Response types
A typical response to a target step and foveofugal motion is shown in Fig. 1b (left). Here, a saccade is initiated after a latency of approximately \(200\,\hbox {ms}\) in the direction of motion of the pursuit target. In trials with foveopetal motion (toward the fovea), several different responses can be observed: (1) an initial saccade before the target crosses the fixation location, (2) direct initiation of smooth pursuit without an initial saccade, or (3) direct initiation of smooth pursuit followed by a small corrective saccade that compensates for inaccuracies in pursuit (Fig. 1b). In the following analysis, smooth responses and responses with a corrective saccade are collapsed (other responses). A response is considered to exhibit an initial saccade (saccade response) if the saccade occurs before the pursuit target reaches the zero position (central position before the step).
The proportion of responses with initial saccades in the foveopetal condition is expected to depend on the step amplitude and speed of the pursuit target (de Brouwer et al. 2002b). Smooth responses are expected to occur when the target reaches the zero position early, that is, for small step amplitudes and high speeds. Saccadic responses are expected to occur when the target reaches the zero position late, i.e., for large amplitudes and low speeds. To verify this, the proportion of trial types were computed across all subjects and step amplitudes separately for each velocity condition.
Fig. 2a shows histograms of observed responses. The results show that smooth/corrective (other) responses occurred primarily for short step amplitudes and that responses with initial saccades occurred primarily for large step amplitudes. The results show that saccadic responses constituted the majority (>50 %) for steps equal to or larger than 8° in the 20°/s condition and 4° in the 10°/s condition.
Saccade reaction times
We compared SRTs of initial saccades in foveopetal and foveofugal trials. SRTs were only compared between conditions in which responses with initial saccades constituted the majority in foveopetal trials (see previous section). The RTs of these saccades were expected to be influenced directly by the properties of the target (eccentricity, speed, movement direction) rather than auxiliary factors such as adjustments of pursuit gain or cancellation delays (see “Introduction” section). SRTs of both velocity conditions were analyzed separately because of the different distributions of response types between both conditions. The results are presented in turn.
For trials in the 20°/s condition, a \(2\times 3\) repeated-measures ANOVA was conducted. The tested factors include the target motion direction (petal, fugal) and three step amplitudes (8°, 10°, 12°). These were the step amplitudes where the predominant response was an initial saccade in foveopetal trials (>50 %). Figure 2b (left) shows the average SRTs and tested conditions. The analysis shows significantly longer SRTs in saccades to foveopetal targets (\(230\,\hbox {ms}\)) in comparison with saccades to foveofugal targets [\(185\,\hbox {ms}\), \(F(1,15)=41.8\), \(p<0.01\)]. Furthermore, the analysis reveals a significant main effect of step amplitude [\(F(2,30)=3.5\), \(p<0.05\)] and a significant interaction between both factors [\(F(2,30)=12.6\), \(p<0.01\)].
A linear regression of step amplitude and SRT shows a negative relationship for saccades in foveopetal trials [−4.4 ms/°, \(t(15)=3.1\), \(p<0.01\), average \(r^{2}=0.7\)] but not for saccades in foveofugal trials. In other words, SRTs decreased with increasing step amplitude for saccades to foveopetal targets but not for saccades to foveofugal targets.
For trials in the 10°/s condition, the range of step amplitudes that were considered in the analysis was extended from 4° to 12° (Fig. 2b, right). Again, these were the step amplitudes where the predominant response was an initial saccade in foveopetal trials. A \(2\times 5\) repeated-measures ANOVA shows significantly longer SRTs in saccades to foveopetal targets (\(209\,\hbox {ms}\)) in comparison with saccades to foveofugal targets [\(186\,\hbox {ms}\), \(F(1,15)=50.7\), \(p<0.01\)]. The analysis also shows a significant main effect of step amplitude [\(F(4,60)=7.4\), \(p<0.01\)] and a significant interaction between both factors [\(F(4,60)=16.7\), \(p<0.01\)].
A linear regression of step amplitude and SRT shows a negative relationship for saccades to foveopetal targets (−3.8 ms/°, \(t(15)=3.6\), \(p<0.01\), average \(r^{2}=0.66\)) but not for saccades to foveofugal targets.
Post hoc comparisons of both motion directions (petal, fugal) were performed for each step amplitude. This comparison shows significant differences in both speed conditions for the relevant step amplitudes (8°–12° in 20°/s trials, 4°–12° in 10°/s trials, \(p<0.01\), Bonferroni corrected).
Saccade amplitudes
Previous research has shown that the displacement of the target during the saccade preparation period is taken into account by the saccade planning process (Guan et al. 2005): For example, after the initial step, as the target travels further into the periphery during foveofugal trials, saccade amplitudes become larger. The current data show that saccade amplitudes are predicted by the target displacement of the initial step and the target’s motion during the SRT (see also Fig. 3a): For trials in the 20°/s condition, the average difference between predicted and actual amplitude was 0.08°. For trials in the 10°/s condition, the average difference between predicted and actual amplitude was 0.03°.
A linear regression analysis of saccade amplitude and SRT was conducted to examine the relationship between saccade amplitude and SRT in greater detail (see also Fig. 3b). Linear regression slopes were computed per participant and condition. Repeated-measures ANOVA was employed to analyze the slope parameters (same conditions as in “Saccade reaction times” section). In line with previous results (Guan et al. 2005), this analysis shows that saccade amplitudes incorporate the displacement of the target during the saccade preparation period: For trials in the 20°/s condition, the analysis shows a negative relationship for saccades in foveopetal trials [−16°/s, \(F(1,15)=240\), \(p<0.01\)] and a positive relationship for saccades in foveofugal trials (26°/s). For trials in the 10°/s condition, the analysis also shows a negative relationship for saccades in foveopetal trials [−7°/s, \(F(1,15)=367\), \(p<0.01\)] and a positive relationship for saccades in foveofugal trials (15°/s). For both target speed conditions, the results neither showed a main effect of step amplitude nor an interaction between motion direction and step amplitude (\(p>0.1\)).
Eccentricity-matched SRTs
The differences in saccade amplitudes between both motion direction conditions suggest one potential explanation for the obtained SRT results, namely differences in the eccentricities of targets prior to saccade onset. Previous work on saccades to static targets has shown that target eccentricity affects SRTs (Kalesnykas and Hallett 1994). The results presented in the previous section demonstrate that saccade amplitudes vary as a function of time, in line with a change in eccentricity due to the target’s constant movement. For example, the eccentricity of a target shortly before the saccade becomes larger if the target moves foveofugally and smaller if it moves foveopetally. To test whether the obtained differences in SRTs of initial saccades were independent from the differences in target eccentricity during the saccade preparation period, a comparison of eccentricity-matched conditions was conducted. To select matching step amplitude conditions from the available conditions of our experiment, we assumed a baseline saccade latency of \(200\,\hbox {ms}\). This is a typical average saccade latency (Kalesnykas and Hallett 1994). For example, in the current experiment, target eccentricity following a 12° step and foveopetal motion was approximately 8° after \(200\,\hbox {ms}\) of motion at a speed of 20°/s. This eccentricity condition was matched by a 4° step and foveofugal motion at the same speed.
It should be noted that these predicted eccentricities approximate the actual target eccentricities, for example, due to differences in actual SRTs. In contrast to the unmatched comparison, eccentricities in both motion conditions are now reversed in the matched comparison: on average slightly larger in the foveopetal motion condition and slightly smaller in the foveofugal condition (see Fig. 4a). If target eccentricity is the main determinant of saccade latencies, saccades to foveopetal targets should exhibit shorter rather than longer SRTs in this matched comparison. The results show that this is not the case: For 20°/s trials, the conditions selected for comparison were 2° and 4° steps for foveofugal trials and 10° and 12° steps for foveopetal trials. The targets in these two conditions were approximately at 6° and 8° eccentricity at saccade onset, respectively (Fig. 4a). A \(2\times 2\) repeated-measures ANOVA shows significantly longer SRTs in saccades to foveopetal targets (\(225\,\hbox {ms}\)) in comparison with saccades to foveofugal targets [\(195\,\hbox {ms}\), \(F(1,15)=17.9\), \(p<0.01\)].
For 10°/s trials, the selected conditions were 2°, 4°, 6°, and 8° steps for foveofugal trials and 6°, 8°, 10°, and 12° steps for foveopetal trials. The targets in these conditions were approximately at 4°, 6°, 8°, and 10° eccentricity at saccade onset, respectively (Fig. 4a). Again, a \(2\times 4\) repeated-measures ANOVA shows significantly longer SRTs in saccades to foveopetal targets (\(209\,\hbox {ms}\)) in comparison with saccades to foveofugal targets [\(186\,\hbox {ms}\), \(F(1,15)=50.7\), \(p<0.01\)].
Post hoc comparisons of both motion directions (petal, fugal) were performed for each matched step amplitude, showing significant differences in both speed conditions for the relevant step amplitudes (6° and 8° in 20°/s trials, 4°–10° in 10°/s trials, \(p<0.05\), Bonferroni corrected).
Together, this suggests that the measured SRT differences are a result of the difference in the target’s motion direction rather than differences in its eccentricity prior to saccade onset.
Pre-saccadic pursuit
Small, pre-saccadic movements in the direction of pursuit can sometimes be observed in saccades to moving targets (Tychsen and Lisberger 1986). The occurrence of these eye movements could be related to saccade onsets. Saccades to foveopetal targets are made against the motion of occurring pre-saccadic pursuit. This means that the eyes are first decelerated before they are accelerated in the opposite direction. This could potentially affect the measurements of saccade onsets based on velocity and acceleration thresholds and thus lead to prolonged SRT measurements.
To examine the occurrence and relationship of these eye movements with the measured SRTs, we computed the average eye velocity (pre-saccadic velocity, PSV) \(50\,\hbox {ms}\) prior to the saccadic eye movements (see also Guan et al. 2005). Statistical analyses were performed for conditions in which the predominant response was an initial saccade in foveopetal trials. PSV values are reported relative to the pursuit target’s velocity, i.e., positive values indicate that pre-saccadic pursuit moved the eye in the target’s motion direction.
For trials in the 20°/s condition, a \(2\times 3\) repeated-measures ANOVA was conducted. The tested factors include the target motion direction (petal, fugal) and three step amplitudes (8°, 10°, 12°, the same as in “Saccade reaction times” section). In both motion conditions, PSVs occurred in the direction of target motion. For foveopetal movements, PSVs were faster (2.4°/s) than for foveofugal movements [0.7°/s, \(F(1,15)\)
\(=18.0\), \(p<0.01\)]. Furthermore, the analysis reveals a significant main effect of step amplitude [\(F(2,30)=12.1\), \(p<0.01\)] and a significant interaction between both factors [\(F(2,30)=16.3\), \(p<0.01\)].
For trials in the 10°/s condition, a \(2\times 5\) repeated-measures ANOVA was conducted. The range of step amplitudes that were considered in the analysis was extended from 4° to 12° (see “Saccade reaction times” section). For this target speed, PSVs did not differ significantly between both conditions (on average 0.81°/s). The analysis shows a significant main effect of step amplitude [\(F(4,60)=25.1\), \(p<0.01\)] and a significant interaction between both factors [\(F(4,60)=14.7\), \(p<0.01\)].
Linear regression of step amplitude and PSV shows that, similar to the SRT results, PSVs decreased with increasing step amplitude for foveopetal target motion [20°/s motion: −0.4°/s per degree, \(t(15)=4.3\), \(p<0.01\), average \(r^{2}=0.67\); 10°/s motion: −0.17°/s per degree, \(t(15)=5.1\), \(p<0.01\), average \(r^{2}=0.68\)].
A detailed analysis of the relationship between SRTs and PSVs was conducted. First, linear regression slopes were computed per participant and condition. Next, for trials in the 20°/s condition, a \(2\times 3\) repeated-measures ANOVA was conducted with the slope parameter as dependent variable (for factor levels, see “Saccade reaction times” section). In both motion conditions, PSVs increased slightly during saccade preparation. For foveofugal movements, PSVs increased by 0.75° per \(100\,\hbox {ms}\) and by 3.7° per \(100\,\hbox {ms}\) for foveopetal movements [\(F(1,15)=50.2, p<0.01\)]. The analysis also shows a significant interaction between the step and motion direction factors [\(F(4,60)=14.0\), \(p<0.01\)].
For trials in the 10°/s condition, a \(2\times 5\) repeated-measures ANOVA was conducted with the slope parameter as dependent variable. Again, PSVs increased slightly during saccade preparation in both motion conditions. For foveofugal movements, PSVs increased by 0.65° per \(100\,\hbox {ms}\) and by 1.7° per \(100\,\hbox {ms}\) for foveopetal movements [\(F(1,15) =52.5, p<0.01\)]. The analysis also shows a significant interaction between the step and motion direction factors [\(F(4,60)=6.5\), \(p<0.01\)].
Linear regressions of step amplitude and slope parameters confirm the general results: As step amplitudes increased, slopes became more shallower for foveopetal target motion [20°/s motion: −0.42° per \(100\,\hbox {ms}\) per degree, \(t(15)=4.0\), \(p<0.01\), average \(r^{2}=0.32\); 10°/s motion: −0.21°/s per degree, \(t(15)=5.6\), \(p<0.01\), average \(r^{2}=0.48\)].
These results can be explained by assuming that PSVs (as SRTs) are affected by the target’s eccentricity and speed (e.g., Tychsen and Lisberger 1986) but do not elucidate the causal relationship between both.
A subset of trials was analyzed to examine whether the measured SRT asymmetries depend on the occurrence of PSVs. The subset comprises of trials with absolute PSVs smaller than 1°/s, i.e., trials wherein the eye fixation was relatively static (Guan et al. 2005). This analysis was only performed for 10°/s trials with target step amplitudes larger or equal to 6°, to assure that data points were available for the analysis for all participants and conditions (\(70\,\%\) of datapoints).
The average PSV in this subset was 0.07°/s. A \(2\times 4\) repeated-measures ANOVA shows significant differences in SRTs between both motion conditions also in this subset. SRTs were longer in saccades to foveopetal targets (\(198\,\hbox {ms}\)) in comparison with saccades to foveofugal targets [\(185\,\hbox {ms}\), \(F(1,15)=31.3\), \(p<0.01\)].
Post hoc comparisons of both motion directions (petal, fugal) were performed for each step amplitude of the subset. This shows significantly longer SRTs for saccades to foveopetal targets for the relevant step amplitudes (6°–12°, \(p<0.05\), Bonferroni corrected).
These results suggest that, although pre-saccadic responses appear to be similarly affected by the target’s motion and eccentricity as SRTs, they do not necessarily cause the measured SRT effects.