Ziad M Hafed
email: ziad.m.hafed@cin.uni-tuebingen.de

Laurent Goffart
email: laurent.goffart.int@gmail.com

Werner Reichardt

Gaze direction as equilibrium: more evidence from spatial and temporal aspects of small-saccade triggering in the rhesus macaque monkey

Keywords: Microsaccades, saccadic latency, fovea, superior colliculus, cerebellum, fixational eye movements, ocular drift

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Introduction

The sudden appearance of a visual target is often followed by a saccadic movement of the eyes. In non-pathological conditions, this movement brings the image of the target within the central visual field. During the subsequent fixation, small saccades can still be triggered, even though the target location in space has not changed. This suggests that gaze fixation is a highly active process requiring continuous regulation of the contraction of extraocular muscles, and also constant coordination among them. This physiological fact can sometimes be overlooked, especially given that in the majority of studies using monkeys as behavioral research subjects, so-called computer-controlled "fixation windows" are used to make sure that the animal effectively looks at the appropriate target, and not elsewhere, for a period of time.

While such windows can constrain the range of saccade sizes that the monkey is allowed to make during fixation, they do not completely eliminate them. Moreover, the generation of fixational saccades in the monkey is not a mere function of computer-controlled constraints on fixation accuracy. Their amplitude remains small even when large fixation windows are used (e.g. [START_REF] Guerrasio | Fastigial oculomotor region and the control of foveation during fixation[END_REF], and high acuity visual tasks often require that small saccades are directed in highly precise manners. In addition, monkeys can make microsaccades that accurately and consistently orient a restricted zone of their retina toward the location of tiny visual spots [START_REF] Tian | Dynamics of fixational eye position and microsaccades during spatial cueing: the case of express microsaccades[END_REF]2016). Another aspect that influences the generation of "fixational" saccades is the target size. Minuscule targets indeed elicit smaller saccades than larger targets [START_REF] Goffart | Visual fixation as equilibrium: evidence from superior colliculus inactivation[END_REF].

Besides these spatial aspects, there are also temporal aspects, such as variabilities in the timing of saccade onset. From the excitation of ganglion cells in the retina to the recruitment of motor neurons and the contraction of extraocular muscles, action potentials are transmitted through several relays in the brain (thalamus, cerebral cortex, superior colliculus, and reticular formation). The latency of saccades reflects the time (duration) taken by the action potentials to recruit a sufficient number of neurons to ultimately contract the agonist muscles while relaxing the antagonist ones, and rotate the eyeballs. Thus, any lesion that compromises the visuomotor transmission leads to increasing the oculomotor reaction time. In humans, the visuomotor delay depends upon the eccentricity of the target in the visual field [START_REF] Kalesnykas | Fixation conditions, the foveola and saccadic latency[END_REF][START_REF] Kalesnykas | Retinal eccentricity and the latency of eye saccades[END_REF]Wyman and Steinman 1973) insofar as the latency of saccades towards foveal targets is much longer, on average, than other saccades. However, since these observations were made, it was not entirely clear whether the origin of these longer latencies was visual or motor. Later experiments testing saccades towards auditory targets (Zambarbieri et al. 1995) or gaze shifts that were rendered dysmetric by a cerebellar pharmacological perturbation [START_REF] Goffart | Changes in initiation of orienting gaze shifts after muscimol inactivation of the caudal fastigial nucleus in the cat[END_REF] suggested that the dependency might be motor-related: the smaller the saccade, the longer the time to initiate it. We hypothesize that this effect is related to a recent proposal that gaze direction is not a passive state, but an active equilibrium, and that an eye movement (saccadic or slow) is not initiated as long as the visuo-oculomotor system is within a mode where opposing commands (or movement tendencies) counterbalance each other [START_REF] Goffart | Kinematics and the neurophysiological study of visually-guided eye movements[END_REF][START_REF] Goffart | Neurophysiology of visually guided eye movements: critical review and alternative viewpoint[END_REF]Krauzlis et al. 2017).

Here we document the timing of saccade triggering in rhesus macaque monkeys in a variety of behavioral tasks. We particularly focus on very small saccades, as well as differences between saccade directions, in order to investigate hypotheses related to recent neurophysiological findings [START_REF] Chen | The Foveal Visual Representation of the Primate Superior Colliculus[END_REF][START_REF] Goffart | Neurophysiology of visually guided eye movements: critical review and alternative viewpoint[END_REF][START_REF] Guerrasio | Fastigial oculomotor region and the control of foveation during fixation[END_REF][START_REF] Hafed | Sharper, Stronger, Faster Upper Visual Field Representation in Primate Superior Colliculus[END_REF]Krauzlis et al. 2017) and also motivate future ones.

Our results are consistent with the model positing that saccade triggering, or lack thereof, depends on balance of different opposing oculomotor commands, and with particular dependence on spatial visuomotor maps magnifying the representation of the central visual field.

Methods

Ethics approvals

All monkey experiments were approved by ethics committees at the Regierungspräsidium Tübingen. The experiments were in line with the European Union directives and the German laws governing animal research. Some monkey data were analyzed from [START_REF] Willeke | Memory-guided microsaccades[END_REF] for the new purposes of this article. In these cases, the same committees had approved the experiments.

We also analyzed anew human data from the same study [START_REF] Willeke | Memory-guided microsaccades[END_REF], as well as collected additional data from one author (ZH) and three naïve subjects (2 males and 1 female, aged 25-33 years). These human experiments were approved by ethics committees at the Medical Faculty of Tübingen University, and the subjects provided informed consent.

Laboratory setups

Monkey experiments were performed in the same laboratory environment as that described recently [START_REF] Buonocore | Eye Position Error Influence over "Open-Loop" Smooth Pursuit Initiation[END_REF]Chen and Hafed 2018;Chen et al. 2018;[START_REF] Skinner | Transfer function of the rhesus macaque oculomotor system for small-amplitude slow motion trajectories[END_REF][START_REF] Willeke | Memory-guided microsaccades[END_REF]. Human experiments were done in the laboratory described in [START_REF] Grujic | Peri-saccadic perceptual mislocalization is different for upward saccades[END_REF][START_REF] Hafed | Alteration of visual perception prior to microsaccades[END_REF].

Briefly, the monkeys viewed stimuli on a cathode-ray-tube (CRT) display running at 120 Hz refresh rate. The humans viewed stimuli on a CRT display running at 85 Hz refresh rate. In all cases, the display used was gamma-corrected (linearized), and the stimuli were grayscale. Background and stimulus luminance values are described below with the behavioral tasks. Stimulus control for both monkeys and humans was achieved using the Psychophysics Toolbox [START_REF] Brainard | The Psychophysics Toolbox[END_REF]Kleiner et al. 2017;[START_REF] Pelli | The VideoToolbox software for visual psychophysics: transforming numbers into movies[END_REF]). In the monkey experiments, the toolbox acted as a slave device receiving display update commands from a master device and sending back confirmation of display updates. The master system consisted of a real-time computer from National Instruments controlling all aspects of data acquisition (including digitization of eye position signals) and reward of the animals (in addition to display control). The realtime computer communicated with the Psychophysics Toolbox using direct Ethernet connections and universal data packet (UDP) protocols [START_REF] Chen | Postmicrosaccadic enhancement of slow eye movements[END_REF]). In the human experiments, the Psychophysics Toolbox was used as the primary controller, and it synchronized display updates with eye tracker data samples [START_REF] Hafed | Alteration of visual perception prior to microsaccades[END_REF].

Monkey eye movements were recorded at 1kHz using electromagnetic induction of electrical current in a scleral eye coil [START_REF] Fuchs | A method for measuring horizontal and vertical eye movement chronically in the monkey[END_REF][START_REF] Judge | Implantation of magnetic search coils for measurement of eye position: an improved method[END_REF].

As stated in [START_REF] Willeke | Memory-guided microsaccades[END_REF], we used video-based eye tracking for the human subjects, again sampling at 1kHz (EyeLink 1000; desktop mount). For best eye tracking performance, we fixed the heads of the monkeys and humans during the sessions. For the former, this was achieved with surgically-implanted head-holders [START_REF] Chen | Postmicrosaccadic enhancement of slow eye movements[END_REF]. For the latter, we used a custom-built chin-and-forehead rest with additional head position guides on the temples and behind the head [START_REF] Hafed | Alteration of visual perception prior to microsaccades[END_REF].

Animal preparation

We collected behavioral data from 2 adult, male rhesus macaques (Macaca Mulatta).

Monkeys M and N (aged 7 and 10 years, and weighing 8 and 11.5 kg, respectively) were implanted with a scleral coil in one eye to allow measuring eye movements using the electromagnetic induction technique [START_REF] Fuchs | A method for measuring horizontal and vertical eye movement chronically in the monkey[END_REF][START_REF] Judge | Implantation of magnetic search coils for measurement of eye position: an improved method[END_REF]. The monkeys were also implanted with a head holder to stabilize their head during the experiments, with details on all implant surgeries provided earlier [START_REF] Chen | Postmicrosaccadic enhancement of slow eye movements[END_REF][START_REF] Skinner | Transfer function of the rhesus macaque oculomotor system for small-amplitude slow motion trajectories[END_REF]. They were part of a larger neurophysiology project beyond the scope of the current manuscript.

Monkey behavioral tasks

The monkeys were trained to perform a visually-guided saccade task. Each trial started with the presentation of a central white fixation spot (86 cd/m 2 ) over a uniform gray background (29.7 cd/m 2 ). The fixation spot was a square of 5.3 x 5.3 min arc dimensions. After 300-900 ms of fixation (i.e. maintaining eye position within a prescribed distance from the spot; see below), the fixation spot was jumped to a new location, instructing the monkeys to generate a visually-guided saccade to follow the spot. The size of the jump was varied randomly across trials. Target locations were chosen from among 96 predefined possibilities, as follows: the target could jump by a distance of 0.06, 0.1, 0.2, 0.3, 0.5, 0.7, 1, 1.5, 2, 3, 5, or 10 deg in either the horizontal or vertical dimension, or it could jump obliquely along a diagonal (in which case we used the same sampling resolution of each of the horizontal and vertical dimensions of any given jump: 0.06, 0.1, 0.2, 0.3, 0.5, 0.7, 1, 1.5, 2, 3, 5, or 10 deg of each of the horizontal and vertical components). Moreover, the jump could be to either side of display center (rightward or leftward in the horizontal dimension; upward or downward in the vertical dimension). Therefore, we sampled horizontal, vertical, and diagonal target locations of different eccentricities, with denser sampling of foveal and perifoveal locations. In all data analyses and graphs, we used the convention of positive target locations being to the right of or above display center (for either horizontal or vertical dimension, respectively), and negative target locations being to the left of or below display center. If the monkeys fixated the new spot location within 500 ms after it had jumped, and held their eye position there for another approximately 300 ms, they were rewarded with liquid reward.

We controlled the monkeys' fluid reward system in real-time by employing a virtual, computer-controlled window around target location. If eye position entered the virtual window within the prescribed "grace" period, a reward was triggered. Otherwise, the trial was aborted, and a new trial was initiated. Our virtual "target windows" across trials had radii of 2-2.5 deg. Note that a radius of 2-2.5 deg was still employed even for foveal target locations of smaller eccentricities. This means that for such small target eccentricities, we exploited the natural tendency of the monkeys to perform the task without any computer monitoring to ensure that they generated the required saccades. This was not a problem at all, because after the monkeys were trained on the task with eccentricities of 5 deg and higher, they very naturally generalized their trained rule when tested on smaller target eccentricities. This was also the case in more complicated variants of the task [START_REF] Willeke | Memory-guided microsaccades[END_REF], and it was also consistent with human results (e.g. see Fig. 10). We felt that this approach of large virtual target windows was better than the alternative of enforcing tiny target windows, because in the latter case, any potential increases in reaction times of saccades could have been interpreted as being the consequence of increased task difficulty or a potential speed-accuracy tradeoff.

We analyzed a total of 928 trials from monkey M in this task, and 1246 trials from monkey N.

We also analyzed visually-guided delayed saccades and memory-guided delayed saccades made by the same two monkeys. These data were collected during an earlier experiment, with detailed methods described elsewhere [START_REF] Willeke | Memory-guided microsaccades[END_REF].

The purpose of the present re-analysis was to explore saccade latency as a function of target eccentricity, and to examine how this relationship might be affected by task instruction. We also wanted to directly compare results from the same animals used in the (immediate) visually-guided saccade experiments described above. Briefly, the delayed saccade task was similar to the (immediate) visually-guided saccade task described above, except that there was a delay period of 500-1000 ms during which the fixation spot remained visible when the saccade target was visible. The presence of the central spot instructed the monkeys to maintain fixation, despite the presence of the peripheral target. When the fixation spot disappeared, the monkeys could make the saccade to the peripheral target. This task allowed us to investigate whether increased saccadic latencies for small target eccentricities (see Results) were necessarily linked to sudden visual onsets in the (immediate) visually-guided saccade task.

The memory-guided saccade task was similar to the delayed, visually-guided saccade task, except that the target duration was brief (duration: 58 ms). When the fixation spot disappeared, the monkeys generated an eye movement to the remembered location of the earlier target flash. This task was useful to dissociate increased reaction times for small target eccentricities from the presence of a visual target.

In all tasks, we started out with the monkeys already being experts in oculomotor tasks requiring fixation of a small target (similar to author ZH in Fig. 10). The monkeys were used in earlier studies demonstrating their level of precision in eye movement control (e.g. [START_REF] Tian | Dynamics of fixational eye position and microsaccades during spatial cueing: the case of express microsaccades[END_REF]2016 for monkey N and[START_REF] Buonocore | Eye Position Error Influence over "Open-Loop" Smooth Pursuit Initiation[END_REF][START_REF] Skinner | Transfer function of the rhesus macaque oculomotor system for small-amplitude slow motion trajectories[END_REF] for monkey M). Therefore, even though we analyzed thousands of trials in the present study, we did not characterize learning processes.

From personal observation, the naïve monkeys naturally fixated similarly sized fixation spots to a precision significantly higher than that required by computercontrolled virtual windows. The quality of their fixation therefore started out being good, and improved fairly quickly within a matter of a few trials within a single session.

Human behavioral tasks

For supporting comparisons of the results from our monkeys in the (immediate) visually-guided saccade task to those reported in the literature on human subjects (e.g. [START_REF] Kalesnykas | Fixation conditions, the foveola and saccadic latency[END_REF][START_REF] Kalesnykas | Retinal eccentricity and the latency of eye saccades[END_REF]Wyman and Steinman 1973), we ran one human expert (author ZH) and three naïve subjects on the same task as that performed by our two expert monkeys (see Figs. 10,11). We analyzed 1966 trials from subject ZH and 783-974 trials from each of the naïve subjects. In separate sessions, we also ran a variant of the same task, but the fixation spot now remained visible after target jump. The subjects' task was to maintain fixation and press a button (with the right thumb) as quickly as possible after target onset. The goal was to measure manual reaction times for perceptual detections not requiring an eye movement. This allowed us to compare and contrast manual reaction times to saccadic reaction times from the original variant of the task. We analyzed 1924 from author ZH in this task variant, and 799-945 trials from each of the three naïve subjects. In all experiments, the fixation spot and target were a small square of 4.4 x 4.4 min arc. Their luminance was 97.3 cd/m 2 , and the background luminance was 20.5 cd/m 2 . In addition, two of the subjects (ZH and MB) were instructed to perform the manual task first before the saccade task, and two other subjects (FK and HB) performed the saccade task first before the manual task. The results (see Figs. 10,11) did not depend on the order in which the two tasks were performed, and therefore cannot be explained by learning or practice effects in one or the other task.

Because we were particularly interested in the monkey memory-guided saccade reaction time results as a function of target eccentricity (see Results below), we also decided to explore their generalizability to human memory-guided saccades, an aspect that was not well-explored in the existing human saccade literature so far.

Therefore, we re-analyzed human data that we had collected earlier [START_REF] Willeke | Memory-guided microsaccades[END_REF] with the same task. Briefly, the human subjects made the same memoryguided saccade task with target locations being chosen randomly across trials from among 480 possibilities, with heavy sampling of small eccentricities. Specifically, target eccentricities in this experiment ranged from 6 min arc to 12 deg, with 288 out of the 480 target locations lying within the square of eccentricities within +/-0.8 deg (horizontally) by +/-0.8 deg (vertically).

Behavioral analyses

We detected saccades and microsaccades using established methods reported elsewhere [START_REF] Bellet | Human-level saccade detection performance using deep neural networks[END_REF][START_REF] Chen | Postmicrosaccadic enhancement of slow eye movements[END_REF]. Both methods rely on a mathematical differential (i.e. speed) or more (i.e. acceleration) of the digitized eye position signals acquired by our systems, with specific parameters for the classification of saccadic events depending on the specific signal noise levels in the digitized signals. We manually inspected each trial to correct for false alarms or misses by the automatic algorithms, which were rare. We also marked blinks or noise artifacts for later removal. In scleral eye coil data, blinks are easily discernible due to well-known blink-associated changes in eye position. In video-based eye tracking, blinks are equally easy to detect because they are associated with an absence of eye position data due to the closed eyelids.

In the (immediate) visually-guided saccade task, we analyzed the first saccade that was triggered after the target jump. We excluded all trials in which there was a blink within +/-100 ms from target jump, since this could impair visual detection of the jump. We also excluded all trials in which a microsaccade occurred within the period from -100 ms to 60 ms relative to target jump occurrence. Our reason was that microsaccades around stimulus onset reduce target visibility and increase reaction time [START_REF] Beeler | Visual threshold changes resulting from spontaneous saccadic eye movements[END_REF][START_REF] Bellet | Sequential hemifield gating of alpha-and betabehavioral performance oscillations after microsaccades[END_REF][START_REF] Chen | A neural locus for spatial-frequency specific saccadic suppression in visual-motor neurons of the primate superior colliculus[END_REF][START_REF] Chen | Neuronal Response Gain Enhancement prior to Microsaccades[END_REF][START_REF] Hafed | Microsaccadic suppression of visual bursts in the primate superior colliculus[END_REF][START_REF] Tian | A Microsaccadic Account of Attentional Capture and Inhibition of Return in Posner Cueing[END_REF]Zuber and Stark 1966). Similar exclusion criteria were also used in human analyses (e.g. Figs. 10,11). We defined as a successful reaction any eye movement made within 70-500 ms after target jump (throughout this article, we interchangeably refer to the time interval between target jump and saccade onset as the "saccadic latency" or "saccadic reaction time"). When plotting reaction time as a function of target eccentricity or direction, or both, we binned nearby eccentricities, and we only showed summary measurements (e.g. mean and s.e.m.) if each bin contained at least five measurements. We also only included saccades if the measurements had movements with direction error relative to the target (defined as the difference in the angular direction of a saccade relative to the angular direction of the target displacement vector) of less than 45 deg (this was the great majority of data; e.g. Fig. 9 in Results).

For the re-analysis of the delayed, visually-guided and memory-guided saccade data of [START_REF] Willeke | Memory-guided microsaccades[END_REF], we used similar procedures to those described above. Since the sampling of target locations in these tasks was slightly different from that performed in the present experiments (i.e. for the visually-guided saccade task), we adjusted the binning windows accordingly, and we only included any measurement bins in which there were at least 7 saccades per bin. We also accepted as a minimum reaction time 100 ms instead of 70 ms, since we observed that reaction times in these "delayed" types of saccade tasks were generally longer than in the immediate visually-guided saccade task.

For the re-analysis of the human memory-guided saccade data of [START_REF] Willeke | Memory-guided microsaccades[END_REF], we again used similar procedures. Like in the monkey memory-guided saccade task, we considered a minimum reaction time of 100 ms. In reality, this was conservative, since the human reaction times were significantly longer, in general, than those of the monkeys in the same task (as described in Results and also in [START_REF] Willeke | Memory-guided microsaccades[END_REF].

We additionally binned trials in the delayed, visually-guided saccade task according to the length of the delay period used in the task. For analyzing trends of reaction time as a function of delay period duration, we used a running average spanning the total range of delay periods (500 to 1000 ms). The running average started at a delay period of 600 ms with time bin steps of 50 ms until 900 ms. At each of these time bin steps, we averaged trials with +/-100 ms delay period duration from the current bin step. For example, the average in the first bin step of 600 ms had all trials with delay period durations of 500-700 ms, and the average of the next bin step had all trials with delay period durations of 550-750 ms, and so on.

Finally, for the visually-guided saccade task, we plotted saccade amplitude and direction error as a function of target eccentricity, using similar binning procedures to those described above for reaction times.

In all analyses, we were interested in comparing saccades to upper and lower visual field target locations, since eye-movement related structures like the superior colliculus (SC) represent them differently [START_REF] Hafed | Sharper, Stronger, Faster Upper Visual Field Representation in Primate Superior Colliculus[END_REF]. Specifically, SC visual responses to stimulus onsets (as well as neuronal contrast sensitivity) are both significantly stronger and earlier in SC neurons representing the upper visual field than in neurons representing the lower visual field [START_REF] Hafed | Sharper, Stronger, Faster Upper Visual Field Representation in Primate Superior Colliculus[END_REF], and there is a concomitant reflection of this difference in saccade reaction times; this corroborates a very strong correlation between SC visual response strength/latency and saccadic reaction times in general and under a variety of conditions (Chen et al. 2018;[START_REF] Chen | A neural locus for spatial-frequency specific saccadic suppression in visual-motor neurons of the primate superior colliculus[END_REF]. We therefore divided trials according to whether the target location was in the lower visual field (one group) or otherwise (that is, purely horizontal or in the upper visual field; the second group).

Statistical analyses

Our purpose was to document patterns of rhesus macaque reaction time values as a function of visual-field location across a variety of well-established oculomotor tasks.

We therefore largely present descriptive statistics in all figures, showing mean and s.e.m. measurements, as well as numbers of observations. All trends that we focus on are immediately visible in the mean and s.e.m. plots that we present.

Results

Monkeys exhibit increased saccadic reaction times for foveal target eccentricities

Our goal was to document the saccadic reaction times of rhesus macaque monkeys when target displacements are small. We were motivated by the fact that in humans, it is known that small-eccentricity target displacements are associated with increased saccadic reaction times [START_REF] Vries | The saccadic size-latency phenomenon explored: Proximal target size is a determining factor in the saccade latency[END_REF][START_REF] Kalesnykas | Fixation conditions, the foveola and saccadic latency[END_REF][START_REF] Kalesnykas | Retinal eccentricity and the latency of eye saccades[END_REF]Wyman and Steinman 1973). Figure 1 shows example eye position and velocity traces from one monkey (monkey M) when the target displacement was small (Fig. 1a) or when it was much larger (Fig. 1b). In both cases, the target displacement was to the right of central fixation, and we plotted horizontal eye position as well as radial eye velocity in the interval around target jump (labeled target onset in the figure). In both cases, a saccade was made to the target, which scaled appropriately in size with target eccentricity (also see Fig. 9 in a later section of Results). However, when the target eccentricity was small (Fig. 1a), the small saccades had significantly longer reaction times than the big saccades generated when the target eccentricity was large (Fig. 1b). This is illustrated in Fig. 1 with dashed vertical lines delineating the reaction times of the fastest small (Fig. 1a, blue dashed line) and large (Fig. 1b, red dashed line) saccades in the two shown data sets. As can be seen, there was a clear difference between fastest reaction times as a function of target eccentricity.

Moreover, the overall distribution for the small saccades was shifted towards longer and more variable reaction times when compared to the bigger saccades. These examples demonstrate that rhesus macaque monkeys exhibit the same latency increase for small visually-guided saccades as human subjects (De [START_REF] Vries | The saccadic size-latency phenomenon explored: Proximal target size is a determining factor in the saccade latency[END_REF][START_REF] Kalesnykas | Fixation conditions, the foveola and saccadic latency[END_REF][START_REF] Kalesnykas | Retinal eccentricity and the latency of eye saccades[END_REF]Wyman and Steinman 1973).

We summarized the above results across the entire set of measurements. In Fig. 2a that for the foveal target eccentricities. This strong increase for the foveal targets is more vivid in the middle panel of Fig. 2a, zooming in on only the central 1.5 deg of target eccentricities. Similarly, the rightmost panel of Fig. 2a plots the same data as in the leftmost panel but now on a logarithmic eccentricity scale, again demonstrating the longer saccadic reaction times associated with small target eccentricities. Similar results were obtained in monkey N, except that this monkey showed an even more dramatic increase in reaction times for foveal target eccentricities (from a minimum mean reaction time of <150 ms to a peak of approximately 300 ms). Therefore, across all target locations and eccentricities that we measured, there was a clear and consistent increase in saccadic reaction times of the two monkeys for foveal targets.

There was another increase in reaction times, albeit weaker, for large target eccentricities, as also observed in human subjects [START_REF] Kalesnykas | Fixation conditions, the foveola and saccadic latency[END_REF][START_REF] Kalesnykas | Retinal eccentricity and the latency of eye saccades[END_REF].

To statistically confirm the above interpretations (Fig. 2), we binned target eccentricities into three groups: <1 deg, 2-5 deg, and >7 deg. Reaction times were significantly faster for the <1 deg group than for the 2-5 deg (monkey M: p=1.6x10 -17 ; monkey N: p=1.6x10 -41 ; t-test). Moreover, reaction times were significantly faster for the 2-5 deg group than for the >7 deg group (monkey M: p=1.3x10 -32 ; monkey N: p=6.2x10 -43 ; t-test).

We also inspected overall reaction time distributions to confirm that our method for accepting successful trials during the experiments did not artificially penalize specific ranges of reaction times. Specifically, our monkeys were rewarded based on the use of virtual, computer-controlled windows surrounding target location. If the eye position was not inside the virtual target window within 500 ms from target onset on a given trial (Methods), then the trial was aborted and the monkey was not rewarded. It is therefore conceivable (although unlikely; Methods) that we artificially truncated reaction time distributions at 500 ms, especially for target eccentricities showing increased reaction times (Fig. 2). However, this was not the case. For example, the top panels of Fig. 3a,b show the reaction time distributions when foveal target eccentricities of 12-36 min arc were tested. The distributions were not truncated at 500 ms, suggesting that the monkeys were still able to generate visually-guided saccades to these foveal targets within the prescribed "grace" period of 500 ms.

Similarly, the bottom panels of Fig. 3a, b demonstrate that for another range of target eccentricities in which reaction times increased (Fig. 2), the increase was again not affected by the truncation at 500 ms forced by our grace period.

Targets in the lower visual field are associated with increased reaction times, also for foveal eccentricities

Because the SC exhibits a strong asymmetry between the representation of the upper and lower visual fields [START_REF] Hafed | Sharper, Stronger, Faster Upper Visual Field Representation in Primate Superior Colliculus[END_REF], with direct consequences on saccadic reaction times for large saccades, we next analyzed the reaction times of small visually-guided saccades to foveal targets in the upper and lower visual fields. Specifically, it was not known so far whether differences in saccadic reaction times between upper and lower visual field target locations also occur for very small eye movements. For the same data as in Fig. 2, we divided trials according to whether the target was in the lower visual field (Fig. 4a,c; red) or whether it was along the horizontal meridian or in the upper visual field (Fig. 4a,c; blue). Using the same formatting conventions as in Fig. 2, we found that there was, essentially, a global upward shift in the relationship between saccadic reaction time and target eccentricity for targets in the lower visual field. That is, the reaction time increase associated with lower visual field target locations also happened for tiny foveal eccentricities (middle panels in Fig. 4a,c). This was confirmed statistically when we tested reaction times across the two groupings of target locations in Fig. 4a,c (monkey M: p=2x10 -8 ; t-test comparing the two groups of data in Fig. 4a; monkey N: p=1.6x10 -28 ; t-test comparing the two groups of data in Fig. 4c). Moreover, this effect was not restricted to cardinal target/saccade directions. For example, in Fig. 4b,d, we plotted, for each monkey, the saccadic reaction time as a function of oblique target location. We plotted target location bins on log-polar coordinates [START_REF] Hafed | Similarity of superior colliculus involvement in microsaccade and saccade generation[END_REF], in order to cover the large span of eccentricities tested, and we colorcoded each binned target location (z-axis) with the mean saccadic reaction time for that location. In both monkeys, the same general dependence of saccadic reaction time on target eccentricity (Figs. 2,3,4a,c) occurred for all target directions. That is, foveal locations had the longest reaction times; there was a minimum of reaction times at intermediate eccentricities; and there was then a more modest increase in reaction times once again for larger eccentricities. Moreover, lower visual field locations (including foveal ones) were associated with the longest reaction times (also see Figs. 10, 11 for a human replication of all of these observations).

Delayed, visually guided saccades show largely similar reaction time patterns to (immediate) visually-guided saccades

To demonstrate that increased reaction times for small saccades are indeed related to motor programming (our equilibrium hypothesis) rather than only due to visual processing of foveal targets, we also ran our monkeys on a delayed saccade task. In this task, the target remained persistent for a certain delay period while the fixation spot was visible. Only when the fixation spot was removed were the monkeys allowed to make the saccade (Methods).

We found a similar increase in reaction time in the delayed condition as in the immediate visually-guided saccade task for small target eccentricities. This happened even though the target was persistent, and the instruction to trigger the saccade was the offset of a fixation spot instead of the onset of the target. The task also had temporal expectation inherently built into it (discussed further below), since the longer the delay period was, the more likely it was that the "go" signal for the saccade was to come; there was also sufficient time with short delay periods to plan a saccade.

Figure 5 plots reaction time data from this task in a format identical to that in Fig. 4 for both monkeys. The same general pattern of results was observed. Namely, small, foveal target eccentricities were associated with the longest reaction times, and lower visual field locations were also associated with long reaction times when compared to horizontal and upper visual field locations.

An interesting difference that emerged in this condition relative to the (immediate) visually-guided saccade condition was the behavior of saccadic reaction times for large eccentricities (e.g. >10 deg). In this variant of the task, the increase in saccadic reaction times with increasing target eccentricities was less consistent than with the (immediate) visually-guided saccade task (Figs. 234). Instead, lower visual field targets of intermediate eccentricities (e.g. between ~4 and 10 deg) exhibited a small increase in reaction time relative to larger target eccentricities (and upper visual field target locations). Thus, in the same two animals, changing the task seemingly modified the pattern of results for large eccentricities.

We also explicitly investigated the potential role of temporal expectations in this task.

We divided our trials based on the length of the delay period. That is, we asked whether saccadic reaction times decreased when the delay period was long, since longer delay periods necessarily increase the likelihood of the instruction to generate the required saccade. For each monkey, we plotted in Fig. 6a, c reaction time as a function of target eccentricity (pooling upper and lower visual field locations together), but after dividing the trials into different bins based on the duration of the delay period (different colors). There was indeed an effect of temporal expectations (faster reaction times for longer delay period durations), but this effect was absent for the most foveal target eccentricities. We confirmed this in Fig. 6b,d by plotting reaction time as a function of delay period duration for different target eccentricity bins. In both monkeys, targets within <1 deg of eccentricity did not show a dependence of reaction time on delay period duration. In monkey N, such a dependence emerged for more eccentric targets as close as 2 deg; in monkey M, this dependence emerged for more eccentric targets approximately >7 deg in eccentricity. These effects were the same whether targets were in the upper or lower visual fields (except for the globally elevated reaction times of lower visual field targets shown in Fig. 5).

Thus, even though knowledge of target location and expectation to generate a saccade altered the detailed patterns of saccadic reaction times for extra-foveal target locations (Figs. 5,6), the same increases in reaction times for foveal targets were evident in this task just like in the (immediate) visually-guided saccade task.

Small memory-guided saccades are also associated with increased reaction times, despite the absence of a visual target

To further demonstrate the independence of small saccade reaction times from foveal visual responses (whether in SC or elsewhere), we also trained our monkeys to generate small memory-guided saccades [START_REF] Willeke | Memory-guided microsaccades[END_REF]. In this case, the instruction to generate a saccade was the offset of a fixation spot displayed on an otherwise blank screen. The saccade itself was not directed to a visual stimulus, but instead to a remembered location [START_REF] Willeke | Memory-guided microsaccades[END_REF]. We found similar increases in saccadic reaction times for foveal target eccentricities (Fig. 7; formatted identically to Figs. 4,5). Interestingly, for foveal target eccentricities (middle panels of Fig. 7a,c), there was no clear difference in reaction times between locations in the upper and lower visual fields, unlike when there was a visual stimulus as the target for the saccade (Figs. 4,5). Thus, even with memory-guided "microsaccades" [START_REF] Willeke | Memory-guided microsaccades[END_REF], there was an increase in saccadic reaction times, although the presence or absence of a visual target could alter the detailed properties of such an increase. It is also worth noting that the reaction time in this condition did not increase for larger eccentricities as in the (immediate) visually-guided saccade task. Instead, and as in the delayed, visually-guided saccade task, it was specifically the lower visual field saccades for intermediate eccentricities that seemed to increase.

Small memory-guided saccades in humans show patterns similar to small memoryguided saccades in monkeys

Intrigued by the results in Fig. 7, we sought to test whether similar observations could also be made in human subjects. We had human subjects perform the same task as the monkeys [START_REF] Willeke | Memory-guided microsaccades[END_REF]) and found very similar results (Fig. 8). Small memory-guided "microsaccades" [START_REF] Willeke | Memory-guided microsaccades[END_REF] were associated with the longest reaction times relative to all other eccentricities, just like in the monkeys.

Therefore, in all tasks, small saccades were always associated with the longest average latencies, regardless of whether the saccades were reflexive (Figs. 1234), delayed (Figs. 5,6), or memory-guided (Figs. 7,8).

Small visually-guided saccades show differences in spatial accuracy for upward and downward targets

Because of the global changes in reaction times in the (immediate) visually-guided saccade task for different visual field locations (Fig. 4), we searched for other asymmetries in saccade parameters that also depended on foveal (or extra-foveal) target location. We found that saccade amplitude and direction differentially depended on visual field target location for foveal targets. Specifically, when we plotted saccade amplitude as a function of target eccentricity (Fig. 9a,c), we found that amplitude scaled nicely with target eccentricity even for foveal target locations, but there was larger overshoot in saccade amplitude for foveal targets in the lower visual field than in the upper visual field or along the horizontal meridian. On the other hand, when we plotted saccade direction error relative to target direction (Fig. 9b,d), we found that the overshooting lower visual field small saccades were more directionally accurate than the saccades to foveal targets in the upper visual field or along the horizontal meridian. Therefore, besides strong increases in reaction times for foveal target eccentricities (Figs. 1234), small visually-guided saccades showed differential effects of amplitude versus directional accuracy as a function of target visual field location. These effects (Fig. 9) were not so clearly visible in the other variants of the task, such as the delayed, visually-guided saccade task or the memory-guided saccade task.

Increased reaction times for small eccentricities are specific to eye movements and absent in manual reactions

Finally, we were further investigated the absence of increased reaction times for large saccades made in the memory-guided task when compared to the visuallyguided saccade task. We hypothesized that the increase in the latter task might critically depend on the perceptual detectability of the appearing target. Specifically, we used a small spot as the target in all of our experiments, even for eccentricities of 10 or 15 deg. This means that, at these eccentricities, the small spot would be harder to perceptually detect than in the foveal or parafoveal regions (due to limits of the contrast sensitivity function). Therefore, even without saccadic responses, decreased perceptual detectability at far eccentricities could delay reaction times.

We explicitly tested this hypothesis by performing additional experiments with one of us (ZH) being the experienced subject (similar to our two experienced monkey subjects). In Fig. 10a, we replicated the findings of human saccadic reaction times as a function of target eccentricity [START_REF] Kalesnykas | Fixation conditions, the foveola and saccadic latency[END_REF][START_REF] Kalesnykas | Retinal eccentricity and the latency of eye saccades[END_REF]. Note how, in addition to the dramatic increase for small saccades, saccadic reaction times increased with increasing target eccentricity for extra-foveal targets (curved black arrow in the figure; similar to our monkeys in Fig. 2). Critically, for Fig. 10b, we ran the same subject on a perceptual detection task, in which no saccade was required at all. Instead, the subject had to press a button as soon as the target appeared in the periphery (Methods), and we confirmed that no microsaccades occurred between target onset and button press. Two notable observations are clear from the data.

First, there was no strong increase in reaction times for foveal target eccentricities, suggesting that the increased reaction times of small saccades are specific to the fact that the motor behavior was to generate small saccades. Second, the same increase in reaction times for larger target eccentricities as in Fig. 10a was still evident (curved black arrow). This latter observation is much more obvious when the two curves are superimposed together in Fig. 10c using the same y-axis scaling (but with arbitrary y-axis positioning of the curves due to the different absolute values of saccadic and manual reaction times). Both tasks were associated with increased reaction times for peripheral targets, but only the saccadic task was associated with increased reaction times for foveal targets. Therefore, the increases in Fig. 2 and Fig. 10a for large eccentricities were not specific to saccade generation. These same conclusions were reached when we repeated these same experiments on 3 additional naïve subjects (Fig. 11a). Interestingly, all 4 subjects also showed the dependence of saccadic reaction times on upper versus lower visual field target locations (Fig. 10d and Fig. 11b) that we observed in our monkeys (Fig. 4), but this effect was again specific only to saccade generation (Fig. 10e and Fig. 11c).

Discussion

We investigated spatial and temporal aspects of triggering small saccades in the rhesus macaque monkey and compared our results to those obtained in human subjects both from the existing literature and through our own additional measurements. We specifically found that, in the monkey, small saccades require more time than larger saccades to be triggered. This observation is true whether the small saccades are visually-driven, delayed (but still visually-driven), or memoryguided. We also found a strong asymmetry in the reaction times of small visuallyguided saccades to upper and lower visual field locations, similar to larger saccade results [START_REF] Hafed | Sharper, Stronger, Faster Upper Visual Field Representation in Primate Superior Colliculus[END_REF][START_REF] Schlykowa | Monkey saccadic latency and pursuit velocity show a preference for upward directions of target motion[END_REF]Zhou and King 2002). For larger saccades, there was a gradual increase in reaction times with increasing target eccentricities, but primarily in the (immediate) visually-guided saccade task and not in the delayed, visually-guided saccade task or the memory-guided saccade task.

Our results are important to document in the oculomotor system literature because there has been no systematic attempt to investigate small-saccade triggering properties in the rhesus macaque monkey. In humans, it is well-known that smallsaccade reaction times are long [START_REF] Kalesnykas | Fixation conditions, the foveola and saccadic latency[END_REF][START_REF] Kalesnykas | Retinal eccentricity and the latency of eye saccades[END_REF]Wyman and Steinman 1973), although the mechanistic reasons for this phenomenon seem to be still not fully understood. In the monkey, there have basically been only casual inferences about small-saccade reaction times in macaques [START_REF] Boch | Express-saccades of the monkey: reaction times versus intensity, size, duration, and eccentricity of their targets[END_REF][START_REF] Skinner | Transfer function of the rhesus macaque oculomotor system for small-amplitude slow motion trajectories[END_REF][START_REF] Willeke | Memory-guided microsaccades[END_REF]), but either with tasks that were not explicitly designed for such analyses or without sufficient sampling of small target eccentricities. Therefore, our results provide an important reference catalog of smallsaccade triggering in macaque monkeys. This is especially important nowadays to guide investigations of neural mechanisms associated with foveal visual and motor processing [START_REF] Chen | The Foveal Visual Representation of the Primate Superior Colliculus[END_REF][START_REF] Guerrasio | Fastigial oculomotor region and the control of foveation during fixation[END_REF][START_REF] Willeke | Memory-guided microsaccades[END_REF].

One interesting aspect of our results is the observation that the reaction times of small saccades are shorter for upper visual field target locations than for lower visual field target locations (e.g. Fig. 4). This was in addition to the observation of increased reaction times in general for small saccades (Figs. 123). Therefore, not only are foveal targets associated with long saccadic reaction times (Figs. 123), but longer times are particularly prominent with foveal targets located in the lower visual field (Fig. 4). Interestingly, in one of their control conditions, Wyman and Steinman (1973) required a small downward saccade, which exhibited prolonged reaction times in humans as well, although this aspect of the data was not explicitly mentioned in that study. This is consistent with our human results of Figs. 10,11. It is also consistent with the asymmetric representations of upper and lower visual fields in the SC, in such a manner that can directly affect gaze direction, saccadic reaction times, and landing errors [START_REF] Hafed | Sharper, Stronger, Faster Upper Visual Field Representation in Primate Superior Colliculus[END_REF][START_REF] Goffart | Influence of background illumination on fixation and visually guided saccades in the rhesus monkey[END_REF]). As we elaborate more below, these effects are also consistent with our theory of gaze direction as an equilibrium insofar as an eye movement is not initiated as long as the visuooculomotor system is within a state of balance among opposing commands [START_REF] Goffart | Kinematics and the neurophysiological study of visually-guided eye movements[END_REF][START_REF] Goffart | Neurophysiology of visually guided eye movements: critical review and alternative viewpoint[END_REF][START_REF] Goffart | Visual fixation as equilibrium: evidence from superior colliculus inactivation[END_REF]Krauzlis et al. 2017).

We also noticed interesting contrasts between the reaction times of small and large saccades. For example, immediate visually-guided saccades showed a marked increase in reaction times for large saccades (e.g. Fig. 2), but this effect was not as strong as that for small saccades. It has been reported in humans that large saccades also become associated with increased reaction times [START_REF] Kalesnykas | Fixation conditions, the foveola and saccadic latency[END_REF][START_REF] Kalesnykas | Retinal eccentricity and the latency of eye saccades[END_REF]. However, are the causes similar to the causes of increased reaction times of small saccades? This issue remains unaddressed. Based on our data, we believe that the two increases are driven by quite different underlying causes. Specifically, in the delayed and memory-guided saccade tasks, the increase in reaction times for large saccades was much less obvious than in the (immediate) visually-guided saccade task, even though small saccades showed strong increases in all three tasks. Therefore, increased reaction times for large saccades are likely to be driven by different mechanisms from those affecting small-saccade reaction times. Indeed, our experiments of Figs. 10, 11 demonstrate that perceptual detectability of far peripheral targets might explain the increased reaction times associated with large eccentricities.

If perceptual detectability can affect reaction times of large target eccentricities (Figs. 10,11), we think that equilibrium states in the oculomotor system explain the long reaction times of small saccades. Specifically, evidence from pharmacological inactivation experiments in either the SC or the caudal fastigial nucleus suggests that gaze direction is an equilibrium, and that an eye movement (saccadic or slow) is not initiated as long as the visuo-oculomotor system is within a state of balance where opposing commands counterbalance each other [START_REF] Goffart | Kinematics and the neurophysiological study of visually-guided eye movements[END_REF][START_REF] Goffart | Neurophysiology of visually guided eye movements: critical review and alternative viewpoint[END_REF][START_REF] Goffart | Visual fixation as equilibrium: evidence from superior colliculus inactivation[END_REF]Krauzlis et al. 2017). Thus, the longer reaction times of small saccades are the signature of enhanced times to create a symmetry-breaking condition, which puts the downstream premotor neurons into a push-pull regime that is responsible for the firing rates of motor neurons innervating the agonist and antagonist extraocular muscles (reciprocal innervation). Such enhanced times can occur because of the following reason. Prior to bursting during both contralateral and ipsilateral saccades, saccade-related neurons in the rostral SC and caudal fastigial nucleus fire in a sustained manner during visual fixation [START_REF] Hafed | Similarity of superior colliculus involvement in microsaccade and saccade generation[END_REF][START_REF] Kleine | Saccade-related neurons in the primate fastigial nucleus: what do they encode?[END_REF]. More importantly, they also increase firing before and during both contralateral and ipsilateral saccades. Such bilateral activity carries, at the level of saccade-related premotor neurons, commands that are antagonist to each other (see Fig. 10 in [START_REF] Goffart | Deficits in saccades and fixation during muscimol inactivation of the caudal fastigial nucleus in the rhesus monkey[END_REF]). Thus, the longer reaction times of small saccades result from the fact that the bilateral and conflicting drives exerted by collicular and fastigial neurons become stronger as the activity becomes more rostral in the SC and/or as the ipsilateral and contralateral presaccadic spikes emitted by fastigial neurons are simultaneous. The longer lead times of firing activity (before saccade bursts) that some inhibitory premotor neurons emit prior to small saccades strikingly illustrate this concept (e.g. see Fig. 8 in [START_REF] Scudder | Characteristics and functional identification of saccadic inhibitory burst neurons in the alert monkey[END_REF].

A second mechanistic reason for enhanced times is related to spatial representation itself. Consistent with the large amount of foveal magnification in the SC [START_REF] Chen | The Foveal Visual Representation of the Primate Superior Colliculus[END_REF], the equilibrium idea is actually a natural extension of SC population coding of saccade metrics, but this time to aid in the specification of gaze direction during fixation. Specifically, Sparks and colleagues proposed that "precise saccadic movements are not produced by the discharge of a small population of finely tuned neurons but result from the weighted sum of the simultaneous movement tendencies produced by the activity of a large population of less finely tuned neurons" [START_REF] Sparks | Size and distribution of movement fields in the monkey superior colliculus[END_REF]). If the deep SC is a continuum representing different movement tendencies, then the absence of movement during fixation may be viewed as the simple result of simultaneous movement tendencies for small saccades counterbalancing each other. Indeed, rostral SC neurons active during fixation do individually represent small movement vectors [START_REF] Hafed | Similarity of superior colliculus involvement in microsaccade and saccade generation[END_REF]. Thus, the foveal magnification in the SC contributes not only to ensure precise microsaccades [START_REF] Chen | The Foveal Visual Representation of the Primate Superior Colliculus[END_REF][START_REF] Guerrasio | Fastigial oculomotor region and the control of foveation during fixation[END_REF][START_REF] Ko | Microsaccades precisely relocate gaze in a high visual acuity task[END_REF][START_REF] Tian | Dynamics of fixational eye position and microsaccades during spatial cueing: the case of express microsaccades[END_REF]), but it does also imply that a sizable population of neurons is active at any one moment in time to represent the current fixated goal [START_REF] Goffart | Visual fixation as equilibrium: evidence from superior colliculus inactivation[END_REF]Hafed et al. 2008;Hafed and Krauzlis 2008).

The implication of this is that a given displacement (in anatomical coordinates) of the center of mass of such active population would correspond to only a tiny displacement of the represented "movement vector" in visual coordinates (the same displacement in the caudal SC would correspond to much larger changes in the represented movement vector). Thus, achieving a shifted center of mass to create sufficient imbalance in the downstream readout of SC activity is harder because of the tiny visual field locations represented by the rostral SC. Movements effected by readout of the rostral SC would indeed be infinitesimally small for very small shifts of rostral SC populations.

If balance among multiple gaze commands is what maintains gaze stability and increases reaction times for small saccades, then one might wonder how an imbalance may be generated at all during fixation in the first place. In other words, why is reaction time not infinite once balance among competing gaze shift commands is achieved? One possible explanation is behavioral and invokes the slow fixational eye movements that often happen in between saccades. These ocular drifts change the retinotopic location of the fixated object and thus create the imbalance needed to activate the colliculoreticular streams innervating the eye muscles. In fact, we recently found that the generation of tiny microsaccades during fixation is highly consistently associated with small, instantaneous retinotopic gaze position errors, even in the presence of peripheral "attention-capturing" cues [START_REF] Tian | Dynamics of fixational eye position and microsaccades during spatial cueing: the case of express microsaccades[END_REF]2016).

Another explanation is physiological and lies upon the fluctuations of the activity of neurons, which, from the foveal ganglion cells to the saccade-related premotor burst neurons, exhibit sustained firing rates whenever gaze is held stable. Among this immense number of neurons, we find not only long-lead burst neurons in the pontine reticular formation, but also neurons in the caudal fastigial nucleus [START_REF] Kleine | Saccade-related neurons in the primate fastigial nucleus: what do they encode?[END_REF][START_REF] Sun | Individual neurons in the caudal fastigial oculomotor region convey information on both macro-and microsaccades[END_REF]. After unilateral inactivation of this nucleus, fixational saccades are not only dysmetric [START_REF] Guerrasio | Fastigial oculomotor region and the control of foveation during fixation[END_REF]), but the direction of gaze during fixation and pursuit is also always deviated towards the lesioned side [START_REF] Bourrelly | Pursuit disorder and saccade dysmetria after caudal fastigial inactivation in the monkey[END_REF][START_REF] Goffart | Deficits in saccades and fixation during muscimol inactivation of the caudal fastigial nucleus in the rhesus monkey[END_REF][START_REF] Guerrasio | Fastigial oculomotor region and the control of foveation during fixation[END_REF]. The fact that the head can also be deviated following a unilateral SC or fastigial lesion indicates that the balancing of activity is a process that is not restricted to the determination of eye gaze direction [START_REF] Goffart | Neurophysiology of visually guided eye movements: critical review and alternative viewpoint[END_REF]; head direction is also an equilibrium. Thus, gaze and head movements, instead of reducing putative signals encoding the angular distance between gaze (or head) and target locations in physical space, may be separate processes which consist of restoring symmetries [START_REF] Goffart | Kinematics and the neurophysiological study of visually-guided eye movements[END_REF]Goffart et al. 2018).

An interesting additional consequence of the oculomotor balance idea is that we can predict express, rather than slow, reaction times for small saccades under the right conditions related to instantaneous gaze position error. Indeed, so-called "express microsaccades" can happen when peripheral stimulus onsets momentarily bias a state equivalent to "unstable equilibrium" out of equilibrium [START_REF] Tian | Dynamics of fixational eye position and microsaccades during spatial cueing: the case of express microsaccades[END_REF].

Specifically, in that study, it was found that a peripheral stimulus onset during fixation was sometimes associated with a distinct population of so-called express microsaccadic reactions, which were highly precise in their timing and direction relative to the appearing stimulus. These movements had latencies significantly <100 ms even though they were small eye movements (like in the present study), but it was found that they occurred under very specific conditions of lack of prior microsaccades for a prolonged period of time as well as eye position being in a state of almost "zero" position error relative to the fixated spot [START_REF] Tian | Dynamics of fixational eye position and microsaccades during spatial cueing: the case of express microsaccades[END_REF].

Of course, the oculomotor balance referred to in all of the above can be implemented in different forms in different oculomotor nuclei. For example, omnipause neurons (OPN's) in the nucleus raphe interpositus exhibit tonic activity in the absence of saccades, similar in principle to other neurons in other brain areas (e.g. rostral deep SC neurons or caudal fastigial nucleus neurons) (Krauzlis et al. 2017). Because these OPN's completely pause during saccades, they are believed to be an all-ornone mechanism for "fixing gaze". However, OPN's do show evidence for reflecting the state of balance among multiple movement tendencies, which is consistent with our equilibrium hypothesis. For example, OPN's clearly modulate their tonic rate with eye velocity in a continuous manner [START_REF] Missal | Common inhibitory mechanism for saccades and smoothpursuit eye movements[END_REF]. It is thus conceivable that even during so-called "gaze fixation", their tonic rate is systematically variable, reflecting fixational drift eye movements. In that case, even these neurons would show variability that is inconsistent with a theoretical "command to fix gaze". These neurons, like other brainstem premotor neurons, can be part of a network likely coordinating balance or imbalance from among multiple competing movement tendencies. However, there is no convincing evidence to date that inactivating OPN's results in impairments in gaze fixation or even saccade latency [START_REF] Soetedjo | Evidence that the superior colliculus participates in the feedback control of saccadic eye movements[END_REF][START_REF] Kaneko | Effect of ibotenic acid lesions of the omnipause neurons on saccadic eye movements in rhesus macaques[END_REF].

Naturally, the role of vision needs to be also considered when thinking about oculomotor behaviors, and that is why we performed our delayed and memoryguided saccade tasks. Previous experiments in humans have attempted to dissociate between visual and oculomotor (or other) sources of increased reaction times for small target eccentricities, and they attributed the increase to a difficulty in specifying the saccade metrics [START_REF] Kalesnykas | Fixation conditions, the foveola and saccadic latency[END_REF]Wyman and Steinman 1973).

Similarly, in the rhesus macaque SC, while some visual bursts for foveal target onsets might show dependence on foveal eccentricity in their response latency (firstspike latency), this does not seem to be a general property of foveal SC neurons [START_REF] Chen | The Foveal Visual Representation of the Primate Superior Colliculus[END_REF]. Specifically, superficial SC neurons (which generally exhibit marginally shorter visual response latencies than deeper SC neurons) show decreases in first-spike latency of the visual response with increasing foveal eccentricity (consistent with our behavioral findings above); on the other hand, deeper SC neurons show no such dependence of visual burst latency on foveal target eccentricity [START_REF] Chen | The Foveal Visual Representation of the Primate Superior Colliculus[END_REF]). Since it is the deeper SC neurons that show higher correlations between visual burst latency and saccadic reaction times [START_REF] Chen | A neural locus for spatial-frequency specific saccadic suppression in visual-motor neurons of the primate superior colliculus[END_REF][START_REF] Marino | Linking visual response properties in the superior colliculus to saccade behavior[END_REF], this might suggest that increased reaction times for small target eccentricities may not be intrinsically visual in nature (i.e. caused purely by visual-only mechanisms). Consistent with this, other studies showed that the latencies of gaze shifts increase for the smallest gaze displacements, though not for the smallest target eccentricities [START_REF] Goffart | Changes in initiation of orienting gaze shifts after muscimol inactivation of the caudal fastigial nucleus in the cat[END_REF]Zambarbieri et al. 1995), suggesting that saccade triggering can depend on premotor signals related to the impending movement in addition to incoming visual signals from the retina. Our results from the delayed and memory-guided saccade tasks (e.g. Fig. 5) further corroborate these ideas. 2a for monkey M. However, here, we separated targets as being located in the lower visual field relative to the line of sight (red) or otherwise (that is, located horizontally or in the upper visual field; blue). Reaction times were longer for lower visual field targets, consistent with [START_REF] Hafed | Sharper, Stronger, Faster Upper Visual Field Representation in Primate Superior Colliculus[END_REF]. This also happened for small target eccentricities (middle panel of a). (b) Log-polar plot of the same data as in a demonstrating how intermediate eccentricities had the lowest reaction times in all directions, and how lower visual field target locations were associated with longer reaction times than upper visual field target locations at all eccentricities tested. (c, d) Same as a, b but for monkey N. Error bars denote s.e.m. Figure 5 Increased reaction times for small delayed, visually-guided saccades in the rhesus macaque monkey. (a) Similar analyses to those in Fig. 4a for monkey M, but now during the delayed, visually-guided saccade task. As in the (immediate) visually-guided saccade task, small saccades had increased reaction times compared to larger saccades. Also like in the visually-guided saccade task, upper visual field target locations were associated with faster reaction times than lower visual field target locations. However, an increase in reaction times for large target eccentricities was less clear here than in the (immediate) visually-guided saccade task. Instead, lower visual field targets of intermediate eccentricities (e.g. (c,d) Same as a, b, but for monkey N. In this monkey, the dependence of reaction time on delay period duration emerged for targets as close as 2 deg in eccentricity (d). Like in monkey M, more foveal targets (<1 deg) still showed reaction times that were largely independent of delay period duration. Error bars denote s.e.m. Figure 7 Increased reaction times for small memory-guided saccades in the rhesus macaque monkey. (a, b) Similar analyses to Fig. 4a, b for monkey M but during the memory-guided saccade task. Small memory-guided saccades were associated with increased reaction times (compared to larger saccades) despite the absence of a visual target for the saccades. Note that for memory-guided saccades, the increase in reaction time for larger target eccentricities that was obvious for (immediate) visually-guided saccades (e.g. Fig. 2) did not take place so clearly. Instead, lower visual field saccades of intermediate sizes (e.g. 5-12 deg amplitudes; red curves) showed elevated reaction times compared to upper visual field saccades. Also note that there was no strong difference in reaction time between upper and lower visual field targets for small amplitudes (middle panel in a), unlike for visuallyguided saccades (Figs. The same data but now with upper and lower visual field target locations separately, as in Fig. 7. Similar results to those in the monkeys were obtained. Note that for small amplitudes (middle panel), there was a clearer difference between upper and lower visual field saccades than in the monkeys (Fig. 7). Thus, the data appeared more similar to those in visually-guided saccades (Fig. 4a,c; middle panels). (c) The same data but in a format similar to that of Fig. 7b,d, demonstrating that, in humans as well, small memory-guided "microsaccades" in all directions are associated with increased reaction times. Figure 9 Small visually-guided saccades in the rhesus macaque monkey were more accurate in size for upper visual field targets but more accurate in direction for lower visual field targets. (a) Saccade amplitude as a function of target eccentricity in monkey M. We used logarithmic axes to display the data such that the effects with small eccentricities are more visible. Small saccades to lower visual field targets (red) overshot the target significantly more than small saccades to horizontal and upper visual field targets (blue). n=928 trials. (b) For the same data as in a, we plotted saccade direction error (relative to target direction) as a function of target eccentricity. Direction error was smaller for small saccades to lower visual field targets (red) than for small saccades to horizontal and upper visual field targets (blue). (c, d) Similar results for monkey N. n=1246 trials. In all panels, error bars denote s.e.m. Figure 10 Both saccadic and manual reaction times increased for large target eccentricities in a human subject; only saccadic, but not manual, reaction times increased for small saccades as well as for lower visual field target locations. (a) Author ZH performed the same task as in Fig. 2. Small saccades had very long reaction times. Large saccades also showed a modest reaction time increase (curved black arrow). (b) Results from the same subject in the manual version of the task (Methods). (c) Same data from a, b but now using the same yaxis scaling (see vertical scale bar) but arbitrary y-axis placement to visually align the curves. Both tasks showed increased reaction times for large target eccentricities (black curved arrows), but only saccadic responses had strong increases for small target eccentricities (gray rectangle). (d) Same data as in a but separating upper and lower visual field target locations, as in Fig. 4. (e) Similar to d but for the manual task's data. Error bars denote s.e.m. Figure 11 shows similar results from three additional naïve subjects. 10c showing a comparison between manual and saccadic reaction times. The same y-axis scale bar applies to both tasks, but absolute values are not presented (for reference, absolute values are shown from one data point per curve). (b) Same data as in a from the saccade task, but separating targets as being either in the upper or lower visual fields, as in Fig. 10d. (c) Same data as in a from the manual task, but separating targets as being either in the upper or lower visual fields, as in Fig. 10e. For each subject, the same y-axis scaling was used in b, c to facilitate comparison of effect sizes between the two tasks. All other conventions are identical to those in Fig. 10.

  , we plotted in the leftmost panel the mean (surrounded by s.e.m. boundaries) saccadic reaction time of monkey M as a function of target eccentricity. The smallest target eccentricities (<1 deg) were associated with long reaction times, reaching a mean of approximately 240 ms. Reaction time then dropped down to approximately 150 ms for eccentricities >1 deg. Larger eccentricities (approximately >5 deg) were associated with another increase in saccadic reaction times, albeit not as large as

Finally

  , future experiments could investigate the neural mechanisms for learning to fixate visual objects under different visual and oculomotor conditions, and in which various amounts of asymmetry would be incorporated. For example, if target shape is changing, whether for the currently fixated position or for next target positions, what are the consequences on the oculomotor balance? How does this change alter the SC and caudal fastigial nucleus population activity? It will also be important to characterize the neural mechanisms underlying the coordination between saccades and slow eye movements (including the ocular drifts), with or without a concurrent head movement.

Figure legends Figure 1

 1 Figure legends

Figure 4

 4 Figure 4 Dependence of monkey visually-guided saccade reaction times on upper versus lower visual field target location. (a) Similar analyses as in Fig.2afor monkey M. However, here, we separated targets as being located in the lower visual field relative to the line of sight (red) or otherwise (that is, located horizontally or in the upper visual field; blue). Reaction times were longer for lower visual field targets, consistent with[START_REF] Hafed | Sharper, Stronger, Faster Upper Visual Field Representation in Primate Superior Colliculus[END_REF]. This also happened for small target eccentricities (middle panel of a). (b) Log-polar plot of the same data as in a demonstrating how intermediate eccentricities had the lowest reaction times in all directions, and how lower visual field target locations were associated with longer reaction times than upper visual field target locations at all eccentricities tested. (c, d) Same as a, b but for monkey N. Error bars denote s.e.m.

  Figure5Increased reaction times for small delayed, visually-guided saccades in the rhesus macaque monkey. (a) Similar analyses to those in Fig.4afor monkey M, but now during the delayed, visually-guided saccade task. As in the (immediate) visually-guided saccade task, small saccades had increased reaction times compared to larger saccades. Also like in the visually-guided saccade task, upper visual field target locations were associated with faster reaction times than lower visual field target locations. However, an increase in reaction times for large target eccentricities was less clear here than in the (immediate) visually-guided saccade task. Instead, lower visual field targets of intermediate eccentricities (e.g. 5-12 deg; red reaction time curves in a) were associated with increased reaction times relative to eccentricity-matched upper visual field targets. n=3265 trials; error bars denote s.e.m. (b) Log-polar plot showing the underlying data of a across space. (c, d) Similar results were obtained with monkey N. n=4277 trials.

  Figure8Memory-guided saccades in humans showed the same eccentricitydependencies as monkey memory-guided saccades. (a) Similar analyses to Fig.2but for our human subjects' data combined. The smallest saccades were associated with the longest reaction times, as in the monkeys (Fig.7). n=13531 trials; error bars denote s.e.m. (b) The same data but now with upper and lower visual field target locations separately, as in Fig.7. Similar results to those in the monkeys were obtained. Note that for small amplitudes (middle panel), there was a clearer difference between upper and lower visual field saccades than in the monkeys (Fig.7). Thus, the data appeared more similar to those in visually-guided saccades (Fig.4a, c; middle panels). (c) The same data but in a format similar to that of Fig.7b, d, demonstrating that, in humans as well, small memory-guided "microsaccades" in all directions are associated with increased reaction times.

Figure 11

 11 Figure 11 Same observations as in Fig. 10, but with data from three additional naïve subjects. Each row of plots represents data from a single subject. (a) Same as Fig.10cshowing a comparison between manual and saccadic reaction times. The same y-axis scale bar applies to both tasks, but absolute values are not presented (for reference, absolute values are shown from one data point per curve). (b) Same data as in a from the saccade task, but separating targets as being either in the upper or lower visual fields, as in Fig.10d. (c) Same data as in a from the manual task, but separating targets as being either in the upper or lower visual fields, as in Fig.10e. For each subject, the same y-axis scaling was used in b, c to facilitate comparison of effect sizes between the two tasks. All other conventions are identical to those in Fig.10.

Acknowledgements

ZMH was funded by the Werner Reichardt Centre for Integrative Neuroscience (CIN).

The CIN is an Excellence Cluster (EXC307) funded by the Deutsche Forschungsgemeinschaft (DFG). ZMH was also supported by the Hertie Institute for Clinical Brain Research at Tuebingen University, and DFG-funded Research Unit (FOR1847; project: HA6749/2-1). LG was supported by CNRS and Fondation pour la Recherche Médicale. We thank Aya Tarek, Antimo Buonocore, and Konstantin Willeke for help with data collection.

Data availability

All data presented in this paper are stored in institute computers and are available upon reasonable request.

Author contributions

ZMH collected the data. ZMH and LG analyzed the data and wrote the manuscript.

Declaration of interests

The authors declare no competing interests.