Introduction

Decision making – both perceptual and value-based – is shaped by the information that we sample from the environment. Information sampling is not a passive process but is instead determined by where we decide to look. We actively fixate the eyes on objects that we might act upon, and it is well-established that these fixations can influence the eventual choices we make (Cavanagh et al., 2019; Eum et al., 2023; Gluth et al., 2020; Shimojo et al., 2003; Smith & Krajbich, 2019). However, it has long been recognized that information can be processed covertly as well as overtly, and that shifts in covert attention can precede – as well as occur independently of – overt eye movements (Buschman & Miller, 2010; Carrasco, 2011; Li et al., 2021; Posner, 1980; Yeshurun & Carrasco, 1998, 1999). In other words, covert attention might facilitate evidence accumulation even at locations that are not currently fixated, and in turn influence the eventual decision made.

Despite its potential importance, the interplay between covert attention, overt fixation, and decision-making remains poorly understood. This is because covert attention has been difficult to index directly. For example, one popular and widely-used model of choice, the attentional drift diffusion model (aDDM), uses fixation data to make implicit claims about the processing of unfixated – and thus, potentially covertly attended – options during evidence integration and choice (Eum et al., 2023; Krajbich et al., 2012; Krajbich & Rangel, 2011; Yang & Krajbich, 2023). The aDDM captures many features of the relationship between overt attention, reaction times and choices. Strikingly, however, it proposes that unfixated options are downweighted using a single static parameter – held constant across all trials, all timepoints, and all peripheral options. In other words, the level of covert attention is assumed not to vary over space nor time. This common assumption is a necessary consequence of there being no behavioral index (to date) of how covert attention might vary during choice.

In this study, we introduce an attentional probe paradigm to directly measure covert attention to peripheral options during free-viewing choice; incorporating this paradigm (Dugué et al., 2015; Gaspelin et al., 2015) into a free-viewing choice task allows us to ask how attention to both fixated and unfixated options is dynamically modulated throughout the decision process. Our results reveal key insights into the relationship between covert attention, overt fixations, and choice. First, they demonstrate that covert attention is shaped by decision-relevant factors such as option value and choice-relevance, as well as a competitive relationship with overt attention, whereby increased covert attention to high-value peripheral options comes at the expense of attention to the overtly fixated location. Control analyses found that the covert attention indexed by our task was dissociable from presaccadic attention. Finally, we show that covert attention has downstream consequences for choice behavior, attenuating the effect of fixation-related choice biases. These results provide a foundation for the study of dynamic shifts in covert attention during choice.

Results

2.1 Choice task with attention probes

We designed a task to directly index covert attention as participants freely saccaded and chose between options presented at different locations on the screen. Participants completed a choice task with simultaneous eye-tracking, where they freely saccaded and chose between differently valued patches to earn rewards. To behaviorally index covert attention during the decision, we used a secondary probe detection task (Dugué et al., 2015; Gaspelin et al., 2015) in which probe letters were momentarily flashed at the spatially distinct patch locations. This allowed us to ask how covert attention – indexed by probe detection – at each location is influenced by factors such as the value, choice-relevance, and visibility of peripheral options, as well as how such covert attention influences choice downstream.

In this task, participants’ goal was to choose the patch that contained the most dots of a designated target colour, and doing so earned them a reward on that trial (Figure 1). As fixation effects on valuation and choice are essentially identical between food-based (subjective value) and dot-based (objective value) choice tasks (Sepulveda et al., 2020), we considered it appropriate to use a dot-based task to assess interactions between attention, valuation and choice. This allowed us to more directly manipulate objective value compared to choices between options with variable subjective values (e.g., snack foods).

Items were either presented in a fixation-contingent manner (i.e., non-fixated items were hidden) or were presented simultaneously (i.e., non-fixated items were visible) (Figure 1). These two conditions build directly upon the findings of Eum et al. (2023), who previously used this design to show that non-fixated information has a greater influence on participants’ choices when it remains visible rather than hidden (but did not index covert attention directly, as in the present study).

Figure 1:

Together, these elements comprised the incentivized primary choice task that participants had to complete – sampling information between the available locations via eye-gaze, and choosing the location with more goal-relevant dots. In Experiment 1 (N = 31), participants chose between two options, but we included a third, equidistant location that contained no decisionrelevant information during the trial, to serve as a choice-irrelevant control location. In Experiment 2 (N = 30), the third location was instead a valid choice option.

After training participants on this primary choice task, we integrated a secondary attentional probe task which allowed us to directly probe participants’ covert attention (Dugué et al., 2015; Gaspelin et al., 2015). While participants completed the primary choice task, we momentarily flashed probe letters for 150 ms at each of the three onscreen patches simultaneously. The timing of the probe presentation was saccade-contingent, occurring shortly after participants visited their 1^st, 2^nd, or 3^rd patch (probes appearing following the 3^rd patch existed in Experiment 2 only). Immediately after completing the primary choice task on each trial, participants were asked to report as many of the probe letters as possible (Figure 1, probe report). The accuracy of probe reports allowed us to index attention towards the fixated option (overt attention), unfixated option (covert attention), and irrelevant location (also covert attention) on the screen, and relate this to (i) the value of options presented; (ii) the visibility of unfixated option/s (i.e. the hidden vs. visible conditions); (iii) the participant’s choice on each trial.

2.2 Covert attention is dynamically shaped by decision-relevant factors

2.2.1 Covert attention is value-modulated, and competes with the overtly fixated location

We first asked if attention at both the currently fixated and peripheral options was modulated by their relative value, operationalized by the difference in proportion of target-colour dots of the peripheral option relative to the fixated option.

To this end, we examined probe report accuracy at the covertly attended, unfixated option. As shown in Figure 2C-D, the likelihood of correct probe-letter report for the relevant unfixated option increased, as that option’s relative value compared to the fixated option increased. This was true in both Experiment 1 (Figure 2C; main effect of unfixated option’s value relative to fixated: β = 0.24, CI_95% [0.095, 0.384], SE = 0.074, z = 3.24, p = .001) and Experiment 2 (Figure 2D; main effect of unfixated option’s value relative to fixated: β = 0.43, CI_95% [0.277, 0.585], SE = 0.079, z = 5.49, p < .001).

Figure 2:

We then examined whether probe report accuracy at the fixated option was also modulated by this relative value. In Experiment 1, we found a significant main effect of relative value (value of unfixated option minus value of fixated option; β = -0.52, CI_95% [-0.831, -0.217], SE = 0.157, z = -3.34, p < .001) on probe report correctness of the fixated option, as shown in Figure 2E. Similarly, in Experiment 2, we found a significant main effect of relative value (mean value of the two unfixated options minus value of fixated option; β = -0.88, CI_95% [-1.164, -0.587], SE = 0.147, z = -5.95, p < .001), as shown in Figure 2F.

The full model for both these analyses additionally included peripheral option visibility, probe timing condition, and their interactions with relative value as the regressors (for full model specification and results, and disaggregated versions of Figures 2C-F, see Supplementary Tables S1–S2 and Figure S1). We found mixed results regarding the contribution of peripheral option visibility and probe timing on peripheral probe report accuracy. In Experiment 1, the value modulation effect increased from the 1^st to 2^nd visit (relative value x probe timing interaction: β = 0.28, SE = 0.162, z = 3.24, p = .001), but this interaction between relative value and probe timing was not significant in Experiment 2 (p’s > .23). Experiment 2 found that value modulation of peripheral probe reports was weaker when peripheral options were hidden (relative value x visibility condition: β = -0.28, SE = 0.098, z = -2.85, p = 0.004), and that this interaction diminished from the 2^nd to 3^rd visit (β = 0.31, SE = 0.13, z = 2.50, p = .014). Hiding the peripheral option, however, did not affect the value modulation of peripheral probe reports in Experiment 1 (p = .699). We note that this was possibly due to the standalone value of options being correlated with its relative value in Experiment 1 (but not in Experiment 2), such that participants could have inferred the relative value of an option before having seen the peripheral option’s value.

Similarly, we found mixed evidence for the effects of peripheral option visibility and probe timing on probe report accuracy at the fixated option (Supplementary Tables S3–S4). Across both experiments, fixated probe reports became more accurate from the 1^st to 2^nd visit (Exp 1: β = 0.60, SE = 0.21, z = 2.85, p = .004; Exp 2: β = 0.52, SE = 0.164, z = 3.16, p = .002); and from the 2^nd to 3^rd visit in Experiment 2 (Exp 2: β = 0.51, SE = 0.187, z = 2.73, p = .006). In Experiment 2, we found that value modulation effect on the fixated option was weaker when the peripheral option was hidden (β = -0.50, SE = 0.176, z = -2.86, p = .004); but this effect was nonsignificant in Experiment 1 (β = -0.12, SE = 0.12, z = -0.96, p = .340).

To separate the effects of the fixated and unfixated values on probe response accuracy, we replicated the value modulation findings using separate regressor terms for each option’s value, rather than using relative value as a regressor (see Supplementary Tables S5–S6 for full model specification). In both experiments, an unfixated option’s value had a positive effect on the likelihood of correctly reporting the probe appearing there (main effect of unfixated option value; Experiment 1: β = 0.323, CI_95% [0.122, 0.523], SE = 0.102, z = 3.149, p = .002; Experiment 2: β = 0.361, CI_95% [0.217, 0.504], SE = 0.073, z = 4.925, p < .001), while the fixated option’s value on the same trial had an opposite, negative effect (Exp 1: β = -0.335, CI_95% [-0.549, -0.122], SE = 0.109, z = -3.077, p = .002; Experiment 2: β = -0.238, CI_95% [-0.395, -0.081], SE = 0.080, z = -2.97, p = .003). Similarly, a fixated option’s value had a positive effect on the likelihood of correctly reporting the probe appearing there (Experiment 1: β = 0.657, CI_95% [0.216, 1.098], SE = 0.225, z = 2.921, p = .003; Experiment 2: β = 0.807, CI_95% [0.532, 1.082], SE = 0.140, z = 5.750, p < .001), while the value of the unfixated option/s on that trial had an opposite, negative effect (Experiment 1: β = -0.746, CI_95% [-1.147, -0.344], SE = 0.205, z = -3.642, p < .001; Experiment 2: β = -0.321, CI_95% [-0.589, -0.053], SE = 0.140, z = -2.350, p = .019).

In Experiment 2, we also examined the influence of the value of an unfixated option on covert attention at the other unfixated alternative – in other words, how the value of one unfixated option influenced correctly reporting the probe at the other unfixated option. We found that the value of the lower-valued unfixated option negatively influenced the likelihood of participants correctly reporting the probe at the higher-valued unfixated option (β = -0.096, CI_95% [-0.168, - 0.024], SE = 0.037, z = -2.597, p = .009), over and above the effects of the higher-valued unfixated option’s value itself (β = 0.217, CI_95% [0.144, 0.290], SE = 0.037, z = 5.808, p < .001) and the value of the currently fixated option (β = -0.243, CI_95% [-0.306, -0.179], SE = 0.032, z = -7.486, p < .001). We similarly found that the higher-valued unfixated option negatively influenced the likelihood of participants correctly reporting the probe at the lowervalued unfixated option (β = -0.080, CI_95% [-0.156, -0.003], SE = 0.039, z = -2.038, p = .042), over and above the effects of the lower-valued unfixated option’s value itself (β = 0.138, CI_95% [0.062, 0.213], SE = 0.039, z = 4.563, p < .001) and the value of the fixated option (β = -0.163, CI_95% [-0.229, -0.097], SE = 0.034, z = -4.843, p < .001). The full models for both these analyses additionally controlled for the effects of peripheral option visibility, probe timing, and their interactions; for the results of these additional regressors, please see Supplementary Tables S9–S10.

2.2.2 Attentional downweighting is sensitive to choice-relevance

As further confirmation that our probe report measure indeed captured covert attention, we asked whether the mere presence of task-relevant stimuli at a location affected probe report accuracy to that location – as one would expect from a sensible measure of covert attention. To pre-empt our results, this was the case.

In Experiment 1, participants were more likely to correctly detect probe letters that appeared at the choice-relevant unfixated option relative to the choice-irrelevant unfixated option (Figure 3C; irrelevant vs. unfixated choice-relevant: β = -1.19, CI_95% [-1.773, -0.599], SE = 0.299, z = -3.96, p < .001. (Unsurprisingly, probe letters were reported most accurately at the currently fixated location; fixated vs. unfixated choice-relevant: β = 2.05, CI_95% [1.488, 2.618], SE = 0.288, z = 7.12, p < .001). To ensure that this was not due to the subjects’ gaze potentially being closer to the choice-relevant unfixated option, we confirmed that the same results replicated when controlling for distance between the probe-letter and gaze location (irrelevant vs. unfixated choice-relevant: β = -1.11, SE = 0.309, CI_95% [-1.714, -0.502], z = 3.58, p < .001; fixated vs. unfixated choice-relevant: β = 2.33, SE = 0.319, CI_95% [1.706, 2.958], z = 7.30, p < .001).

Figure 3:

In the full model, we additionally tested for the effect of peripheral option visibility, probe timing (presentation at first or second fixation), and their interactions with probe location type on probe response correctness (Supplementary Table S11; for a version of Figure 3C disaggregated by probe timings, see Supplementary Figure S2). None of these additional regressors were significant (p’s all > .05), with the exception that probe responses were overall less accurate when the peripheral option was hidden (β = -0.20, SE = 0.092, z = -2.19, p = .029) - though this effect did not survive when additionally controlling for the distance between gaze location and the unfixated option’s probe letter (Supplementary Table S12; β = - 0.15, SE = 0.098, z = -1.52, p = .128).

These initial results confirm that covert attention is itself modulated by choice-relevance. In Experiment 2 - given that there were always task-relevant stimuli present at two peripheral locations outside the current target of fixation – we could ask: was covert attention allocated to the locations that were more choice-relevant because of their higher relative value? To do so, we classified the two unfixated options on each trial (again defined at the time of probe presentation) as the higher- vs. lower-valued option (Figure 3D). We asked if the higher-valued unfixated option was more likely to be reported correctly than the lower-valued unfixated option. We found a significant effect of probe location, such that the accuracy for the highervalued unfixated option was higher than the lower-valued unfixated option (unfixated_low vs. unfixated_high: β = -0.48, CI_95% [-0.747, -0.206], SE = 0.138, z = -3.46, p < .001; see Figure 3D).

In the full model, we additionally tested for the effects of peripheral option visibility, probe timing, and their interactions with probe location type on probe response correctness (Supplementary Table S13; for a version of Figure 3D disaggregated by probe timings, see Supplementary Figure S2). Probe responses were again overall less accurate when the peripheral options were hidden (β = -0.44, SE = 0.126, z = -3.52, p < .001). From the 1^st to 2^nd visit, the higher-valued unfixated option became less downweighted relative to the lower-valued unfixated option (fixated probe location x 1^st-visit probe timing interaction: β = -0.58, SE = 0.197, z = -2.93, p = .003). We additionally found that this effect was stronger when the peripheral option was hidden, compared to when it was visible (β = 0.79, SE = 0.252, z = 3.14, p = .002), which could be explained by the fact that when peripheral options were hidden rather than visible, participants had no information at the first-visited option about peripheral options but gained more information as they made subsequent visits. No other regressors were significant (all p > .05).

In summary, we found that covert attention was modulated by a target location’s relative value compared to the currently fixated option, as well as its choice-relevance, and that increased covert attention to higher-valued peripheral options came at the expense of overt attention to fixated options.

2.3 Covert attention influences choice behavior downstream and attenuates choice biases

Next, we asked whether covert attention – as indexed by probe report accuracy – influenced choice behavior. We did so by assessing how covert attention to alternative option/s affects two different choice biases that have been shown to arise from fixating on a given option – the lastfixation and time advantage choice biases. Results revealed converging evidence that covert attention to alternative options attenuates both choice biases.

2.3.1 Attenuation of a choice bias associated with the last fixation

We first replicated a choice bias towards the last-fixated option, whereby people were more likely to choose an option that they were fixating on at the time of choice, when controlling for relative value. A main effect of last-fixated option was found in both Experiment 1 (β = 3.44, CI_95% [2.497, 4.374], SE = 0.479, z = 7.18, p < .001) and in Experiment 2 (β = 3.07, CI_95% [2.240, 3.896], SE = 0.422, z = 7.26, p < .001). Replicating results by Eum et al. (2023), this bias increased when peripheral visual information was hidden compared to when it was visible (last-fixated option x visibility condition interaction; Exp 1: β = 2.12, CI_95% [1.663, 2.568], SE = 0.231, z = 9.16, p < .001; Exp 2: β = 2.06, CI_95% [1.413, 2.712], SE = 0.33, z = 6.23, p < .001; for disaggregated versions of Figure 4C and D, please see Supplementary Figures S3 and S4 respectively).

Figure 4:

To assess whether covert attention drives choice, we then asked whether covert attention – as captured by the probe display during each trial – modulated the aforementioned choice bias downstream. Specifically, we considered whether attention towards the last-unfixated option affected the choice bias associated with the last-fixated option (reflected in participants’ choice at the end of the trial). Across both experiments, we found that the choice bias was attenuated whenever the probe at the last-unfixated option was correctly reported. In other words, when the probe letter at the last-unfixated option was correctly reported, people were less biased towards choosing the last-fixated option. This interaction between the last-fixated option and probe report correctness for the last-unfixated option was significant in both Experiment 1 (β = -2.49, CI_95% [-3.422, -1.566], SE = 0.47, z = -5.27, p < .001) and Experiment 2 (β = -1.53, CI_95% [-2.186, -0.867], SE = 0.34, z = -4.54, p < .001).

To more strictly ascertain whether specifically covert attention at the last-unfixated option reduced the downstream choice bias against it, we asked whether the choice bias attenuation effect survived when considering only trials where the last-unfixated option was also the unfixated option at the time of probe presentation (i.e., when probe report correctness indexed covert attention only). We found the choice bias attenuation effect survived with this subsetted data in both experiments (last-fixated option x probe report correctness for the last-unfixated option interaction; Experiment 1: β = -1.63, CI_95% [-2.335, -0.928], SE = 0.359, z = -4.55, p < .001; Experiment 2: β: p = -1.59, CI_95% [-2.519, -0.668], SE = 0.472, z = -3.38, p < .001). Full model results are reported in Supplementary Tables S14–S17.

2.3.2 Attenuation of a choice bias associated with excess fixation time (‘time advantage’)

A second choice-bias has been revealed in previous work, showing that increased cumulative fixation time towards one option over another (previously termed ‘time advantage’; e.g., Eum et al., 2023; Krajbich et al., 2010; Krajbich & Rangel, 2011) increases the probability of choosing it, even when controlling for relative value. To seek converging evidence for the claim that covert attention influences downstream choice – supplementing the findings revealing effects of covert attention on choice behavior in Section 2.3.1 - we asked if the time advantage choice bias was likewise affected by covert attention to alternative options on a given trial.

Our analysis used corrected choice probability for a given choice option (‘Option 1’) as the dependent variable, as has been done in previous literature (Eum et al., 2023; Krajbich et al., 2010; Krajbich & Rangel, 2011). We arbitrarily defined an ‘Option 1’ on each trial, and defined the other option/s as the comparator option for that trial (for full details on comparator option definition, see Supplementary Section 4.1: Supplementary Methods). Time advantage of Option 1 was then defined as the excess fixation time relative to the comparator option, and analyses focused only on trials where the comparator option was unfixated at probe (i.e., where probe correctness at that location indexed covert attention).

Hypothetically, if an attentional bias did not exist, the corrected choice probability for an option should hence be zero independent of time advantage to that option (horizontal gray line, Figure 5B-C). Contrary to this, we found that increasing time advantage towards an option increased its choice probability. This was the case both in Experiment 1 (β = 0 .068, CI_95% [0.045, 0.091], SE = 0.012, t = 5.90, p < .001]) and in Experiment 2 (β = 0 .085, CI_95% [0.065, 0.105], SE = 0.010, t = 8.37, p < .001).

Figure 5:

We then asked if the choice bias linked to increased cumulative fixation time towards a given option (time advantage) was attenuated by covert attention towards a peripheral, other option. We found evidence for this in both experiments, via a significant two-way interaction between time advantage and whether the probe letter for a peripheral comparator option was correctly reported. In Experiment 1, the effect of time advantage on choosing Option 1 was weaker when Option 2’s probe letter was correctly reported (β = -0.028, CI_95% [-0.050, -0.006], SE = 0.011, t = -2.54, p = .011). In Experiment 2, the effect of time advantage on choosing Option 1 was weaker, when the probe letter was correctly reported at the longer-dwelled peripheral, other option (β = -0.026, CI_95% [-0.047, -0.005], SE = 0.011, t = -2.49, p = .013). The full model additionally controlled for the effect of peripheral option visibility; full results, as well as the disaggregated versions of Figure 5B and 5D, are reported in Supplementary Section 4.1: Supplementary Results. Overall, these results suggested that the time-advantage-linked choice bias towards a given option was attenuated when participants correctly reported the probe letter appearing at another, peripheral option.

In summary, we found converging evidence that covert attention influences downstream choice across two experiments; results revealed strong evidence that correct probe reports for a peripheral comparator option reduced the last-fixation bias (Figure 4), and significant but weaker evidence that this attenuated the time-advantage choice bias (Figure 5).

2.4 Correct probe reports for peripheral options indexed covert attention that is dissociable from presaccadic attention

Could the value-related effects on our probe report measure be wholly accounted for by pre-saccadic attention rather than true covert attention? For instance, do we see higher probe report accuracy at high-value peripheral locations (Section 2.2) simply because people are more likely to saccade to higher-value options next? The trinary-option task design of Experiment 2 allowed us to directly address this question as it isolated instances where covert attention was not presaccadic. In Experiment 1, the option that a participant is saccading from is, in most cases, the same as the option that they saccade to next (after the probe onsets), as there were only two options. However, in Experiment 2, although this is still the case on some trials (for participants who make a ‘return visit’; Figure 6C), there are other instances where the option that a participant saccades from is distinct from the option that they saccade to next – i.e., covert attention is purely post-saccadic (Figure 6B; scenario depicted in Figure 6A). We therefore sought to confirm whether covert attention was still value-modulated in this case.

Figure 6:

We found that probe report accuracy was generally higher when the location was about to be fixated (Figure 6C) than when it was not (Figure 6B) (β = 1.593, CI_95% [1.085, 2.101], SE = 0.259, z = 6.146, p < .001). However, even when covert attention at an option was not pre-saccadic, it was still modulated by value (analysis subset to data from Figure 6B; main effect of relative value: β = 0.154, CI_95% [0.006, 0.303], SE = 0.076, z = 2.038, p = .042). For full model details, please see Supplementary Tables S19–S20.

We conducted a further control analysis and asked – in both Experiments 1 and 2 - how the time to an upcoming saccade to an option influenced probe report accuracy there. If probe report accuracy solely indexed presaccadic attention, one would expect that probe report accuracy monotonically decreases at a peripheral location, as the time until an upcoming saccade there increases. In contrast to this, we found a U-shaped relationship between the time to an upcoming saccade to an unfixated option and the probe report accuracy at that option (Experiment 1: β for second-order polynomial regressor = 20.23, CI_95% [16.192, 25.282], SE = 2.063, z = 9.81, p < .001; Experiment 2: β for second-order polynomial regressor = 17.22, CI_95% [13.141, 21.326], SE = 2.087, z = 8.25, p < .001; see Supplementary Tables S21–S22 for full modeling details, and Figure S6 for visualization).

In sum, our findings converged to indicate that the covert attention that was indexed by our probe task could not solely be explained by – and was dissociable from – presaccadic attention to upcoming gaze targets.

Discussion

In the present study, we examined how covert attention is allocated during value-guided decision making and whether it plays a functional role in shaping choice. By combining a valuebased choice task with a secondary attentional probe, we were able to directly index covert attention during ongoing decisions. Across two experiments, the results highlight two central features of the relationship between covert attention and choice: first, covert attention itself is dynamically shaped by decision-relevant factors, such as the decision relevance and value of peripheral options, as well as through competition with overt attention; and second, covert attention exerts downstream consequences for choice behavior, attenuating choice biases linked to overt fixations.

Together, these results demonstrate that attentional influences on decision making extend beyond eye gaze and cannot be fully captured by gaze-based accounts alone. Rather than reflecting a static attentional downweighting relative to the currently-gazed option, covert attention is dynamically and flexibly allocated to peripheral options. Participants were more likely to correctly report a peripheral probe letter when it appeared at an option that was both task-relevant and more valuable relative to other options – including both the currently-fixated and the alternative peripheral option. Results demonstrated that value modulation of covert attention was robust both across binary and trinary choice sets. Additionally, not only did the choice process influence covert attention, but covert attention also – in turn – influenced downstream choice behavior.

Our study draws parallels with previous work while representing a unique advance in the relationship between covert attention, overt fixations, and choice. Recently, for example, Siems et al. (2026) showed how the overall strength of covert attention might be rhythmically modulated (at ~11Hz) during a perceptual decision task in which participants were required to maintain central fixation. While our present study cannot directly examine rhythmicity in covert attention (due to the fixed temporal onset of the probes used), the study of Siems et al. (2026) leaves unexamined how covert attention interacts with other decision-relevant factors, most notably overt information gathering via fixations. On the other hand, our findings are in line with other work employing free-viewing two-alternative choice tasks which have suggested that attention may be paid to non-fixated items at the same time as foveated items during free-viewing choice (Butler et al., 2021; Eum et al., 2023; Munet & Wallis, 2026). However, such work has left unclear both the factors modulating covert attention, and the contribution of covert attention to choice. The present study therefore demonstrates, for the first time, how covert attention may be dynamically shaped by decision-relevant factors during choice, as well as how covert attention to peripheral choice alternatives competes with overt attention to influence choice behavior.

Our results further show that value-related modulation of covert attention during choice cannot be explained solely by presaccadic attention to whichever option that is fixated next. A large body of work has demonstrated that attention is deployed to a future gaze location immediately prior to saccade execution. This presaccadic attention enhances perceptual performance at that location (Blangero et al., 2010; Deubel & Schneider, 1996). Combined with evidence that higher-valued options are more likely to attract gaze (Anderson et al., 2011; Le Pelley et al., 2015), this would raise the possibility that value effects observed at peripheral locations could solely reflect presaccadic attention to high-value options. If this were the case, value modulation of covert attention should be absent at peripheral locations that are not the target of the upcoming saccade. We were able to test this possibility in control analyses, as Experiment 2 provided a multialternative choice context where we could dissociate presaccadic and postsaccadic peripheral locations. Crucially, value modulation in probe report accuracy at peripheral options persisted, regardless of whether it was subsequently or previously fixated. Taken together, our results demonstrate that covert attention is allocated in a value-dependent way that is dissociable from presaccadic attention, consistent with past work suggesting presaccadic and covert attention are separable (see Li et al., 2021 for a review).

Beyond demonstrating that covert attention to peripheral locations is modulated by both choice relevance and relative value, our results further establish a novel link between covert attention and choice behavior. Previous work has shown that overt attention – indexed by gaze – is associated with increased choice probability for a given option, producing so-called “choice biases” linked to overt gaze (Cavanagh et al., 2019; Molter et al., 2022; Sepulveda et al., 2020; Shimojo et al., 2003; Smith & Krajbich, 2018, 2019; Thomas et al., 2021). Here, we show that increased covert attention to peripheral options can attenuate these choice biases. Across both binary and trinary choice scenarios, choice biases – towards choosing the last option which was fixated on at the time of choice. as well as towards options that received more cumulative fixation time – were reduced when participants accurately reported the probe letter at the other option/s. Building on work that has previously shown that humans and non-human primates can covertly evaluate options during choice (Butler et al., 2021; Cavanagh et al., 2019; Munet & Wallis, 2026; Perkovic et al., 2023) and that covert sampling amplifies choice probability (Siems et al., 2026), our findings illustrate – for the first time - how covert attention to peripheral choice alternatives competes with overt attention in a manner that is consequential for choice behavior.

The finding that covert attention has downstream consequences on choice behavior may also provide an additional clue in an enduring debate: does choice and value influence attention, or does attention influence perceived value and, consequently, choice? The former view – which argues that correlations between gaze and choice arise because individuals prefer attending to options that they consider favorable – has received substantial empirical support across both choice and attention literatures. This support has included evidence for value-modulated attentional capture in human attention, whereby gaze is attracted to higher-value stimuli even when they are task-irrelevant (Anderson et al., 2011; Le Pelley et al., 2015). Further, humans exhibit a form of confirmation bias in overt attention, sampling information to support existing beliefs about more favorable options and those that are previously selected (Hunt et al., 2016, 2018; Kaanders et al., 2022). The influence of value on overt attention and information sampling has been instantiated in models in which gaze is attracted to higher-value items during decision-making (e.g., Callaway, Rangel, & Griffiths, 2021; Gluth et al., 2018).

In contrast, other work has argued the view that attention itself amplifies the perceived value of an option and therefore directly biases choice (Smith & Krajbich, 2019; Thomas et al., 2021), and have been supported by findings which have attempted to establish causal directionality by using experimenter-manipulated information sampling (e.g., Armel, Beaumel, & Rangel, 2008; Fromer, Callaway, Griffiths, & Shenhav, 2025; Newell & Le Pelley, 2018). Consistent with proposals in attentional economics suggesting that choice can be influenced by value-modulated attentional biases (Pearson et al., 2022), our findings provide evidence that covert attention likewise influences choice behavior. Specifically, we show that an estimate of covert attention earlier in the decision process can influence the final choice. Therefore, while our results also support a causal link from value and choice to attention – demonstrating that covert attention is attracted to high-value locations – they additionally suggest that a reverse link from attention to choice may also operate during value-guided decisions. Thus, our work goes beyond prior research by demonstrating that covert attention, independent of overt gaze and without experimental manipulation, can naturally influence choice behavior.

The present findings show that covert attention plays a non-trivial role in decision making, and thus highlight the need for covert attention to be integrated as a key mechanism into models of value-guided choice. While models have begun formalizing the causal link between value and attention, they have typically equated attention and gaze. As a result, these models – along with models where attention is not operationalized as gaze, but more abstractly defined (e.g., Roe, Busemeyer, & Townsend, 2001; Trueblood, Brown, Heathcote, & Busemeyer, 2013; Usher & McClelland, 2004) - have avoided making explicit claims about how attention may be covertly allocated to peripheral options. One notable exception is the attention drift diffusion model (Krajbich et al., 2010; Krajbich & Rangel, 2011), which makes implicit assumptions about covert attention, by including parameters which suggest that unfixated options are downweighted via a static parameter which is held constant across all trials and all timepoints within a decision. Although a less literal interpretation of this parameter could allow for value-sensitive attentional weighting, such an interpretation requires additional inferences equating decision weights with attentional weights, which is beyond the model’s original formulation. Taken together, our findings show that attention is neither confined to gaze, nor reducible to a uniform downweighting of the non-fixated options. This highlights a set of theoretically important attentional dynamics that future models of decision-making will need to account for.

In our study, introducing a probe report task to a choice task allowed us to examine how covert attention – as indexed by probe detection at each location – is itself influenced by decisionrelevant factors, as well as the influences on choice that it exerts downstream. While we achieved these aims, the probe task necessarily introduced dual-task demands which involved working memory as well as attention. A potential consequent weakness of our approach is that value may not only influence attention to a location, but also the strength of the working memory trace at a spatial location (and hence, its probability of being reported) - as such, it is not possible to rule out a contribution of working memory to the findings in the present study. Future work could obtain a continuous readout of covert attention during the decision using neuroimaging – by, for example, using alpha lateralization (Gresch et al., 2025) or frequency tagging (Marshall et al., 2024; Seijdel et al., 2023) as indices of covert visual attention. The use of high-temporal resolution neuroimaging methods may also help elucidate the nature of the covert attention captured in this study; for instance, whether value-modulated attentional selection is involuntary and stimulus-driven, or voluntary and top-down, as the two are characterised by different time-courses (Hickey, Van Zoest, & Theeuwes, 2010).

Methods

4.1 Participants

31 participants (M_age = 23.6 years, 15 male, 16 female, 0 other) took part in Experiment 1, and 30 participants (M_age = 29.7 years, 7 male, 22 female, 1 other) took part in Experiment 2. Participants were recruited at the University of Oxford. All participants had normal or corrected-to-normal vision (including colour vision), did not have a current psychiatric diagnosis, and provided informed consent prior to participating in the study.

Participants received £15/hour minimum payment, plus a bonus of up to £1.50 commensurate with performance in the choice task (Experiment 1: M = £1.50; Experiment 2: M = £1.45). The research protocol received ethics approval from the University of Oxford Central University Research Ethics Committee (Approval Number R92139).

4.2 Sample size determination

Sample size planning was guided by previous studies using a similar choice paradigm (Eum et al., 2023; Sepulveda et al., 2020) or probe detection task (Dugué et al., 2015; Gaspelin et al., 2015). Given that ours is the first study to combine both paradigms, effect sizes to run a-priori power analyses were difficult to determine and therefore we used these previous studies as a guide.

4.3 Apparatus

Stimuli were presented using PsychoPy (Peirce et al., 2019) on a 23-inch ASUS monitor (1920 x 1080 pixels) at a viewing distance of 73 cm. Eye position was recorded at 1 kHz using an SR Research EyeLink 1000+ desk-mounted system; a nine-point calibration procedure was used for Experiment 1, and a five-point calibration procedure was used for Experiment 2. Binocular recording was used whenever possible, while monocular recording was used for participants who encountered challenges with binocular recording. We used the EyeLink Toolbox (Cornelissen et al., 2002) to interface the eyetracker system with the stimulus presentation system. The interfacing between experiment code and the eyetracker was necessary for gazecontingent elements of the experiment: peripheral option visibility conditions, changing patch border colors for fixated options across both peripheral option visibility conditions, and probe onset timing (see Task Details and Design sections for more details).

4.4 Task details

In both experiments, participants completed a value-guided choice task, where they repeatedly chose between circular patches filled with equiluminant colored dots (RGB values: orange [255, 137, 5], cyan: [23, 188, 173]) which indicated each option’s value. One colour was designated as the target colour, which was counterbalanced across participants. On each trial, participants’ goal was to select the patch with most dots of the target colour; doing so earned the participants a virtual gemstone which was converted to a bonus at the end of the task (none, £0.90, or £1.50; corresponding to 0-49%, 50-79% and 80%+ correct trials, respectively). As such, the task was both perceptual and value-guided.

To incentivize performance during the task, a progress bar was shown throughout the experiment showing the running cumulative total number of virtual gemstones earned, together with “benchmarks” corresponding to the threshold for earning the £0.90 and £1.50 bonus payments (corresponding to 50% and 80% correct trials, respectively). During a practice phase, participants observed how gemstone earnings and the progress bar functioned; the progress bar then reset and began for real for the main experiment.

Participants were first given instructions for the pure-choice task, before completing two practice blocks of 20 trials containing only pure-choice trials. This was done as previous piloting (Gaspelin et al., 2015) found that participants needed extensive practice with the primary task before the probe-detection task was added. Following the first two practice blocks, participants viewed instructions about the choice-with-probe-trials, before completing two further practice blocks of 20 trials, which consisted of half pure-choice trials intermixed with half choice-with-probe trials.

After the practice trials, participants reviewed the task instructions before commencing the main experiment. It was reiterated to participants that their goal was to complete the choice task, and that the probe task would not be relevant to their gemstone earnings and thus their bonus payment from the experiment. Participants then completed 8 blocks of 40 trials in the main experiment, consisting wholly of choice-with-probe trials. This yielded 320 trials excluding practice block trials.

4.4.1 Pure-choice trials

On each trial, a fixation cross (1.2° by 1.2° visual angle) was first presented for 1s to signal the participant that the trial was about to begin. Three circular patches were then presented on the computer screen; the circular patches were 5° in diameter and were equidistantly spaced 6.5° apart, appearing at the top, bottom-left, and bottom-right of the screen respectively.

Trials belonged to one of two peripheral option visibility conditions (Figure 1), in a replication of the design used by Eum et al., (2023). On visible trials, the contents of the decision-relevant patches remained onscreen regardless of which patch was currently fixated. On hidden trials, only the content of the currently fixated decision-relevant patch was visible (i.e., patch contents were gaze-contingent).

Participants had unlimited time to select a patch and could do so at any point during the trial. To select a patch, participants used the up, left, or right arrow keys on their keyboard, to select the top, left, or right patches respectively; however, participants were blocked from choosing the irrelevant patch in Experiment 1. After making their selection, participants received the feedback “You received a gemstone!” if they correctly selected the patch with the higher proportion of target dots, or “You did not receive a gemstone.” if they did not.

4.4.1.1 Experiment 1

Two of the circular patches were decision-relevant, each containing 100 smaller dots (0.15° by 0.15°) that were either cyan or orange in colour. One of the circular patches was empty and thus decision-irrelevant. The locations of the relevant and irrelevant patches were pseudorandomized between trials, with the constraint that one-third of all trials had each possible assignment of patch location to decision-irrelevance.

For each pair of decision-relevant patches on each trial, the difference in the proportion of target dots between the patches (i.e., value differences) varied in ten percentage levels, ranging from 2% to 20% with 2% steps. The maximum proportion of target dots in a patch was 80% and the minimum proportion was 20%.

4.4.1.2 Experiment 2

All three patches contained colored dots which indicated each options’ value. On each trial, the proportion of target dots (option value) in each of the three patches was pseudo-randomly drawn from a uniform distribution from 20% to 80%, with the constraint that for any given pair, the difference in target dot proportions had to exceed 2%. This meant that unlike Experiment 1, we did not sample evenly across the value-difference space, and the range of value differences now spanned 2% to 60% (though most trials still had a value difference between 2 to 20%); however, this sampling method had the benefit that option absolute values were now decorrelated from relative value.

4.4.2 Choice-with-probe trials

In two practice blocks, and for all trials in the main experiment, probe letters were presented during the trial. These ‘choice-with-probe’ trials were identical to pure-choice trials, with the only difference being the presentation of i) probe letters at one point during the trial, and ii) a probe response screen after patch selection. On these trials, the choice task remains the primary task, and responses on the probe task did not affect participants’ gemstone earnings. To assess the effect of decision time course on attention, probe letter onset (probe timing condition) varied between trials.

After letter-probe presentation, the trial continued as normal. After patch selection, the response screen appeared which consisted of the full English alphabet in white. Participants then used the computer mouse to select letters they recalled from the probe display. When a letter was selected, it turned yellow; and when it was deselected, it turned white again. Participants clicked an “OK” box to submit their response and continue. Probe report was untimed, and participants received no direct feedback on the accuracy of probe report. After submitting the probe report, participants received feedback on their patch selection (“You received a gemstone!”/ “You did not receive a gemstone.”).

4.4.2.1 Experiment 1

The letter-probes could either appear at 220 ms following the first fixation on the first-visited option on the given trial (1^st-visited probe) or at 220 ms following the first fixation on the second-visited option on the given trial (2^nd-visited probe). To control probe presentation, the experiment code obtained samples of gaze position from the eye-tracker at 1 kHz and monitored these samples in real-time, presenting the probe only after cumulative gaze-time at the corresponding option location had exceeded a 220 ms threshold. During probe display, letters were superimposed over each patch for 150 ms. The letters were three letters from the English alphabet that were randomly selected without replacement. Letters were white in Arial typeface (0.8° height).

4.4.2.2 Experiment 2

In addition to letter-probes appearing after 220 ms of sampling the first-visited or second-visited option, they could also appear after 220 ms of sampling the third-visited option. As such, approximately a third of trials belonged to each of the three probe timing conditions.

4.5 Design

The study contained two within-subject conditions: peripheral option visibility (visible or hidden) and probe timing (Experiment 1: 1^st-visited or 2^nd-visited probe; Experiment 2: 1^st-visited, 2^nd- visited, or 3^rd-visited probe). Trials were counterbalanced across different conditions, and trials were randomly assigned to each condition combination. Additionally, value difference (i.e., the difference between the two options presented on each trial in their proportion of target dots) was a continuous within-subject variable that varied between trials.

4.6 Data analysis

We processed and analyzed all data using R (R Core Team, 2024), and visualized data using the ggplot2 package (Wickham, 2016; Wickham et al., 2019). Generalized linear mixed models were fitted using the lme4 package (Bates et al., 2015), and likelihood ratio tests were conducted using the stats package (R Core Team, 2024). Only data from the main task, which consisted of wholly choice-with-probe trials, were used for analysis.

4.6.1 Random-effects structure selection for LMMs

For each linear mixed model (LMM) analysis, we performed a systematic random-effects structure selection procedure which retained the most maximal random-effects structure while preventing overfitting. The procedure was consistent across analyses. i) For each analysis, model selection started with the maximal random-effects structure, which included subject random intercepts, as well as by-subject random slopes for all main effects included in the model (as these were always within-subject factors). ii) Following this, we identified possible overparameterization by performing PCA using the rePCA() function on the fitted maximal LMM’s random effect variance-covariance matrix. iii) If overparameterization was identified, we identified the random effect with the smallest associated variance, and iv) then fit a new reduced model without this random effect. Steps ii) and iii) were repeated until we reached a model where both the PCA results no longer identified overparameterization and the model fit was not singular, v) Once no overparameterization is identified in the present iteration’s model, we used the current model as the final model from which statistics are reported.

For robustness, in Supplementary Materials Sections 1 to 4, we report results from an alternative model selection scenario where analyses use the simplest possible random-effects structure containing only subject random intercepts (the fixed effects structure remained the same as in the main text). Unless otherwise specified, the reported results do not qualitatively differ between the main text and this alternative analysis.

4.6.2 G/LMM reporting

For all linear mixed models (LMMs), and generalized linear mixed models (GLMMs), we report the regression coefficient β, the standard error, the z-statistic for GLMMs or t-statistic otherwise, as well as the p-value. P-values are based on asymptotic Wald tests for GLMMs, and based on Satterthwaite’s degrees of freedom method using the lmerTest package (Kuznetsova et al., 2017) for LMMs. For all models, we applied a two-tailed criterion corresponding to a 5% error criterion for significance. Note that for GLMMs, β coefficients serve as a standardized measure of effect size, as the exponentiated β coefficient represents the odds ratio in generalized linear regression; we report β and its 95% Wald confidence interval in-text, and the associated odds ratios in the supplementary tables corresponding to each result. For GLMMs, we assume that the binary outcome variable (i.e., correctness of probe report) is Bernoulli (i.e., Binomial-distributed) and therefore assume that a logit link function is appropriate, as is common for generalized linear models; we do not perform any other transformations on the outcome variable. All continuous predictor variables including value differences were z-transformed (i.e., the mean subtracted from each observation, divided by the standard deviation).

4.7 Exclusion criteria

Exclusion criteria. We implemented the following trial-wise exclusion criteria for our analyses, as these analyses were dependent on results from the probe-detection task. Altogether, 31.4% of the data were excluded in Experiment 1, and 44.0% of the data were excluded in Experiment 2.

4.7.1 Experiment 1

1.93% of trials were excluded due to participants choosing a patch prior to probe onset (resulting in a no-show of probe letters). 7.39% of trials were excluded due to participants saccading away from a patch before the probe appeared. 24.10% of trials were excluded due to participants’ gaze moving to either of the unfixated options during probe presentation. 0.5% of trials were excluded for belonging in the top 99.5^th percentile of choice reaction times, as this may have indicated that participants’ attention had lapsed or were performing the task differently from instructed (e.g., counting dots).

4.7.2 Experiment 2

2.3% of trials were excluded due to participants choosing a patch prior to probe onset (resulting in a no-show of probe letters). 10.9% of trials were excluded due to participants saccading away from a patch before the probe appeared. 35.4% of trials were excluded due to participants’ gaze moving to either of the unfixated options during probe presentation. 0.5% of trials were excluded for belonging in the top 99.5^th percentile of choice reaction times, as this may have indicated that participants’ attention had lapsed or were performing the task differently from instructed (e.g., counting dots). Finally, we excluded trials during which the experimenter recalibrated the eyetracker, but this did not lead to the additional removal of any more trials.

Supplementary results

1 Supplementary results relating to Section 2.2.1 (“Covert attention is value-modulated, and competes with the overtly fixated location”)

Effect of peripheral option value, relative to the fixated option, on peripheral and fixated location probe letter reports

Figure S1.

Table S1.

Table S2.

Table S3.

Table S4.

Effect of option absolute value on peripheral and fixated location probe letter reports

Table S5.

Table S6.

Table S7.

Table S8.

Covert attention is also influenced by value of other peripheral alternatives

Table S9.

Table S10.

2 Supplementary results relating to Section 2.2.2 (“Attentional downweighting is sensitive to choice-relevance”)

Figure S2.

Table S11.

Table S12.

Table S13.

3 Supplementary results relating to Section 2.3.1 (“Attenuation of a choice bias associated with the last fixation”)

Table S14.

Table S15.

Figure S3:

Figure S4:

Table S16.

Table S17.

4 Supplementary information and analyses relating to Section 2.3.2 (“Attenuation of a choice bias associated with excess fixation time - ‘time advantage’”)

4.1 Supplementary Methods

We assessed the relationship between excess fixation time (‘time advantage’) and the corrected probability of choosing a given option. We asked if this relationship (i.e., choice bias) was affected by covert attention to another option on that trial.

In Experiment 1, we arbitrarily defined an ‘Option 1’ on each trial, and defined the other option as ‘Option 2’. Time advantage of Option 1 was then defined as the excess fixation time relative to the comparator Option 2, and analyses focused only on trials where Option 2 was unfixated at probe (i.e., where probe correctness at that location indexed covert attention). In Experiment 2, we again arbitrarily defined an ‘Option 1’ on each trial, and defined the option with the longer dwell time out of the two remaining options as the comparator for the time advantage calculation; analyses focused only on trials where the comparator option was unfixated at probe.

We used corrected choice probability for Option 1 as the dependent variable, as has been done in previous literature (Eum et al., 2023; Krajbich et al., 2010; Krajbich & Rangel, 2011).

In Experiment 2, we again arbitrarily defined an ‘Option 1’ on each trial, and defined the option with the longer dwell time out of the two remaining options as the comparator for the time advantage calculation; analyses focused only on trials where the comparator option was unfixated at probe. The corrected probability of choosing Option 1 was defined by: i) obtaining the proportion with which option 1 is chosen at each bin (i.e., level) of relative value - 10 bins (ranging from 2 to 20%) for Experiment 1, and 8 bins (ranging from 2 to 60%) in Experiment 2; then ii) subtracting this proportion from each choice observation (coded as 1 if option 1 chosen, and 0 otherwise).

4.2 Supplementary Results

Figure S5.

Table S18.

5 Supplementary results relating to Section 2.4 (“Correct probe reports for peripheral options indexed covert attention that is dissociable from presaccadic attention”)

Upcoming gaze target

Table S19.

Table S20.

U-shaped relationship between time to upcoming saccade and probe report accuracy at the saccade target

To check if probe report correctness may have purely indexed presaccadic attention, we asked how temporal proximity to the upcoming saccade to the unfixated option following the probe presentation affected the accuracy of probe report at the unfixated option. If the attention indexed by probe reports were accounted wholly by presaccadic attention, we should expect to see that the probe report accuracy of the unfixated option decrease monotonically with the time to an upcoming saccade to that option; otherwise, we would expect a non-monotonic relationship.

In both experiments, we found evidence of a non-monotonic relationship between the time to an upcoming saccade to an unfixated option, and the probe report accuracy at the unfixated option. For each of the two experiments, we compared two GLMs with probe report correctness at the unfixated option as a binary outcome variable, and peripheral option visibility condition and time to the subsequent saccade to that unfixated option as regressors. A polynomial model (where the time regressor was polynomial with degree two) outperformed a linear model (where the time regressor was linear) on multiple model comparison metrics (AIC_polynomial = 5668.87, AIC_linear = 5762.43; BIC_polynomial = 5694.33, BIC_linear = 5781.52), suggesting the presence of a non-monotonic second-degree relationship between the time regressor and probe report accuracy.

The polynomial models found both first- and second-degree effects for the time regressor, suggesting that though probe report for the unfixated option did become less accurate as the subsequent saccade to that option happened later (1^st degree time regressor; Experiment 1: β = -22.19, SE = 2.072, z = -10.71, p < .001; Experiment 2: β = -13.63, SE = 2.097, z = -6.50, p < .001), there was a U-shape relationship between time and probe accuracy characterized by an increase in probe report accuracy when the subsequent saccade to the unfixated option happened even further later (2^nd -degree time regressor; Experiment 1: β = 20.23, SE = 2.063, z = 9.81, p < .001; Experiment 2: β = 17.22, SE = 2.087, z = 8.25, p < .001). The full model additionally controlled for the effect of peripheral option visibility as we were aware that it affected peripheral probe report accuracy (Supplementary Table S22).

Figure S6.

Table S21.

Table S22.

Data availability

All raw data, as well as the preprocessed forms of the data, have been made available at the Open Science Framework at https://osf.io/3b6xv/. All code needed to reproduce the analyses reported in both the main text and supplementary information have been made available at the Open Science Framework at https://osf.io/3b6xv/. Experiment code and task stimuli are publicly available at https://github.com/CCNHuntLab/covert-decision-exp.

Acknowledgements

AXL was supported by a Clarendon Scholarship, The Queen’s College Waverley Scholarship, and a Department of Experimental Psychology Studentship from the University of Oxford. Data collection for this study was funded by a Wellcome/Royal Society Sir Henry Dale Fellowship (208789/Z/17/Z) awarded to LH, who was also supported by a strategic Longer and Larger award from the BBSRC (BB/W003392/1).

Additional information

Contributions

AXL: Conceptualisation, Formal Analysis, Investigation, Project administration, Software, Supervision, Writing – original draft, Writing – review & editing; BC: Investigation, Project administration; Writing – review & editing; SD: Investigation, Project administration, Writing – review & editing; SB: Conceptualisation, Supervision, Writing – review & editing; LH: Conceptualisation, Funding acquisition, Supervision, Writing – review & editing.

Funding

Wellcome Trust (WT)

https://doi.org/10.35802/208789

• Laurence T Hunt

Royal Society (The Royal Society) (208789/Z/17/Z)

• Laurence T Hunt

UKRI | Biotechnology and Biological Sciences Research Council (AFRC) (BB/W003392/1)

• Laurence T Hunt