The first of these additional analyses addresses the fact that the analysis so far is based on responses averaged over many trials. With such data, the WTA outcome is manifest
only when the Contrast Ratio is
outside the Transition Zone. However, if the motion signals are very noisy then it is possible that a WTA situation also prevails
inside the Transition Zone. For example, a mean Response Ratio of 0.5 might have resulted because torsional eye movements were effectively driven exclusively by the 5
f component in half of the trials and exclusively by the 3
f component in the other half of the trials. If this were the case, then we would expect the distribution of the tOFRs to a given 3
f5
f stimulus to be bimodal inside the Transition Zone and unimodal outside. In the previous studies, the response distributions were always unimodal and well fit by Gaussian functions with comparable
SDs, even near the center of the Transition Zone when the competing sine waves were of similar contrast, and the response distributions with the pure 3
f and 5
f stimuli showed only minor overlap. We found the same in the present study: see the sample data in
Figure 7A obtained from subject FAM when the 3
f grating (contrast, 37.5%) rotated CCW and the 5
f grating (contrast, 31.6%) rotated CW. The response distributions here with all three stimuli were well fit by a Gaussian function (smooth curves in
Figure 7A), with
r 2 values ranging from 0.88 to 0.97, and the
SD was actually smaller with the dual (3
f5
f) stimuli than with the single (pure 3
f, pure 5
f) stimuli: see the orange, green, and gray histograms/curves, respectively, in
Figure 7A. Very similar data were obtained from the other two subjects and, significantly, the standard deviation of the actual response distributions (rather than of the best-fit Gaussians) with the 3
f5
f stimuli for which the Response Ratio was closest to 0.5 (the center of the Transition Zone) were never significantly larger—and in 3/12 cases were significantly smaller—than those of the response distributions with the pure 3
f and pure 5
f stimuli of matching contrast (Fischer test). Also, in 10/12 cases, the
SDs of the 3
f5
f distributions near the center of the Transition Zone were not significantly different from the
SDs of the distributions for which the Response Ratios were closest to zero or unity (Fischer test). This all strongly suggests that the WTA situation does
not operate inside the Transition Zone, and in order to confirm this we ran a simulation. For this, we first used the
mean responses to the three stimuli and
Expression 4 to estimate the Response Ratio and then simulated the response distribution predicted by the WTA model for the 3
f5
f stimuli by summing the response distributions obtained with the pure 3
f and 5
f stimuli, weighted in accordance with this Response Ratio. It was clear from this that the
simulated 3
f5
f response distributions were indeed bimodal and extended well beyond the extremes of the
actual 3
f5
f response distributions, which were unimodal: see
Figure 7B for an example, with the actual distribution in gray and its best-fit Gaussian function in black line (reproduced from
Figure 7A) and the simulated distribution in blue. Overall, when the Response Ratios were closest to 0.5, the distributions of the “real” and the “simulated” responses to the 3
f5
f stimuli for the data obtained from two out of three subjects were significantly different (
p < 0.01 on the Kolmogorov–Smirnov two-sample test). For the third subject (JKM), the “simulated” distributions also tended to be broader than the “real” ones, but only by 0.2% and 16% for CW and CCW stimuli, respectively, and these differences were not statistically significant.
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