April 2015
Volume 15, Issue 4
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Article  |   June 2015
The antisaccade task: Vector inversion contributes to a statistical summary representation of target eccentricities
Author Affiliations
  • Matthew Heath
    School of Kinesiology, The University of Western Ontario, London, ON, Canada,
    Graduate Program in Neuroscience, The University of Western Ontario, London, ON, Canada
    mheath2@uwo.ca
  • Caitlin Gillen
    School of Kinesiology, The University of Western Ontario, London, ON, Canada,
    cgillen@uwo.ca
  • Jeffrey Weiler
    School of Kinesiology, The University of Western Ontario, London, ON, Canada,
    jweiler2@uwo.ca
Journal of Vision June 2015, Vol.15, 4. doi:10.1167/15.4.4
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      Matthew Heath, Caitlin Gillen, Jeffrey Weiler; The antisaccade task: Vector inversion contributes to a statistical summary representation of target eccentricities. Journal of Vision 2015;15(4):4. doi: 10.1167/15.4.4.

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Abstract

Antisaccades require the top-down suppression of a stimulus-driven prosaccade (i.e., response suppression) and the inversion of a target's spatial location to mirror-symmetrical space (i.e., vector inversion). Moreover, recent work has shown that antisaccade amplitudes are characterized by a statistical summary representation (SSR) of the target eccentricities included in a stimulus-set—a result suggesting that antisaccades are supported via the same relative visual information as perceptions. The present investigation sought to determine whether response suppression and the disruption of real-time control or vector inversion contribute to a SSR in oculomotor control. Participants completed pro- and antisaccades (target eccentricities of 10.5°, 15.5°, and 20.5°) in blocks of trials that differed with regard to the frequency that individual target eccentricities were presented. The manipulation of target eccentricity frequency was used to determine whether the most frequently presented target within a stimulus-set (i.e., the SSR) influences saccade amplitudes. Moreover, we disrupted the real-time control of prosaccades by requiring participants to suppress their response for a brief visual delay (i.e., 2000 ms: so-called delay prosaccade). As expected, antisaccades and delay prosaccades produced equivalent reaction times. In turn, amplitudes for delay prosaccades were refractory to the manipulation of target eccentricity frequency, whereas antisaccades were biased in the direction of the most frequently presented target within a stimulus-set. Accordingly, we propose that vector inversion contributes to the mediation of target eccentricities via a SSR and that such a phenomenon provides convergent evidence that a relative visual percept mediates antisaccades.

Introduction
One of the primary roles of the human visual system is to develop short- and long-term representations to support perceptual judgments. Ample evidence has shown that the ventral visual pathway mediates perceptual judgments by comparing the properties of an object (e.g., distance, orientation, shape, size) to other items in the visual scene (i.e., relative visual processing) (Goodale & Milner, 1992; Ungerleider & Mishkin, 1982). Relative processing is an important attribute of the ventral pathway because it permits the development of cognitive maps that promote the temporally stable identification of objects based on their visual properties (i.e., a grape is “relatively” small compared to an apple). Moreover, an accumulating body of evidence has shown that a consequent feature of the ventral stream's relative processing is that perceptual judgments are, in part, represented by a statistical summary representation (SSR). In the first direct demonstration of this phenomenon, Ariely (2001) presented a set of differently sized circles for 500 ms and asked participants to report whether a subsequent test circle was a member of the set (experiment 1) or represented the average of the set (experiment 2). Results showed that participants were unable to identify whether the test circle was a member of the set but were able to reliably discriminate when the test circle represented the average of the set. Accordingly, Ariely proposed that the visual system creates a SSR without accurate information related to the individual items contained within the set. More recent work has shown that a SSR (a) occurs for exposure durations as brief as 50 ms and persists in memory for an appreciable period of time (i.e., 2000 ms) (Chong & Treisman, 2003) and (b) occurs across a range of stimulus-sets that differ with regard to their density and distribution type (Chong & Treisman, 2003, 2005; Im & Chong, 2009). As well, a SSR continuously operates over transforming objects (Albrecht & Scholl, 2010) and characterizes perceptions for items within a stimulus-set that are presented concurrently or serially (Corbett & Oriet, 2011). As such, a SSR provides a parsimonious strategy by which perceptual judgments accommodate for limited visual-attentive resources.1 
The second primary role of the visual system is to execute movements. Notably, although a growing body of evidence supports the contention that visual perceptions are mediated by a SSR, a paucity of work has examined whether actions are similarly influenced. One framework to address this issue is to investigate whether a target property (e.g., eccentricity) representing the SSR of a stimulus-set facilitates the latency and/or amplitude of goal-directed saccades. In one examination of this issue, work by our group (Gillen & Heath, 2014b; see also Gillen & Heath, 2014a) had participants complete prosaccades (i.e., saccade to veridical target location) and antisaccades (i.e., saccade to the target's mirror symmetrical location) to briefly presented targets (i.e., 50 ms) located 10.5° (“proximal” target), 15.5° (“middle” target), and 20.5° (“distal” target) left and right of a common fixation. Importantly, pro- and antisaccades were completed across conditions that differed with regard to the weighting of target eccentricity frequency. In the control-weighting condition, target eccentricities were presented with equal frequency whereas in the proximal- and distal-weighting conditions the “proximal” and “distal” targets were, respectively, presented five times as often as the other eccentricities. It was reasoned that if a SSR influences oculomotor control then the proximal- and distal-weighting conditions should produce amplitudes that are biased in the direction of the most frequently presented target (i.e., the target that represents the “average” eccentricity of the stimulus-set). Results showed that prosaccades were refractory to the different target-weighting conditions. This was an expected finding and one attributed to their mediation via absolute (i.e., metrically precise) sensorimotor transformations specified via retinotopically organized motor maps in the superior colliculus (SC) (Wurtz & Albano, 1980). In other words, the absolute visual information supporting prosaccades is incompatible with the development of a SSR. More notably, antisaccades in the proximal-weighting condition undershot target eccentricity more than their control condition counterpart, whereas the converse pattern was true for the distal-weighting condition. Thus, antisaccade amplitudes were biased in the direction of the most frequently presented target—a result that is entirely compatible with the representation of a stimulus-set via a SSR. In accounting for this finding, we note that antisaccades produce longer reaction times (RTs) (Fischer & Weber, 1992; Hallett, 1978) and less accurate and more variable amplitudes than prosaccades (Dafoe, Armstrong, & Munoz, 2007; Evdokimidis, Tsekou, & Smyrnis, 2006; Heath, Weiler, Marriott, & Welsh, 2011). Further, neuroimaging and electrophysiological evidence from humans and nonhuman primates has shown that the aforementioned antisaccade behavioral “costs” are related to the top-down and two-component process of suppressing a stimulus-driven prosaccade (i.e., response suppression) (Connolly, Goodale, Menon, & Munoz, 2002; Curtis & D'Esposito, 2003; Ford, Goltz, Brown, & Everling, 2005), and the visual remapping of a target's spatial location to mirror-symmetrical space (i.e., vector inversion) (Moon et al., 2007; Zhang & Barash, 2000; for comprehensive review, see Munoz & Everling, 2004). Thus, our group proposed that the observed SSR for antisaccades evinces that top-down control renders sensorimotor transformations via the same relative visual information as perceptions.2 Moreover, we note that our conclusion is consistent with work demonstrating that the spatial location of a target on trial N-1 or N-2 influences the endpoint location for a to-be-performed trial (Rastgardani, Lau, Barton, & Abegg, 2012; see also Abegg, Rodriguez, Lee, & Barton, 2010; Cheng, De Grosbois, Smirl, Heath, & Binsted, 2011; DeSimone, Everling, & Heath, 2015). 
An issue that remains to be addressed is whether response suppression and the introduction of a memory delay or vector inversion contributes to the mediation of saccade endpoints via a SSR. To that end, we had participants complete pro- and antisaccades cued by a briefly presented target (i.e., 50 ms; eccentricities of 10.5°, 15.5°, and 20.5°) across distal-, control-, and proximal-weighting conditions (i.e., the same task and weighting conditions as employed by Gillen & Heath, 2014b). In addition, target-weighting conditions were performed in a delay prosaccade task wherein a 2000-ms interval was introduced between target extinction and movement onset. The basis for the delay prosaccade task was twofold. First, delay prosaccades require the top-down inhibition of an automatic and stimulus-driven response (visual grasp reflex; see Pierrot-Deseilligny, Rivaud, Gaymard, & Agid, 1991) and are therefore associated with response-suppression demands that are similar to antisaccades (Olk & Kingstone, 2003; Weiler, Holmes, Mulla, & Heath, 2011; Weiler, Mitchell, & Heath, 2014). Second, the manual aiming and oculomotor literature have shown that a response implemented following a period of visual delay requires that the spatial location of a target is held in memory (Heath, 2005; White, Sparks, & Stanford, 1993)—a top-down manipulation that some work has shown to result in the specification of target eccentricity via relative visual information (e.g., Westwood & Goodale, 2003; but see Elliott & Madalena, 1987). More specifically, Westwood and Goodale's (2003) real-time control hypothesis asserts that actions planned and executed following even the briefest period of visual delay are mediated via a perception-based target representation (see also Goodale & Westwood, 2004). Thus, if the top-down demands associated with disrupting real-time control contributes to endpoints mediated via a SSR, then antisaccades and delay prosaccades in the proximal- and distal-weighting conditions should produce amplitudes that are, respectively, shorter and longer than their control condition counterparts. In other words, antisaccade and delay prosaccade amplitudes should be biased in the direction of a most frequently presented target. 
As an alternative prediction, it is possible that a SSR is selectively related to vector inversion. Indeed, vector inversion is an attention-dependent process requiring that the visual distance between the central gaze and a visual target is computed to a perceived location in mirror-symmetrical space (Collins, Vergilino-Perez, Delisle, & Doré-Mazars, 2008; Nyffeler, Hartmann, Hess, & Müri, 2008; Nyffeler, Rivaud-Pechoux, Pierrot-Deseilligny, Diallo, & Gaymard, 2007; Moon et al., 2007; Zhang & Barash, 2000). It is therefore possible that antisaccade endpoints are mediated via a SSR in order to diminish the complexity and noise associated with vector inversion. As such, if vector inversion contributes to the mediation of endpoints via a SSR, then the different target-weighting conditions used here should selectively influence antisaccades. Thus, the research question addressed here provides a framework to determine whether a SSR is unique to the antisaccade task or reflects a general consequence of top-down oculomotor control. 
Methods
Participants
Sixteen participants (age range: 19–29 years; 11 female and five male) from the University of Western Ontario community volunteered for this investigation. All participants were self-declared right-hand dominant, had normal or corrected-to-normal vision, and reported no current or previous neurological impairment. Participants provided written consent approved by the Office of Research Ethics, University of Western Ontario, and this work was conducted according to the ethical standards outlined in the Declaration of Helsinki. 
Apparatus and procedures
Participants sat in front of a normal tabletop (height 775 mm) for the duration of the experiment with their head placed in a head/chin rest. A 30-in. LCD monitor (60 Hz, 8 ms response rate, 1280 × 960 pixels; Dell 3007WFP, Round Rock, TX) located at participants' midline and 550 mm from the front edge of the tabletop was used to present visual stimuli. The gaze location of participants' left eye was measured via a video-based eye-tracking system (Eye-Trac6, Applied Sciences Laboratories, Bedford, MA) sampling at 360 Hz. In addition to the stimulus monitor, two additional monitors that were visible only to the experimenter provided real-time point of gaze location, trial-by-trial saccade kinematics (e.g., displacement, velocity), and information related to the accuracy of the eye tracking system (i.e., to perform a recalibration when necessary). Computer events and the presentation of visual stimuli were controlled via MATLAB (7.6; The MathWorks, Natick, MA) and the Psychophysics Toolbox extensions (ver. 3.0; see Brainard, 1997). The lights in the experimental suite were extinguished throughout data collection. 
Visual stimuli were presented against a high-contrast black background and included a white fixation cross (1°, 135 cd/cm2) located at the center of the monitor as well as yellow target crosses (1°, 127 cd/cm2) located 10.5° (i.e., “proximal” target), 15.5° (i.e., “middle” target) and 20.5° (i.e., “distal” target) left and right of the fixation cross and on the same horizontal meridian. At the start of each trial, the fixation cross was presented and signaled that participants should direct their gaze to its location. Once a stable gaze was attained (i.e., ±1.5° for 420 ms) a randomized fore-period was initiated (i.e., 1000 to 2000 ms) after which time one of the target stimuli was presented for 50 ms. Figure 1 shows that responses were completed in each of three distinct trial-types (i.e., prosaccade, antisaccade, delay prosaccade). For prosaccade (i.e., saccade directly to veridical target location) and antisaccade (i.e., saccade mirror-symmetrical to target location) trial-types, the extinction of the fixation cross and the simultaneous onset of the target stimulus served as the movement imperative. For the delay prosaccade trial-type, the target was extinguished and participants were subsequently cued to initiate a response to the remembered target location following a 2000-ms delay. Importantly, Figure 1 shows that the fixation cross remained visible during the delay interval, and its extinction served as the movement imperative. For all trial-types, participants were instructed to complete their response as quickly and accurately as possible. Further, a 50-ms target presentation was used to ensure that retinal feedback related to response accuracy was equated across trial-types (Heath et al., 2011). Additionally, in selecting the delay interval used here we were guided by previous work reporting that sufficiently brief delays do not differentially influence equivalence in pro- and antisaccade response-suppression demands. In particular, previous work has shown that pro- and antisaccades exhibit equivalent RTs regardless of whether task instructions (i.e., pro- vs. antisaccade) are withheld until response cuing (i.e., 0-ms delay condition; see Olk & Kingstone, 2003; Weiler & Heath, 2014) or are preformed following a 2000-ms delay (Weiler et al., 2011). Moreover, because prosaccade endpoint bias is not modulated following sufficiently brief delays (i.e., <5600 ms; see White et al., 1993), the 2000-ms interval used here provided a stable basis to determine whether disrupting real-time control renders prosaccade endpoints that are mediated by a SSR. 
Figure 1
 
Schematic of the timeline of visual and movement-related events for prosaccades, antisaccades, and delay prosaccades. For all trial-types, a central fixation was presented for a randomized fore period after which time one of the three target eccentricities was presented for 50 ms (note: for simplicity, the figure shows one target presented in the left visual field). For pro- and antisaccades (see left panel), the fixation cross was extinguished concurrent with target presentation, and the fixation extinction (and simultaneous target onset) served as the imperative to saccade to the target's veridical (i.e., prosaccade: depicted as a solid line with arrow) or mirror-symmetrical (i.e., antisaccade: depicted as a hatched line with arrow) location. For delay prosaccades (see right panel), the same target presentation duration was used after which time a 2000-ms delay interval was introduced—the fixation cross was visible during the delay interval. Following the delay interval, the fixation cross extinction served as the cue to saccade to the target's remembered location.
Figure 1
 
Schematic of the timeline of visual and movement-related events for prosaccades, antisaccades, and delay prosaccades. For all trial-types, a central fixation was presented for a randomized fore period after which time one of the three target eccentricities was presented for 50 ms (note: for simplicity, the figure shows one target presented in the left visual field). For pro- and antisaccades (see left panel), the fixation cross was extinguished concurrent with target presentation, and the fixation extinction (and simultaneous target onset) served as the imperative to saccade to the target's veridical (i.e., prosaccade: depicted as a solid line with arrow) or mirror-symmetrical (i.e., antisaccade: depicted as a hatched line with arrow) location. For delay prosaccades (see right panel), the same target presentation duration was used after which time a 2000-ms delay interval was introduced—the fixation cross was visible during the delay interval. Following the delay interval, the fixation cross extinction served as the cue to saccade to the target's remembered location.
The different trial-types were completed in separate blocks within each of three conditions that differed with regard to target eccentricity weighting. For the control-weighting condition, an equal number of trials (i.e., eight) were completed to each target eccentricity by visual space combination (i.e., 48 trials for each of the prosaccade, antisaccade, and delay prosaccade trial-types). For the proximal-weighting condition, the proximal target was presented five times as often as the middle and distal target eccentricities. Thus, 40 trials were completed to each left and right visual field proximal target whereas eight trials were completed to each left and right visual field middle and distal target. For the distal-weighting condition, the distal target was presented five times as often as the proximal and middle targets. As such, 40 trials were completed to each left and right visual field distal target whereas eight trials were completed to each left and right visual field proximal and middle target. Therefore, for each trial-type (i.e., prosaccade, antisaccade, delay prosaccade), participants completed 112 trials in each of the proximal- and distal-weighting conditions. In total, participants completed 816 trials. 
The three weighting conditions were completed in separate and randomly ordered sessions that were separated by a minimum of 24 h. Owing to the number of trials used here, we included the different sessions to reduce mental fatigue and eye strain. As well, recall that within each weighting condition the different trial-types (i.e., prosaccade, antisaccade, delay prosaccade) were completed in separate and randomly ordered blocks. Prior to each trial-type block, an instruction screen was presented, which informed participants as to the nature of the upcoming trials. Target presentation (i.e., target eccentricity by visual field combination) within each block was pseudorandomized and based on the criterion that a single target could not appear on more than three consecutive trials. During data collection, a trial associated with a signal loss (i.e., an eyeblink) or a directional error was discarded, and that trial was reentered into the trial matrix. Less than 1% of pro- and delay prosaccade trials and less than 4% of antisaccade trials were associated with a directional error. The low antisaccade error rate is attributed to the use of an overlap paradigm and the use of separate trial-type blocks (Weiler & Heath, 2014). 
Data analysis
Gaze position data were filtered offline via a dual-pass Butterworth filter employing a low-pass cutoff frequency of 15 Hz. Filtered displacement data were used to compute instantaneous velocities via a five-point central finite difference algorithm. Acceleration data were similarly obtained from the velocity data. Movement onset was determined when saccade velocity and acceleration values exceeded 30°/s and 8000°/s2, respectively. Saccade offset was marked when saccade velocity fell below a threshold value of 30°/s for 15 consecutive frames (i.e., 42 ms). 
Dependent variables and statistical analysis
Dependent variables included RT (time between fixation cross extinction and movement onset) and saccade amplitude in the primary (i.e., horizontal) movement direction. RT data were excluded if less than 85 ms (Wenban-Smith & Findlay, 1991) or were greater than 650 ms; less than 2% of trials for any participant were excluded based on the aforementioned criteria. Post hoc contrasts involving trial-type or weighting condition were completed via paired-samples t tests, and significant effects involving target eccentricity were decomposed via power-polynomials (i.e., trend analysis; see Pedhazur, 1997). 
Results
Reaction time
Figure 2 provides RT frequency histograms as a function of trial-type and target-weighting condition. The histograms provide a qualitative demonstration that for each trial-type the proximal- and distal-weighting conditions did not result in an increased frequency of express saccades compared to the control-weighting condition. Thus, the different target-weighting conditions were not associated with distinct presaccade motor preparation processes (Dorris & Munoz, 1998; Rolfs & Vitu, 2007). RT data were examined quantitatively via 3 (trial-type: prosaccade, antisaccade, delay prosaccade) × 3 (weighting condition: proximal-weighting, control weighting, distal-weighting) × 3 (target eccentricity: 10.5° [proximal], 15.5° [middle], 20.5° [distal]) repeated-measures ANOVA. Results elicited a main effect for trial-type, F(2, 30) = 70.38, p < 0.001. Prosaccades (236 ms, SD = 32) produced shorter RTs than antisaccades (300 ms, SD = 32) and delay prosaccades (309 ms, SD = 24), all ts(15) = 10.37 and 10.04, all ps < 0.001. RTs for the latter trial-types did not reliably differ, t(15) = 1.34, p = 0.20. 
Figure 2
 
RT (ms) percentage frequency histograms for prosaccades, antisaccades, and delay prosaccades as a function of distal- (top panels), control- (middle panels), and proximal-weighting (lower panels) conditions. Bins widths are 20 ms and begin at 80 ms and end at 640 ms. The vertical dashed line in each panel represents the bin containing mean RT.
Figure 2
 
RT (ms) percentage frequency histograms for prosaccades, antisaccades, and delay prosaccades as a function of distal- (top panels), control- (middle panels), and proximal-weighting (lower panels) conditions. Bins widths are 20 ms and begin at 80 ms and end at 640 ms. The vertical dashed line in each panel represents the bin containing mean RT.
Amplitude
Amplitude data were examined via the same ANOVA model as RT. Results produced main effects for trial-type, F(2, 30) = 14.51, p < 0.001; weighting condition, F(2, 30) = 5.69, p < 0.01; and target eccentricity, F(2, 30) = 863.27, p < 0.001 as well as interactions involving trial-type by target eccentricity, F(4, 60) = 165.03, p < 0.001, and trial-type by weighting condition, F(4, 60) = 9.90, p < 0.001. 
In terms of the trial-type by target eccentricity interaction, Figure 3 shows that amplitudes increased linearly with increasing target eccentricity for each trial-type; only linear effects were significant: all Fs(1, 15) = 1709.84, 45.69, and 719.15, respectively, for prosaccades, antisaccades, and delay prosaccades, and all ps < 0.001. To further decompose the interaction, we computed participant-specific slopes relating amplitude to target eccentricity separately for each trial-type. Prosaccades produced a steeper slope (0.92, SD = 0.04) than antisaccades (0.28, SD = 0.15) or delay prosaccades (0.81, SD = 0.11), all ts(15) = 17.02 and 3.85, all ps < 0.01. As well, delay prosaccades produced a steeper slope than antisaccades, t(15) = 15.66, p < 0.001. In complement to the slope analysis, the top panels of Figure 4 provide target eccentricity difference scores (i.e., amplitude minus veridical target eccentricity) for each trial-type. This figure demonstrates that all trial-types produced an increased undershooting bias with increasing target eccentricity; however, the magnitude of the bias was largest for antisaccades. 
Figure 3
 
Amplitude (degrees) for prosaccades, antisaccades, and delay prosaccades as a function of weighting condition (proximal-weighting [triangle symbol], control-weighting [circle symbol], and distal-weighting [square symbol]) and target eccentricity. The dashed line represents the regression of each weighting condition to target eccentricity, and associated regression equations are presented at the top of each panel. The solid line in each panel represents veridical target eccentricity. Error bars represent the 95% within-participant confidence interval computed as a function of the mean-squared error term for target eccentricity for individual trial-type and weighting condition combinations (Loftus & Masson, 1994).
Figure 3
 
Amplitude (degrees) for prosaccades, antisaccades, and delay prosaccades as a function of weighting condition (proximal-weighting [triangle symbol], control-weighting [circle symbol], and distal-weighting [square symbol]) and target eccentricity. The dashed line represents the regression of each weighting condition to target eccentricity, and associated regression equations are presented at the top of each panel. The solid line in each panel represents veridical target eccentricity. Error bars represent the 95% within-participant confidence interval computed as a function of the mean-squared error term for target eccentricity for individual trial-type and weighting condition combinations (Loftus & Masson, 1994).
Figure 4
 
The top panel shows target eccentricity amplitude difference scores (degrees, i.e., amplitude for each target eccentricity minus veridical target eccentricity) for each trial-type (prosaccade, antisaccade, delay prosaccade). The bottom panel shows weighting condition difference scores (degrees; distal-weighting/proximal-weighting condition minus control-weighting condition) for each trial-type. Error bars represent 95% between-participant confidence intervals (Cumming, 2013). The absence of overlap between error bars and zero represent a reliable difference that can be interpreted inclusive to a test of the null hypothesis. Thus, the figures graphically depict that (a) target eccentricity difference scores for all trial-type by target eccentricity combinations—with the exception of antisaccades to the 10.5° target—show a reliable undershooting bias and (b) weighting-condition difference scores show that prosaccade and delay prosaccade amplitudes for the proximal- and distal-weighting conditions did not reliably differ from their control condition counterparts, whereas antisaccade amplitudes for the proximal- and distal-weighting conditions were, respectively, less than and greater than their control condition counterpart.
Figure 4
 
The top panel shows target eccentricity amplitude difference scores (degrees, i.e., amplitude for each target eccentricity minus veridical target eccentricity) for each trial-type (prosaccade, antisaccade, delay prosaccade). The bottom panel shows weighting condition difference scores (degrees; distal-weighting/proximal-weighting condition minus control-weighting condition) for each trial-type. Error bars represent 95% between-participant confidence intervals (Cumming, 2013). The absence of overlap between error bars and zero represent a reliable difference that can be interpreted inclusive to a test of the null hypothesis. Thus, the figures graphically depict that (a) target eccentricity difference scores for all trial-type by target eccentricity combinations—with the exception of antisaccades to the 10.5° target—show a reliable undershooting bias and (b) weighting-condition difference scores show that prosaccade and delay prosaccade amplitudes for the proximal- and distal-weighting conditions did not reliably differ from their control condition counterparts, whereas antisaccade amplitudes for the proximal- and distal-weighting conditions were, respectively, less than and greater than their control condition counterpart.
In terms of the trial-type by weighting condition interaction, Figure 5 presents frequency histograms for each trial-type by weighting condition combination. Notably, prosaccades and delay prosaccades demonstrated separate distributions and separate peaks for the different target eccentricities included in each weighting condition. In contrast, antisaccades demonstrated a single distribution and a single peak for each weighting condition. Thus, the frequency histograms provide a qualitative demonstration that antisaccade endpoints were mediated via a SSR. Moreover, quantitative analyses (Figure 3 and lower panels of Figure 4) show that prosaccades and delay prosaccades did not reliably differ as function of the different weighting conditions, all Fs(2, 30) < 1. In contrast, antisaccades produced an effect of weighting condition, F(2, 30) = 16.25, p < 0.001, such that amplitudes for proximal- and distal-weighting conditions were respectively less than and greater than their control condition counterpart, all ts(15) = −3.43 and 2.82, ps = 0.003 and 0.012. In other words, responses requiring vector inversion were characterized by a SSR. 
Figure 5
 
Amplitude (degrees) percentage frequency histograms for prosaccades, antisaccades, and delay prosaccades as a function of distal- (top panels), control- (middle panels), and proximal-weighting (lower panels) conditions. The bin containing the mean for each target eccentricity is denoted via a vertical hatched line, and the top (or side) of each line presents the numerical mean (i.e., lines moving from left to right, respectively, represent means for the 10.5°, 15.5°, and 20.5° target eccentricities). Prosaccades and delay prosaccades across each weighing condition demonstrate distributions and peaks for individual target eccentricities. In contrast, antisaccades across each weighting condition demonstrate a single distribution and a single peak.
Figure 5
 
Amplitude (degrees) percentage frequency histograms for prosaccades, antisaccades, and delay prosaccades as a function of distal- (top panels), control- (middle panels), and proximal-weighting (lower panels) conditions. The bin containing the mean for each target eccentricity is denoted via a vertical hatched line, and the top (or side) of each line presents the numerical mean (i.e., lines moving from left to right, respectively, represent means for the 10.5°, 15.5°, and 20.5° target eccentricities). Prosaccades and delay prosaccades across each weighing condition demonstrate distributions and peaks for individual target eccentricities. In contrast, antisaccades across each weighting condition demonstrate a single distribution and a single peak.
Reaction and amplitude correlations
We computed correlation coefficients relating mean RT and amplitude values for each trial-type by weighting condition by target eccentricity combination. Results showed that prosaccades to the 15.5° and 20.5° targets in the distal-weighting condition produced a reliable—and positive—correlation (i.e., p < 0.05). Notably, however, the remaining experimental conditions did not elicit reliable relationships (see Table 1 for coefficients and p values). Thus, amplitudes across the different trial-types were neither reliably nor consistently related to a speed–accuracy tradeoff in movement planning. 
Table 1
 
Correlation coefficients (R) and p values for the relationship between pro- and antisaccade RTs and amplitudes in the control-, proximal-, and distal-weighting conditions for each target eccentricity.
Table 1
 
Correlation coefficients (R) and p values for the relationship between pro- and antisaccade RTs and amplitudes in the control-, proximal-, and distal-weighting conditions for each target eccentricity.
Discussion
The present study tested the competing predictions that disrupting real-time control (i.e., via response suppression and a concurrent memory delay) or vector inversion render a SSR for antisaccade amplitudes. More specifically, we examined the expression of a SSR to determine the mechanism by which top-down cognitive control influences the nature of the visual information (i.e., relative vs. absolute) mediating antisaccades. 
Reaction time: Trial-type—but not target weighting—influences response planning
Results for RT yielded two main findings. First, RTs for antisaccades and delay prosaccades were equivalent and were longer than for prosaccades. As mentioned in the Introduction, that antisaccades produced longer RTs than prosaccades indicates that the top-down nature of response suppression and vector inversion is a measureable and time-consuming process (Hallett, 1978; for review, see Munoz & Everling, 2004). In turn, that antisaccades and delay prosaccades exhibited comparable RTs is directly in line with previous work reporting that response suppression is the primary determinant leading to increased antisaccade latencies (Olk & Kingstone, 2003; Weiler, Hassall, Krigolson, & Heath, 2015; Weiler & Heath, 2014). Most notably, the equivalent RTs for antisaccades and delay prosaccades provides the requisite framework by which to determine whether disrupting real-time control contributes to the mediation of saccade amplitudes via a SSR (see Antisaccade and delay prosaccade amplitudes: Vector inversion renders sensorimotor transformation via a SSR). Second, the different target-weighting conditions did not reliably influence RTs. Of course, we are aware that previous work has shown that manipulating the probabilistic location of a target (i.e., left or right and/or above or below a central fixation) influences pro- and antisaccade RTs—a result single-cell recording studies have linked to an enhanced target detection process and activation of SC motor-related neurons in the receptive field of the most frequently presented target (Dorris & Munoz, 1998; see also Geng & Behrmann, 2005; Liu et al., 2010). Moreover, Rolfs and Vitu (2007) have shown that enhanced movement planning is characterized by an increased frequency of express saccades for the most frequently presented target (i.e., latencies with a peak distribution around 100 ms; Fischer & Ramsperger, 1984). It is, however, important to note that the present study differs from previous work in that we manipulated target eccentricity frequency independent of the visual field in which the target was presented. Thus, and in spite of the increased frequency of the proximal and distal targets in their respective blocks, participants could not a priori predict a target's visual location (i.e., left or right of the central fixation). In support of this view, Figure 2 shows that the proximal- and distal-weighting conditions across each trial-type (i.e., prosaccade, antisaccade, delay prosaccade) did not yield separate express saccade peaks. Accordingly, target eccentricity frequency did not influence movement planning and therefore does not account for trial-type differences in saccade amplitudes (see below). 
Prosaccade sensorimotor transformations are mediated via absolute visual information
Prosaccades undershot veridical target location across each target eccentricity. The undershooting bias cannot be accounted for by a speed–accuracy tradeoff given that prosaccade RT and amplitude values were not reliably nor consistently related. Instead, results support the contention that undershooting is an invariant control strategy designed to minimize energy expenditure (Becker, 1989) and/or saccade flight time (Harris, 1995; Gillen et al., 2013). Additionally, amplitudes were refractory to the different target-weighting conditions (see also Gillen & Heath, 2014b) and is a result demonstrating that absolute and retinotopically organized visual information mediates prosaccade sensorimotor transformations (Wurtz & Albano, 1980). In other words, the absolute visual information supporting prosaccades is incompatible with a SSR. 
Antisaccade and delay prosaccade amplitudes: Vector inversion renders sensorimotor transformations via a SSR
As mentioned above, antisaccades and delay prosaccades exhibited equivalent RTs. Thus, the present study provides the appropriate framework to determine whether the mediation of endpoints via a SSR relates to (a) disrupting real-time control or (b) the process of vector inversion. Concerning results for the control condition, Figure 3 shows that delay prosaccades undershot each target eccentricity—a result indicating that such actions were mediated via the same invariant control strategy as their stimulus-driven counterparts (see Prosaccade sensorimotor transformations are mediated via absolute visual information). In contrast, antisaccades to the 10.5° target exhibited a null endpoint bias, whereas the 15.5° and 20.5° targets produced an undershooting bias. Moreover, the slope relating antisaccade amplitude to target eccentricity was markedly shallower than either prosaccade task. Thus, for control condition antisaccades, the presentation of target eccentricities with equal frequency resulted in the middle target (i.e., the target representing the SSR) determining the direction and magnitude of endpoint bias for the other targets in the stimulus-set. Of course, such a finding on its own provides prima facie evidence that antisaccades were mediated via a SSR. What is more, results for the proximal- and distal-weighting conditions showed that antisaccade amplitudes were biased in the direction of the most frequently presented target (i.e., proximal-weighting = 10.5°; distal-weighting = 20.5°) whereas delay prosaccade amplitudes did not vary with target weighting. As such, it is proposed that antisaccades are governed by a SSR representation of the perceived target eccentricities included within a stimulus-set. Further, the observation that delay prosaccades were refractory to the manipulation of target weighting demonstrates that disrupting real-time control does not contribute to a SSR. Instead, the selective SSR for antisaccades indicates that the top-down and obligatory nature of vector inversion results in sensorimotor transformations mediated by the same relative visual information as perceptions. 
There are three final issues from the results that require addressing. The first relates to the finding that delay prosaccades exhibited a greater undershooting bias than their (no delay) prosaccade counterparts. As discussed above, the difference is not likely related to their mediation via distinct visual information (i.e., absolute vs. relative) as delay prosaccades were not influenced by the different target-weighting conditions. A more parsimonious explanation is that a delay decreases motor-related activity of SC neurons (Basso, Krauzlis, & Wurtz, 2000; Hikosaka & Wurtz, 1985) and contributes to reduced visual “drive” (Krappmann, Everling, & Flohr, 1998). Furthermore, Powers, Basso, and Evinger (2013) have shown that the occurrence of gaze-evoked blinks during a delay interval increases saccade curvature and leads to decreased amplitudes. Thus, evidence suggests that the manner in which a delay prosaccade is structured—and not the transition from absolute to relative information—accounts for their increased undershooting bias. The second issue relates to the finding that the antisaccade undershooting bias increased with target eccentricity to a greater magnitude than prosaccades or delay prosaccades. In accounting for this result, it is important to recognize that perceptual judgments (i.e., oral reports) of target distance exhibit a systematic rise in underestimation bias with increasing target eccentricity (e.g., Bingham & Pagano, 1998; Foley, 1980). For example, the classic work of von Helmholtz (1910/1962) reported that the length of a line presented in the visual periphery was inversely related to its distance from a central fixation. Accordingly, underestimation may reflect that the proportional increase in “noise” associated with increasing stimulus magnitude (i.e., target eccentricity; for an outline of Weber's law see Marks & Algom, 1998) renders a compression of visual space toward a common stable frame of reference (Heath & Binsted, 2007; Sheth & Shimojo, 2001; Westwood, Heath, & Roy, 2003). Perhaps most notably, that antisaccades exhibited the same eccentricity-related undershooting bias provides convergent evidence that the top-down demands of vector inversion result in oculomotor control that is supported by the same relative visual information as perceptions. The third issue to address relates to the target presentation paradigm used here. In particular, each trial in the current investigation entailed the presentation of a discrete and single target. In contrast, the majority of the SSR literature has employed a paradigm wherein each item within a stimulus-set is concurrently presented (e.g., Ariely, 2001; Corbett & Melcher, 2014; Corbett, Wurnitsch, Schwartz, & Whitney, 2012; Chong & Treisman, 2003, 2005; Im & Chong, 2009; but see Albrecht & Scholl, 2010). The basis for the concurrent presentation is that the limited capacity of the visual system renders the processing of a stimulus-set via a SSR rather than retaining metrical information about each individual item. Notably, however, Corbett and Oriet (2011) demonstrated a SSR for a set of items presented in a rapid serial visual presentation paradigm. Thus, the present findings complement those of Corbett and Oriet's in demonstrating that a SSR can represent a stimulus-set when individual items are ordered in a discrete and/or serial fashion. 
A neural correlate for a SSR in oculomotor control
To our knowledge, Albrecht, Scholl, and McCarthy's (2013)3 work represents the only directed study to examine the neural correlate of perceptual averaging and the construction of a SSR. In that work, a posterior suppression of the EEG waveform occurred when participants were asked to judge whether a test stimulus matched the mean characteristic of a previously presented display. The posterior suppression of the EEG can be interpreted as indirect evidence that a sensory-related cortical region mediates a SSR. As well, electrophysiological, neuroimaging, and clinical neuropsychology evidence from the antisaccade literature have reported that the parietal cortex is the candidate structure associated with vector inversion (Nyffeler et al., 2007; Zhang & Barash, 2000).4 Thus, results from the present study attributing a SSR to vector inversion suggest that the parietal cortex may serve as the integral structure in mediating a SSR for oculomotor control. 
Conclusions
Antisaccades and delayed prosaccades were evaluated to determine whether disrupting real-time control or vector inversion contributes to the mediation of endpoints via a SSR. In spite of the equivalent response planning times, antisaccade amplitudes were selectively influenced by the manipulation of target eccentricity frequency. Thus, we propose that the top-down nature of vector inversions renders the processing of relative visual information via a SSR. 
Acknowledgments
Supported by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada and Major Academic Development Fund and Faculty Scholar Awards from the University of Western Ontario. 
Commercial relationships: none. 
Corresponding author: Matthew Heath. 
Email: mheath2@uwo.ca. 
Address: School of Kinesiology and Graduate Program in Neuroscience, The University of Western Ontario, London, ON, Canada. 
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Footnotes
1  Although the Introduction focuses on work in the visual domain, it is important to recognize that a SSR influences tactile-based perceptions of size (Davarpanah Jazi & Heath, 2014; Davarpanah Jazi, Hosang, & Heath, 2015) and the pitch from a sequence of tones (Albrecht, Scholl, & Chun, 2012). Thus, a SSR is a multisensory perceptual characteristic.
Footnotes
2  Kapoula (1985) proposed that prosaccades exhibit a range effect such that the proximal and distal targets contained within a stimulus set respectively over- and undershoot veridical target location (see also Kapoula & Robinson, 1986). Notably, however, our group's (Gillen, Weiler, & Heath, 2013) quantitative analysis of Kapoula's data showed that her results provide no evidence for a range effect, and our work provided further evidence to support the overwhelming contention that prosaccades produce an invariant undershooting bias (Becker, 1989; Harris, 1995). What is more, the range effect is entirely incompatible with our group's previous work showing that antisaccades do not overshoot veridical target eccentricity regardless of the range and magnitude of target eccentricities included within a stimulus set (Gillen & Heath, 2014a; 2014b).
Footnotes
3  Published abstract from the 2013 Annual Meeting of the Vision Sciences Society.
Footnotes
4  The distributed peaks of neural activity within the parietal cortex that reflect individual target eccentricities (cf. Georgopoulos, Schwartz, & Kettner, 1986) may become partially aggregated into a single peak (Cisek, 2007) that represents the statistical summary of the stimulus set.
Figure 1
 
Schematic of the timeline of visual and movement-related events for prosaccades, antisaccades, and delay prosaccades. For all trial-types, a central fixation was presented for a randomized fore period after which time one of the three target eccentricities was presented for 50 ms (note: for simplicity, the figure shows one target presented in the left visual field). For pro- and antisaccades (see left panel), the fixation cross was extinguished concurrent with target presentation, and the fixation extinction (and simultaneous target onset) served as the imperative to saccade to the target's veridical (i.e., prosaccade: depicted as a solid line with arrow) or mirror-symmetrical (i.e., antisaccade: depicted as a hatched line with arrow) location. For delay prosaccades (see right panel), the same target presentation duration was used after which time a 2000-ms delay interval was introduced—the fixation cross was visible during the delay interval. Following the delay interval, the fixation cross extinction served as the cue to saccade to the target's remembered location.
Figure 1
 
Schematic of the timeline of visual and movement-related events for prosaccades, antisaccades, and delay prosaccades. For all trial-types, a central fixation was presented for a randomized fore period after which time one of the three target eccentricities was presented for 50 ms (note: for simplicity, the figure shows one target presented in the left visual field). For pro- and antisaccades (see left panel), the fixation cross was extinguished concurrent with target presentation, and the fixation extinction (and simultaneous target onset) served as the imperative to saccade to the target's veridical (i.e., prosaccade: depicted as a solid line with arrow) or mirror-symmetrical (i.e., antisaccade: depicted as a hatched line with arrow) location. For delay prosaccades (see right panel), the same target presentation duration was used after which time a 2000-ms delay interval was introduced—the fixation cross was visible during the delay interval. Following the delay interval, the fixation cross extinction served as the cue to saccade to the target's remembered location.
Figure 2
 
RT (ms) percentage frequency histograms for prosaccades, antisaccades, and delay prosaccades as a function of distal- (top panels), control- (middle panels), and proximal-weighting (lower panels) conditions. Bins widths are 20 ms and begin at 80 ms and end at 640 ms. The vertical dashed line in each panel represents the bin containing mean RT.
Figure 2
 
RT (ms) percentage frequency histograms for prosaccades, antisaccades, and delay prosaccades as a function of distal- (top panels), control- (middle panels), and proximal-weighting (lower panels) conditions. Bins widths are 20 ms and begin at 80 ms and end at 640 ms. The vertical dashed line in each panel represents the bin containing mean RT.
Figure 3
 
Amplitude (degrees) for prosaccades, antisaccades, and delay prosaccades as a function of weighting condition (proximal-weighting [triangle symbol], control-weighting [circle symbol], and distal-weighting [square symbol]) and target eccentricity. The dashed line represents the regression of each weighting condition to target eccentricity, and associated regression equations are presented at the top of each panel. The solid line in each panel represents veridical target eccentricity. Error bars represent the 95% within-participant confidence interval computed as a function of the mean-squared error term for target eccentricity for individual trial-type and weighting condition combinations (Loftus & Masson, 1994).
Figure 3
 
Amplitude (degrees) for prosaccades, antisaccades, and delay prosaccades as a function of weighting condition (proximal-weighting [triangle symbol], control-weighting [circle symbol], and distal-weighting [square symbol]) and target eccentricity. The dashed line represents the regression of each weighting condition to target eccentricity, and associated regression equations are presented at the top of each panel. The solid line in each panel represents veridical target eccentricity. Error bars represent the 95% within-participant confidence interval computed as a function of the mean-squared error term for target eccentricity for individual trial-type and weighting condition combinations (Loftus & Masson, 1994).
Figure 4
 
The top panel shows target eccentricity amplitude difference scores (degrees, i.e., amplitude for each target eccentricity minus veridical target eccentricity) for each trial-type (prosaccade, antisaccade, delay prosaccade). The bottom panel shows weighting condition difference scores (degrees; distal-weighting/proximal-weighting condition minus control-weighting condition) for each trial-type. Error bars represent 95% between-participant confidence intervals (Cumming, 2013). The absence of overlap between error bars and zero represent a reliable difference that can be interpreted inclusive to a test of the null hypothesis. Thus, the figures graphically depict that (a) target eccentricity difference scores for all trial-type by target eccentricity combinations—with the exception of antisaccades to the 10.5° target—show a reliable undershooting bias and (b) weighting-condition difference scores show that prosaccade and delay prosaccade amplitudes for the proximal- and distal-weighting conditions did not reliably differ from their control condition counterparts, whereas antisaccade amplitudes for the proximal- and distal-weighting conditions were, respectively, less than and greater than their control condition counterpart.
Figure 4
 
The top panel shows target eccentricity amplitude difference scores (degrees, i.e., amplitude for each target eccentricity minus veridical target eccentricity) for each trial-type (prosaccade, antisaccade, delay prosaccade). The bottom panel shows weighting condition difference scores (degrees; distal-weighting/proximal-weighting condition minus control-weighting condition) for each trial-type. Error bars represent 95% between-participant confidence intervals (Cumming, 2013). The absence of overlap between error bars and zero represent a reliable difference that can be interpreted inclusive to a test of the null hypothesis. Thus, the figures graphically depict that (a) target eccentricity difference scores for all trial-type by target eccentricity combinations—with the exception of antisaccades to the 10.5° target—show a reliable undershooting bias and (b) weighting-condition difference scores show that prosaccade and delay prosaccade amplitudes for the proximal- and distal-weighting conditions did not reliably differ from their control condition counterparts, whereas antisaccade amplitudes for the proximal- and distal-weighting conditions were, respectively, less than and greater than their control condition counterpart.
Figure 5
 
Amplitude (degrees) percentage frequency histograms for prosaccades, antisaccades, and delay prosaccades as a function of distal- (top panels), control- (middle panels), and proximal-weighting (lower panels) conditions. The bin containing the mean for each target eccentricity is denoted via a vertical hatched line, and the top (or side) of each line presents the numerical mean (i.e., lines moving from left to right, respectively, represent means for the 10.5°, 15.5°, and 20.5° target eccentricities). Prosaccades and delay prosaccades across each weighing condition demonstrate distributions and peaks for individual target eccentricities. In contrast, antisaccades across each weighting condition demonstrate a single distribution and a single peak.
Figure 5
 
Amplitude (degrees) percentage frequency histograms for prosaccades, antisaccades, and delay prosaccades as a function of distal- (top panels), control- (middle panels), and proximal-weighting (lower panels) conditions. The bin containing the mean for each target eccentricity is denoted via a vertical hatched line, and the top (or side) of each line presents the numerical mean (i.e., lines moving from left to right, respectively, represent means for the 10.5°, 15.5°, and 20.5° target eccentricities). Prosaccades and delay prosaccades across each weighing condition demonstrate distributions and peaks for individual target eccentricities. In contrast, antisaccades across each weighting condition demonstrate a single distribution and a single peak.
Table 1
 
Correlation coefficients (R) and p values for the relationship between pro- and antisaccade RTs and amplitudes in the control-, proximal-, and distal-weighting conditions for each target eccentricity.
Table 1
 
Correlation coefficients (R) and p values for the relationship between pro- and antisaccade RTs and amplitudes in the control-, proximal-, and distal-weighting conditions for each target eccentricity.
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