cues. However, the effect of eye eccentricity is well documented in auditory and visual localization and in the perception of the head straight ahead (Bohlander, 1984; Lewald, 1997; Lewald & Ehrenstein, 2000a; Razavi et al.,2007; Cui et al., 2010) and so is the effect of head eccentricity (Lewald & Ehrenstein, 1998;

Lewald et al., 2000b). Moreover, the effects of eye- and head-eccentricity are equivalent in their influence on visual and auditory stimuli (Lewald et al., 2000b). When eye- or head-eccentricity is of short duration, the auditory median plane and perceived straight ahead of the head shift in the direction of eccentric gaze. This leads to a shift of free-field sound localization in the opposite direction (Lewald&Geltzmann, 2006). However, when eye position is maintained eccentrically for longer periods both perceived head straight ahead and perceived free-field sound localization shift toward eye eccentricity with a larger shift of perceived straight ahead than sound localization (Cui et al., 2010).