Visual Space is Compressed in Prefrontal Cortex Before Eye Movements

Abstract

We experience the visual world through a series of saccadic eye movements, each one shifting our gaze to bring objects of interest to the fovea for further processing. Although such movements lead to frequent and substantial displacements of the retinal image, those displacements go unnoticed. It is widely assumed that a primary mechanism underlying this apparent stability is an anticipatory shifting of visual receptive fields (RFs) from their presaccadic to their postsaccadic locations prior to movement onset 1 . Evidence of this predictive “remapping” of RFs has been particularly apparent within brain structures involved in gaze control 2-4 . However, critically absent among that evidence are detailed measurements of visual RFs prior to movement onset. Here we show that during saccade preparation, rather than remap, RFs of neurons in a prefrontal gaze control area massively converge toward the saccadic target. We mapped the visual RFs of prefrontal neurons during stable fixation and immediately prior to the onset of eye movements, using multi-electrode recordings in monkeys. Following movements from an initial fixation point to a target, RFs remained stationary in retinocentric space. However, in the period immediately before movement onset, RFs shifted by as much as 18 degrees of visual angle (dva), and converged toward the target location. This convergence resulted in a 3-fold increase in the proportion of RFs responding to stimuli near the target region. In addition, like human observers 5,6 , the population of prefrontal neurons grossly mislocalized presaccadic stimuli as being closer to the target. Our results show that RF shifts do not predict the retinal displacements due to saccades, but instead reflect the overriding perception of target space during eye movements. We recorded from neurons within the FEF of monkeys (macaca mulatta) using linear electrode arrays (Fig. 1a) (Methods). The FEF is an area of prefrontal cortex with a known involvement in gaze control 7 and visual attention 8-11 . Previous studies have found evidence that visual RFs of FEF neurons predictively remap prior to saccades 1,4 . That is, this body of evidence suggests that FEF RFs shift from their presaccadic locations to their anticipated, postsaccadic locations prior to onset of each saccade (Extended Data Fig. 1). However, because these studies inferred RF shifts from visual responses to stimuli presented at only a few locations, the validity of the remapping framework remains uncertain. We therefore mapped the RFs of simultaneously recorded FEF neurons with flashed (25 ms) “probe” stimuli while monkeys performed a standard saccade task 4 (Methods, Extended Data Fig. 2). To obtain detailed measurements of RFs during the task, we used a dense array of visual probes: 10 by 9 positions covering an area of 36 by 32 dva (Fig. 1b). Using this arrangement, we mapped RFs during 3 separate periods: during fixation at each of two fixation points (FP1 and FP2) and just prior (69 ms, SD = 35) to a saccade from FP1 to FP2. Fig. 1c shows four examples of FEF RFs mapped during fixation at FP1 and FP2, and their corresponding RF centers (RF1s and RF2s) (Methods). In each example, the change in fixation from one location to the other was accompanied by a RF displacement that was equivalent to the displacement of fixation, reflecting the retinocentric property of FEF RFs. RFs measured at FP2 also served as empirical estimates of the expected shifts due to predictive remapping. When measured while monkeys were still fixating at FP1, but preparing saccades to FP2, RFs were remarkably different from those measured during stable fixation. As shown in the examples, presaccadic RF centers (PRFs) differed both from the RF1s and the RF2s (Fig. 1d). Furthermore, PRFs tended to be much closer to the saccade target (FP2), in some cases shifting from their RF1 location in a direction orthogonal (example 3) or opposite (example 4) to the saccade direction, and thus were inconsistent with remapping. We measured the changes in RF2s and PRFs from their corresponding RF1s (ΔFIX and ΔPRE) for a population of 179 RFs mapped in two monkeys (Fig. 2a) (Methods). As expected, the average displacement of RF2s (11.2 dva, SD = 1.5) was approximately equal to the saccade amplitude (12 dva, SD = 0.2), and was independent of the RF1 distance to the saccade target (ε’RF1 ) (r = 0.05, p = 0.49) (Methods). Without presaccadic RF modulation, we would expect PRFs to be identical to their corresponding RF1s, given that retinal stimulation is essentially identical in these two conditions. However, FEF RFs are dramatically altered during saccade preparation, and are shifted by an average of 8.4 dva (SD = 3.6) and as much as 18 dva (Methods, Extended Data Figure 3). This shift was greater (p < 10-10) than the small variations in RFs measured between the fixation conditions (Extended Data Fig. 4). Furthermore, in contrast to RF2s, PRFs depended on the RF1 distance to the saccade target (r = 0.44, p < 10-9), with larger PRF shifts occurring for more distant RFs. Note that this dependence should not occur if the presaccadic RFs predictively shift from RF1s to their postsaccadic RF2s. Moreover, the angular differences (ϕ’) between the RF2 displacement vectors and the PRF shift vectors were not uniform as expected with remapping, but depended on the angular deviation (θ) of RF1 from the saccade vector (r = 0.75, p < 10-10) (Fig. 2b). Thus, we observed substantial presaccadic shifts that were inconsistent with the remapping prediction (Extended Data Fig. 5). Furthermore, the overall pattern of RF shifts reveals how individual shifts can appear consistent with remapping at some locations in space (Methods, Extended Data Fig. 10). To further understand the presaccadic RF modulation, we examined PRF shift vectors across the entire distribution of measured RF locations (Fig. 2c) (Methods, Extended Data Fig. 6). We observed that PRFs shifted in the direction of the saccade target independent of their corresponding RF1 location. On average, PRFs were 6.1 dva closer to the saccade target than the RF1s (p < 10-10). We further compared PRFs to the remapping prediction, using the RF2s as an empirical estimate, and found PRFs to be closer to the saccade target than expected with remapping (p < 10-10). Thus, PRFs deviated from the remapping prediction and instead converged toward the saccade target. This pattern of results was the same when considering only single neurons, indicating that the convergence reflected the shifting of individual neuronal RFs rather than a differential gain change across multiple neurons (Methods, Extended Data Fig. 7,8). We next examined how presaccadic changes in RFs altered the representation of visual space by the population of recorded FEF neurons. Rather than focus solely on RF centers, however, we instead measured how saccade preparation altered the degree to which each visual probe elicited responses from the neuronal population (Methods). Fig. 3a shows the percentage of “population RFs” yielding responses across all probe locations during fixation and saccade preparation. These distributions of “RF density” illustrate how the representation of visual space is displaced by the change in fixation from FP1 to FP2 in the population. Moreover, these RF density distributions revealed a substantial effect of saccade preparation on the representation of space. Specifically, we observed an increase in RF density centered on the saccade target. Within a 20 by 20 dva region around the saccade target, RF density increased more than twofold (106.4 %, p < 10-3). Note the more than threefold increase in the proportion of RFs with responses at locations nearest the target (Fig. 3b). These changes in RF density were accompanied by alterations in the presaccadic spike count correlations of simultaneously recorded neurons (Methods, Extended Data Figure 10), suggesting changes in effective connectivity 12,13 during saccade preparation. The above observations point toward a substantial enhancement in the representation of visual space at the saccade target. Finally, we considered whether the presacaddic convergence of RFs to the saccade target results in a distorted “read-out” of stimulus location. In human observers, stimulus location during saccade execution is grossly misjudged. This mislocalization results in a “compression of visual space”, with observers reporting stimuli as appearing much closer to the saccade target than they actually are 5,6 . Therefore, we decoded probe positions from the full population of recorded FEF neurons during fixation at FP1 (Fig. 4a) and during saccade preparation (Fig. 4b) (Methods). During fixation, the location of probe stimuli near FP1 (x = [-10, -2], y = [-10, 6]), where most of the RFs were sampled, could be accurately decoded from the population response (average error = 1.3 dva). In contrast, during saccade preparation, probe locations within the same region of space were grossly mislocalized by the population of neurons (average error = 7 dva). Furthermore, the error was systematic in that the population response consistently mislocalized probes as being closer to the saccade target (Fig. 4c). The distance between the population estimate of probe location and the saccade target was reduced by 47% compared to fixation (-3.7 dva, p < 10-5) and by 46% compared to veridical (-3.6 dva, p < 10-4). Thus, the convergence of RFs resulted in a compression of visual space toward the target. Predictive remapping of RFs is widely assumed to be the mechanism by which perceptual stability is achieved during saccades 1 , specifically by a global anticipatory updating of visual space. Although our results demonstrate robust presaccadic shifts of FEF RFs, those shifts clearly violate the remapping prediction, and instead reveal a compression of visual space toward the saccade target. This observation raises an important question about the role of RF shifts in maintaining stability across eye movements. Specifically, how, if at all, might the convergence of RFs, rather than remapping, contribute to stable vision? It has been hypothesized by some that visual stability may be due to a strong bias of perceptual processing toward the targets of saccades 14 . This hypothesis argues that the failure to detect retinal image displacements results from a reduced representation of non-target locations, as compared to the overriding perception of target space 15 . Consistent with this hypothesis is psychophysical evidence of enhanced perception at the saccade target prior to movement onset 16,17 , as well as enhanced visual cortical signals 18-21 . Furthermore, the perception of visual space is massively compressed prior to saccades 5,6 . Our results reveal a neuronal correlate of these perceptual effects. In particular, we found that populations of FEF neurons grossly mislocalize stimuli as being closer to the target, resembling psychophysical compression. Thus, regardless of the role of the above perceptual phenomena in visual stability, the representation within the FEF mirrors them. FEF neurons have been causally implicated in the control of visual attention 8 and the corresponding modulation of stimulus-driven activity in posterior visual cortex 9,10,22-24 . Several recent studies suggest that the influence exerted by FEF neurons on visual cortex during attention originates from predominantly visual signals 11,25 . Our results indicate that FEF visual signals conveyed to posterior areas prior to saccades grossly overrepresent the space occupied by the target. Thus, prior to each eye movement, or during covert attention 26,27 , feedback from FEF neurons may impose the same distortion onto visual cortex 28-30 , and this biased representation of target space could result in the aforementioned attentional enhancement within that space. Methods General surgical and electrophysiological procedures We used two male adult rhesus monkeys (Macaca mulatta, 8 and 12 kg), Monkey N and Monkey B, in the experiments. All experimental procedures were in compliance with the US Public Health Service policy on the humane care and use of laboratory animals, the Society for Neuroscience Guidelines and Policies, and Stanford University Animal Care and Use Committee. Each animal was surgically implanted with a titanium head post, a scleral search coil, and a cylindrical titanium recording chamber (20 mm diameter) overlaying the arcuate sulcus. A craniotomy was performed on each animal, allowing access to the FEF. All surgeries were conducted using aseptic techniques under general anesthesia (isoflurane), and analgesics were provided during postsurgical recovery. Electrodes were lowered into the cortex using a hydraulic microdrive (Narishige International). Activity was recorded extracellularly using linear array electrodes (U-Probe, Plexon) with 16 contacts spaced 150 μm apart. Neural activity was sampled at 40 kHz. Waveforms were sorted using offline techniques. The FEF was confirmed by the ability to evoke fixed-vector, short latency saccadic eye movements with stimulation at low currents 31,32 . U-Probes were then lowered for simultaneous recordings of visual RFs at the same coordinates. RF measurements and monkey behavior We measured visual RFs of FEF neurons by randomly presenting a single probe stimulus out of a 10 by 9 probe grid extending 36 by 32 degree of visual angle (dva). In each recording session we placed the probe grid to cover the area where we expected most of the RF locations based on the evoked saccade vectors by microstimulation of a given recording site. The probes consisted of white squares with an area of 1 dva 2 resulting in a positive luminance contrast of 60% (Michelson) and 3 (Weber) to the gray background (23.7 cd/m2). The probe duration was less than 25 ms as measured with a photodiode and thus comparable in duration to previous studies 4,29. In all three conditions (fixation 1, fixation 2, and presaccadic) the monkey was required to fixate one out of two fixation points (FP1 and FP2) placed 12 dva apart along the horizontal meridian. The fixation points FP1 and FP2 consisted of small (0.5 dva in diameter) red disks (23.6 cd/m2). The saccade task consisted of a standard step task 4 in which the fixation point (FP1) was displaced to a new location and the monkey rewarded for shifting its gaze to it. The fixation and presaccadic conditions differed in terms of the timing of the visual probe stimulus with respect to the saccade. In the two fixation conditions, the probe stimulus was presented at least 500 ms before a saccade. In the presaccadic condition, the probe presentation occurred while the monkey was still fixating at the location of FP1 but already planning a saccade to FP2. The monkey was rewarded with a drop of juice if he was still fixating at the required location at the end of the trial (> 500 ms after probe presentation). Fixation and saccade accuracy was excellent in both monkeys with an average horizontal error of 0.01 dva (SD = 0.29) and an average vertical error of -0.02 dva (SD = 0.29) in fixation. The average saccade vector was 11.98 dva (SD = 0.52) with an horizontal landing error of -0.19 (SD = 0.35) and a vertical error of -0.05 dva (SD = 0.4). The average saccadic reaction time, i.e. the time between target onset and saccade initiation, for Monkey N was 113 ms (SD = 35) and 229 ms (SD = 37) for Monkey B. We observed little or no evidence that monkeys were distracted by the probe appearance during saccade preparation. First, for both monkeys the rate at which stray saccades were made to probes was well below 1% (0.26% for monkey B and 0.11% for monkey N. Second, there was no systematic dependency of saccadic reaction time and probe location across the two monkeys (Extended Data Fig. 2). For all reported analyses we used the responses to probes that were presented within a time window of 150 ms prior to saccade onset. The average probe onset time was 64 ms before saccade onset (SD = 32) for Monkey N and 82 ms (SD = 38) for Monkey B. RF maps and centers We computed RF maps as shown in Fig. 1 as follows. For a given probe location k we obtained the neuronal activity akn for the time interval (50, 350] ms after probe onset for a given trial n. We then computed the average activity āk for each k as the arithmetic mean across n. This was done separately for the two fixation and the presaccadic conditions. Within each of these three conditions we then normalized mean activities āk by a ¯ k ′ = a ¯ k − min k ( a ¯ k ) max k ( a ¯ k ) − min k ( a ¯ k ) , with a ¯ k ′ ∈ { 0 , … , 1 } and linearly interpolated across space to obtain RF maps with a resolution of 0.1 by 0.1 dva. The center (x̄,ȳ) in Cartesian coordinates for a given RF was then computed as the center of mass for all locations with responses greater or equal than 75 % of the maximum, that is x ¯ = 1 α ( ∑ x ∑ y a ¯ x y ′ x ) y ¯ = 1 α ( ∑ x ∑ y a ¯ x y ′ y ) , with α = ∑ x ∑ y a ¯ x y ′ , ∀ a ¯ x y ′ ( a ¯ x y ′ ≥ λ ) , and λ =0.75. Dataset In total, 27 experimental sessions yielded 179 recordings with measurable RFs in all of the three behavioral conditions (fixation 1, fixation 2, presaccadic) and were used for further analyses. We found no significant differences regarding the main results between RFs of well-isolated single neurons with stable waveforms and remaining RFs and thus combined all RFs for further analyses. Statistical Analyses Statistical analyses were performed using Mathematica (Wolfram Research) and R. In general, statistical tests were two-tailed. All reported p values regarding mean differences are based on t-tests. Non-parametric controls using Wilcoxon signed rank tests were significant as well for all reported effects regarding central tendencies (p values not shown). All reported correlations are based on Pearson's r. For all significant correlations Spearman's rho and Kendall's tau yielded the same result (p values not reported). Finally, all reported linear regressions are based on ordinary least square fits. Time dependency of PRF shifts Although our experiment was designed specifically to obtain spatially detailed measurements of presaccadic RFs, rather than to explore their temporal dynamics, we nonetheless considered whether the RF shifts were time dependent with respect to saccade onset. To address this question, we divided the distribution of probe presentation times into two periods by the median for each of the 179 presaccadic RFs. This reduced the data by half in each of the two periods. Nevertheless, we were able to obtain clear presaccadic RFs in 68 cases. The average probe presentation for the “earlier” half was 103 ms before saccade onset; whereas the average time for the “later” half was 55 ms. For the former, earlier period, we found that the average PRF shift was 8.09 dva, and for the latter, later period, the average PRF shift was 9.65 dva from their respective RF1s. The difference between these two shift amplitudes was significant (p < 10-4) (Extended Data Figure 3a), as was the difference in the distance of the PRFs to the saccade target, the later PRFs being closer on average by 1.26 dva (p < 10-4) (Extended Figure 3b). These data indicate that while there was already a substantial PRF shift as of the earlier time period, there was still significant shifting of the PRF in the later time period. RF shift across space To illustrate the average shift of RFs across space as shown in Fig. 2c, we averaged adjacent RF centers. Visual space was divided into equally sized bins (6 by 6 dva) ranging from −16 to 8 dva horizontally and from −24 to 24 dva vertically centered around the saccade target (FP2) (Fig. 2c lower right). This range included all RF1s, that is, centers of RFs measured while the monkey was fixating at FP1 long before and after a saccade. RF1s were than simply averaged (arithmetic mean) if they fell inside the same bin. The respective average RF2 and PRF was obtained accordingly based on the pairings obtained by the binned RF1s. Extended Data Fig. 6 shows all individual RF1s, RF2s, and PRFs. Shifting of RFs in single neurons We considered that the observed convergence of RFs toward the saccade target might be the result of two different processes. First, it could result from RF shifts in individual neurons toward the saccade target. A second, though less likely possibility, is that it reflects a differential gain change across multiple neurons. Specifically, it could result from a relative increase in the activity of neurons with RFs adjacent to the target, together with a simultaneous decrease in the activity of neurons with RFs at more distant locations. Importantly, RFs measured from multi unit activity do not allow one to easily distinguish between these two possibilities as this activity by definition includes the visual responses from multiple neurons. We therefore carried out separate analyses of RF shifts on a subpopulation of well-isolated, single neurons and confirmed that the spike waveforms from these neurons were identical across stimulus location and experimental conditions (fixation and presaccadic). To accomplish this, we first considered a set of well-clustered waveforms (Extended Data Fig. 7a) as potential single-neuron isolations depending on the distribution of inter-spike intervals (ISI), and the corresponding estimated rate of false positive occurrences 33 (Extended Data Fig. 7b). Out of the pool of well-isolated clusters, we identified 23 single neurons for which we were able to measure RFs in all 3 conditions. For these neurons the estimated false positive rates averaged 3.5% (1.5 ms refractory period) 34 . However, to directly assess the degree to which multiple neurons contributed differently to the fixation and presaccadic RFs, we systematically compared the waveforms of isolated neurons across the two conditions, specifically fixation 1 and presaccadic. In order to do so, we first subtracted the average waveforms (arithmetic mean) obtained from the two conditions by comparing waveforms obtained from responses at the most effective probe location for each condition (Extended Data Fig. 7c). Each waveform comparison yielded 40 differences (40 samples/ms) that were tested independently for statistical significance by constructing Bonferroni corrected 95% confidence intervals (α’ = α /40, α = 0.05). Thereafter, we projected waveforms for each neuron into principal component (PC) space (Extended Data Fig. 7d). For each PC dimension (40 in total) we fitted a logistic regression to test the separability of the two sets of waveforms independently within each dimension (Extended Data Fig. 7e). We accessed the statistical significance of the Pseudo R2 using Bonferroni correction again for each independent test. Finally, to test how well waveforms can be separated using all 40 PC dimensions simultaneously, we trained a linear Support Vector Machine (SVM) for each neuron using a “leave-one-out” cross validation based on all unique combination of fixation and presaccadic waveforms. We then compared the resulting estimate of classification performance to a distribution of performance estimates based on 10000 samples in which both fixation and presaccadic waveforms have been randomly assigned to one out of two groups for classification (Extended Data Fig. 7f). We found that 21 of the 23 isolations satisfied all of above criteria and thus allowed us to interpret the visual responses elicited during fixation and in the presaccadic period as coming from a single neuron. Extended Data Fig. 7g shows the corresponding fixation RFs and the presaccadic RF for the example neuron. Extended Data Fig. 7h,i shows the distributions of Pseudo R2s and the SVM performance for all neurons meeting the above criteria. Finally, we compared the RF shifts observed in the above-selected neurons (well-isolated neurons with stable waveforms) to the remaining RFs in the overall population (Extended Data Fig. 8). This comparison revealed that for both populations the nature of the PRF shifts were statistically indistinguishable. First, the average displacement of RF2s from RF1s (ΔFIX) in both populations was approximately equal to the amplitude of the saccade, and was independent of the distance of RF1s to the saccade target (ε’RF1 ) (RFs of selected neurons: r = 0.36, p = 0.1; remaining RFs: r = 0.03, p = 0.66 ) (Extended Data Fig. 8a). More importantly, for both populations, the PRFs (ΔPRE) depended on the distance of RF1 to the saccade target (RFs of selected neurons: r = 0.48, p = 0.02; remaining RFs: r = 0.46, p < 10−8), with larger presaccadic shifts occurring for more distant RFs in both cases. Moreover, neither the intercepts (b0,p = 0.3) nor the slopes (b1, p = 0.42) of the fitted regressions were significantly different between the two populations. For the combined data shown in Fig. 2a we estimate for ΔFIX , b0 = 10.9 (p < 10−10 ) and b1 = 0.03 (p = 0.49 ) and for ΔPRE, b0 = 3.8 (p = 7.1·10−7) and b1 = 0.4 (p = 6·10−10). Second, the angular differences (ϕ’) between the RF2 displacement vectors and the PRF shift vectors in both populations depended on the angular deviation (θ) of the RF1 from the saccade vector (RFs of selected neurons: r = 0.87, p < 10−6; remaining RFs: r = 0.77, p < 10−9) (Extended Data Fig. 8b). Again, neither the intercepts (p = 0.43) nor the slopes (p = 0.06) of the fitted regressions were significantly different between the two populations. For the combined data shown in Fig. 2b we estimate b0 = −0.4 (p = 0.9) and b1 = 0.8 (p < 10−10). Lastly, in both populations, the PRFs were located closer to the saccade target (Extended Data Fig. 8c). Thus, overall the presaccadic RF shifts in both populations deviated from the remapping prediction, and instead converged toward the saccade target. Relationship of our results to previous evidence of predictive remapping Our results clearly demonstrate that rather than predictively remap, RFs in the FEF converge toward the saccade target. However, it is important to consider how previous evidence of predictive remapping in this area, and perhaps other areas, might have instead been indicative of RF convergence. Below, we summarize two key ways in which the present results provide a means of reinterpreting past studies in terms of RF convergence. Our results illustrate the importance of obtaining a broad sampling of RF position across the visual field in a sample of neurons in order to understand the nature of presaccadic RF shifts. As illustrated in Figure 2a-c, both the shift direction and amplitude depend heavily on the initial RF position. Moreover, it illustrates how evidence consistent with remapping can be obtained within some portions of the visual field. The remapping hypothesis predicts that the PRF shifts to a neuron's post-saccadic location, sometimes called its “future field” 4 , in anticipation of the impending movement. Our results illustrate how evidence consistent with the remapping hypothesis can be obtained within select portions of the visual field, particularly locations near the fovea where RF convergence toward the saccade target, and shifts toward a hypothetical future field will look similar. Our results can also explain how previous experiments using only a single presaccadic probe stimulus found evidence consistent with the remapping hypothesis. In the absence of a complete RF map, any observations of visual responses at or near the expected future field can be interpreted as consistent with remapping, even when the actual presaccadic RF shift is not predictive, and instead moves in an alternative manner, e.g. toward the saccade target. As is evident in Figures 1a and 1b, the deviation of the empirical presaccadic shift from the remapping prediction depends on the position of the RF within the visual field. At many RF locations, the results clearly deviate from remapping. However, at others locations the differences between remapping and convergence are smaller, and thus measurement of the presaccadic RF with only 1 probe stimuli cannot distinguish between them. This ambiguity is depicted in two additional examples shown in Extended Data Fig. 9. See also Zirnsak et al. 35 for a discussion of this topic. RF density To provide an estimate of how the representation of visual space by FEF RFs changes prior to a saccade, we first averaged RFs with adjacent centers. Visual space was divided into the same bins as described in Methods, ‘RF shift across space’. However, instead of just averaging the centers of RFs falling in a given bin we averaged the whole RFs. That is, based on the normalized RFs as described in Methods, ‘RF maps and centers’, the ith activity with i ∈ {1,...,22} to a probe stimulus at location k was computed as A i k = 1 n ∑ j n a ¯ j k ′ , where n is the number of RFs with RF1s falling in the same bin. Thereafter activities were again normalized by A i k ′ = A i k − min k ( A i k ) max k ( A i k ) − min k ( A i k ) , with Aik ' ∈ {0,...,1}. This was done for the two fixation and the presaccadic conditions and we refer to the resulting RFs as “population RFs”. We then counted the number of the population RFs for which the normalized activity to a given probe location k was equal to, or exceeded 50% of the maximum normalized activity. That is, d k R F = ∑ i f ( A i k ′ ) with f ( A i k ′ ) = { 1 i f A i k ′ ≥ 0.5 0 e l s e } . We refer to this quantity dRF as “RF density”. Note that this measure is minimally affected by the sampling bias of measured RFs. Spike count correlations Our multi-electrode recordings enabled us to explore the extent to which the RF convergence during saccade preparation is accompanied by changes in correlated neuronal responses. Correlated fluctuations in neuronal responses have been interpreted as reflecting effective connectivity 12,13 , so we hypothesized that the presaccadic RF convergence might lead to increases in these correlated fluctuations. From the 179 neuronal RFs, we computed spike count correlations from responses to all 90 probes in 677 neuronal pairs recorded simultaneously at varying inter-neuronal distances (Extended Data Fig. 10a). The spike count correlation was computed as r i j k S C = ∑ n ( a i k n − a ¯ i k ) ( a j k n − a ¯ j k ) ∑ n ( a i k n − a ¯ i k ) 2 ∑ n ( a j k n − a ¯ j k ) 2 , where r i j k S C is simply the Pearson product-moment correlation coefficient between the ith and jth neuronal response a over n trials for a given probe location k. The respective sample mean response is denoted by ā. Spikes were counted in the same time interval (50,350] ms after probe onset that was used to estimate the RF maps. Given the known property of the Pearson product-moment correlation as a biased estimator of the true population correlation ρ for small samples and given the systematically fewer trials in the presaccadic condition as compared to the fixation condition (n̄pre = 9.5, n̄fix = 11.7), spike count correlations in the fixation condition have been computed as follows to match the number of trials in the presaccadic condition. For a given presaccadic correlation coefficient r i j k S C , p r e the corresponding fixation correlation coefficient r i j k S C , f i x was computed as the arithmetic mean of all r i j k S C , f i x ′ which are based on all unique combinations of n k p r e neuronal responses a i k n f i x and a j k n f i x if n k p r e < n k f i x . For a given pair ij and k the rSC was only considered for further analyses if the number of trials was the ≥3. The hypothesized increase in spike count correlation during saccade preparation should be observed particularly when neurons are visually driven. Thus, we related spike count correlations to driven activity, relative to baseline activity. To do so, we combined the responses of a given neuronal pair ij to a particular probe k, and normalized those responses to the baseline activity. That is, we first divided the individual mean response āk to a given probe by the respective baseline activity b̄, which was obtained from the average (arithmetic mean) of the spike rate bn , during fixation at the beginning of each trial n, before probe presentation, across all trials of a recording session. The time window within which spikes were counted for a given n to get bn was of the same size (300 ms) as was the window to obtain the probe related activity akn . The normalized response for a given pair and probe was then computed as a ¯ i j k ′ = ln ( a ¯ i k b ¯ i ) + ln ( a ¯ j k b ¯ j ) , with ln(·) denoting the natural logarithm. Note that combined responses driven by the probe stimulus were thus > 0, with 0 indicating no change in the combined response compared to baseline. The bins used in Extended Data Fig. 10b are based on data obtained during the fixation conditions, and were broken into quintiles for all a ¯ i j k ′ ≤ 0 , and deciles otherwise, given the higher number of normalized responses greater than 0. The same bins were then applied to compute the average spike count correlations in the presaccadic condition. For each bin, we also determined the percentage of combined responses for which both individual responses in the pair exceeded baseline activity (Extended Data Fig. 10b, middle. First, we observed that the average spike count correlation decreased overall as a function of electrode distance between recorded responses (Extended Data Fig. 10a). Second, whereas the spike count correlation was reduced during saccade preparation, compared to fixation, when the combined response was at or below baseline (−0.06, p < 10−10), there was an increase when the combined response exceeded baseline (0.02, p < 10−7) (Extended Data Fig. 10b, top and bottom). Although the majority of combined above-baseline responses consisted of pairs in which both neuronal responses exceeded baseline (Extended Data Fig. 10b, middle), we also computed the overall change in spike count correlation for those pairs exclusively. The observed presaccadic increase in spike count correlation for those pairs was significantly greater than that of fixation (0.03, p < 10−10). Thus, as hypothesized, an increase in spike count correlation was observed when neuronal pairs were driven above baseline. This increase in spike count correlation during saccade preparation is consistent with the increase in the shared representation of visual space among neurons (Fig. 3), at least insofar as correlated fluctuations in neuronal responses reflect effective connectivity between pairs of neurons. Population decoding To decode the population activity of the recorded FEF neurons with respect to stimulus location during stable fixation and shortly before saccade onset we maximized the term ∑ i N a i k n a ¯ i l [ ∑ i N a i k n 2 ] 1 2 [ ∑ i N a ¯ i l 2 ] 1 2 over probe location l 36 . That is, for all N = 179 RFs we compare the vector a consisting of single responses a to a given probe location k on the nth trial to all vectors a ¯ consisting of the averaged activity to l across all trials. The decoded location is simply the probe l that maximizes the above term, which is equivalent in finding the minimal angle between a given a and each a ¯ . We did so by randomly and independently sampling aik with respect to n 10000 times for each the fixation condition (fixation 1) and the presaccadic condition. Note we assume that the same activity space ( a ¯ ) is used to infer the location of a stimulus that is presented just prior to a saccade as it is used to infer the location of a stimulus that is presented during stable fixation. That is, all a ¯ are exclusively based on the neuronal activity recorded during the fixation condition. When decoding the stimulus location during fixation, a ¯ representing the averaged activity to a stimulus at location l did not include a if k = l.