Speed-accuracy tradeoffs influence the main sequence of saccadic eye movements

Abstract

Several studies have proposed that an optimal speed-accuracy tradeoff underlies the stereotyped relationship between amplitude, duration and peak velocity of saccades (main sequence). To test this theory, we asked 8 participants to make saccades to Gaussian-blurred spots and manipulated the task's accuracy constraints by varying target size (1, 3, and 5°). The largest targets indeed yielded more endpoint scatter (and lower gains) than the smallest targets, although this effect subsided with target eccentricity. The main sequence depended on several interacting factors: saccade latency, saccade gain and target size. Early saccades, which were faster than amplitude-matched late saccades, followed the target-size dependency one would expect from a speed-accuracy tradeoff process. They had higher peak velocities and shorter durations for larger targets than for smaller targets. For late saccades, however, the opposite was found. Deviations from the main sequence also covaried with saccade gain, in line with the idea that motor noise underlies part of the endpoint variability. Thus, our data provide partial evidence that the saccadic system weighs the detrimental effects of motor noise on saccade accuracy against movement duration and speed, but other factors also modulate the kinematics. We discuss the possible involvement of parallel saccade pathways to account for our findings.

Figure 1

Endpoint variability. (a) Individual dots show the endpoints of the saccades made to the different target locations and different target sizes (color coded) by one of our subjects. The lines represent the average saccade trajectories from the fixation point (+) to the peripheral targets. The ellipses represent the distributions of the endpoints. Only rightward saccades of the subject’s right eye are shown. (b) Amplitude gain of the same rightward saccades as a function of target eccentricity. A gain of 1 corresponds to a saccade that lands at the center of the briefly (100 ms) flashed target. Solid lines indicate the mean, error bars indicate ± 1 standard deviation. (c) Effect of target eccentricity and target size on endpoint variability. Larger ellipse areas reflect more scatter among the endpoints. The solid lines are the result of a mixed effects model fitted to all data (both eyes and both target directions) from all subjects. Dashed lines are grand averages from all 8 subjects. Error bars indicate ± 1 standard deviation of the grand means. (d) Grand mean of the saccade gain and the grand mean of the gain variance for different target eccentricities. Error bars indicate ± 1 standard deviation of the grand means.

Figure 2

Latency and gain. (a) Scatter plot (center) showing saccade gain as a function of saccade latency for a single subject. Data are stratified by target size (color code). Solid lines are linear regression lines fitted to each of the data sets. The latency histograms (bottom) show bimodal distributions for a single subject with a group of early saccades and a group of late saccades. There are fewer late saccades than early ones. The gain histograms (left), which peak close to 1, illustrate the variability in saccade gain. This is also data from a single subject. (b) The percentage of saccades that were late for each target eccentricity and each target size. This is the average for all subjects. Error bars indicate ± 1 SEM.

Figure 3

Main sequence. (a,b) Average eye position (a) and eye velocity (b) traces for saccades to each of the nine different target locations, stratified by target size (color code). (c,d) The main sequence relationships of duration (c) and peak velocity (d) against saccade amplitude for rightward saccades of the participant’s right eye. The faded dots represent the late saccades. Solid lines are fit to the data for saccades with latencies < 250 ms and a gain ranging between 0.9 and 1.1 (i.e., a subset of the brighter dots). (e) The Peak velocity*Duration is the same for early and late saccades.

Figure 4

Normalized duration and peak velocity. Data in this plot are from the same individual (Subject Number 4) as in Fig. 3, and pooled across target location and recorded eye. The data are normalized with respect to the main sequence for normometric (i.e., 0.9 > gain > 1.1) saccades towards 1° wide targets with regular (< 250 ms) latencies (i.e., pink main sequence curves in Fig. 3). (a,b) Normalized duration and the normalized peak velocity as a function of the latency for each of the three target sizes (color coded). (c,d) Same kinematics data as in (a) and (b) but now plotted as a function of saccade gain.

Figure 5

Normalized main sequence regression. Scatter plots of the regression coefficients which quantify how the normalized duration (horizontal axis) and the normalized peak velocity (vertical axis) depend either on target size and saccade latency (a–c) or on target size and saccade gain (d–f). Each numbered dot in the plots represents a single subject. (a–c) Regression coefficients when saccade latency, target size, and the interaction of the two are taken into account, and saccade gain is not. (as in Fig. 4a,b) The applied regression equations were (Wilkinson Notation): Normalized saccade duration ~ Target size + Saccade latency + Target size × Saccade latency. Normalized saccade peak velocity ~ Target size + Saccade latency + Target size × Saccade latency. (d–f) Regression results considering only saccade gain, target size, and the interaction of the two, but not saccade latency (as in Fig. 4c,d). The applied regression equations were: Normalized saccade duration ~ Target size + Saccade gain + Target size × Saccade gain, Normalized saccade peak velocity ~ Target size + Saccade gain + Target size × Saccade gain.

Figure 6

Effects of gain and latency on the main sequence. These plots show the relation between amplitude and duration and between amplitude and peak velocity that our respective regression models predict for different saccade gains, latencies and target sizes. Target size is color coded. The three columns are for different gains: hypometric (gain = 0.75), normometric (gain = 1.00), and hypermetric (gain = 1.25). The dotted lines represent the late saccades (latency 100 ms longer than the median latency) and the solid lines represent early saccades (latency 50 ms shorter than the median latency).

Figure 7

Main sequence differences between target sizes. Here we plot the change in duration and peak velocity between the target sizes. The blue lines show the difference between the 1° and the 3° target. The green lines show the difference between the 1° and the 5° target. Positive values indicate an increase in duration or peak velocity compared with saccades to the 1° wide targets.