Spatial vision by macaque midbrain

Visual brain areas exhibit tuning characteristics that are well suited for image statistics present in our natural environment. However, visual sensation is an active process, and if there are any brain areas that ought to be particularly “in tune” with natural scene statistics, it would be sensory-motor areas critical for guiding behavior. Here we found that the primate superior colliculus, a structure instrumental for rapid visual exploration with saccades, detects low spatial frequencies, which are the most prevalent in natural scenes, much more rapidly than high spatial frequencies. Importantly, this accelerated detection happens independently of whether a neuron is more or less sensitive to low spatial frequencies to begin with. At the population level, the superior colliculus additionally over-represents low spatial frequencies in neural response sensitivity, even at near-foveal eccentricities. Thus, the superior colliculus possesses both temporal and response gain mechanisms for efficient gaze realignment in low-spatial-frequency dominated natural environments.


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Chih-Yang Chen 1,2,3 , Lukas Sonnenberg 4 , Simone Weller 4 , Thede Witschel 4 , and Ziad M. Summary 45 Visual brain areas exhibit tuning characteristics that are well suited for image statistics 46 present in our natural environment. However, visual sensation is an active process, and if 47 there are any brain areas that ought to be particularly "in tune" with natural scene 48 statistics, it would be sensory-motor areas critical for guiding behavior. Here we found 49 that the primate superior colliculus, a structure instrumental for rapid visual exploration 50 with saccades, detects low spatial frequencies, which are the most prevalent in natural 51 scenes, much more rapidly than high spatial frequencies. Importantly, this accelerated 52 detection happens independently of whether a neuron is more or less sensitive to low 53 spatial frequencies to begin with. At the population level, the superior colliculus 54 additionally over-represents low spatial frequencies in neural response sensitivity, even at 55 near-foveal eccentricities. Thus, the superior colliculus possesses both temporal and 56 response gain mechanisms for efficient gaze realignment in low-spatial-frequency 57 dominated natural environments. 58 59 60 61 62 63 64

Introduction 66
The superior colliculus (SC) is a visual-motor structure important for transforming visual 67 signals into behaviorally-appropriate gaze shift commands (Boehnke and Munoz, 2008; 68 Gandhi and Katnani, 2011;Optican, 2005;Sparks and Mays, 1990;Veale et al., 2017;69 Wurtz, 1996). Even though much is known about the SC's afferent and efferent 70 connections, as well as its physiological visual and eye-movement-related neural 71 response characteristics, such knowledge has predominantly been obtained using highly 72 Schaaf, 1998). Curiously, such observations are often also used to account for motor 85 rather than perceptual effects, for example on manual and saccadic reaction times 86 (Breitmeyer, 1975;Ludwig et al., 2004;White et al., 2008), even though these early 87 visual areas may be viewed as being more relevant for perception rather than action. 88

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In this study, we hypothesized that the SC's importance in guiding action (Gandhi and 90 Katnani, 2011; Veale et al., 2017) should make it as well matched to spatial properties 91 present in natural scenes as early visual areas, if not more so, and in a manner that is 92 highly conducive of behavioral motor effects. We specifically tested the ability of SC 93 neurons to detect low spatial frequency visual stimuli. We found that these neurons do so 94 much earlier than for high spatial frequencies, and independently of neural sensitivity to a 95 given spatial frequency. Moreover, we found that at the population level, SC neural 96 sensitivity to spatial frequency was primarily low-pass in nature, meaning that both SC 97 response time and SC response strength are particularly efficient when visually analyzing 98 the low spatial frequencies that are abundantly present in natural scenes. These 99 observations have allowed us to predict, with high fidelity, our animals' saccadic reaction 100 time patterns as a function of spatial frequency based solely on SC visual response 101 strength and latency measurements obtained from completely different experimental 102 sessions not involving saccadic responses. We believe that our findings clarify important 103 visual functions of the SC, complementary to this structure's more well-studied motor 104 (Gandhi and Katnani, 2011) and cognitive (Krauzlis et al., 2013) functions. Such findings 105 not only allow better understanding of visual-motor behavior under more naturalistic 106 conditions than with impoverished laboratory stimuli, but they also help clarify potential 107 underlying mechanisms for pathological cases in which the SC's role in vision may be 108 magnified. For example, in blindsight (Weiskrantz et al., 1974), patients with V1 loss 109 exhibit spatial frequency tuning properties remarkably similar to those that we describe 110 here (Sahraie et al., 2010;Sahraie et al., 2002;Trevethan and Sahraie, 2003). 111

Results 112
Faster SC responses to low spatial frequencies irrespective of neural sensitivity 113 We recorded visual responses in macaque monkeys that were passively fixating a small 114 spot of light (Chen and Hafed, 2013;Chen et al., 2015). During such passive fixation, we 115 presented a high contrast sine wave grating filling the visual response field (RF) of a 116 recorded neuron (Materials and Methods). We randomly varied the spatial frequency of 117 the presented grating from trial to trial and noticed a systematic rank ordering of neural 118 response latencies as a function of spatial frequency. For example, in the neuron depicted 119 in Fig. 1A, visually-evoked action potentials arrived earliest for gratings of 0.56 or 1.11 120 cycles/deg (cpd), and their latency progressively increased for higher spatial frequencies. response sensitivity (i.e. response gain) that has been reported in both the SC (Marino et 125 al., 2012) and in early cortical visual areas (Maunsell and Gibson, 1992 (Fig. 1C, bottom) as a function of spatial frequency revealed a dissociation 132 between the two neural response properties: the preferred spatial frequency in terms of 133 response sensitivity was ~4 cpd, whereas the preferred spatial frequency in terms of 134 response latency was much lower.

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is illustrated by plotting firing rates for the same neuron, since it is easier to infer response amplitudes from 147 firing rates. The neuron emitted the strongest visual responses for 4.44 cpd gratings even though these 148 strong responses came later than for lower spatial frequencies. Thus, there was a dissociation between 149 response latency and response sensitivity. (C) Tuning curves illustrating the dissociation. The top panel 150 plots the tuning curve of the neuron according to response sensitivity (i.e. response amplitude as a function 151 of spatial frequency; Materials and Methods). Visual responses were strongest for 4.44 cpd gratings with 152 both lower and higher spatial frequencies (e.g. the colored arrows) evoking significantly weaker responses.

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On the other hand, in the lower panel, the latency to first visually-evoked spike (Materials and Methods) at 154 4.44 cpd was longer than for lower spatial frequencies but shorter than for higher spatial frequencies (e.g. , and following a very simple rule: for 0.56, 1.11, and 2.22 cpd spatial frequencies, 176 response latencies were shorter than for 4.44 cpd, whereas response latencies were longer 177 for 11.11 cpd. Again, for all these spatial frequencies, response sensitivity was weaker 178 than for 4.44 cpd. Thus, faster SC detection of low spatial frequencies occurs 179 independently of visual sensitivity to a given spatial frequency.    resulting in a broad spectrum of low and high spatial frequencies in their stimuli. When 245 we plotted our observed SC visual response latencies along with these authors' results as 246 a reference (Fig. 4D), we found that the SC consistently exhibited very early responses 247 (for example, compare our 2.22 cpd latencies to those in V1 from their measurements). 248 Moreover, even when we measured SC visual response latencies using small bright spots, 249 that is, still activating a broad spectrum of spatial frequencies, the SC still exhibited early

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(Materials and Methods) in our recorded neurons, separated by spatial frequency. For each neuron, we 262 measured the average first-spike latency of the evoked visual response after a given spatial frequency 263 grating was presented on multiple trials. We then repeated the measurement for other spatial frequencies.

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The evoked response consistently came earlier for low spatial frequencies than for high spatial frequencies.

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(B) The rank-ordering of spatial frequencies in A is also seen when plotting the mean first-spike latency 266 across all neurons as a function of spatial frequency. Low spatial frequencies evoked a visual response 267 earlier than high spatial frequencies. Error bars denote s.e.m. across neurons, and the asterisks indicate 268 p<0.001 when comparing first-spike latency for 0.56 cpd to that in each of the other spatial frequencies. (C)

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Variability of first-spike latency was higher for higher spatial frequencies. We plotted the slope of the 270 cumulative histograms in A between the 20 th and 80 th data percentiles as a function of spatial frequency.

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This slope progressively decreased, suggesting progressive increase in first-spike latency variability across 272 neurons with higher spatial frequencies. (D) Our data from A plotted along with data from multiple visual 273 areas in gray; copied with permission from (Schmolesky et al., 1998). SC visual responses for low spatial 274 frequencies were among the earliest responses in the visual system, but it has to be noted that the

Over-representation of low spatial frequencies in SC neural sensitivity 283
Besides rapidly detecting low spatial frequencies, being able to efficiently guide behavior 284 implies that the SC's pattern analysis machinery might also be more sensitive to such low 285 spatial frequencies, at the population level, and not just be faster in responding to them. 286 Indeed, when we plotted all tuning curves as done in Fig. 1C (top), we found primarily 287 low-pass characteristics in the population even at near-foveal eccentricities. Specifically, 288 low-pass (black curves in Fig. 5B). This suggests that the SC over-represents low spatial 293 frequencies in terms of visual response sensitivity in addition to its boosting of such 294 spatial frequencies in terms of response latency.

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Preferred spatial frequency as a function of neuronal preferred eccentricity. Near-foveal neurons had a 312 broad range of preferred spatial frequencies, but there was still low spatial frequency preference at these 313 eccentricities. Preferred spatial frequency was selected in this figure as the peak in fitted tuning curves, like 314 those shown in A. Thus, for extremely low-or high-pass neurons, the preferred spatial frequency indicated 315 in this analysis was only an estimate that was cut-off by the end of the fitted curves constrained by our 316 sampled spatial frequencies (dashed horizontal lines).
We explored the over-representation of low spatial frequencies further by first counting 319 the number of neurons responding the most for 0.56 cpd spatial frequencies as opposed to 320 other spatial frequencies. These neurons accounted for 42% of our population, and no 321 other single spatial frequency recruited as many neurons (Fig. 6A). Interestingly, this 322 over-representation of low spatial frequencies became even more obvious when assessing responses for the lowest spatial frequency that we presented (Fig. 6B, C). This effect can 330 also be better appreciated when inspecting raw LFP traces from the same 3 example (as well as sustained response) for 0.56 and 1.11 cpd gratings (Fig. 6D, leftmost panel). 336 In other words, at the population level, even near-foveal SC eccentricities over-represent 337 low spatial frequencies. Similar effects were also observed for the other two example 338 eccentricities in Fig. 6D. Therefore, the SC over-represents low spatial frequencies both 339 in terms of neural sensitivity (Figs. 5-6) as well as neural response latency (Figs. 1-4). 340

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We then wanted to relate our results above to human performance. We performed human 395 behavioral experiments testing the predictions of our SC-based observations. We ran a 396 visual search task exercising different spatial frequencies in active gaze behavior, but 397 with highly visible stimuli even at high spatial frequencies. Subjects had to freely search 398 for a grating with an oddball orientation from among many other ones having the same 399 spatial frequency but a slightly different orientation from the oddball stimulus ( Fig. 8A; 400 Materials and Methods). The task was demanding enough that subjects had to generate 401 many saccades to search for the oddball target, and example scan paths of these saccades 402 are shown in green in Fig. 8A. We found that inter-saccadic intervals increased in 403 duration when the search array consisted of high spatial frequencies as opposed to low 404 spatial frequencies (Fig. 8B), consistent with our neural and behavioral results above. 405 Importantly, this effect was not due to a speed-accuracy tradeoff, in which it may have 406 been the case that faster inter-saccadic intervals were associated with worse task 407 performance. Instead, Fig. 8C demonstrates that target detection performance was almost 408 constant (and at high levels) for the spatial frequencies (for example, between ~1 and ~4 409 cpd) in which inter-saccadic intervals showed the biggest changes in duration. Moreover, 410 for all but the very last 1-2 inter-saccadic intervals in Fig. 8B, the oddball target was not 411 yet identified by the subjects, so the shorter intervals for low spatial frequencies were not 412 because oddball targets were already identified or recognized. Therefore, even in natural 413 searching gaze behavior with a stimulus that is less prone to visual masking as in (

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The left panel shows a search array of targets with a low spatial frequency, and the right panel shows a 423 search array of targets with a higher spatial frequency. In all cases, subjects searched for an oddball 424 orientation in the array, which was slightly different from the orientation that was present in all other 425 gratings; the task was made difficult enough to require many scanning saccades of the array before the We found preferential representation of low spatial frequencies in the SC in terms of both 438 response latency and response strength. We believe that these results place the SC in an 439 ideal position to facilitate orienting behavior in natural environments, which are 440 dominated by low image spatial frequencies (Ruderman and Bialek, 1994;Tolhurst et al., 441 1992). Consistent with this, White and colleagues recently found that saccadic RT's are 442 significantly faster in natural scenes, after ensuring matched stimulus visibility (White et 443 al., 2008). We also performed a visual search task with high target visibility (Fig. 8), and 444 we found strong dependence of saccadic timing on spatial frequency, consistent with our 445 SC results. In this regard, our analysis of monkey saccadic RT's in Fig. 7 is particularly  446 intriguing, because it further suggests that the SC may indeed be instrumental in 447 facilitating these human observations. Specifically, we were able to account for each 448 animal's RT patterns with high fidelity based solely on SC visual responses collected 449 from different experimental sessions and during passive fixation. We believe that this 450 result makes sense in hindsight. If one were to expect any visual brain areas to be 451 optimized for natural scene statistics dominated by low spatial frequencies, then it should 452 be those areas that have privileged access to the motor output, like the SC. This is 453 imperative given that we are active observers and would normally orient our sensory 454 apparati very frequently under natural scene scenarios. In all, we believe that our results demonstrate that spatial vision capabilities of the 507 primate SC are specifically organized to facilitate exploring natural scenes with rapid 508 gaze shifts. The monkeys performed a pure fixation task while we recorded the activity of 526 visually-responsive SC neurons, as described in detail before (Chen and Hafed,527 2017; Chen et al., 2015). Briefly, in each trial, we displayed a white fixation spot 528 (8.5x8.5 min arc) over a gray background. Fixation spot and background luminance 529 were described earlier (Chen and Hafed, 2013). After an initial fixation interval (400-530 550 ms), the fixation spot transiently dimmed for ~50 ms, which reset microsaccadic 531 rhythms (Hafed and Ignashchenkova, 2013;Tian et al., 2016) and also attracted attention 532 to the spot rather than to the response field (RF) stimulus. After an additional 110-320 533 ms, a stationary, vertical Gabor patch with 80% relative contrast (defined as Lmax-534 Lmin/Lmax+Lmin) appeared for 300 ms within the neuron's RF. The RF was estimated 535 earlier in the session using standard saccade tasks Hafed and Chen, 536 2016), and the Gabor patch size was chosen to fill as much of the RF as possible. The 537 spatial frequency of the patch, in cycles/deg (cpd), was varied randomly across trials 538 (from among 0.56, 1.11, 2.22, 4.44, and 11.11 cpd). Grating phase was randomized from 539 trial to trial, and the monkey was rewarded only for maintaining fixation; no orienting to 540 the grating or any other behavioral response was required. We used only vertical gratings, 541 but we confirmed that they elicit robust responses in the SC. In pilot data, we also 542 confirmed that any potential orientation tuning in the SC was broad and included robust 543 responses to vertical gratings Marrocco and Li, 1977;Schiller and 544 Koerner, 1971). 545

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We recorded from 115 neurons (monkey N: 60; monkey P: 55) with preferred 547 eccentricities up to 24 deg. We excluded trials with microsaccades occurring within +/-548 100 ms from stimulus onset because such occurrence can alter neural activity. In fact, the 549 trials with microsaccades near stimulus onset were analyzed recently, from the same set 550 of neurons, to explore spatial-frequency dependence of saccadic suppression in the SC 551 . Our focus here was to only analyze baseline visual activity and 552 not activity modulated due to the presentation of peri-movement stimuli. We excluded 9 553 neurons from further analyses because they did not have >25 repetitions per tested spatial 554 frequency after excluding the microsaccade trials. This number was our chosen threshold 555 for the minimum number of observations in order to have sufficient confidence in our 556 interpretations of the results. For the remaining 106 neurons that were included in the 557 analyses, we collected >295 trials per neuron (average: 935 +/-271 s.d.). 558 559

Monkey saccade reaction time task 560
In completely different purely behavioral sessions, we ran our monkeys on a simple 561 saccade reaction time task, which we recently described in detail (Chen and Hafed, 562 2017). Briefly, the monkeys fixated, and a Gabor patch of 2 deg diameter could appear at 563 3.5 deg eccentricity either to the right or left of fixation. The patch was otherwise 564 identical to that used in the recording task described above, and the fixation spot 565 disappeared simultaneously with patch appearance in order to cue the monkeys to 566 generate a targeting saccade towards the patch. We measured reaction time (RT) and 567 correlated it with SC visual responses collected from completely different sessions and 568 critically not involving a saccadic response at all (i.e. the recording task above). We 569 analyzed 2,522 trials from Monkey N and 3,392 trials from Monkey P. As with the neural 570 data above, we only analyzed trials without any microsaccades within 100 ms before or 571 after Gabor patch onset, to avoid peri-movement effects on RT that were described in 572 detail elsewhere from the same experimental sessions . 573 574

Human visual scanning task 575
Subjects sat in a dark room facing a computer display (41 pixels per deg; 85 Hz), and 576 head fixation was achieved through a custom-made chin/forehead rest (Hafed, 2013). We 577 collected data from 8 subjects (3 females and 5 males; 5 subjects were authors of the 578 study). 579 580 Each trial started with an initial fixation spot presented at display center. After ~1030 ms 581 of steady fixation, a search array consisting of 4x4 Gabor patches appeared. Each patch 582 was 6.1 deg in diameter, and all 16 patches were distributed evenly in a grid layout across 583 the display. Grating contrast was set to maximum (100%), and all patches had the same 584 spatial frequency within a given trial. Spatial frequency was altered randomly across 585 trials from among 6 possible values (0.33, 0.66, 1.31, 1.97, 3.93, and 5.9 cpd). Moreover, 586 all but one patch had the same orientation within a given trial (picked randomly across 587 trials from all possible orientations with a resolution of 1 deg). The odd patch was tilted 588 by 7 deg either clockwise or counter-clockwise from the orientation of all other patches, 589 and the subjects' task was to search for the oddly oriented patch and indicate whether it 590 was tilted to the right or left from all other patches. The task was very difficult to perform 591 during fixation, and therefore required prolonged scanning of the entire grid array of 592 patches with many saccades until the odd patch was found and correctly discriminated. 593 This allowed us to obtain sufficient search performance data, with many inter-saccadic 594 intervals that were the focus of our analysis (i.e. our goal was to investigate how inter-595 saccadic intervals were affected by spatial frequency). We collected 180 trials per subject 596 (i.e. 30 trials per spatial frequency), but each trial had many more inter-saccadic intervals 597 that could be analyzed (as detailed below). 598 599 600

Neuron classification 601
We used similar neuron classification criteria to those used in our recent studies (Chen et 602 al., 2015;Hafed and Chen, 2016). Briefly, a neuron was labeled as visual if its activity 0-603 200 ms after target onset in a delayed saccade task (Hafed and Chen, 2016;Hafed and 604 Krauzlis, 2008) was higher than activity 0-200 ms before target onset (p<0.05, paired t-605 test). The neuron was labeled as visual-motor if its pre-saccadic activity (-50-0 ms from 606 saccade onset) was also elevated in the delayed saccade task relative to an earlier fixation 607 interval (100-175 ms before saccade onset) (Li and Basso, 2008). Our results (e.g. spatial 608 frequency rank ordering of response latencies) were similar for either visual or visual-609 motor neurons (except for small quantitative differences in visual response latency). As a 610 result, we combined neuron types in analyses unless otherwise explicitly stated. 611 612

Eye movement analyses 613
We measured eye movements in monkeys using scleral search coils (Fuchs and  For the monkey recordings, we detected microsaccades in order to exclude trials with 620 such movements occurring near stimulus onset (see above). For the monkey saccade 621 reaction time task, we detected the targeting saccade after grating onset and measured its 622 RT. We only considered trials in which there were no microsaccades within +/-100 ms 623 from target onset, because microsaccades near target onset alter RT (Chen and Hafed,624 2017; Hafed and Krauzlis, 2010), and because these trials with peri-microsaccadic stimuli 625 were analyzed separately elsewhere . 626 627 For the human scanning task, we measured inter-saccadic intervals during search. The 628 inter-saccadic interval was defined as the time period between the offset of one saccade 629 and the onset of the next. We only considered saccades occurring between search array 630 onset and trial end (i.e. button press) when computing inter-saccadic intervals. Moreover, 631 we only analyzed trials in which there were no blinks during the entire period from which 632 we were collecting inter-saccadic intervals. Because trials were long until subjects found 633 the odd patch, meaning that we had many inter-saccadic intervals within any trial, 634 removal of blink trials did not reduce our data set dramatically; in the end, we had a total 635 of 3,325-4,743 accepted inter-saccadic intervals per spatial frequency in our analyses 636 (from a total of 145-182 accepted trials per spatial frequency). 637 638

Firing rate analyses 639
We analyzed SC visual bursts by measuring peak firing rate 20-150 ms after stimulus 640 onset (Chen and Hafed, 2017). We then obtained spatial frequency tuning curves by 641 plotting peak visual response as a function of grating spatial frequency (Hafed and Chen, 642 2016). We performed a least squares fit of the measurements to the following difference- where f is firing rate, x is spatial frequency, a 1 and a 2 represent the amplitude of each 648 Gaussian function, b 1 and b 2 represent the mean of each Gaussian function, c 1 and c 2 are 649 the bandwidth of each Gaussian function, and B is the baseline firing rate (obtained from 650 all trials as the mean firing rate in the interval 0-50 ms before Gabor patch onset). The 651 goodness of fit was validated by computing the percentage of variance across stimuli 652 accounted for by the model (Carandini et al., 1997). Only neurons that had >80% 653 explained variance by the fit were included in summaries of tuning curve fits in Results 654 (97 out of 106 neurons), but all neurons were included in all other analyses. We should 655 also note here that the tuning curves from the same neurons in this study were presented 656 earlier in brief format to provide support for the conclusions of another independent study 657 out of our laboratory (Hafed and Chen, 2016); however, the conclusions and analyses 658 shown in the present study are novel and were not described elsewhere before, whether 659 by our laboratory or by other laboratories. 660

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We estimated the preferred spatial frequency of each neuron as the spatial frequency 662 within the sampled range of 0.56-11.11 cpd for which the fitted tuning curve from the 663 above equation peaked. To combine different neurons' tuning curves (e.g. Fig. 5B), we 664 first normalized the peak of the tuning curve of each neuron to 1. We then combined 665 neurons and obtained a mean curve across neurons along with s.e.m. estimates. 666

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We estimated first-spike latency using Poisson spike train analysis (Legendy and 668 Salcman, 1985). Most of our neurons had very little or no baseline activity, meaning that 669 our estimate of first-spike latency using this method was very robust, and it gave us a 670 sense of how quickly our neurons responded to the onset of a given stimulus. 671 672 Local field potential analyses 673 We obtained local field potentials from wide-band neural signals using methods that we 674 described recently Hafed and Chen, 2016). We then aligned LFP 675 traces on Gabor patch onset, and we measured evoked responses in two ways. First, we 676 measured the strongest deflection occurring in the interval 20-150 ms after stimulus 677 onset, to obtain a measure that we called the transient LFP response. Second, we 678 measured the mean deflection in the period 150-250 ms after stimulus onset, to obtain 679 what we referred to as the sustained LFP response. Since the LFP evoked response is 680 negative going, when we refer to a "peak" LFP response, we mean the most negative 681 value of the measured signal. where x is spatial frequency, PV(x) is the average peak visual response of all included 693 neurons for spatial frequency x; FSL(x) is the average first-spike latency of all included 694 neurons for spatial frequency x; and a, b, c are model parameters. Since the behavioral 695 RT's were experimentally obtained from horizontal targets at 3.5 deg eccentricity, we 696 only included neurons with preferred RF locations centered within the range of 2-10 deg 697 in eccentricity and +/-45 deg in direction from horizontal (i.e. 46 neurons). Moreover, we 698 separated each monkey's neurons so that its own neural activity was used to predict its 699 behavioral variability. Since we obtained similar conclusions when relating RT to either 700 visual neurons alone or visual-motor neurons alone, we combined neuron types in the 701 shown analyses to maximize the numbers of neurons used. 702 703 For modeling mean RT as a function of neural response properties, we normalized the 704 range of RT values that we observed to the range from 0 to 1, with 0 corresponding to the 705 shortest RT (e.g. that obtained from the lowest spatial frequency). We similarly 706 normalized the range of peak visual response and first-spike latency. We then fit the best 707 parameters to equation 2 above that matched the data. To test whether including either 708 first-spike latency or peak visual response alone gave similar model fits to the case where 709 both quantities were part of the model, we also ran the fitting with either parameter a or b 710 in equation 2 pegged at 0.

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Cumulative histograms of first-spike latency as in Fig. 4, but after separating neurons as either being purely 884 visual (blue) or visual-motor (red). To reduce clutter, only 3 spatial frequencies are shown. As can be seen, 885 the dependence of response latency on spatial frequency was similar whether neurons were purely visual or