May 2015
Volume 15, Issue 6
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Letters to the Editor  |   May 2015
Saccadic inhibition and the remote distractor effect: One mechanism or two?
Author Affiliations
  • Aline Bompas
    INSERM U1028 and CNRS, UMR5292, Lyon Neuroscience Research Center, Brain Dynamics and Cognition Team, Lyon, France
    aline.bompas@gmail.com
  • Petroc Sumner
    Cardiff University Brain Research Imaging Centre, School of Psychology, Cardiff University, Cardiff, Wales, UK
    sumnerp@cardiff.ac.uk
Journal of Vision May 2015, Vol.15, 15. doi:10.1167/15.6.15
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      Aline Bompas, Petroc Sumner; Saccadic inhibition and the remote distractor effect: One mechanism or two?. Journal of Vision 2015;15(6):15. doi: 10.1167/15.6.15.

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Abstract

It has been hotly debated whether a single mechanism underlies two established and highly robust oculomotor phenomena thought to index the competitive nature of eye movement plans: the remote distractor effect and saccadic inhibition (SI). It has been suggested that a transient mechanism underlying SI would not be able to account for the shift in the saccade latency distribution produced by early distractors (e.g., those appearing 60 ms before target onset) without additional assumptions or a more sustained source of inhibition. Here we tested this prediction with a model previously optimized to capture SI for late distractors. Where behavioral studies have intermingled stimulus onset asynchronies (SOAs) within the same block, the model captures the pattern of RDEs and SI effects with no parameter changes. Where SOAs have been blocked behaviorally, the pattern of RDEs can also be captured by the same model architecture, but requires changes to the inputs of the model between SOAs. Such changes plausibly reflect likely changes in participants' expectations and attentional strategy across block types.

The remote distractor effect (RDE) is a well-established phenomenon thought to reflect competitive processes in eye movement planning. An irrelevant distractor delays saccadic latency to a target appearing in a different location (Walker, Deubel, Schneider, & Findlay, 1997). Typically a target and distractor are presented simultaneously and mean latency increases by 20 to 40 ms; error rate may also increase (Bompas & Sumner, 2009a, 2009b; Casteau & Vitu, 2012; Ludwig, Gilchrist, & McSorley, 2005; Trappenberg, Dorris, Munoz, & Klein, 2001; Walker & Benson, 2013). Similar effects can occur for early distractors, presented up to around 100 ms prior to the target (though such stimuli can also carry a warning effect). 
Late distractors (presented typically 20–100 ms after target onset), on the other hand, only marginally increase error rate and can produce a bimodal latency distribution (Buonocore & McIntosh, 2008; Edelman & Xu, 2009; Reingold & Stampe, 2002). Saccades executed within about 70 ms of distractor onset escape interference, while many subsequent saccade plans are transiently delayed, causing a dip in the latency distribution. This is followed by a recovery period where these saccades reappear with delayed latencies later in the distribution. The dip is precisely time-locked to the distractor, beginning ∼70 ms after distractor onset and peaking about 100 ms from distractor onset. This phenomenon, referred to as saccadic inhibition (SI), is also highly robust. The short delay of the dip suggests it to be caused by a rapid automatic signal triggered by the onset of visual distractors, mediated via fast pathways to the superior colliculus (Reingold & Stampe, 2002). 
Some authors have argued strongly that SI and the RDE reflect the same mechanism (Buonocore & McIntosh, 2008; McIntosh & Buonocore, 2014), and others have implicitly or explicitly accepted that the mechanism producing SI produces at least the major component of the RDE (Bompas & Sumner, 2011; Edelman & Xu, 2009). What appears to be a shift in the latency distribution for simultaneous distractors could be regarded as a dip on the leading edge of the distribution. However, other authors have argued that a mechanism transient enough to produce brief dips in the distribution would be too transient to explain the RDE from early distractors appearing 60 ms before the target (Walker & Benson, 2013); the dip would no longer be on the leading edge of the distribution, but should be finished by the time the latency distribution even starts. Therefore, a different, more sustained source of inhibition might better explain much of the RDE. The source of this might be stimulus-induced modulation of fixation activity or the tonic inhibition of superior colliculus from basal ganglia. 
Modeling RDE and SI with a single model
Three related issues and potential meanings of RDE and SI have been discussed in the previous debates: phenomena, measurement, and mechanism. Although the term RDE has most often been associated with the measurement of mean (or median) delay, here, in order to draw a clear distinction between two phenomena, we will restrict RDE to mean the phenomenon of an overall shift (and possible skew) in latency distribution (as opposed to a dip). Similarly, we will restrict SI to mean the phenomenon of transient dips in the latency distribution, rather than the mechanism that might underlie it. So defined, the phenomena are at least superficially distinct, but may still reflect a continuum of distractor effects caused by the same mechanism. Shifts tend to occur with early or simultaneous distractors, while dips tend to occur with late distractors (and the magnitude of both effects varies with distractor timing). 
Here we test the extent to which a model previously optimized to produce SI with late distractors might also produce the RDE for early distractors with no additional assumptions or changes to parameter settings. The model is identical to that described in Bompas and Sumner (2011), which was based on a previously published model intended to simulate key features of the superior colliculus (Trappenberg et al., 2001), including firing rate data with early distractors (−100 ms; see figure 1 in Trappenberg et al., 2001). It is a competing interactive leaky accumulator (Usher & McClelland, 2001) that simulates a saccade motor map of 200 nodes with local facilitation and long-range inhibition. The model integrates transient exogenous signals produced by both target and distractor stimuli with endogenous signals supporting fixation and then saccades to the target. When the activity for one node reaches a threshold, a saccade is produced to that location. The model produces SI because the sharp transient exogenous activity for late distractors briefly hinders the accumulation of activity for the target, meaning that any saccade's activity that has not yet reached threshold when the distractor signal arrives is delayed and appears later in the distribution instead. 
First we did not adjust any parameters of the model from the settings previously used to create SI for late distractors in Bompas and Sumner (2011). We simply set the distractors to occur at seven different times relative to the target from early to late (stimulus onset asynchrony [SOA] of −60, −40, −20, 0, 20, 40, and 60 ms, where negative SOA means early distractors and positive SOA means late distractors). We found that DINASAUR (Bompas & Sumner, 2011) readily produces a shift in the latency distribution for early distractors as well as dips for late distractors (Figure 1, Column 3). The simulations compare reasonably well to previous behavioral data where these distractor SOAs were used (Bompas & Sumner, 2009b; Sumner, Edden, Bompas, Evans, & Singh, 2010; see Figure 1, Columns 1 and 2). 
Figure 1
 
Columns 1 and 2 plot data from two previous studies (high distractor contrast condition in Bompas & Sumner, 2009b; Sumner et al., 2010) where target direction was randomized, distractors appeared opposite to targets, and early and late distractors were intermingled in the same blocks (data are combined over three and 12 participants, respectively). For early distractors (negative SOA) the latency distribution with distractor present (black) is shifted relative to without distractor (gray). For late distractors, there is a dip (SI) time-locked to distractor onset. The thin line shows the latency distribution of errors towards the distractor, which is also time-locked to distractor onset as would be expected if they were driven by automatic visual signals. Mean (and median) delays for each SOA were, respectively: 9, 23, 28, 31, 27, 28, and 18 ms (12, 24, 28, 36, 28, 32, and 24 ms) for Column 1 and 5, 14, 20, 21, 25, 19, and 14 ms (8, 18, 23, 23, 28, 23, and 19 ms) for Column 2. Error rates were 24%, 19%, 11%, 7%, 3%, 3%, and 1% and 35%, 31%, 26%, 17%, 9%, 3%, and 2%. Note that large differences in error rate (10%–80%) across participants for the earliest distractors in Sumner et al. (2010) explains why the distractor and no-distractor distributions appear more separated than a mean delay of 5 ms would suggest; participants with high error rates contribute few saccades to the distractor distribution, but still make a full contribution to the no-distractor distribution, and these participants tend to have the lowest no-distractor latencies. Column 3 shows simulations using DINASAUR (1,200 trials per condition) with settings identical to those in Bompas and Sumner (2011)—that is, we made no attempt to fit it to the actual data for early distractors or late distractors here, but simply inherited the settings used to simulate late distractors previously. Column 4 shows the delay caused by the distractor for individual trials, simulated with identical noise with and without distractor, plotted against the latency that would have occurred without a distractor. Many saccades that would have occurred even 200 ms after the distractor (i.e., after visible dips are over) were still delayed. See Figure 2 for more information for the modeled data.
Figure 1
 
Columns 1 and 2 plot data from two previous studies (high distractor contrast condition in Bompas & Sumner, 2009b; Sumner et al., 2010) where target direction was randomized, distractors appeared opposite to targets, and early and late distractors were intermingled in the same blocks (data are combined over three and 12 participants, respectively). For early distractors (negative SOA) the latency distribution with distractor present (black) is shifted relative to without distractor (gray). For late distractors, there is a dip (SI) time-locked to distractor onset. The thin line shows the latency distribution of errors towards the distractor, which is also time-locked to distractor onset as would be expected if they were driven by automatic visual signals. Mean (and median) delays for each SOA were, respectively: 9, 23, 28, 31, 27, 28, and 18 ms (12, 24, 28, 36, 28, 32, and 24 ms) for Column 1 and 5, 14, 20, 21, 25, 19, and 14 ms (8, 18, 23, 23, 28, 23, and 19 ms) for Column 2. Error rates were 24%, 19%, 11%, 7%, 3%, 3%, and 1% and 35%, 31%, 26%, 17%, 9%, 3%, and 2%. Note that large differences in error rate (10%–80%) across participants for the earliest distractors in Sumner et al. (2010) explains why the distractor and no-distractor distributions appear more separated than a mean delay of 5 ms would suggest; participants with high error rates contribute few saccades to the distractor distribution, but still make a full contribution to the no-distractor distribution, and these participants tend to have the lowest no-distractor latencies. Column 3 shows simulations using DINASAUR (1,200 trials per condition) with settings identical to those in Bompas and Sumner (2011)—that is, we made no attempt to fit it to the actual data for early distractors or late distractors here, but simply inherited the settings used to simulate late distractors previously. Column 4 shows the delay caused by the distractor for individual trials, simulated with identical noise with and without distractor, plotted against the latency that would have occurred without a distractor. Many saccades that would have occurred even 200 ms after the distractor (i.e., after visible dips are over) were still delayed. See Figure 2 for more information for the modeled data.
Figure 2
 
Metrics of the distraction effects for modeled data. Note that mean and median delays (the standard RDE measures, top plot) track each other for early distractors, but diverge for late distractors because the median of a bimodal distribution is greatly influenced by whether the dip comes before or after the median of the baseline condition; hence median delay can be misleading for late distractors (see McIntosh & Buonocore, 2014). Conversely, dip amplitude (maximum distraction ratio, after Bompas & Sumner, 2011) is only useful once bimodality appears in the distribution; a value of 1 means that for at least one time bin, 100% of the saccades in the baseline condition have disappeared from that time bin in the distractor distribution). The middle plot provides further information for the individual trial delays (modeled distractor condition minus identical modeled trial without distractor) as depicted in Figure 1, Column 4. Note that the overall mean delay is accounted for more by the proportion of trials affected than by the mean delay or standard deviaton of those affected trials. The lower plot shows histograms of these individual trial delays (i.e., collapsing over the x-axes of Column 4 in Figure 1). It is clear that small effects are much more common than medium or large ones, and that the pattern is similar for early (red), simultaneous (black), and late distractors (blue).
Figure 2
 
Metrics of the distraction effects for modeled data. Note that mean and median delays (the standard RDE measures, top plot) track each other for early distractors, but diverge for late distractors because the median of a bimodal distribution is greatly influenced by whether the dip comes before or after the median of the baseline condition; hence median delay can be misleading for late distractors (see McIntosh & Buonocore, 2014). Conversely, dip amplitude (maximum distraction ratio, after Bompas & Sumner, 2011) is only useful once bimodality appears in the distribution; a value of 1 means that for at least one time bin, 100% of the saccades in the baseline condition have disappeared from that time bin in the distractor distribution). The middle plot provides further information for the individual trial delays (modeled distractor condition minus identical modeled trial without distractor) as depicted in Figure 1, Column 4. Note that the overall mean delay is accounted for more by the proportion of trials affected than by the mean delay or standard deviaton of those affected trials. The lower plot shows histograms of these individual trial delays (i.e., collapsing over the x-axes of Column 4 in Figure 1). It is clear that small effects are much more common than medium or large ones, and that the pattern is similar for early (red), simultaneous (black), and late distractors (blue).
Lasting effects of transient distractor on individual trials
Thus, even though the dip for late distractors is transient (only about 50-ms wide and over by 130 ms from distractor onset), early distractors can, by the same mechanism, delay a latency distribution that only starts 150 ms after distractor onset. Column 4 of Figure 1 shows that in the modeled data, many individual trials that would have produced a saccade with latency even up to 200 ms are still delayed by an early distractor (note that this analysis can be done for the model because each simulation with a distractor can be paired with an identical simulation—with identical noise—without a distractor; with behavior data, this analysis cannot be done). Figure 2 summarizes this same data to directly compare the pattern of individual trial delays for different SOAs, confirming that the most common effects are small ones, and this pattern does not change for early versus late distractors. 
For the same reason that early distractors affect saccades at all, late distractor signals affect not only saccade plans that would have reached threshold during the dip, but also saccade plans that would have reached threshold throughout the distribution beyond the dip. The end of the visible dip is not the end of distractor influence, but merely the point when the number of recovering saccades from the earliest part of the dip starts to outnumber the delayed saccades, as previously emphasized by McIntosh and Buonocore (2014, p. 4). 
Figure 3 clarifies the mechanisms underlying these effects by showing the neural activity within the three nodes of interest (fixation in blue, target in gray or black, and distractor in red) for SOAs of −60, 0, and +60 ms. In the case of early distractors, activity is inhibited in the target node for saccade plans that have not even started yet, and at the same time, activity in the distractor node persists and is still inhibiting the target node when target signals arrive. In this way the model echoes and formalizes a point also made by McIntosh and Buonocore (2014) that distractors could, via the same mechanism, affect both early and late points in the saccade planning process. 
Figure 3
 
Time course of exogenous and endogenous inputs and consequences on the neural activities within the fixation (blue), target (black), and distractor (red) nodes at SOA −60, 0, and 60 ms. The neural activities are represented for the distractor present condition. For comparison, the neural activity within the target node is also given in the absence of distractor (gray). B = Baseline activity during fixation before peripheral stimulus onset. Th = Threshold of the accumulation process. NB = At SOA 0, bursts of exogenous activity in target and distractor nodes fully overlap. NB2 = At SOA 60, the delay is large on this noise-free trial, but only a smaller proportion of saccades will be affected compared to SOA 0. NB3 = The slight reduction in activity for the target node in the presence of an early distractor (bottom left plot) is reminiscent of neurophysiological data observed in the SC by Dorris, Olivier, and Munoz (2007).
Figure 3
 
Time course of exogenous and endogenous inputs and consequences on the neural activities within the fixation (blue), target (black), and distractor (red) nodes at SOA −60, 0, and 60 ms. The neural activities are represented for the distractor present condition. For comparison, the neural activity within the target node is also given in the absence of distractor (gray). B = Baseline activity during fixation before peripheral stimulus onset. Th = Threshold of the accumulation process. NB = At SOA 0, bursts of exogenous activity in target and distractor nodes fully overlap. NB2 = At SOA 60, the delay is large on this noise-free trial, but only a smaller proportion of saccades will be affected compared to SOA 0. NB3 = The slight reduction in activity for the target node in the presence of an early distractor (bottom left plot) is reminiscent of neurophysiological data observed in the SC by Dorris, Olivier, and Munoz (2007).
It therefore seems necessary to distinguish between different meanings of “transient.” The SI effect for late distractors is transient, in the sense that the dip tends to last under 50 ms in the distribution. The distractor signal in the model is also transient (it decays back to near zero in less than 50 ms), but because the model is an accumulator, its effect on activity across the distractor and target nodes can last 120 ms (depending on leakage; for instance, with the current model settings, the RDE is 3 ms for distractor SOA of −120 ms). Thus the effect of the distractor on saccade plans spreads further than either the length of the dip or the length of the modeled signal might imply (the effect of modulating signal transience in the model is further explored in Figure 4). 
Figure 4
 
Columns 1 and 2 show the effect of making the exogenous signal more or less transient (all settings the same as in Figure 1 except the decay rate of exogenous signals decreased to 8 or increased to 12; original setting was 10). Mean (median) delays are 8, 17, 25, 28, and 20 ms (8, 18, 26, 31, and 25 ms) for Column 1 and 16, 40, 52, 26, and 11 ms (15, 40, 56, 24, and 0 ms) for Column 2. Columns 3 and 4 show the delay caused by the distractor for individual simulated trials plotted against the latency that would have occurred without a distractor (same analysis as in Figure 1, Column 4). While there is lower density of medium and long delays for shorter distractor signals, the reach of the distractor is not more limited with respect to the where the saccade would have appeared in the latency distribution with no distractor (x-axis).
Figure 4
 
Columns 1 and 2 show the effect of making the exogenous signal more or less transient (all settings the same as in Figure 1 except the decay rate of exogenous signals decreased to 8 or increased to 12; original setting was 10). Mean (median) delays are 8, 17, 25, 28, and 20 ms (8, 18, 26, 31, and 25 ms) for Column 1 and 16, 40, 52, 26, and 11 ms (15, 40, 56, 24, and 0 ms) for Column 2. Columns 3 and 4 show the delay caused by the distractor for individual simulated trials plotted against the latency that would have occurred without a distractor (same analysis as in Figure 1, Column 4). While there is lower density of medium and long delays for shorter distractor signals, the reach of the distractor is not more limited with respect to the where the saccade would have appeared in the latency distribution with no distractor (x-axis).
Changing the transience of distractor signals
To further enlighten the above discussion about the lasting effects of transient signals on later saccades, we tested the effect of increasing or reducing the decay rate of the exogenous signal from the distractor. Note that in the model, the duration of the distractor stimulus does not make a difference because there is no sustained signal for its continued presence and no signal associated with distractor offset. However, the duration of distractor-related activity is governed by the amplitude and decay rate of the onset-induced exogenous signal (Figure 3). Note also that the same exogenous signal parameters also apply to the target, so both exogenous signals were changed together. As Figure 4 (Column 1) shows, more transient signals reduce both RDE and SI, as well as reducing errors and lengthening mean latency, all for the same reason that there is now less power in the exogenous signals to affect the accumulation process. Decreasing the transience of distractors has opposite effects. Crucially, the patterns of RDE for early distractors and SI for late distractors are preserved despite these changes. 
Columns 3 and 4 of Figure 4 show the delays for individual trials as for the final column of Figure 1. Although shorter lasting distractor signals (Column 3) introduce fewer medium to long saccade delays compared to longer lasting distractor signals (Column 4), these effects are not more restricted on the x-axis. In other words, it is not the case that more transient signals only affect the first portion of the baseline latency distribution. This is because what matters most to whether a saccade is affected is the distractor activity when target accumulation begins, not when it would have ended. 
Task design and the relative size of early and simultaneous distractor effects
While early distractors produced RDEs in both the model and the data depicted in Figure 1, the magnitude of the mean delay for −60-SOA was consistently about a third that for simultaneous distractors (a similar reduction is present in Bompas & Sumner, 2009a; see their figure 2). In the model, early distractors are able to produce more activity because they are not competing against target activity (see Figure 3), but there is still fixation activity inhibiting them, and the distractor effects always remain less than for simultaneous distractors. This was not the case for the data in Walker and Benson (2013), where the RDEs for contralateral distractors with −60-ms SOA were equivalent to (or even larger than) those for simultaneous distractors. We therefore tested whether any simple adjustments to the model could reduce the difference between early and simultaneous distractor RDEs. If all settings have to stay constant between SOAs, this is not possible, for the reasons already illustrated in Figure 4: Any parameter that increases the relative strength of distractor signals causes more errors for early distractors, which remove themselves from the latency distributions used to define RDE, and thus have less effect on the RDE for early distractors than for simultaneous ones (Figure 4, Column 2). 
However, the different SOAs in Walker and Benson's (2013) study were blocked, which frees up the model to make plausible parameter changes between blocks. Since blocked early distractors provide a warning signal, and target location was also kept constant for miniblocks (while target onset was jittered), we provided the model with some anticipatory endogenous signal for the target when the distractor precedes it. Secondly, for SOA 0 to +60, we attenuated the distractor signal, because target location is known, and thus we can assume some attentional filtering for nontarget locations (despite the target locations also being known for early distractors, we did not reduce the distractor signal because it must be attended in order to provide the warning effect; in other words, the hypothesis that the distractors suffer from attentional attenuation only applies if they are also not used as warning signals). If these changes are deemed plausible as factors that can change due to attention and expectancy, rather than reflecting distinct mechanisms, then a single modeled mechanism can accommodate the existing data (see Figure 5; further changes to endogenous signals could provide an even better fit to the exact latencies, but here we stick to the minimum changes to capture the pattern; note that it is the exogenous distractor signal that has been attenuated, because this is the only signal produced by distractors in the model). 
Figure 5
 
Simulations providing a closer fit to experiment 2 in Walker and Benson (2013). For the early distractors (SOA −60) the target node received anticipatory endogenous signal (a third of the strength of the full endogenous signal that follows target onset). This speeded up saccade latency to the values found by Walker and Benson (2013; median target-only latency = 112 ms, median latency with distractor = 130 ms). Note that, perhaps counterintuitively, this anticipatory activity did not reduce the RDE (18 ms); the decrease in baseline latency is mainly provided by many more saccades in the express mode (where exogenous activity is sufficient to reach threshold), and since distractors markedly reduce this express mode, they still produce a marked RDE. Error rate is also reduced (5%), though not the very low levels in Walker and Benson's data. For SOA zero, we attenuated the distractor signal (by half), which provided an RDE of 16 ms, less than that for −60 SOA, as in the data of Walker and Benson (median target-only latency = 137 ms, median latency with distractor = 153 ms). The simulation for +60 SOA used the same settings as 0 SOA.
Figure 5
 
Simulations providing a closer fit to experiment 2 in Walker and Benson (2013). For the early distractors (SOA −60) the target node received anticipatory endogenous signal (a third of the strength of the full endogenous signal that follows target onset). This speeded up saccade latency to the values found by Walker and Benson (2013; median target-only latency = 112 ms, median latency with distractor = 130 ms). Note that, perhaps counterintuitively, this anticipatory activity did not reduce the RDE (18 ms); the decrease in baseline latency is mainly provided by many more saccades in the express mode (where exogenous activity is sufficient to reach threshold), and since distractors markedly reduce this express mode, they still produce a marked RDE. Error rate is also reduced (5%), though not the very low levels in Walker and Benson's data. For SOA zero, we attenuated the distractor signal (by half), which provided an RDE of 16 ms, less than that for −60 SOA, as in the data of Walker and Benson (median target-only latency = 137 ms, median latency with distractor = 153 ms). The simulation for +60 SOA used the same settings as 0 SOA.
Neither our paradigm nor Walker and Benson's (2013) were ideal for directly comparing the magnitude of the RDE across SOAs. As discussed above, blocking allows differences in anticipatory, alerting, or attentional factors. Our paradigm had a different drawback: Distractors always appeared in the opposite position to the target, and thus early distractors were predictive of the target location. Again therefore, alerting/expectancy processes may come into play in different ways. Note also that we did not manipulate locations in our paradigm to explore the spatial characteristics of RDE or SI, nor have we tested whether the current model is able to account for extant spatial data. 
Conclusions
In sum, we found that a model previously optimized to produce the dips of SI also produces a clear RDE for early distractors with no parameter changes, providing a reasonable fit to our previous data. Parsimony would then favor the conclusion that RDE and SI are two manifestations of a single mechanism (McIntosh & Buonocore, 2014). However, to fit Walker and Benson's (2013) data, where SOAs were blocked rather than intermingled, some settings in the model must be changed between SOAs, namely an adjustment in the exogenous and endogenous signals. If we equate the word “mechanism” with the structural properties of the decision network, then such simple adjustments in the inputs to the decision units would not qualify as a distinct mechanism. However, if a mechanism is equated with the inputs feeding the decision process, then it is possible to conclude that distractor effects, when studied under differing conditions (e.g., different SOA) in separate blocks, result from distinct combinations of mechanisms. Last, the model makes a strong prediction: If the RDE and SI emerge from the same mechanism, then when block-wise changes between SOAs are ruled out, the RDE will always be smaller for earlier distractors. 
Acknowledgments
This research was funded by the ESRC (ES/K002325/1). 
Commercial relationships: none. 
Corresponding author: Petroc Sumner. 
Email: sumnerp@cardiff.ac.uk. 
Address: School of Psychology, Cardiff University, Cardiff, Wales, UK. 
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Figure 1
 
Columns 1 and 2 plot data from two previous studies (high distractor contrast condition in Bompas & Sumner, 2009b; Sumner et al., 2010) where target direction was randomized, distractors appeared opposite to targets, and early and late distractors were intermingled in the same blocks (data are combined over three and 12 participants, respectively). For early distractors (negative SOA) the latency distribution with distractor present (black) is shifted relative to without distractor (gray). For late distractors, there is a dip (SI) time-locked to distractor onset. The thin line shows the latency distribution of errors towards the distractor, which is also time-locked to distractor onset as would be expected if they were driven by automatic visual signals. Mean (and median) delays for each SOA were, respectively: 9, 23, 28, 31, 27, 28, and 18 ms (12, 24, 28, 36, 28, 32, and 24 ms) for Column 1 and 5, 14, 20, 21, 25, 19, and 14 ms (8, 18, 23, 23, 28, 23, and 19 ms) for Column 2. Error rates were 24%, 19%, 11%, 7%, 3%, 3%, and 1% and 35%, 31%, 26%, 17%, 9%, 3%, and 2%. Note that large differences in error rate (10%–80%) across participants for the earliest distractors in Sumner et al. (2010) explains why the distractor and no-distractor distributions appear more separated than a mean delay of 5 ms would suggest; participants with high error rates contribute few saccades to the distractor distribution, but still make a full contribution to the no-distractor distribution, and these participants tend to have the lowest no-distractor latencies. Column 3 shows simulations using DINASAUR (1,200 trials per condition) with settings identical to those in Bompas and Sumner (2011)—that is, we made no attempt to fit it to the actual data for early distractors or late distractors here, but simply inherited the settings used to simulate late distractors previously. Column 4 shows the delay caused by the distractor for individual trials, simulated with identical noise with and without distractor, plotted against the latency that would have occurred without a distractor. Many saccades that would have occurred even 200 ms after the distractor (i.e., after visible dips are over) were still delayed. See Figure 2 for more information for the modeled data.
Figure 1
 
Columns 1 and 2 plot data from two previous studies (high distractor contrast condition in Bompas & Sumner, 2009b; Sumner et al., 2010) where target direction was randomized, distractors appeared opposite to targets, and early and late distractors were intermingled in the same blocks (data are combined over three and 12 participants, respectively). For early distractors (negative SOA) the latency distribution with distractor present (black) is shifted relative to without distractor (gray). For late distractors, there is a dip (SI) time-locked to distractor onset. The thin line shows the latency distribution of errors towards the distractor, which is also time-locked to distractor onset as would be expected if they were driven by automatic visual signals. Mean (and median) delays for each SOA were, respectively: 9, 23, 28, 31, 27, 28, and 18 ms (12, 24, 28, 36, 28, 32, and 24 ms) for Column 1 and 5, 14, 20, 21, 25, 19, and 14 ms (8, 18, 23, 23, 28, 23, and 19 ms) for Column 2. Error rates were 24%, 19%, 11%, 7%, 3%, 3%, and 1% and 35%, 31%, 26%, 17%, 9%, 3%, and 2%. Note that large differences in error rate (10%–80%) across participants for the earliest distractors in Sumner et al. (2010) explains why the distractor and no-distractor distributions appear more separated than a mean delay of 5 ms would suggest; participants with high error rates contribute few saccades to the distractor distribution, but still make a full contribution to the no-distractor distribution, and these participants tend to have the lowest no-distractor latencies. Column 3 shows simulations using DINASAUR (1,200 trials per condition) with settings identical to those in Bompas and Sumner (2011)—that is, we made no attempt to fit it to the actual data for early distractors or late distractors here, but simply inherited the settings used to simulate late distractors previously. Column 4 shows the delay caused by the distractor for individual trials, simulated with identical noise with and without distractor, plotted against the latency that would have occurred without a distractor. Many saccades that would have occurred even 200 ms after the distractor (i.e., after visible dips are over) were still delayed. See Figure 2 for more information for the modeled data.
Figure 2
 
Metrics of the distraction effects for modeled data. Note that mean and median delays (the standard RDE measures, top plot) track each other for early distractors, but diverge for late distractors because the median of a bimodal distribution is greatly influenced by whether the dip comes before or after the median of the baseline condition; hence median delay can be misleading for late distractors (see McIntosh & Buonocore, 2014). Conversely, dip amplitude (maximum distraction ratio, after Bompas & Sumner, 2011) is only useful once bimodality appears in the distribution; a value of 1 means that for at least one time bin, 100% of the saccades in the baseline condition have disappeared from that time bin in the distractor distribution). The middle plot provides further information for the individual trial delays (modeled distractor condition minus identical modeled trial without distractor) as depicted in Figure 1, Column 4. Note that the overall mean delay is accounted for more by the proportion of trials affected than by the mean delay or standard deviaton of those affected trials. The lower plot shows histograms of these individual trial delays (i.e., collapsing over the x-axes of Column 4 in Figure 1). It is clear that small effects are much more common than medium or large ones, and that the pattern is similar for early (red), simultaneous (black), and late distractors (blue).
Figure 2
 
Metrics of the distraction effects for modeled data. Note that mean and median delays (the standard RDE measures, top plot) track each other for early distractors, but diverge for late distractors because the median of a bimodal distribution is greatly influenced by whether the dip comes before or after the median of the baseline condition; hence median delay can be misleading for late distractors (see McIntosh & Buonocore, 2014). Conversely, dip amplitude (maximum distraction ratio, after Bompas & Sumner, 2011) is only useful once bimodality appears in the distribution; a value of 1 means that for at least one time bin, 100% of the saccades in the baseline condition have disappeared from that time bin in the distractor distribution). The middle plot provides further information for the individual trial delays (modeled distractor condition minus identical modeled trial without distractor) as depicted in Figure 1, Column 4. Note that the overall mean delay is accounted for more by the proportion of trials affected than by the mean delay or standard deviaton of those affected trials. The lower plot shows histograms of these individual trial delays (i.e., collapsing over the x-axes of Column 4 in Figure 1). It is clear that small effects are much more common than medium or large ones, and that the pattern is similar for early (red), simultaneous (black), and late distractors (blue).
Figure 3
 
Time course of exogenous and endogenous inputs and consequences on the neural activities within the fixation (blue), target (black), and distractor (red) nodes at SOA −60, 0, and 60 ms. The neural activities are represented for the distractor present condition. For comparison, the neural activity within the target node is also given in the absence of distractor (gray). B = Baseline activity during fixation before peripheral stimulus onset. Th = Threshold of the accumulation process. NB = At SOA 0, bursts of exogenous activity in target and distractor nodes fully overlap. NB2 = At SOA 60, the delay is large on this noise-free trial, but only a smaller proportion of saccades will be affected compared to SOA 0. NB3 = The slight reduction in activity for the target node in the presence of an early distractor (bottom left plot) is reminiscent of neurophysiological data observed in the SC by Dorris, Olivier, and Munoz (2007).
Figure 3
 
Time course of exogenous and endogenous inputs and consequences on the neural activities within the fixation (blue), target (black), and distractor (red) nodes at SOA −60, 0, and 60 ms. The neural activities are represented for the distractor present condition. For comparison, the neural activity within the target node is also given in the absence of distractor (gray). B = Baseline activity during fixation before peripheral stimulus onset. Th = Threshold of the accumulation process. NB = At SOA 0, bursts of exogenous activity in target and distractor nodes fully overlap. NB2 = At SOA 60, the delay is large on this noise-free trial, but only a smaller proportion of saccades will be affected compared to SOA 0. NB3 = The slight reduction in activity for the target node in the presence of an early distractor (bottom left plot) is reminiscent of neurophysiological data observed in the SC by Dorris, Olivier, and Munoz (2007).
Figure 4
 
Columns 1 and 2 show the effect of making the exogenous signal more or less transient (all settings the same as in Figure 1 except the decay rate of exogenous signals decreased to 8 or increased to 12; original setting was 10). Mean (median) delays are 8, 17, 25, 28, and 20 ms (8, 18, 26, 31, and 25 ms) for Column 1 and 16, 40, 52, 26, and 11 ms (15, 40, 56, 24, and 0 ms) for Column 2. Columns 3 and 4 show the delay caused by the distractor for individual simulated trials plotted against the latency that would have occurred without a distractor (same analysis as in Figure 1, Column 4). While there is lower density of medium and long delays for shorter distractor signals, the reach of the distractor is not more limited with respect to the where the saccade would have appeared in the latency distribution with no distractor (x-axis).
Figure 4
 
Columns 1 and 2 show the effect of making the exogenous signal more or less transient (all settings the same as in Figure 1 except the decay rate of exogenous signals decreased to 8 or increased to 12; original setting was 10). Mean (median) delays are 8, 17, 25, 28, and 20 ms (8, 18, 26, 31, and 25 ms) for Column 1 and 16, 40, 52, 26, and 11 ms (15, 40, 56, 24, and 0 ms) for Column 2. Columns 3 and 4 show the delay caused by the distractor for individual simulated trials plotted against the latency that would have occurred without a distractor (same analysis as in Figure 1, Column 4). While there is lower density of medium and long delays for shorter distractor signals, the reach of the distractor is not more limited with respect to the where the saccade would have appeared in the latency distribution with no distractor (x-axis).
Figure 5
 
Simulations providing a closer fit to experiment 2 in Walker and Benson (2013). For the early distractors (SOA −60) the target node received anticipatory endogenous signal (a third of the strength of the full endogenous signal that follows target onset). This speeded up saccade latency to the values found by Walker and Benson (2013; median target-only latency = 112 ms, median latency with distractor = 130 ms). Note that, perhaps counterintuitively, this anticipatory activity did not reduce the RDE (18 ms); the decrease in baseline latency is mainly provided by many more saccades in the express mode (where exogenous activity is sufficient to reach threshold), and since distractors markedly reduce this express mode, they still produce a marked RDE. Error rate is also reduced (5%), though not the very low levels in Walker and Benson's data. For SOA zero, we attenuated the distractor signal (by half), which provided an RDE of 16 ms, less than that for −60 SOA, as in the data of Walker and Benson (median target-only latency = 137 ms, median latency with distractor = 153 ms). The simulation for +60 SOA used the same settings as 0 SOA.
Figure 5
 
Simulations providing a closer fit to experiment 2 in Walker and Benson (2013). For the early distractors (SOA −60) the target node received anticipatory endogenous signal (a third of the strength of the full endogenous signal that follows target onset). This speeded up saccade latency to the values found by Walker and Benson (2013; median target-only latency = 112 ms, median latency with distractor = 130 ms). Note that, perhaps counterintuitively, this anticipatory activity did not reduce the RDE (18 ms); the decrease in baseline latency is mainly provided by many more saccades in the express mode (where exogenous activity is sufficient to reach threshold), and since distractors markedly reduce this express mode, they still produce a marked RDE. Error rate is also reduced (5%), though not the very low levels in Walker and Benson's data. For SOA zero, we attenuated the distractor signal (by half), which provided an RDE of 16 ms, less than that for −60 SOA, as in the data of Walker and Benson (median target-only latency = 137 ms, median latency with distractor = 153 ms). The simulation for +60 SOA used the same settings as 0 SOA.
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