We trained two monkeys to perform a value-based decision task in which they used eye movements to view the choice options and used a manual response lever to indicate their decision (Figure 1A). To begin a trial, the monkeys were required to fixate on the center of the task display while holding down the center of three response levers. After the required eye fixation and lever hold period was satisfied, two targets were presented on the left and right of the task display, each associated with a reward ranging from 1 to 5 drops of juice. Following the initial fixation period, gaze was unrestricted, allowing the monkeys to look at each target as many times and for as long as they liked before indicating a choice. To encourage the monkeys to look directly at the targets, and to limit their ability to perceive the targets using peripheral vision, the targets were initially masked until the first saccade away from the central fixation point was detected (see Methods). To indicate their choice, the monkeys first lifted their hand off the centrally-located response lever, and then pressed the right or left lever to indicate which of the two targets they chose. The reaction time (RT) in each trial was defined as the period between the onset of the targets and the lift of the center lever. We collected data from a total of 54 sessions: 29 from Monkey C (N = 15,613) and 25 for Monkey K (N = 14,433).

Overall choice performance is illustrated in Figure 1D. Choices were nearly optimal for the easiest trials (value difference of +/-3 or 4 drops of juice,>98% of choices in favor of higher value target) and occasionally suboptimal for more difficult trials (value difference of +/-1 or 2 drops of juice, 86% higher-value choices for both Monkey C and Monkey K). When the targets were of equal value, the probability of the monkeys choosing the left or right target was near chance (50% left choices for Monkey C, 46% for Monkey K). This pattern of choices indicates that the monkeys were behaving according to the incentive structure of the task, with a very low rate of guesses or lapses (Fetsch, 2016). Further, choice behavior was well-described by a logistic function parameterized by the difference between the values of the left and right items (fit lines in Figure 1D are from a logit mixed effects regression: β_{value-difference} = 1.37, CI = [1.34, 1.40]; F (1,30044)=8411.60, p<1e-10). Additionally, we found that both the average RT and the average number of fixations per trial were modulated by choice difficulty: the monkeys responded slower and made more fixations when the two targets were near in value, compared to when the value difference between the targets was large (RT: Figure 1E, linear mixed effects regression: β_difficulty = -0.032, CI: [-0.039,–0.026]; F (1, 30044)=106.09, p<1e-10. Number of Fixations: Figure 1F, Linear mixed effects regression: β_difficulty = -0.10, CI = [-0.12,–0.09]; F(1, 30044)=126.7, p<1e-10). Together these results are consistent with behavioral patterns seen in both humans and NHPs performing 2-alternative forced choice tasks (e.g. Gold and Shadlen, 2007; Thomas et al., 2019).

In the preceding section, we show that both RT and the number of fixations increase as a function of trial difficulty. However, in high-performing subjects trial difficulty is correlated with chosen value, because the trials with large value differences (low difficulty) are also trials where higher-value offers are chosen. Therefore, the RT and fixation effects originally attributed to difficulty may be explained in part by chosen value. To determine the unique contributions of chosen value and difficulty to RT and the total number of fixations, we used the approach of Balewski et al., 2022. Briefly, we modeled each behavioral metric as a function of one predictor, and then regressed the other predictor against the residuals of the first model. For example, to measure the unique contribution of chosen value to RT, we first ran a linear mixed effects model explaining RT as a function of difficulty. We then took the residuals from this model, which represent the RT after accounting for difficulty, and ran a second mixed effects model explaining these residuals as a function of chosen value.

Consistent with the findings of Balewski and colleagues, RT was modulated more by chosen value than by difficulty (β_chosen-value = -0.026, CI = [-0.034,–0.019]; F (1,30044)=46.35, p<1e-10; CPD = 8%; β_difficulty = -0.011, CI = [-0.012,–0.010]; F (1,30044)=318.44, p<1e-10; CPD = 1.4% Figure 2A/C, Supplementary file 1 rows 4–5). Interestingly, we found the opposite pattern for the total number of fixations per trial: this metric was strongly modulated by difficulty (β_difficulty = -0.065, CI = [-0.086,–0.043]; F (1,30044)=34.46, p=4.41e-9; CPD = 1.8%; Figure 2C), and showed no effect of chosen value (β_chosen-value = -0.028, CI = [–0.095, 0.39]; F (1,30044)=0.66, p=0.42; CPD = 0.69%; Figure 2D, Supplementary file 1 rows 4–5). In sum RTs appear to reflect the size of the upcoming reward (faster responses for higher rewards), whereas the number of fixations reflect choice difficulty, with more fixations associated with more difficult trials.

The following sections characterize the number and durations of the monkeys’ fixations onto the choice targets throughout each trial. A fixation was defined as a period of stable gaze upon one of the two targets. Consistent with fixation analyses in human studies, consecutive fixations upon the same target were merged into a single fixation epoch, and fixations onto non-target locations were not included in the analysis (See Behavior Analysis for details). Following conventions from human studies, final fixation durations are defined as the interval between fixation onset and the center lever lift; in other words, final fixation durations are delimited by the reaction time in each trial (e.g. Krajbich et al., 2010). For non-final fixations, the duration is defined in the conventional way, as the interval between fixation onset and the initiation of the next saccade.

In our task, information about the choice targets was obscured unless the monkey was directly fixating on them. Therefore, the optimal strategy involves a minimum of two fixations, one to each target. Consistent with this, the monkeys almost always looked at both targets on each trial (97.2% of trials for Monkey C, 91.6% for Monkey K). The fraction of trials with 1, 2, 3, or ≥4 total fixations before the RT for Monkey C was 2.8%, 41.2%, 49.2%, and 6.8%; and for Monkey K was 8.4%, 43.0%, 43.8%, 4.8%. Thus, in the vast majority of trials the monkeys either looked at each target exactly once (2 total fixations) or looked at one target once and the other twice (3 total fixations). The average number of fixations per trial for Monkey K was 2.45 SEM 0.02 and for Monkey C was 2.57 SEM 0.04. This average is smaller than in human binary choice tasks, in which the average number of fixations per trial is usually 3 or more. As we discuss below, the difference between human and monkey total fixation numbers has implications for comparing fixation durations between species.

Fixations can be defined by both their absolute and relative order in a trial. Absolute order refers to the serial position in the trial: first, second, third, etc. Relative order refers to when the fixation occurs with regards to the trial start or end: initial, middle, final. Note that these definitions are not independent or mutually exclusive. Instead, they depend on the total number of fixations in the trial. For example, in a trial with a total of two fixations, the second fixation is also the ‘final’ fixation (there are no middle fixations). However, in a trial with three total fixations, the second fixation is considered a ‘middle’ fixation. Because the monkeys usually make either two or three total fixations in a trial, relative and absolute order are conflated. (In contrast, humans typically make three or more fixations per trial, so that second fixations are almost always ‘middle’ fixations.) Consequently, it is necessary to independently analyze the effects of both absolute and relative fixation order.

To assess the effects of absolute order (first, second, third, etc.) independent of relative order (final/non-final), we first fit a linear regression explaining fixation duration as a function of relative order. We then regressed absolute order against the residuals from the first model. Consistent with human fixation patterns, we found that fixation durations decreased as a function of absolute order, after controlling for relative order (β_{relativeOrder} = -0.049, CI = [-0.065,–0.033]; F(1, 7762)=36.06, p<1.92e-9; Figure 3). The decrease is especially notable at the third fixation, which in a binary task is the first ‘re-fixation’ onto a previously sampled target, and is consistent with human fixation patterns (Manohar and Husain, 2013). Next, to assess the effects of relative order independent of absolute order, we fit a linear mixed-effects model comparing fixation durations across absolute positions, treating absolute position as a categorical variable. We then fit a second model explaining the residuals as a function of whether or not the fixation was a final fixation (i.e., relative order). After accounting for serial position, we found that non-final fixations were shorter than final fixations (β_{relativeOrder} = -0.047, CI = [-0.057,–0.037]; F(1, 7762)=86.34, p<1e-10; Figure 3). In sum, we identified two independent order-based effects on duration: a decrease in duration with successive fixations in a trial, as well as a tendency to fixate longer on final fixations.

The monkeys’ prolonged final fixations seem to contradict prior human studies, which typically report shorter final fixations. However, this discrepancy may be explained by the relatively larger number of fixations that humans make (mean ~3.7, computed from freely available data from the study described in Krajbich et al., 2010), compared to the monkeys in the present study (mean ~2.5). Consequently, humans’ final fixations tend to have higher absolute order and are thus nearly always re-fixations onto a target—both factors that are associated with shorter fixation durations, as noted above. In contrast, the monkeys’ final fixations are overwhelmingly either the second or third in the trial. Thus, not only do their final fixations have a lower absolute order, but they are also comprised of a larger fraction of longer initial fixations onto a target (i.e. when the final fixation is the 2nd fixation).

The average fixation duration was dependent on the value of the target being fixated, and upon the order in the trial in which the fixation occurred. For the first fixation in each trial, duration increased as a function of fixated target value (β_fixValue = 0.003, CI = [0.0011,0.0040]; F(1, 28392)=11.37, p=0.0007, Supplementary file 1, row 8). Intuitively, the effect size can be interpreted as the influence of a one-drop change in juice volume; for example, for initial fixations the regression estimate of 0.003 corresponds to a 3ms increase in fixation duration per drop of juice. For middle fixations, defined as any fixation that was neither first nor final, the average duration decreased as a function of the value of the fixated target (β_fixValue = -0.0076, CI = [-0.0086,–0.0067]; F(1, 17580)=231.37, p<1e-10; Supplementary file 1, row 9). At the same time, middle fixation durations were also influenced by the value of the target not currently being viewed (β_nofixValue = -0.035, CI=[-0.040,–0.030]; F(1, 17580)=197.78, p<1e-10; Supplementary file 1, row 10); because most middle fixations were the second fixations in the trial, this means that the value of the first-viewed item ‘carried over’ into the second fixation to influence its duration. Combining the influences of fixated and non-fixated values into a single variable, middle fixation durations increased as a function of relative value, defined here as the value of the fixated target minus the value of the non-fixated target (β_{relativeFixVal} = 0.016, CI = [0.012, 0.021]; F(1, 17580)=48.55, p<1e-10; Supplementary file 1, row 11). Finally, we find that durations decreased as function of the absolute difference in target values (β_difficulty = -0.019, CI = [-0.025,–0.0154]; F(1, 17580)=47.17, p<1e-10; Supplementary file 1, row 12). Together, these results support the notion that fixation behavior and valuation are not independent processes, and that the effects of value on viewing durations must be accounted for when computing and interpreting gaze biases (see Cumulative Gaze-Time Bias, below).

Humans show three core choice biases related to gaze behavior. First, they tend to choose the item that they viewed first (initial fixation bias). Second, they tend to choose the item they spend more time looking at over the course of the trial (cumulative gaze-time bias). Third, they tend to choose in favor of the target they are viewing at the moment they indicate their choice. All three of these biases are evident in our monkey subjects, as detailed below. However, before these biases can be quantified, we must first address the question of whether monkeys show evidence for a two-stage form of gaze bias recently identified in human behavior.

To explain how these gaze biases come about, prior human studies have used modified sequential sampling models (aSSMs) that provide an increase in evidence accumulation for a given item while it is being viewed (see Krajbich, 2019, for review). This bias generally takes one of two forms: Some studies suggest that the gaze amplifies the value of attended targets so that the increase in evidence accumulation is proportional to the attended value (i.e. is multiplicative). Others suggest that gaze acts by providing a fixed increase in evidence accumulation to attended targets, independent of target values (i.e. is additive). Studies directly comparing these two mechanisms are not fully conclusive (Smith and Krajbich, 2019; Thomas et al., 2019), perpetuating debates as to which is ‘correct’. A third, hybrid modeling framework offers a compromise (Manohar and Husain, 2013; Westbrook et al., 2020). Under this framework, a trial can be divided into two stages. The first stage is the decision stage, where evidence accrues for the decision offers, and gaze increases evidence accumulation for attended items in multiplicative fashion. The second stage begins once an internal decision boundary is reached (a choice is made) and continues until the choice is physically reported. During this interval the gaze becomes drawn to the to-be-chosen item, which is captured with an additive gaze bias. In other words, in the first stage, gaze influences choice, whereas in the second stage, the latent choice influences gaze.

Two patterns in the monkeys’ fixation data are consistent with this two-stage model. First, as shown in Figure 3, final fixation durations are longer than non-final fixations even after accounting for absolute order in the trial, suggesting some process that occurs at the end of each trial that prolongs fixation durations. Second, the monkeys’ final fixations were on the to-be-chosen target on nearly every trial (~97% of trials), consistent with gaze being drawn to the to-be-chosen items.

To more directly test the hybrid, two-stage, model in our data, we reasoned that the relative fit of a model with an additive gaze bias compared to one with a multiplicative gaze bias would indicate whether choice reflects one mechanism alone, or a mixture of both. Using the Gaze-Weighted Linear Accumulator Model (GLAM, Thomas et al., 2019), we found that while the multiplicative model provided a slightly better fit than the additive model, the difference was not significant (Figure 4, 0 on the x-axis, Supplementary file 3). This suggests that our data likely reflect a mixture of additive and multiplicative gaze biases, consistent with the hybrid model.

Next, we tested the assumption that the influence of gaze switches between the two biasing mechanisms near the end of the trial, at the moment a decision threshold is met. We reasoned that if this were the case, that the relative fit of one model over the other would increase if we removed increasing amounts of data from the end of the trial. Alternatively, if the multiplicative and additive influences were mixed throughout the trial, this truncation would have little effect on the relative fit of the two model variants. We found that the difference in fit between the two models became significant for truncation values of 100ms and higher, with the multiplicative model providing the better fit (Supplementary file 3). Further, at 100ms the probability that data were generated by a multiplicative, and not an additive, model reaches 100% (Figure 4). Together, this supports the two-stage model put forth by Westbrook, where gaze acts multiplicatively during the first stage before transitioning to additive approximately 100ms before the RT.

Under the two-stage framework, the transition point between the multiplicative and additive stages of the decision process occurs when accumulated evidence reaches the decision boundary. In other words, the additive stage occurs after a decision has been made but before the RT is detected. In standard sequential sampling models, this type of post-decision/pre-report interval is referred to as terminal non-decision time (NDT; Ratcliff and McKoon, 2008; Resulaj et al., 2009). As noted above, we estimated that in our data, this transition occurs approximately 100ms prior to the RT. Because the focus of this study was to characterize the influence of gaze on the decision process itself (i.e. the putative first stage), the remaining analyses were conducted using data that were truncated by 100ms, in order to minimize the influence of post-decision gaze effects. However, as this is merely an estimate of the NDT interval, we repeated each analysis using data truncated over a range of NDT values from 0 to 400ms. The results, presented in Figure 6—figure supplement 1, and Figure 7—figure supplement 1, indicate that the gaze biases described in the following sections are robust to NDT truncation values of up to 200ms.

As is the case in humans, the monkeys were more likely to choose the target that they looked at first in a given trial. To quantify this bias, we used a logit mixed effects regression, which gives an estimate of the effect of an initial leftward fixation on the log odds of a leftward choice: β_{first-is-left}=0.66, CI = [0.32; 1.00]; F(1,30043)=14.36, p=0.00015, see Supplementary file 1, 13. The fact that β_{first-is-left} is significantly greater than zero indicates that an initial leftward fixation is associated with a greater likelihood of a leftward choice. The effect of target value differences computed in this same model was β_{value-difference} = 1.40 (CI = [1.32, 1.43]; F (1,30043)=5349.40, p<1e-10). The ratio between these two regression estimates (β_{first-is-left} / β_{value-difference}), gives the relative influence the initial fixation on choice as compared to the value differences of the targets: 0.66/1.40=0.47. In other words, the monkeys chose as if the first-fixated item was, on average, worth 0.47 drops of juice more than its nominal value. Critically, because the targets were obscured until the monkeys initiated their first saccade (see Methods), their initial fixations were unbiased with regard to target value. Thus, the choice bias in favor of the initially fixated item cannot be attributed to a tendency for the monkeys to look at higher value targets first.

This suggests that the initial fixation direction, whether exogenously or endogenously driven, may have a causal influence in choice. To test this causal role, we conducted additional experimental sessions in which we manipulated initial fixation by staggering the onset of the two targets (Monkey C: 16 sessions, n=6931 trials; Monkey K: 8 sessions, n=5433 trials). Staggered target onsets – either left first or right first – occurred randomly in 30% of the trials in these sessions (Figure 3A), with concurrent onsets in the other 70% of trials (Figure 3B). In the staggered-onset trials, the monkeys almost always directed their initial fixations to the target that appeared first (100% of staggered trials for Monkey C, 94.1% for Monkey K). Trials in which Monkey K did not fixate on the first target (n=99) were removed from analysis. As in the sessions without gaze manipulation described above, we found a main effect of initial fixation on choice (logit mixed effects regression: β_{first-is-left}=0.70, CI = [0.41; 1.00]; F(1,12359)=21.83, p=3.02e-06; β_{first-is-left} / β_{value-difference} = 0.57 drops of juice; see Figure 5 and Supplementary file 1, row 14). Importantly, we found no main effect of trial-type (staggered vs. standard; β_trial-type = -0.07, CI = [–0.33; 0.18]; F(1,12359)=0.32, p=0.57) nor was there a difference in the magnitude of the initial fixation effect across the two trial-types β_{first-is-left:trial-type} = 1.48e-3, CI = [–0.23; 0.24]; F(1,12359)=1.52e-4, p=0.57. Thus, not only could we induce an initial fixation bias by manipulating where the monkey looked first, but the magnitude of this bias is comparable to the bias observed without a manipulation.

Here, we asked whether monkeys were more likely to choose items that were fixated longer in a trial. We first quantified the time spent looking at the two choice targets in every trial. Then, using a logit mixed effects regression, we asked whether choice outcomes were dependent on the relative time spent looking at the left item as compared to the right item (‘Time Advantage Left’). Consistent with human choice patterns, monkeys were more likely to choose the left item as the relative time advantage for the left item increased (Figure 6B and C; β_{time-advantage} = 18.71, CI = [15.07; 22.34]; F(1,28393)=101.76, p<1 e- 10, Supplementary file 1, row 15). Because fixation durations are themselves dependent upon the target values (see Fixation Durations Depend on Target Value, above), we repeated this analysis using choice probabilities that were corrected to account for the target values (see Methods). Using these corrected choice probabilities, the positive relationship between relative viewing times and choice was maintained. (Figure 6D and C; linear mixed effects regression: β_{time-advantage} = 1.07, CI = [0.92; 0.1.21]; F(1, 28393)=208.90, p<1 e- 10, Supplementary file 1, row 16). Intuitively, this effect size would predict a change in choice probability of ~5% given a change in relative viewing time advantage from –0.1s to 0.1s. Thus, the monkeys were more likely to choose items that were fixated longer, independent of the values of the targets in each trial. The corrected cumulative gaze time bias effects were significantly above zero for data truncated up to 200ms (Figure 6—figure supplement 1).

A prediction of earlier aSSM models is that the item being fixated at the end of the trial should be chosen more often than the non-fixated item, due to the net increase in evidence accumulation for fixated items, and consequently the greater likelihood that evidence for a fixated item reaches a bound at any given moment (Krajbich et al., 2010; Krajbich and Rangel, 2011; Tavares et al., 2017). In contrast, the two-stage model described by Westbrook et al., 2020, suggests that the final fixation reflects, rather than influences, the result of the accumulation process. Therefore, we assessed the final fixation bias in our data in a manner similar to prior studies but with one important difference: as detailed above, the fixation data in each trial were truncated by 100ms to minimize the influence of late-stage gaze effects. In the truncated data, the location of the final fixation in each trial is defined as the target being viewed by the monkey at the virtual end of the trial, which in an aSSM framework can be interpreted as an estimate of when the decision boundary was reached (e.g. Resulaj et al., 2009).

Using the truncated data, we found that the monkeys were more likely to choose the target being viewed at the virtual trial end, consistent with the final fixation bias effects observed in humans (Figure 7, logit mixed effects regression: β_last-is-left=3.35, CI = [2.34; 4.37]; F(1,28392)=42.00, p<1e-10, Supplementary file 1, row 17). Note that this effect is present even after removing up to 200ms from the end of the trial (approximately 25% of the full trial duration, Figure 7—figure supplement 1). This means that final fixation biases can be explained at least in part by an effect of gaze on evidence accumulation – as suggested by prior studies (Krajbich et al., 2010)– when assuming a terminal NDT epoch of up to 200ms.

The analyses above show broad consistency between NHP and human data with respect to the association between gaze and choice behavior. The question remains, however, as to whether these patterns emerge from a similar mechanism to those observed in humans. To this end, we asked whether an aSSM framework could explain the gaze and choice patterns we observed in NHPs. We chose the Gaze-weighted Linear Accumulator Model (GLAM; Molter et al., 2019), which was previously used to explain gaze-related choice biases in humans across multiple independent decision studies (Thomas et al., 2019). Using this model, we asked three questions with regards to our NHP data: First, does a model with a gaze bias mechanism fit our data better than a similar model without a gaze bias? Second, how do gaze biases estimated in our monkey subjects compare to prior human work? Third, can the model accurately predict the critical features of choice behavior, such as accuracy, RT, and the influence of gaze on choice?

To answer the first question, we fit two variants of the GLAM to each monkeys’ data. These variants differed only in their treatment of the gaze bias parameter, γ (see Equation 1 for model specification and parameter definitions). Note that since the model was fit using the NDT-truncated data, we exclusively utilized the multiplicative version of the model (See Figure 4 and associated text). In the first GLAM variant, the gaze bias parameter γ was left as a free parameter, allowing gaze to modify the rate of evidence accumulation for fixated items. The second model fixed γ at 1, assuming a priori that gaze has no effect on the decision process. The maximum a posteriori (MAP) and 95% highest posterior density intervals (HPD) for the parameters estimated in both model variants are given in Supplementary file 2. The relative fit of the two variants was assessed using the difference in WAIC score (dWAIC, Vehtari et al., 2017), defined by subtracting the WAIC value for the model with γ fixed at 1 from the WAIC for the model where γ was a free parameter. The dWAIC for Monkey C was –3357.9, and for Monkey K was –8159.7, indicating that the model that allowed for the presence of gaze biases is the better fit of the two model variants. Further, this difference was significant as indicated by nonoverlapping WAIC values ±their standard error (Supplementary file 1). In the gaze-bias model, γ values were as follows: Monkey C: MAP = 0.079, HPD = [0.045, 0.12]; Monkey K: MAP = –0.056, HPD = [-0.087,–0.018].

Since the GLAM had previously been used to explore gaze biases in four human decision-making datasets (Folke et al., 2016; Krajbich et al., 2010; Krajbich and Rangel, 2011; Tavares et al., 2017), we were able to directly compare the extent of the gaze bias by comparing the γ parameters for humans vs. our monkey subjects. Treating each session as an independent sample, we found that the distribution of γ in each of our monkey subjects fully overlapped with the γ distributions from human studies (Figure 8).

Finally, we assessed the model’s predictive accuracy by performing out-of-sample simulations to predict core features of the behavioral data. To do this, the data were first split into even- and odd-numbered trials. Next, the models were estimated using only the even-numbered trials. Finally, these estimates were used to simulate each of the held-out trials 10 times, resulting in a set of simulated choice and reaction time measures that could be compared to the empirically observed behavior in the held out trials. As illustrated in Figure 9, the model predictions closely match the monkeys’ actual performance (see also Supplementary file 1, rows 18–20 and Supplementary file 4). Note that repeating this procedure with γ fixed at 1 (no gaze bias) produces accurate predictions of choices and reaction times but fails to capture the effect of cumulative gaze-bias on choice (not illustrated, see Thomas et al., 2019).

In summary, an aSSM model that includes gaze bias provides a better fit than a model without a gaze bias, and the magnitude of this bias is comparable to that estimated in human data using the same modeling framework. Finally, the model is able to make accurate out-of-sample predictions of choice and gaze behavior.

While our findings are broadly consistent with those from humans, there are two notable differences between the monkeys’ gaze behavior in the present study, and that of humans reported in prior studies. First, monkeys made fewer fixations per trial than humans on average (~2.5 vs 3.7); second, the monkeys’ final fixations in each trial tended to be prolonged compared to non-final fixations—the opposite of what has been reported in many human studies. Critically, these two differences may be related. For both humans and monkeys, fixations made early in the trial are longer than those made later; thus, because the monkeys’ final fixations occur early in the trial (e.g. either 2nd or 3rd), they will be longer on average than final fixations in humans, which tend to occur later in the trial (e.g. 4th, 5th, etc.).

One significant similarity between the current study and prior studies in humans was the positive association between gaze and choices, which was well-explained using an aSSM. As noted in the results, our data are most consistent with a two-stage aSSM in which gaze initially biases the choice process, and then (after a decision boundary is reached) transitions to a mode in which gaze becomes drawn to the intended choice target (Manohar and Husain, 2013; Westbrook et al., 2020). The behavioral feature of this second stage is consistent with a motor-preparatory phenomenon known as a gaze-anchoring, in which gaze becomes ‘locked’ onto the reach target in order to increase the speed and efficiency of the response (Battaglia-Mayer et al., 2001; Dean et al., 2011; Neggers and Bekkering, 2000).

In prior studies of gaze-anchoring in humans and NHPs, the latency between the eyes locking onto target of an upcoming response and the beginning of detected movement ranges between 64 and 100ms (Battaglia-Mayer et al., 2001; Neggers and Bekkering, 2001; Reyes-Puerta et al., 2010; Stuphorn et al., 2000). The terminal NDT estimate that we derived from the model comparison is consistent with these latencies, and with NDT estimates obtained from standard sequential sampling models (e.g. Resulaj et al., 2009). Ultimately, the true duration of the post-decision epoch is difficult to estimate from behavioral data alone. Additional work will be necessary to either measure or infer the plausible range of post-decision/pre-report intervals in our task, in order to confirm the robustness of the gaze bias effects measured here.

Beyond similarities to prior human studies, our results are also consistent with the handful of NHP studies in which some degree of free eye movement was permitted. Among these, both Hunt et al., 2018 and Rich and Wallis, 2016 imposed some restrictions on eye movements, making it difficult to assess the relationship between fully natural gaze patterns and choices. Cavanagh et al., 2019 used a fully free-viewing design, and also observed a bias in favor of initially fixated items.

Our study confirms this result, and provides additional insights, due to novel elements of the study design. First, by manipulating initial fixation direction, we show that initial fixation has a causal effect on the decision process. Second, the results of the aSSM model-fitting provide a mechanistic explanation for our results and permits a direct comparison to model fitting results in human studies.

Finally, unlike many prior studies, the decision task requires the monkeys to sample the targets by fixating them directly, due to the use of a gaze contingent mask that completely obscures the stimuli at the beginning of the trial, and the use of visual crowders that closely surround each target. This subtle design element is crucial, because it permits accurate measurement of the time spent attending to each target, and of the relationship between relative viewing time and choice. In a forthcoming study using this same task, we show that OFC neurons do not begin to reflect the value of the second-fixated stimulus until well after it has been viewed by the monkey, indicating that value information is only available to the monkey once a target is fixated (McGinty and Lupkin, 2021). In contrast, in tasks where value-associated targets are easily perceived in peripheral vision, even targets that are not fixated influence prefrontal value signals and decision behavior (e.g. Cavanagh et al., 2019; Xie et al., 2018). High-value peripheral targets are also implicated in value-based attentional capture, in which overt or covert attention becomes drawn to objects that are reliably associated with reward (Anderson et al., 2011; Kim et al., 2015). Thus, the task used in the present study minimizes value-based capture effects.

The impetus for developing this animal model is to explore the neural underpinnings of the relationship between gaze and value-based choice. Given the fact that a sequential sampling model provides objectively good fits to the observed behavior, one potential approach for understanding neural mechanisms is to identify brain regions that correspond to different functions in a sequential sampling framework. Such an approach has been used in perceptual dot motion discrimination, where extrastriate cortical area MT is thought to provide the ‘input’ signal (encoding of visual motion) and neurons in parietal area LIP are thought to represent the accumulated evidence over time (see Gold and Shadlen, 2007, for review). One note of caution, however, is that brain activity that outwardly appears to implement accumulator-like functions may not be causally involved in the choice (e.g. Katz et al., 2016). Nonetheless, it is still useful to consider the neural origins of two core computations suggested by sequential sampling models: the representation of the target values (corresponding to the input signals), and neural signals that predict of the actions performed to obtain the reward (reflecting the decision output).

For the encoding of accumulated evidence, findings from NHP neurophysiology point to regions involved in the preparation of movement. In motion discrimination tasks that use eye movements to report decisions, accumulated evidence signals can be observed in oculomotor control regions such as area LIP, frontal eye fields, and the superior colliculus. Because the decision in our task is reported with a reach movement, potential sites for accumulator-like activity include motor cortical areas such as the arm representations within dorsal pre-motor cortex (Chandrasekaran et al., 2017). In addition, human imaging studies have identified several other candidate regions with accumulator-like activity, including in the intraparietal sulcus, insula, caudate, and lateral prefrontal cortex (Gluth et al., 2012; Hare et al., 2011; Pisauro et al., 2017; Rodriguez et al., 2015). Interestingly, several studies find accumulator-like signals in cortical areas in the dorsal and medial frontal cortex, but these are not consistently localized. For example, whereas Pisauro et al., 2017 find accumulator-like activity in the supplementary motor area, Rodriguez et al., 2015 identify a more anterior region in the medial frontal cortex. Additional studies in both humans and NHPs will be necessary to understand the specializations of these regions with respect to encoding decision evidence.

Because decision behavior in this study was value-dependent, regions encoding economic value are strong candidates for signals that provide input to an accumulator. Value-related signals have been observed in numerous cortical and subcortical regions, including the amygdala (e.g. Paton et al., 2006), the ventral striatum (Kable and Glimcher, 2009; Lim et al., 2011), and the ventromedial frontal lobe (VMF), including both the orbitofrontal and ventromedial prefrontal cortices (Padoa-Schioppa and Assad, 2006; Rich and Wallis, 2016; Vaidya and Fellows, 2015). Of these regions, the VMF has received the most scrutiny with regard to gaze-biases. In humans, there is evidence of BOLD activity in this region related to attention-guided decision-making (Gluth et al., 2012; Hare et al., 2011; Leong et al., 2017; Lim et al., 2011; Pisauro et al., 2017; Rodriguez et al., 2015), and patients with lesions to this area show impairments in such tasks (Vaidya and Fellows, 2015).

In NHPs, the orbitofrontal portion of the VMF (the OFC) has been demonstrated to contain value-signals that are dependent on whether gaze is directed towards a reward-associated visual target (Hunt et al., 2018; McGinty et al., 2016; McGinty and Lupkin, 2021) a mechanism fully consistent with the effects of gaze posited by aSSM frameworks. However, the precise neural mechanisms explaining how gaze biases choice outcomes are still unknown. One hypothesis is that the value-coding regions inherit gaze-modulated information from visual cortical regions sensitive to shifts in visual attention. For instance, neurons in the anterior inferotemporal cortex, which projects directly to the OFC (Carmichael and Price, 1995; Kravitz et al., 2013), selectively encode features of attended objects to the exclusion of others in the same receptive field (DiCarlo and Maunsell, 2000; Moore and Armstrong, 2003; Moran and Desimone, 1985; Richmond et al., 1983; Sheinberg and Logothetis, 2001). Therefore, the similar fixation-driven effects on OFC value-coding shown by McGinty and colleagues (McGinty et al., 2016; McGinty and Lupkin, 2021) may be inherited from this structure. Another candidate region for the top-down influences on gaze-dependent value-coding, is the frontal eye fields (FEF). In a recent study from Krajbich et al., 2021, focal disruption of FEF leads to a reduction in the magnitude of gaze-biases. Prior work in both humans and NHPs has shown that the FEF can influence perceptual sensitivity through the top-down modulation of early visual areas (Moore and Armstrong, 2003; Moore and Fallah, 2004; Ruff et al., 2006; Silvanto et al., 2006; Taylor et al., 2007), suggesting that it may exert similar influence on value-encoding regions.

In real-world decision scenarios, both humans and NHPs depend heavily on active visual exploration to sample information in the environment and make optimal decisions. In this way, even simple decisions require dynamic sensory-motor coordination. The importance of these gaze dynamics is underscored by the growing number of human studies showing that gaze systematically biases the decision process. We have developed a novel value-based decision-making task for macaque monkeys and found that monkeys spontaneously exhibit gaze biases that are quantitatively similar to humans’, while also showing the high level of behavioral control necessary for neurophysiological study. This novel paradigm will therefore make it possible to identify the cell- and circuit-level mechanisms of these biases.

The subjects were two adult male rhesus monkeys (Macaca Mulatta), referred to as Monkey C and Monkey K. Both subjects weighed between 13.5 and 15 kg during data acquisition, and both were 11 years old at the start of the experiment. They were implanted with an orthopedic head restraint device under full surgical anesthesia using aseptic techniques and instruments, with analgesics and antibiotics given pre-, intra-, and post-operatively as appropriate. Data from Monkey K were collected at Stanford University (25 sessions, 14,433 trials); data from Monkey C were collected at Rutgers University—Newark (29 sessions, 15,613 trials). All procedures were in accordance with the Guide for the Care and Use of Laboratory Animals (National Research Council, 2011) and were approved by the Institutional Animal Care and Use Committees of both Stanford University and Rutgers University—Newark.

The subjects performed the task while head-restrained and seated in front of a fronto-parallel CRT monitor (120 Hz refresh rate, 1024x768 resolution), placed approximately 57 cm from the subjects’ eyes. Eye position was monitored at 250 Hz using a non-invasive infrared eye-tracker (Eyelink CL, SR Research, Mississauga, Canada). Three response levers (ENV- 612 M, Med Associates, Inc, St. Albans, VT) were placed in front of the subjects, within their reach. The ‘center’ lever was located approximately 17 cm below and 35 cm in front of the display center, and the center points of the two other levers were approximately 9 cm to the left and right of the center lever. The behavioral paradigm was run in Matlab (Mathworks, Inc, Natick, MA) using custom scripts using the Psychophysics Toolbox extensions (Brainard, 1997; Cornelissen et al., 2002) . Juice rewards were delivered through a sipper tube placed near the subjects’ mouths.

To test the causal nature of the relationship between initial fixation and choice, we conducted additional sessions in which we temporally staggered the onset of the two targets (Monkey C: 16 sessions, n=6931 trials; Monkey K: 8 sessions, n=5433 trials). During these sessions, in 30% of the trials the first target array would appear randomly on either the left or right of the screen. The second target array appeared 250ms after the onset of the first, or when the monkeys began their initial saccade away from the central fixation point, whichever came first. The location of the first target array was randomized across trials. This manipulation was intended to encourage the monkeys to direct their attention towards the target that appeared first, as shown in prior human studies (Tavares et al., 2017). As expected, the monkeys directed their initial fixation to the cued target on 96% of the staggered-onset trials.

With the exception of the computational modeling, analyses were performed in Matlab v. R2022a (Mathworks, Inc, Natick, MA). All graphs, except Figure 3, were generated within the Matlab environment. For Figure 3, the violin plots were generated using the Seaborn v. 0.12.2 library for Python (Waskom, 2021). Unless otherwise noted, analyses were conducted using generalized mixed-effects regressions with random effects for monkey-specific slopes and intercepts. To fit these models, data were collapsed across sessions, unless otherwise noted. Full specifications for all models are given in Supplementary file 1. Regression estimates (β’s) and 95% confidence intervals (CI) are reported for each effect. Significance for each effect was determined using a post-hoc ANOVA in which the regression estimates were compared to 0 (F- and p- values, reported in the text).

The onset and duration of fixations, defined as periods of stable gaze upon one of the two targets, were recorded by the Eyelink CL software. For analysis purposes, a fixation was considered to be on a given target if it was located within 3–5 degrees of the target center. Two consecutive fixations made onto the same target were merged into one continuous fixation. Fixations that were not onto either target were discarded; however, these were extremely rare: in the vast majority of trials, the monkeys fixated exclusively upon the targets.

For analysis purposes, fixations were designated as ‘first’, ‘final’ or ‘middle’. First fixations were defined as the first target that was fixated after the onset of the target arrays; final fixations were defined as the target being fixated at the moment the monkey initiates a choice by lifting the center lever; and middle fixations were defined as all on-target fixations that were neither first nor final. Fixation durations were measured in the conventional manner, except for final fixations, which were considered to be terminated at the time of choice in each trial, consistent with previous human studies (Krajbich et al., 2010; Krajbich and Rangel, 2011; Tavares et al., 2017; Westbrook et al., 2020). When using truncated data (see Estimation and Truncation of Terminal Non-Decision Time (NDT), below) final fixations were terminated at the virtual trial end point.

For analyses of the final fixation bias and the cumulative gaze-time bias, trials containing only a single fixation were excluded (Monkey C: N=447 trials (2.8% of total), Monkey K: N=1217 trials (8.4% of total)), as they could artificially inflate either or both of these biases. For the latter analysis, we computed in every trial the time advantage for the left item by subtracting the total duration of fixations onto the right target from the total duration of fixations onto the left target (Krajbich et al., 2010). Thus, for trials where the monkey allocated more gaze time to the left target, the time advantage takes a positive value, whereas it takes a negative value for trials where the monkey allocated more gaze time to the right.

Finally, for the cumulative gaze bias analyses shown in Figure 6D and E, choice proportions were corrected using the same procedure set forth in Krajbich et al., 2010. For each trial, we coded the choice outcome as 0 for a right choice and 1 for a left choice. Then from each trial’s choice outcome we subtracted the average probability of choosing left for all trials in that same condition, where the condition was defined as the left minus right target values. This correction removes from the choice data any variance attributable to the differences in the target values; as a result, Figure 4C and E reflect the effect of cumulative gaze after accounting for the influence of the target values on gaze durations.

To gain insight into potential mechanisms underlying choice and gaze behavior in this task, we employed the Gaze Weighted Linear Accumulator Model (GLAM, Thomas et al., 2019). The GLAM modeling was conducted in Python version 3.7 using the glambox toolbox (see Code Availability for details). The GLAM is an aSSM characterized by a series of parallel accumulators racing to a single bound. These accumulators are co-dependent, such that their combined probability of reaching the bound is equal to 1. For two choice options, this formulation is mathematically equivalent to a single accumulator drifting between two bounds (Thomas et al., 2019; Krajbich and Rangel, 2011). The effect of gaze on choice behaviors is implemented as follows: The GLAM posits that over the course of a trial the absolute evidence signal for each item, i, can have two states: a biased state during periods when an item is viewed, and an unbiased state when it is not. The average absolute evidence for each item, A_i, is a linear combination of these two states throughout the trial. As noted in the results, there are two methods through which gaze could bias choice behavior: a multiplicative manner in which gaze amplifies the value of the attended target, and an additive manner in which gaze adds a fixed increase in evidence accumulation to the attended target, independent of its value.

Assuming a multiplicative bias, A_i is defined according to Equation 1a.(1a)Ai=giri + (1-gi) γri

Here, r_i is the veridical value of target i (number of drops of juice), g_i is the fraction of gaze time that the monkey devoted to that target during a given trial, and γ is the crucial gaze bias parameter, which determines the extent to which the non-fixated item is discounted. This parameter has an upper bound of 1, which corresponds to no gaze bias. A value of γ less than 1 indicates biased accumulation in favor of the fixated item.

Under an additive gaze-biasing mechanism, A_i is defined according to Equation 1b.(1b)Ai=ri + γgi

As in the multiplicative model, r_i is the veridical value of target i (number of drops of juice), g_i is the fraction of gaze time that the monkey devoted to that target during a given trial, and γ is the gaze bias parameter. However, in the additive model variant, a γ value of 0 corresponds to no gaze bias, and a nonzero γ value indicates biased accumulation in favor of the fixated item.

The gaze-adjusted absolute evidence signals for each item are then used as inputs to an evidence accumulation process, as follows: First, each absolute value signal (A_i) is converted to a relative evidence signal, R_i, through a logistic transform (see Molter et al., 2019; Thomas et al., 2019 for details and rationale). Then, evidence for each item (E_i) at time t is accumulated according to Equation 2, where ν and σ indicate the speed of accumulation and the standard deviation of the noise, respectively, and R_i is the relative evidence signal. N indicates a univariate normal distribution. A choice is made when the evidence for one of the items reaches the threshold.(2)Ei(t) = Ei(t-1) + vRi +N(0,σ2); Ei(0) = 0

We fit several different variants of the GLAM model to each monkey’s data. To evaluate a hybrid two-stage modeling framework, we compared the relative fit of multiplicative and additive models to the data (Figure 4). Given the overall better fit obtained from the multiplicative models, these were used for the remainder of the analyses. To evaluate the necessity of the gaze bias parameter γ for explaining behavior, we used two variants of the multiplicative model, one in which the gaze bias parameter was left as a free parameter, and another that assumed no gaze bias by setting γ=1 (results in reported in Supplementary file 2). Model fits were compared using the Widely Applicable Information Criterion (WAIC, Vehtari et al., 2017) which accounts for the differences in the complexity of the two model variants. Specifically, we used both the signed difference of WAIC values and the WAIC weights for each model, which can be interpreted as the probability that each model is true, given the data (Vehtari et al., 2017).

In addition, we assessed the model’s predictive accuracy by estimating the parameters for the free- γ model variant using only even numbered trials, and then using these parameter estimates to simulate the results of each of the held-out odd-numbered trials 10 times. We quantified the goodness-of-fit of the simulations by comparing three outcome metrics: choice, RT, and corrected probability of a leftward choice as a function of the cumulative gaze time advantage for the left item (as in Figure 4D and E). Note that since value is removed from the corrected cumulative gaze effect metric (see above), the only input to the model that could modulate it was the relative amount of gaze time devoted to each target. Thus, we can use this metric to assess the model’s ability to emulate the net effect of gaze alone on choice. For each metric we computed a mixed effects regression (logistic for choice, linear for RT and the corrected cumulative gaze effect), in which a vector including both the empirically observed data and the simulations was explained as a function of a binary variable indicating whether a data point came from the empirically observed data, or from the model simulations (i.e. Metric ~1 + isSimulated). If the fixed effect of this variable was not significantly different from 0, then the simulated data did not deviate from the empirically observed data. The mean deviations for each metric are given by the beta-weights and are reported in Supplementary file 4 along with the confidence intervals. As with the other regression models used in this paper, ‘Monkey’ was included as both a random slope and intercept.

All GLAM parameter estimation procedures were identical to those set forth in Thomas et al., 2019, with one exception: Thomas and colleagues assumed a fixed rate of random choice of 5%. This was changed to 1% to reflect the extremely low lapse rate for the easiest trials shown by both monkeys. The lapse rate for each monkey was estimated by finding the percentage of trials in which the monkey chose a 1-drop target when a 5-drop target (the highest possible value) was also available (mean lapse rate: Monkey C=0.64%, Monkey K=0.33%).

In sequential sampling models, the interval between when a decision is reached and when it is detectable to the experimenter is referred to as non-decision time (NDT). To account for and minimize the influence of gaze behavior in this interval, we truncated the gaze data using an estimate of this post-decision epoch. To obtain this estimate, we leveraged the key assumption of the two-stage aSSM, namely that gaze acts in a multiplicative manner prior to a boundary crossing (i.e. reaching a latent decision) and then additively between the boundary crossing and when the decision is reported (i.e. the RT, Manohar and Husain, 2013; Westbrook et al., 2020) Therefore, by removing gaze data from the end of the trial, the probability of the data being better explained by an additive model (and not a multiplicative model) should decrease as more data are removed. We collapsed data across the two monkeys and fit both an additive and a multiplicative variant of the GLAM for data truncated at 0ms, 50ms, 100ms, 150ms, 200ms, 300ms, and 400ms. We then compared the posterior probabilities of the model being correct given the data and the alternative model using the compare function from PyMC. We also compared the WAIC for the two variants, for each level of truncation (Supplementary file 4). The relative probability of the additive model generating the data decreases sharply between 0ms and 100ms of truncation, after which it reaches zero.

Accordingly, we selected 100ms as our NDT estimate, and for the data shown in the main figures we removed gaze data between center lever lift and 100ms before the lever lift in every trial. In other words, in every trial the gaze data were treated as if the trial had actually ended 100ms before the center lever lift; all calculations related to the gaze sequence and timing were calculated with respect to this virtual trial stopping point. For trials where the virtual stopping point occurred during an earlier fixation, we reassigned the final fixation location according to the location of the eyes at the virtual stopping point. In this way, the effects of late-trial gaze effects during the NDT were minimized. The truncated data were used to compute the gaze biases, except the initial fixation bias, and were also used as input to the computational model. Importantly, the main analyses were repeated using truncation values ranging from 0 to 400ms, with results shown in Figure 6—figure supplement 1, and Figure 7—figure supplement 1.

Because the behavioral task was novel, and because there were no published data from free-viewing NHP decision tasks at the time the study began, there were no effect size estimates available to facilitate a power analysis. We therefore began by collecting a pilot sample, and assessing the initial gaze bias and cumulative gaze bias effects as reported in humans by Krajbich et al., 2010. To minimize confirmatory bias stemming from exploratory analyses, these initial analyses procedures were identical to those in Krajbich et al. The first pilot sample, in Monkey K, consisted of 13 sessions (approximately 8000 trials). Using planned analyses from Krajbich et al., we identified statistically significant initial fixation and corrected cumulative gaze biases. Based upon this initial sample, we then targeted a per-monkey sample size of approximately 10–15 sessions or 7000–15,000 trials for detecting behavioral effects of interest in subsequent experiments.

We then collected additional sessions from Monkey K for the purposes of electrophysiological recordings. These were combined with previous behavior-only sessions to create the Monkey K data used in this study (total = 25 sessions). From the second monkey we first collected 13 behavior-only sessions, and then additional 16 sessions for the purpose of electrophysiological recordings, resulting in the 29 sessions for Monkey C reported here.

We defined outlier sessions as those in which the fraction of suboptimal decisions exceeded ~1% for the easiest choices (+/-3 or 4 on the X-axis in Figure 1D), indicating that the monkeys had not yet sufficiently learned the target values; these sessions were excluded from analysis. No exclusions were made on the basis of gaze data, or upon gaze-related outcome measures.

The data and code in this folder are available at https://osf.io/hkgmn/. The glambox toolbox that was used for the computational modeling can be accessed at https://github.com/glamlab/glambox (Molter et al., 2019). The associated documentation can be accessed at https://glambox.readthedocs.io/en/latest/.