Perceptual decisions interfere more with eye movements than with reach movements

Perceptual judgements are formed through invisible cognitive processes. Reading out these judgements is essential for advancing our understanding of decision making and requires inferring covert cognitive states based on overt motor actions. Although intuition suggests that these actions must be related to the formation of decisions about where to move body parts, actions have been reported to be influenced by perceptual judgements even when the action is irrelevant to the perceptual judgement. However, despite performing multiple actions in our daily lives, how perceptual judgements influence multiple judgement-irrelevant actions is unknown. Here we show that perceptual judgements affect only saccadic eye movements when simultaneous judgement-irrelevant saccades and reaches are made, demonstrating that perceptual judgement-related signals continuously flow into the oculomotor system alone when multiple judgement-irrelevant actions are performed. This suggests that saccades are useful for making inferences about covert perceptual decisions, even when the actions are not tied to decision making.

confusions like mine at this sentence would be minimised.
-lines 66-75 are very nice -line 120: can you assess this similarity of psychometric curves statistically? I think that this is critical to show.
-line 134: you might want to also look at Buonocore et al, 2017, 2021 providing a mechanistic explanation for why kinematics might be altered with sensory interference in the citation that you made -line 157: One big difference between reaches and saccades is that the reaches probably have 3x the reaction times of the saccades. So, the lack of effect could simply be because there was too much time between the motion patch and the reach. You do not show the actual manual and saccadic reaction times, but I think you should show them. And, you should consider the possibility that the large difference in reaction time between saccades and reaches could explain your results.
-line 160: I think I expected this result (see comment above about the kinematic alterations) -line 195: again, I cannot see whether they are "nearly identical" because they are put in different panels. Some statistical quantification and/or plotting in the same panel is necessary -line 209: but maybe reach reaction time in the dual task was longer than in the single task. i.e. when required to both reach and look, the reaction times are longer than with only reaching. Similarly for saccades.
Reviewer #2 (Remarks to the Author): This paper report a set of puzzling findings about the interaction between perceptual decisions and the concurrent planning and execution of eye and hand movements that are irrelevant do the decision itself. Previous research (most notably Joo, Katz & Huk 2016) reported that perceptual decisions influenced decision-irrelevant eye movements, concluding it was evidence of motor and decision signals being mixed (multiplexed) in the same neural circuitry. (More specifically, the influence consisted in a modulation of the latency and peak velocity of decision-irrelevant saccadic eye movements.) In the present study the authors tested participants in a similar paradigm but asking participants to perform either individual eye or hand movements, or simultaneous hand+eye movements (in separate experiments). The pattern in the data is rather complex, with the modulation of saccadic peak velocity and modulation of reach movements seemingly absent in the dual-movement task (exp 1) and only a modulation of peak reach velocity being absent in single-movement task (exp 2).
Beside being roughly consistent with previous research showing a link between perceptual decision and eye movements, the take home message of the present study is, in my opinion, unclear. The discussion states that these findings shows how interactions between eye and hand motor planning can occur also when these are made during unrelated perceptual decision (why would they not?), but do not provide mechanistic explanation for the results. Overall, I find that the importance and significance of this study is not communicated clearly. Additionally, the conclusions of the authors depends on interpreting absence of evidence (null NHST tests) as evidence for absence, however it's not obvious that these non-significant tests provide evidence for the null hypothesis (they may well not, given also that the sample size is relatively small, n=11 and n=8). Finally, there is also a potential confounds (related to possible differences in response times between single and dual task conditions) that is not addressed.
Below are some more specific comments: -Was the mean response times (for either saccades and hand reaching) different in the single and dual experiment different? Currently only z-scored times are reported, so this is unclear. I would expect that these may be larger in the dual-task experiment (exp. 1) compared to the exp. 2, and their variance may be larger too. If that is the case, perhaps one complication in interpreting the current results is that the small interference effect due to the perceptual decision simply becomes harder to detect in such conditions? -line 55-onward: the hypothesis seems vague, I think the authors need to do a better job in explaining the rationale and indicating what the hypothesis entails. What does it means that perceptual decision would "prioritize" decision-irrelevant eye movements rather than reach movements? As I understand it, the effects of perceptual decisions on decision-irrelevant movements are considered a side-effects of multiplexing of signals in the neural circuits -a sort of interference. So what does it means that the interference on a certain type of movements would be "prioritized" compared to another, and why would it be the case?
-related to the previous point, I am not aware of studies showing an effect of perceptual decision on decision irrelevant eye movements (e.g. similar to reference n. 9, the study by Joo, Katz & Huk, PNAS 2016) but for hand reaching movements; in fact unless I am missing something none of the references cited shows such an effect. In other words, there is no clear evidence that a similar interference effect occurs for hand movements, so why is it interesting/important to investigate the prioritization of interference effects on eye and hand movements? Note: I don't want to to necessarily say that this is not interesting or important -it may well be -but I think the paper fails to convey why studying this is important/interesting. I think the authors need to do explain more clearly the rationale and scope of the study.
-Supplementary figure 1 is not very informative; it's very hard to tell what is going on with the data. To allow visual comparison of the data I recommend plotting each observer in a separate panel, with their individual functions plotted along the datapoints, using different colors for the same vs different conditions.
-line 120 "almost identical": it's hard to judge whether the functions are almost identical or not From Fig. 2 -it seems there could even be a slightly lower performance in the "Different" condition. Please provide statistical tests and use Bayes factors/equivalence tests to quantify more precisely support for the null hypothesis of no difference between conditions.
-Please provide Bayes factors or equivalence tests for null-results that are important for your conclusions. For example, is is said that coherence do not affect reach reaction times in the same, dual-movement condition, but judging from fig 2e there seems to be a trend, and indeed the p-value here is 0.07 so I doubt this can provide strong evidence in favour of the null hypothesis. Minor: -introduction: it should be acknowledged that whereas many studies showed how decisions influences ongoing hand movements, there is also evidence showing that faster movements like eye saccades, when used to communicate a perceptual decision, seems to be mostly planned *after* the decision is completed -see Lisi, Morgan & Solomon, 2022 (https://doi.org/10.1038/s42003-022-03141-1) -There are some grammatical anomalies, please revise the manuscript to check english language. For instance, at line 45: should be "multiple decision-irrelevant" -in english determiners like multiple, many etc. come before adjectives and other noun modifiers Reviewer #3 (Remarks to the Author): Review of Matsumiya and Furukawa, Nat Comm Biol, 2023 The authors investigated how simultaneous saccades and reach movements are influenced by the formation of a perceptual decision in a motion discrimination task. They report that the latency of saccadic eye movements towards a decision-irrelevant target was systematically affected by the coherence (motion strength) of the decision target, yet reach movement latencies were not. These results were only observed when observers engaged in an active decision task, not when they passively viewed the same target, ruling out that the results could be an effect of any sort of motioninduced drift when viewing the target. Even though the overall logic of the experimental results is strong, I have concerns about the interpretation of the data due to high variability, small sample size, and over-reliance on statistical significance testing in multiple tests. On the upside, the paper is very well written and a pleasure to read.
Overall comments -Approach and logic: at times, it is unclear what the relevance of understanding impact of perceptual decisions on irrelevant / unrelated motor action is. What is this a model of? How are decisionirrelevant action components relevant for our understanding of covert decision processes? It would be helpful to make this more explicit throughout the intro and discussion, especially considering that the main finding is very specific: an irrelevant action is only impacted if it is performed simultaneously with another decision-irrelevant action. Adding to the confusion is the fact that it seems that the overall question really is less about the impact of decision processes on irrelevant actions, but on which action is prioritized -the eye or the hand movement (l.74-75). It would be helpful if the authors clearly stated the relevance of each alternative outcome before summarizing their results. -Interpretation of results: my main concern is with the variability in individual data and the fact that some subjects appear to be at chance performance even at the highest coherence level. How can such results be interpreted? See also more detailed comments re. statistical analysis and reporting below.
Specific (major and minor) comments l.32: please consider replacing "generally" with "often". Many recent studies (as in: published in the last 15 years) do not follow this simple serial model. p.40: this is a nice summary and is consistent with literature on eye movements during decision making, see this recent review, which the authors could consider citing: https://pubmed.ncbi.nlm.nih.gov/35676097/ Suppl. Figure 1 (and others): I'm intrigued by the fact that several subjects appear to perform at around chance even at the highest level of coherence. The variability in the data is enormous, likely owing to individual variabilities in motion sensitivity. Why did the authors choose a constant stimulus design (and why these particular coherence levels) rather than a threshold procedure, which would have accounted for this? As such, it seems that data for observers who perform at chance can hardly be interpreted. Figure 2: fitted lines / model fits seem poor and are particularly misleading for reach reaction times. Why is a linear model used here? l.143-144 and throughout: please report exact p-values. What were the mean saccade latencies here? All figures show standardized data, so it would be helpful to see actual means here. l.151 following (also l.233 etc.): please clarify if these results were all obtained in separate F-tests / repeated-measures ANOVAS, and if yes, why were they not combined (i.e., factors "viewing condition" and "motion strength")? Conducting multiple tests increases the risk of false positives. Also, the authors solely focus on main effects and do not statistically evaluate interactions, yet, the data are interpreted as if there were interactions (effect on latencies in the active vs. passive task in saccades but not reaches). Moreover, some of the p-values are pretty borderline, yet are interpreted alongside much clearer results as indicating "no effect". Please consider supplying effect sizes so the reader can gage the magnitude and meaning of these reported null effects. l.286 following: it is not clear to me what part of the results this interpretation is based on: "We found that simultaneous decision-irrelevant saccade and reach movements suppress the modulation of saccade peak velocities, but not saccade reaction times, by perceptual decisions". Where is the evidence for an inhibitory process here? The authors observe differential effects on saccades and reaches, and differential effects on latency and peak velocity (though this has to be confirmed in a model that includes all these factors in one analysis). But this is not evidence of an inhibitory process per se. Methods: even though this might not have been a concern with the overall finding, it would be helpful to report how stable fixation was during the presentation of the motion stimulus. This type of stimulus typically elicits strong drift or even pursuit. Was this the case here?
Introduction and Discussion sections.
All revisions to the manuscript are highlighted in yellow.
Responses to Reviewer 1 1. Reviewer's comment: The results are generally clear. One missing analysis, in my opinion, is the actual reaction times in the different paradigms. For example, the lack of alteration in reach reaction time relative to saccade reaction time could reflect the fact that reach reactions times are much longer than saccade reaction times.
Response: Thank you for your comments. In accordance with your suggestion, we have changed the reaction times from the z-scores to the actual reaction times in the revised manuscript (see Fig. 2 for experiment 1 and Fig. 5 for experiment 2).
We analysed the actual reaction times to examine whether reach reaction times are much longer than saccade reaction times in the present study. Reaction times for all conditions (e.g., viewing condition in the motion direction discrimination task, motion coherence and movement direction) were averaged for saccade and for reach movements. This result showed that reach reaction times were not significantly longer than saccade reaction times in experiment 1 [ Fig. 6a; F(1, 7) = 3.47, P = 0.10], although the difference in reaction times between saccade and reach was 23.95 ms in experiment 1, as shown in Fig. 6a. This indicates that reach reaction times were not much longer than saccade reaction times. In addition, the standard deviation of reaction times was not significantly different between Saccade reaction times for the same (b) and different (c) tasks as a function of motion coherence. (d and e) Reach reaction times for the same (d) and different (e) tasks as a function of motion coherence. Solid and dashed lines are the fitted lines for the active decision-making and passive viewing conditions, respectively. Results are the mean ± standard error. n = 8.  saccade and reach [ Fig. 6b; F(1, 7) = 0.02, P = 0.89], suggesting that the lack of alteration in reach reaction times with motion coherence cannot be explained by differences in reaction time variability. On the other hand, reach reaction times were significantly longer than saccade reaction times in experiment 2 [ Fig. 6c; F(1, 10) = 45.97, P < 0.01], although the difference in reaction times between saccade and reach was 64.10 ms. The standard deviation of reaction times in experiment 2 was also significantly different between saccade and reach [ Fig. 6d; F(1, 10) = 31.26, P < 0.01]. Nevertheless, reach reaction times were modulated by motion coherence in experiment 2. These results therefore rule out the possibility that the lack of the alteration in reach reaction time relative to saccade reaction time could reflect the fact that reach reaction times are much longer than saccade reaction times. We have added this information and these new data to the revised manuscript. Results are the mean ± standard error. It may be a concern that the lack of alteration in the reach reaction time relative to the saccade reaction time reflected the fact that reach reaction times were much longer than saccade reaction times. We analysed the actual reaction times to examine whether reach reaction times are much longer than saccade reaction times.
Reaction times for all conditions (i.e., viewing condition in the motion direction discrimination task, motion coherence and movement direction) were averaged for both saccade and reach movements. Reach reaction times were not significantly longer than saccade reaction times [ Fig. 6a; F(1, 7) = 3.47, P = 0.10, BF = 1.26, = 0.33], although the difference in reaction times between saccade and reach was 23.95 ms in experiment 1, as shown in Fig. 6a. This indicates that reach reaction times were not much longer than saccade reaction times. In addition, the standard deviation of reaction times was not significantly different between saccade and reach [ Fig. 6b and "interact". For example, in lines 17-18 of the abstract, I'm not sure what the difference is between "motor actions must be related to decision formation" and "perceptual decisions also influence a motor action unrelated to decisions"? Isn't the first already implying the second? I know that you probably want to say something else, but it needs to be crystal clear very early on in the paper. The introduction does a slightly better job of first saying that sometimes, one might think that motor actions are just an output stage, but in reality there might be reach curvatures etc that reflect the internal processing. But, again, the formulation of the entire thing needs to be much more clear.
Returning back to line 43, I again see a statement like "eye movements that are decision irrelevant", but I still do not understand what is meant. I am sure it will get clearer later in the paper, but why leave it a mystery? Clarify as early as possible.
Response: Thank you for your comment. We apologise for the lack of clarity in the difference between 'motor actions must be related to decision formation' and 'perceptual decisions also influence a motor action unrelated to decisions' in the 10. Reviewer's comment: line 157: One big difference between reaches and saccades is that the reaches probably have 3x the reaction times of the saccades. So, the lack of effect could simply be because there was too much time between the motion patch and the reach.
You do not show the actual manual and saccadic reaction times, but I think you should show them. And, you should consider the possibility that the large difference in reaction time between saccades and reaches could explain your results.
Response: As we stated in our response to your first comment above (Reviewer comment #1), we have shown the actual saccade and reach reaction times in the revised manuscript (see Figs. 2 and 5). In addition, we have analysed the actual reaction times to examine whether reach reaction times are much longer than saccade reaction times (see Fig. 6). As shown in Fig. 6, the difference in reaction times between saccade and reach was 23.95 ms in experiment 1 and 64.10 ms in experiment 2. These results indicated that the reaches did not have triple the reaction times of the saccades. In addition, reaction times for all conditions (viewing condition in the motion direction discrimination task, motion coherence and movement direction) were averaged for saccade and for reach movements, and the difference in their average reaction times between saccades and reaches was analysed for both experiments 1 and 2. For experiment 1, reach reaction times were not significantly longer than saccade reaction times [ Fig 13. Reviewer's comment: line 209: but maybe reach reaction time in the dual task was longer than in the single task. i.e. when required to both reach and look, the reaction times are longer than with only reaching. Similarly for saccades.

Response:
We have analysed the difference in reaction time between the dual and single tasks ( Fig. 6a and c), and a two-way analysis of variance was performed with effectors and tasks as factors. There was a significant interaction between results rule out the possibility that the lack of the alteration in the reach reaction time in the dual task could reflect the fact that reach reactions times are much longer in the dual task than in the single task.

Main text, page 16, lines 315-325:
A possible concern is that the lack of alteration in the reach reaction time in the dual task (experiment 1) reflected the fact that reach reaction times were much longer in the dual task (experiment 1) than in the single task (experiment 2). We analysed the difference in reaction times between the dual and single tasks ( Fig. 6a and c). A two-way analysis of variance (ANOVA) was performed with effectors and tasks as factors. There was a significant interaction between effector and task 1. Reviewer's comment: Beside being roughly consistent with previous research showing a link between perceptual decision and eye movements, the take home message of the present study is, in my opinion, unclear. The discussion states that these findings shows how interactions between eye and hand motor planning can occur also when these are made during unrelated perceptual decision (why would they not?), but do not provide mechanistic explanation for the results. Overall, I find that the importance and significance of this study is not communicated clearly. Additionally, the conclusions of the authors depends on interpreting absence of evidence (null NHST tests) as evidence for absence, however it's not obvious that these non-significant tests provide evidence for the null hypothesis (they may well not, given also that the sample size is relatively small, n=11 and n=8). Finally, there is also a potential confounds (related to possible differences in response times between single and dual task conditions) that is not addressed.
Response: Thank you for your comments. In accordance with your suggestion, we have provided a mechanistic explanation for the present results in the revised manuscript. To explain our results in a mechanistic way, we have used the channel modulation hypothesis (Pesaran et al., 2021). Based on this hypothesis, we created a channel modulation model (see Fig. 7). In this model, perceptual decision making consists of the three separate systems in parallel. Each of these systems forms the communication channel to the motor system. Activity in a system of perceptual decisions drives responses in the motor system. In addition, a modulator network exists between the perceptual decision-making system and the motor system. The modulator network is triggered by motor commands from eye and/or reach movements, and activity in the modular network can change the motor system response to input from the perceptual decision system, modulating the communication channel. For example, when simultaneous eye and reach movements are made, the modulator network closes the channel from the system guiding saccade peak velocities to the motor system and the channel from the system guiding reach reaction times to the motor system (Fig. 7b). As a result, the a b The system guiding saccade reaction times Motor system

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The system guiding reach reaction times Motor response 1 Motor response 2

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The system guiding saccade peak velocities Perceptual decision-making systems c d e The system guiding saccade reaction times

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The system guiding reach reaction times

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The system guiding saccade peak velocities The system guiding saccade reaction times

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The system guiding reach reaction times

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The system guiding saccade peak velocities The system guiding saccade reaction times

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The system guiding saccade peak velocities Reward reflected by saccade reaction times Each of these systems forms the communication channel to the motor system. Activity in a system of perceptual decisions drives responses in the motor system. The modulator network is triggered by motor commands from saccade and/or reach movements, and activity in the modular network can change the motor system response to input from the perceptual decision system. (b) Channel modulation during simultaneous saccades and reaches. (c) Channel modulation during saccades. (d) Channel modulation during reaches. (e) The three separate systems of perceptual decision making are related to the expected reward or value associated with a perceptual decision and the ability to have confidence in a perceptual decision.
perceptual decision-making process only affects saccade reaction times (see the Discussion section in the revised manuscript for details). Thus, the present study suggests that the concept of communication channel modulation between the perceptual decision-making system and the motor system may be the key to understanding the mechanisms underlying the link between decision-related activity and decision-unrelated motor processes.
In addition, in response to your suggestion, we have used Bayes factors/equivalence tests to quantify support for the null hypothesis of no significant difference between conditions. For more information, please see our response to Reviewer comment #7 below.
Finally, we have analysed the differences in response times between the single-and dual-task conditions. For more information, please see our response to Reviewer comment #2 below.

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To provide a mechanistic explanation for these complicated results, we consider the channel modulation hypothesis 19 . According to this hypothesis, the communication channel is formed from projections from the perceptual decisionmaking system to the motor system ( Fig. 7a). As a result, activity in the perceptual decision-making system affects responses in the motor system. In addition, a modulator network is placed between the perceptual decision-making system and the motor system. The modulator network works through motor commands from eye and/or reach movements. Activity in the modulator network can alter the motor system response to input from the perceptual decision-making system, modulating the communication channel. Such a channel modulation can produce changes in reaction times and peak velocities for movements by opening the channel that communicates perceptual decision signals to guide a motor response (e.g., saccades) or by closing the channel that communicates perceptual decision signals to guide a different motor response (e.g., reaches).
The present complicated results can be explained by making two assumptions regarding the channel modulation hypothesis (Fig. 7a). First, we assume that perceptual decision-making occurs in three separate systems: (i) the system guiding saccade reaction times, (ii) the system guiding reach reaction times, and (iii) the system guiding saccade peak velocities. Therefore, three communication channels are formed from projections from each of these three systems to the motor system. Second, we assume that a modulator network operates differently depending on the movement task. When simultaneous eye and reach movements are made, the modulator network closes two of the three communication channels: the channel from the system guiding saccade peak velocities to the motor system, and the channel from the system guiding reach reaction times to the motor system (Fig. 7b).
As a result, the perceptual decision-making process only affects saccade reaction times. When a saccade without a reach is made, the modulator network closes the channel from the system guiding reach reaction times to the motor system (Fig. 7c).
As a result, the perceptual decision-making process affects the reaction times and peak velocities of the saccade. When a reach without a saccade is made, the modulator network closes two channels: the channel from the system guiding saccade reaction times to the motor system, and the channel from the system guiding saccade peak velocities to the motor system (Fig. 7d). As a result, the perceptual decision-making process affects reach reaction times.
In addition, we speculate that the three separate systems of perceptual decision making described above may be related to the expected reward or value associated with a judgement and the ability to have confidence in a judgement ( Fig. 7a and e).
Saccade and reach reaction times have been reported to reflect the expectation of the reward or value associated with the movement target 33, 34 . Meanwhile, saccade peak velocities have been reported to reflect the degree of certainty with which a perceptual decision is made (i.e., confidence in a decision) 32 , although an influence on saccade peak velocities from the reward or value associated with the saccade target has been demonstrated in many studies [40][41][42] . Given that reaction time and peak velocity reflect different features of perceptual decisions, our findings suggest that simultaneous saccade and reach movements may be involved in suppressing the channel related to decision confidence in the oculomotor circuitry and the channel related to the expectation of a reward or the value in the manual circuitry, and may interact only with the channel related to the expectation of a reward or the value in the oculomotor circuitry. Thus, the concept of communication channel modulation between the perceptual decision-making system and the motor system may be a key to understanding the mechanisms underlying the link between decision-related activity and decision-unrelated motor processes.
2. Reviewer's comment: Was the mean response times (for either saccades and hand reaching) different in the single and dual experiment different? Currently only z-scored times are reported, so this is unclear. I would expect that these may be larger in the dualtask experiment (exp. 1) compared to the exp. 2, and their variance may be larger too. If that is the case, perhaps one complication in interpreting the current results is that the small interference effect due to the perceptual decision simply becomes harder to detect in such conditions?
Response: Thank you for your comment. Yes, the mean response times differed between the single-and dual-task experiments for both saccades and reaches (Fig.   6). Surprisingly, however, contrary to your expectation, the mean response times were significantly larger in the single-task experiment than in the dual-task experiment for both saccades and reaches [F(1, 17) = 66.93, P < 0.01 for saccades; F(1, 17) = 76.11, P < 0.01 for reaches]. On the other hand, the mean standard deviations of reaction times were not significantly different between the dual-and single-task experiments for both saccades and reaches [F(1, 17) = 1.72, P = 0.21, BF < 0.73 for saccades; F(1, 17) = 2.61, P = 0.12, BF < 0.97 for reaches]. Thus, these results rule out the possibility that the small interference effect due to the perceptual decision simply becomes harder to detect in the dual-task experiment compared with the single-task experiment. We have added these descriptions to the revised manuscript. A possible concern is that the lack of alteration in the reach reaction time in the dual task (experiment 1) reflected the fact that reach reaction times were much longer in the dual task (experiment 1) than in the single task (experiment 2). We analysed the difference in reaction times between the dual and single tasks ( Fig. 6a and c). A two-way analysis of variance (ANOVA) was performed with effectors and tasks as factors. There was a significant interaction between effector and task 0.80]. Thus, these results rule out the possibility that the lack of alteration in the reach reaction time in the dual task could reflect the fact that reach reactions times are much longer in the dual task than in the single task.
Another concern may be that the lack of alteration in the reach reaction time in the dual task (experiment 1) reflected the fact that the variance of reach reaction times was larger in the dual task (experiment 1) than in the single task (experiment 2).
We analysed the difference in the mean standard deviation of reaction times between the dual and single tasks ( Fig. 6b and d) to necessarily say that this is not interesting or important -it may well be -but I think the paper fails to convey why studying this is important/interesting. I think the authors need to do explain more clearly the rationale and scope of the study.
Response: Thank you for raising this important point. As you pointed out, there is no evidence that a similar interference effect occurs for reach movements. In our manuscript, therefore, we considered it necessary to state the hypothesis that a similar interference effect would occur for reach movements. To derive this hypothesis, we introduced a neurophysiological study (de Lafuente et al., 2015) showing that perceptual judgement-related activity arises not only in oculomotor brain areas (e.g., LIP), but also in manual brain areas (e.g., MIP To address this issue, we need to test hypothesis 2. Testing of hypothesis 2 would reveal whether interference between perceptual judgements and judgementirrelevant motor actions is observed in reach movements without eye movements. Therefore, the fact that both hypotheses 1 and 2 are true would suggest that perceptual judgements interfere more with eye movements than with reach movements when simultaneous judgement-irrelevant eye and reach movements are made. These results will provide clues for understanding the mechanisms of communication across motor systems during perceptual decision making 19 .  Furthermore, you pointed out that additional confusion was caused by the fact that the overall question seemed to be less about the impact of decision processes on irrelevant actions, but on which action was prioritised. In accordance with your suggestion, we have clearly stated the relevance of each alternative outcome in the revised manuscript (see lines 95-109).

Main text, page 3, line 29 to page 6, line 109 (introduction):
Studies of perceptual judgements depend on the ability to make inferences about covert cognitive states. To infer such covert cognitive states, overt motor actions are commonly used. Perceptual judgements and motor actions are often modelled as serial stages of processing. In a perceptual judgement task, it is often assumed that first a perceptual judgement is completed and then the subsequent motor output is planned and executed 1, 2 . For example, saccadic eye movements are made after a decision about where to move the eyes based on sensory information.
However, the accumulated literature indicates that motor actions are continuously affected by ongoing perceptual judgement processes that are not yet complete 3, 4 , suggesting an interaction between perceptual judgements and motor actions. In a variety of reach movement tasks, the trajectories of reach movements have been shown to be modulated by a target selection process in visual search 5 , a lexical decision process 6 and the magnitude of a single Arabic numeral 7, 8 . These findings indicate that reach movements are not always the final product of perceptual judgements and that ongoing perceptual judgements continuously affect reach movements, suggesting a continuous interaction between perceptual judgements and reach movements.
Furthermore, the trajectories of saccadic eye movements also elicit systematic deviations in saccade curvature and endpoints when saccadic eye movements are used to report judgements in a perceptual judgement task 9 , indicating that oculomotor output can also be continuously affected by ongoing perceptual judgements. A recent study has demonstrated that saccades are not yet ready to launch when perceptual decision processes terminate 10 , suggesting that perceptual decisions and oculomotor responses rely on temporally distinct streams of evidence.
These findings imply a continuous interaction between perceptual judgements and saccadic eye movements 11 , like reach movements.

Continuous interactions between perceptual judgements and motor actions may be
based on interference of signals in neural circuits. Neural responses in oculomotor brain circuits (e.g., the lateral intraparietal area [LIP]) have been reported to show heterogeneous selectivity for different sources, such as the formation of perceptual judgements and the execution of eye movements, within the same neurons 12-16 .
Neurons in manual brain circuits (e.g., the medial intraparietal area [MIP]) have also been reported to show selectivity for both the formation of perceptual judgements and the execution of reach movements 17 . Thus, the interference of signals related to the formation of perceptual judgements and motor execution in motor brain areas seems to provide a neural basis by which these multiple signals can continuously interact with each other.
Interestingly, interference of perceptual judgement-related signals and judgementirrelevant saccade responses has also been observed in the LIP of monkeys 12-16 .
This neurophysiological observation has been supported by a recent human behavioural study in which the formation of perceptual judgements affected saccadic eye movements, even when the saccadic eye movements were irrelevant to the perceptual judgement task 18 . Thus, the effects of perceptual judgements on judgement-irrelevant motor actions may be considered a side effect of signal interference in motor brain areas.
However, it is not known how the signal interference occurs in dual-task paradigms such as simultaneous eye and reach movements. Such paradigms offer the opportunity to investigate how perceptual judgement-related signals flow between motor systems, which helps to explain the mechanisms of communication across We also found that perceptual judgements did not affect saccade peak velocities when simultaneous judgement-irrelevant saccade and reach movements were made.
No modulation of saccade peak velocities by motion strength was observed in the dual-movement task ( Fig. 3a and b). However, saccade peak velocities were modulated by motion strength in the single-movement task (Fig. 5e). These results indicate that, although perceptual decision-making processes can interfere with the oculomotor system that influences saccade peak velocity, this interference disappears when simultaneous saccade and reach movements are made. This suggests that simultaneous saccade and reach movements are involved in preventing the interference between perceptual decision making and saccade velocity.
In contrast, we found that perceptual judgements did not affect reach peak velocities, regardless of whether reaches were made with or without saccades. No modulation of reach peak velocities by motion strength was observed in both dualand single-movement tasks ( Fig. 3c and d for the dual task; Fig. 5f for the single task). These results suggest that perceptual decision-making processes themselves do not interfere with the manual system that influences reach peak velocity.
(Text partly omitted) Overall, our results show the following: (i) perceptual decision-making processes interfere more with saccade reaction times than with reach reaction times when simultaneous judgement-irrelevant saccade and reach movements are made; (ii) perceptual decision-making processes interfere with reach reaction times when judgement-irrelevant reach movements are made without saccades; (iii) perceptual decision-making processes do not interfere with saccade peak velocities when simultaneous judgement-irrelevant saccade and reach movements are made; and (iv) perceptual decision-making processes do not interfere with reach peak velocities regardless of whether reach movements are made with or without saccades. These findings suggest that perceptual decision-related signals flow between the oculomotor and manual systems in a complicated way.
2. Reviewer's comment: Interpretation of results: my main concern is with the variability in individual data and the fact that some subjects appear to be at chance performance even at the highest coherence level. How can such results be interpreted? See also more detailed comments re. statistical analysis and reporting below.
Response: Thank you for raising this important point. To address this issue, we analysed how perceptual decision accuracy (i.e., motion direction discrimination accuracy) affects saccade reaction times, reach reaction times and saccade peak velocities. The low accuracy of a perceptual judgement is believed to reflect perceptual decisions driven by weaker sensory evidence (Shadlen & Kiani, 2013).
This suggests that participants who have near chance performance at the highest motion coherence level make perceptual judgements based on such weak sensory evidence. Therefore, we expected that decision-irrelevant saccade and reach movements would be less influenced by perceptual decisions if participants had near chance performance at the highest motion coherence level. As expected, these participants had less modulation of saccade and reach reaction times and saccade peak velocities by motion coherence than participants who had high performance at the highest motion coherence level ( Supplementary Fig. 7). Although these results show individual variabilities in motion sensitivity, we believe that these results are also consistent with an explanation that active perceptual decisionmaking processes affect decision-irrelevant motor actions.
The details of the analysis are as follows. In this analysis, the degree of the modulation of reaction time and velocity by motion coherence (we refer to this degree as the modulation index) was calculated as the slope of the reaction time and velocity against motion coherence, respectively (see the caption of the figure below for more details). The modulation indices were classified into high-and lowaccuracy groups. The high-accuracy group consisted of participants with 75% or more perceptual accuracy at the highest motion coherence level. We found that participants in the low-accuracy group had a significantly lower modulation index than participants in the high-accuracy group for saccade reaction times, reach reaction times and saccade peak velocities (Supplementary Fig. 7; t16 = −3.60, P < 0.01 for saccade reaction times; t6 = −2.45, P < 0.05 for reach reaction times; t6 = 2.35, P < 0.05 for saccade peak velocities). Reach reaction time. (c) Saccade peak velocity. The saccade reaction time data were collected from experiments 1 and 2. The reach reaction time data were collected from experiment 2. The saccade peak velocity data were collected from experiment 2. For the saccade movement data in experiment 1, saccade reaction times for the same and different conditions were averaged for each motion coherence. For each of the saccade and reach movement data in experiment 2, reaction times for the short-and long-duration conditions were averaged for each motion coherence. Saccade peak velocities for the short-and longduration conditions were averaged for each motion coherence. The degree of modulation of reaction time and velocity by motion coherence (the modulation index) was calculated as the slope of the reaction time and velocity against motion coherence, respectively. A positive value of the modulation index represents an increase in motor performance with motion coherence. The modulation indices were classified into high-accuracy and lowaccuracy groups. The high-accuracy group consisted of participants with 75% or more perceptual accuracy at the highest motion coherence level. Each circle symbol represents a different participant. Bars represent the mean ± standard error (saccade reaction times: n = 12 for the high-accuracy group; n = 7 for the low-accuracy group; reach reaction times and saccade peak velocities: n = 7 for the high-accuracy group; n = 4 for the low-accuracy group). For statistical evaluation, a t-test of the group mean data was performed.

Supplementary
We have added these descriptions to the revised manuscript and the Supplementary   Information.

Main text, page 22, lines 444-463:
Our results showed that there were individual variabilities in motion direction discrimination accuracy ( Supplementary Figs. 1 and 4). Several participants had near chance performance even at the highest motion coherence. Given that such a low accuracy of motion direction discrimination judgements reflects perceptual decisions driven by weaker sensory evidence 39 , it is possible that these participants may have a smaller influence of motion direction discrimination judgements on judgement-irrelevant saccade and reach movements. To test this possibility, we analysed how motion direction discrimination accuracy affects saccade reaction times, reach reaction times and saccade peak velocities. In this analysis, the degree of modulation of reaction time and velocity by motion coherence (we refer to this degree as the modulation index) was calculated as the slope of reaction time and velocity against motion coherence, respectively (see the caption of Supplementary   Fig. 7 for more details). The modulation indices were classified into high-accuracy and low-accuracy groups. The high-accuracy group consisted of participants with 75% or more perceptual accuracy at the highest motion coherence level. We found that participants in the low-accuracy group had a significantly lower modulation index than participants in the high-accuracy group for saccade reaction times, reach For the saccade movement data in experiment 1, saccade reaction times for the same and different conditions were averaged for each motion coherence. For each of the saccade and reach movement data in experiment 2, reaction times for the short-and long-duration conditions were averaged for each motion coherence.
Saccade peak velocities for the short-and long-duration conditions were averaged for each motion coherence. The degree of modulation of reaction time and velocity by motion coherence (the modulation index) was calculated as the slope of the reaction time and velocity against motion coherence, respectively. A positive value of the modulation index represents an increase in motor performance with motion coherence. The modulation indices were classified into high-accuracy and lowaccuracy groups. The high-accuracy group consisted of participants with 75% or more perceptual accuracy at the highest motion coherence level. Each circle symbol represents a different participant. Bars represent the mean ± standard error (saccade reaction times: n = 12 for the high-accuracy group; n = 7 for the lowaccuracy group; reach reaction times and saccade peak velocities: n = 7 for the high-accuracy group; n = 4 for the low-accuracy group). For statistical evaluation, a t-test of the group mean data was performed.
3. Reviewer's comment: l.32: please consider replacing "generally" with "often". Many recent studies (as in: published in the last 15 years) do not follow this simple serial model.

Response:
We have replaced 'generally' with 'often' in the revised manuscript. Thank you for the suggestion.
Main text, page 3, line 32: In a perceptual judgement task, it is often assumed that 4. Reviewer's comment: p.40: this is a nice summary and is consistent with literature on eye movements during decision making, see this recent review, which the authors could consider citing: https://pubmed.ncbi.nlm.nih.gov/35676097/ Response: Thank you for letting us know about this recent well-written and pertinent review. We have cited this article in the revised manuscript accordingly.

Main text, page 4, lines 51-52:
These findings imply a continuous interaction between perceptual judgements and saccadic eye movements 11 , like reach movements.
5. Reviewer's comment: Suppl. Figure 1 (and others): I'm intrigued by the fact that several subjects appear to perform at around chance even at the highest level of coherence. The variability in the data is enormous, likely owing to individual variabilities in motion sensitivity. Why did the authors choose a constant stimulus design (and why these particular coherence levels) rather than a threshold procedure, which would have accounted for this? As such, it seems that data for observers who perform at chance can hardly be interpreted.

Response:
You are completely correct. The variability in the data is likely due to individual variabilities in motion sensitivity. 6. Reviewer's comment: Figure 2: fitted lines / model fits seem poor and are particularly misleading for reach reaction times. Why is a linear model used here?
Response: Previous studies using a motion discrimination task in which a saccade was made in the perceived motion direction showed that saccade reaction times fit well to a linear model (Roitman & Shadlen, 2002;Joo et al., 2016). For that reason, we used a linear model. As you pointed out, the fitted lines in Fig. 2 seemed poor for reach reaction times. Although we used z-scores in the previous version, we have changed the reaction times from z-scores to the actual reaction times based on the comments from all reviewers. Compared with the z-scores, the fitted lines seem better for the actual reach reaction times (see Fig. 2 in the revised manuscript).
We have added a reason for the use of a linear model to the revised manuscript.   were interactions (effect on latencies in the active vs. passive task in saccades but not reaches). Moreover, some of the p-values are pretty borderline, yet are interpreted alongside much clearer results as indicating "no effect". Please consider supplying effect sizes so the reader can gage the magnitude and meaning of these reported null effects.

Response:
We apologise for the confusion and thank you for your comment. None of these results was obtained with separate F-tests/repeated-measures ANOVAs.
We had already performed a repeated-measures ANOVA with two viewing conditions and five motion strengths as factors. performed with two duration conditions (100 ms and 400 ms) and five motion coherence levels (3%, 6%, 12%, 24% and 48%) as factors. In Figure 6 interpretation is based on: "We found that simultaneous decision-irrelevant saccade and reach movements suppress the modulation of saccade peak velocities, but not saccade reaction times, by perceptual decisions". Where is the evidence for an inhibitory process here? The authors observe differential effects on saccades and reaches, and differential effects on latency and peak velocity (though this has to be confirmed in a model that includes all these factors in one analysis). But this is not evidence of an inhibitory process per se. We also found that perceptual judgements did not affect saccade peak velocities when simultaneous judgement-irrelevant saccade and reach movements were made.
No modulation of saccade peak velocities by motion strength was observed in the dual-movement task ( Fig. 3a and b). However, saccade peak velocities were modulated by motion strength in the single-movement task (Fig. 5e). These results indicate that, although perceptual decision-making processes can interfere with the oculomotor system that influences saccade peak velocity, this interference disappears when simultaneous saccade and reach movements are made. This suggests that simultaneous saccade and reach movements are involved in preventing the interference between perceptual decision making and saccade velocity.
In contrast, we found that perceptual judgements did not affect reach peak velocities, regardless of whether reaches were made with or without saccades. No modulation of reach peak velocities by motion strength was observed in both dualand single-movement tasks ( Fig. 3c and d for the dual task; Fig. 5f for the single task). These results suggest that perceptual decision-making processes themselves do not interfere with the manual system that influences reach peak velocity.
10. Reviewer's comment: Methods: even though this might not have been a concern with the overall finding, it would be helpful to report how stable fixation was during the presentation of the motion stimulus. This type of stimulus typically elicits strong drift or even pursuit. Was this the case here?
Response: That was not the case here. In accordance with your suggestion, we have analysed how stable fixation was during the presentation of the motion stimulus. In this study, participants were instructed to keep their gaze on the fixation point during the presentation of the motion stimulus. The direction of motion was up or down. If the motion stimulus elicited strong eye drift, the direction of the eye drift would change greatly, depending on the motion direction.
The analysis showed that there was no significant difference in the eye drift between the upward and downward motion directions (t19 = −0.45, P = 0.66, d = 0.0066). This result indicates that participants' fixation was stable during the presentation of the motion stimulus (see Supplementary Fig. 8). We have added this information to the revised manuscript and have added Supplementary Fig. 8 Fig. 8).
Supplementary Information, page 9, Supplementary Figure 8: Supplementary Figure 8. Effects of motion direction on eye drift during the presentation of a motion stimulus. Bars represent the mean ± standard error. A positive value of the drift represents the upward direction of the drift. In this study, participants were instructed to keep their gaze on the fixation point during the presentation of the motion stimulus. The fixation point was presented at the centre of the motion stimulus. The direction of motion was up or down. The viewing durations of the motion stimulus were 100 ms in experiment 1 and 100 or 400 ms in experiment 2. We analysed how much the eyes drifted during the presentation of the motion stimulus for experiments 1 and 2. If the motion stimulus elicits strong eye drift, the direction of the eye drift should greatly change depending on the direction of the motion stimulus. There was no significant difference in eye drift between the upward and downward motion directions (t18 = −0.45, P = 0.66, d = 0.0066). These results indicate that the participants' fixation was relatively stable during the presentation of the motion stimulus. For statistical evaluation, a paired t-test of the group mean data was performed. n = 19.  . 4a and c). …. (Fig. 4b and d). regions. While I agree that this seems an appropriate framework, in discussing the present results the authors introduce ad-hoc assumptions arbitrarily and this in my opinion greatly reduce the value of this explanation. Firstly, it is not clear to me what is meant with the assumption that 'perceptual decision-making system occurs in the systems guiding saccade reaction times, reach reaction times, and saccade peak velocity'? Perhaps more importantly, the second assumption ("we assume that a modulator network operates differently depending on the movement task") is pivotal to explaining the result but there is not discussion of its generality or plausibility; it seems introduced ad-hoc to explain the current results. As a result, the whole explanatory mechanism postulated here appears to be a restatement of the findings using different terms borrowed from the channel modulation hypothesis. What is this modulator network, and why it would behave in this way? And more generally, can this mechanisms be used to provide new insight or predictions? Unless these issues are clarified, I think there is no point in making the explanatory account so detailed -it just appear speculative and not very useful-and it may instead be preferable to just mention that these type of interactions (in behaviour) could be the result of channel modulations in multiregional communication.
Response: Thank you for your comment. As you say, we think that it is difficult to clarify the issues that you pointed out. According to your suggestions, we have just stated that the types of interactions in behaviour could be the result of channel modulations in multiregional communication in the revised manuscript. We have also removed Figure 7 from the revised manuscript. Thank you.
Main text, page 24, line 503 to page 25, line 516: These complicated results may be explained based on the channel modulation hypothesis 19 . According to this hypothesis, the communication channel is formed from projections from the perceptual decision-making system to the motor system.
As a result, activity in the perceptual decision-making system affects responses in the motor system. In addition, a modulator network is placed between the perceptual decision-making system and the motor system. The modulator network works through motor commands from eye and/or reach movements. Activity in the modulator network can alter the motor system response to input from the perceptual decision-making system, modulating the communication channel. Such a channel modulation could produce changes in reaction times and peak velocities for movements by opening the channel that communicates perceptual decision signals to guide a motor response (e.g., saccades) or by closing the channel that communicates perceptual decision signals to guide a different motor response (e.g., reaches  (Rouder et al., 2012;Morey et al., 2022), γ values of 0.5, 0.707, and 1.0 correspond to "medium", "wide", and "ultrawide" widths, respectively. Therefore, to analyze Supplementary Figure 4. Bayes factor (BF) as a function of the width of the prior for reach peak velocity. The BF value is the average of 3 iterations of the Markov chain Monte Carlo method with a maximum of 10,000 estimates. The dotted line represents a BF value of 100. To analyze how the BF changes as a function of the width of the prior, we varied the width of the prior from 0.01 to 1. As a result, the BF value decreased significantly when the width of the prior was less than 0.4. However, even though the width of the prior was set to 0.01, the BF was still 120.05. This suggests that the disagreement between p-value and BF for reach peak velocities holds for a wide range of the width of the prior from 0.01 to 1. Results are the mean ± standard error.
how the BF changes as a function of the width of the prior, we varied the γ value from 0.01 to 1. As a result, the BF depended on the width of the prior (see the figure above). Indeed, the BF value decreased greatly when the width of the prior was less than 0.4. However, even though the width of the prior was set to 0.01, the BF was still 120.05. This suggests that the disagreement between p-value and BF for reach peak velocities holds for a wide range of the width of the prior from 0.01 to 1. We have added these descriptions to the revised manuscript and the Supplementary Information.

Main text, page 13, line 249:
(see Supplementary Fig. 4 for the dependence of the BF10 on prior width)

Main text, page 32, lines 676-683:
Bayes factors (BFs) were calculated using an R package for BF analysis 54, 55 . In this package, Cauchy distribution was used as a prior distribution. Except that the scale setting for the prior distribution was set to 0.5, various settings followed the defaults of the package. The maximum number of estimations by the Markov chain Monte Carlo method was 10,000. Following the conventional scales for interpreting BF, cases with a BF less than 3.2 were rated as providing inconclusive evidence of the null or alternative hypothesis 56, 57 . BF01 and BF10 represent indications of null and alternative hypothesis dominance, respectively. However, even though the width of the prior was set to 0.01, the BF was still 120.05.
This suggests that the disagreement between p-value and BF for reach peak velocities holds for a wide range of the width of the prior from 0.01 to 1. Results are the mean ± standard error.
3. Reviewer's comment: additionally, regarding the Bayes factors: if the BF is close to 1, this means that the data are equally likely under the null and alternative hypothesis -in other words, the result of the test is ambiguous/inconclusive and does not provide clear evidence for the null nor alternative hypothesis. This is the case for some tests in the paper -for example see line 172, the BF is 1.04, indicating that the data is equally likely under the null and alternative, however the results is interpreted as evidence for null effect (in this case "indicating that congruency … did not affect psychophysical performance").
This is also the case in other places, e.g. line 333, BF=0.97, taken as evidence that the SD were not different in the two conditions. These tests should be presented and discussed as providing ambiguous or inconclusive evidence, rather than as clear evidence for null or alternative. I would suggests that the author adopt one of the conventional scales for interpreting BF, such as the one provided by Jeffreys (1988), in which the strength of evidence is considered to be "barely worth mentioning" if the BF (or its inverse if we are quantifying the evidence for the null hypothesis) is less than 3.2.
Response: Thank you for giving us the important information about the conventional scales for interpreting BF. Following your suggestion, in the revised manuscript we have stated that cases with the BF less than 3.2 do not provide conclusive evidence for the null or alternative hypothesis.
Main text, page 9, lines 176-178: However, Bayes factor analysis did not provide conclusive evidence for the null hypothesis that the psychometric functions were the same between the two tasks and on the other hand saccade reaction times can also reflect the degree of certainty with which a perceptual decision is made (i.e., confidence in a decision) 40,41 .
Main text, page 25, lines 525-527: Although it is unclear whether reaction time and peak velocity reflect different or similar features of perceptual decisions, Responses to evaluation of author's rebuttal to Reviewer 3 comments 1. Reviewer's comment: Approach & logic. As I mentioned above, I think the revised version of the paper has improved substantially in the clarity with which the research question is introduced and motivated, thanks to some rewording and additions. While I think the paper could still improve in terms of relating the present findings to the bigger picture of sensorimotor decision-making, I think overall the authors have addressed this point adequately.
Response: Thank you.
2. Reviewer's comment: Interpretation of results. The reviewer here raised a very important point, which I had missed in my own evaluation -that some participant's performance was at or near chance in the perceptual task. The authors replied providing additional analyses that shows how that effect they report are seen only (or nearly only) in participants who achieved 75% or more correct responses in the perceptual task. I think this additional analysis clarify the issues with interpretation of the results, although it remains unclear why a relatively large number of participants was at/near chance. Is it possible that these participants were prioritizing the movement task over the perceptual decision task, perhaps because they found it more challenging or engaging?" Response: Yes, we think that it's possible. As you pointed out, those participants may have found it difficult to move their eye and/or hand quickly in the movement