Influence of environmental statistics on inhibition of saccadic return

Abstract

Initiating an eye movement is slowed if the saccade is directed to a location that has been fixated in the recent past. We show that this inhibitory effect is modulated by the temporal statistics of the environment: If a return location is likely to become behaviorally relevant, inhibition of return is absent. By fitting an accumulator model of saccadic decision-making, we show that the inhibitory effect and the sensitivity to local statistics can be dissociated in their effects on the rate of accumulation of evidence, and the threshold controlling the amount of evidence needed to generate a saccade.

Our eyes are constantly moving to sample the visual world. Explaining this complex behavior boils down to the fundamental questions: Where and when do we next shift our gaze? The classic approach to answering these questions is to focus on the “visual” (that is, external) determinants of looking behavior. However, recent studies have shown that the history of preceeding saccades is another important factor. It is now clear that the dynamics of our eye movements are determined not only by the current visual stimulus, but also by the stimuli we have seen and the eye movements we have recently made (1–5).

One example of the influence of saccade history on future saccades is the phenomenon of inhibition of saccadic return (ISR): The fixation duration before a saccade to a previously fixated location is longer than that preceding movement of the eyes to a location that has not been recently visited (6–10). ISR has been related to inhibition of return (IOR), the more general phenomenon whereby attention takes longer to return to a target presented at a previously cued location, when the delay between the cue and the target is sufficiently long (11–14).

A commonly cited and intuitively appealing explanation for IOR and ISR is from the viewpoint of optimality: Because, over time, the visual environment and our behavioral goals will stay relatively unchanged, a location is unlikely to provide any new information if immediately revisited (e.g., refs. 8, 11, 13, and 15). An adaptive system would take advantage of this temporal stability by biasing attention (13) and saccades (8) away from previously attended or fixated locations and toward novel information at new locations. This explanation for why IOR (and ISR) occurs is intuitively appealing but is predicated on the assumption that the world and our goals remain relatively static. Although this assumption may often hold, it is also clear that the utility of inhibition is context-dependent. In dynamic, fast-changing environments (e.g., the classic example of looking for your friend in a moving crowd) refixating previously inspected locations will be more informative. In relatively static situations (e.g., looking for a book in the library) inhibiting previously sampled locations is more adaptive.

A system that is optimized for one set of environmental constraints will not be optimized for another set of constraints. This environmental variability raises an important and fundamental question about the link between the properties of the visual-saccadic system and the statistics of the world. Specifically, does the system flexibly adapt to the statistics of the local environment, or is ISR a more inflexible mechanism for capturing the long-run statistical characteristics of the environment generally?

Is ISR Sensitive to Environmental Statistics?

To address this issue, we asked observers to carry out cued sequences of saccades and manipulated the probability that they would be required to shift their gaze back to a previously visited location. We used the gaze-contingent saccade sequencing paradigm (9) to cue short sequences of two saccades. A schematic of a sequence is shown in Fig. 1. Observers were required to fixate in the center of a single circle. On stable fixation three possible saccade targets (circles) appeared to form a square configuration. Simultaneously, a cue presented at the current fixation location indicated the target of the first saccade through its orientation. Once the observer made a saccade to that target, after a short delay a new cue was presented, indicating the target for the second saccade. This target could cue a saccade to a return (previously visited) location or to a new location (that had not been fixated during that sequence). On fixating this final location, the circles disappeared and a new sequence was initiated by the experimenter.

Fig. 1.

Design of an experimental trial. After fixating on a starting circle (and the experimenter correcting for drift), an additional three circles appear, along with a central cue indicating the next target. After saccading to that target, and without removing the circles, the old cue disappeared and a new cue appeared at fixation to cue either for a return saccade to the starting position, or a saccade to a new location.

Participants completed the task under one of three conditions of environmental probability. In the “Equal” condition, the second saccade was equally often directed to the three possible target locations. Specifically, for the two “new” locations that had not been previously visited, and the “return” location that had been previously visited, the probabilities were 1/3, 1/3, and 1/3 respectively. In the “Low” and “High” conditions, the second saccade target was biased toward the new and return locations, respectively (with return probability 1/6 in the Low condition, and 1/2 in the High condition). The same return probability was maintained across three experimental sessions. Further details of the experiment and scoring are available in the Materials and Methods.

The mean latencies for correct saccades in the three conditions are shown as lines in Fig. 2. A mixed-effects ANOVA revealed a main effect of target location [F_{(1, 33)} = 108.14, P < 0.001], indicating substantial, overall ISR effect, where the mean latency of saccades to return locations (303 ms) was longer than that for new saccades (268 ms). Crucially, there was an interaction between target location and probability condition [F_{(2, 33)} = 15.86, P < 0.001]: ISR increased as return probability decreased. An effect of session was also observed [F_{(2, 66)} = 70.18, P < 0.001]; participants’ overall latencies decreased with practice across the three sessions. Choice accuracy, in terms of the proportion of saccades landing in the quadrant of the target, mirrored the latency results (bars in Fig. 2). Saccades to targets at return locations (mean proportion errors = 0.16) were more likely to be incorrect than for targets at new locations (mean proportion errors = 0.08) [F_{(1, 33)} = 40.71, P < 0.001]. However, this effect was modulated by return probability in that accuracy for return targets increased as return probability increased [F_{(2, 33)} = 4.42, P = 0.02].

Fig. 2.

Mean latency of correct saccades across sessions (lines, with scale on left axis) and mean proportion of saccades that were directed toward one of the nontargets (bars, with scale on right axis), separately for return and new targets, and for the three different return probability conditions. Error bars represent SEs.

These data demonstrate that ISR is not a predetermined characteristic of the system responsible for controlling saccades to explore the visual environment. The system is sufficiently flexible to adapt to the temporal statistics of the local environment. Although the discussion of the nature and role of inhibition of (saccadic) return has generally been conducted in the framework of some broad notions of optimality, our results highlight that such a discussion cannot take place without consideration of the environment in which the observer is situated.

ISR and Return Probability in a Model of Saccadic Decision-Making

What are the implications of such results for theories of inhibition of return and, more generally, for conceptualization of visual-saccadic decision-making? In particular, we ask what mechanisms are responsible for producing ISR and its adaptation to the temporal statistics of the local context?

We conceptualize saccade generation in the more general framework of accumulator models of decision-making (e.g., refs. 16 and 17). The decision about where and when to move the eyes is treated as the accumulation of evidence in favor of different possible saccade alternatives. When the evidence in favor of one alternative crosses a decision criterion, a saccade is initiated to that location. Although a fully specified model would treat space as fully continuous (as in dynamic field theory; e.g., ref. 18), we make the simplifying assumption that several discrete locations compete for action. The broad class of evidence-accumulation models is popular in cognitive psychology (e.g., refs. 16, 19, and 20) and oculomotor physiology (2, 21), partly because neurons in a variety of brain areas involved in perceptual-saccadic decision-making [superior colliculus (SC), frontal eye fields (FEF), and lateral intraparietal area (LIP)] have been found to behave like the theorized accumulators (22–29).

In previous work, we have used one particularly simple, yet effective instantiation from this class of models, namely the linear ballistic accumulator (LBA) (17). The LBA model may be regarded as a generalization of the linear approach to threshold with ergodic rate (LATER) model (2, 30) in which the race between accumulators instantiates the choice of which of several possible movement programs will be carried out. This generalization enables the model to account for both choice and latency, or the when and where in saccade generation, and allows the model to account for the occurrence of errors and the latency of those errors (17). A schematic of the model is shown in Fig. 3. The accumulators begin with a pretarget activation drawn from a uniform distribution with maximum s. After presentation of the cue, the accumulators linearly and deterministically increase their activation. The rate of accumulation is drawn independently for each accumulator and saccade from a normal distribution with standard deviation σ_v; the mean accumulation rate for targets, v_T, is larger than for nontargets, v_D. Once the activation of any accumulator passes the corresponding response threshold, a saccade to the location associated with the winning accumulator is generated, and the saccade latency is given by the sum of the time spent accumulating, and a non-decisional component, T_er.

Fig. 3.

A schematic of the LBA as applied to saccadic decision-making. The three potential targets start with resting levels drawn from a uniform distribution with range 0–s. Sometime after cue presentation, the information from the stimulus starts to accumulate in the three accumulators, with variable rate. The dark line shows the accumulation of evidence for the target (mean accumulation rate = v_T), whereas the light grays show accumulation for the two nontargets (mean accumulation rate = v_D). Once the accumulated evidence in any accumulator passes its corresponding threshold, a saccade is initiated to that location, with the saccadic latency being given by the time to reach the threshold plus the non-decisional component T_er. The experimental manipulations (target location and probability mixture) are allowed to have effects on two components: α, the proportional adjustment of accumulation rate for return saccades; β, the threshold for accumulators corresponding to return saccades. In the figure, the target is presented at a previously visited (return) location, and so has mean accumulation rate = αv_T and threshold βz.

In the context of this class of models, there are two plausible candidate mechanisms to account for the basic ISR effect. First, ISR may be due to a reduction in the rate of accumulation of evidence in favor of making a return saccade. This mechanism is implemented in the model by allowing the accumulation rate to differ between new and return locations; the accumulation rate for alternatives at previously visited locations is scaled by a parameter α. The second mechanism is that ISR results from an increase in the amount of evidence needed to decide in favor of a return saccade (giving non-return accumulators a head start). This possibility was implemented by allowing the decision criterion to vary between return and new alternatives (z for alternatives at new locations, and βz for the return location). Note that this assumption is formally equivalent to allowing the baseline to differ between return and new locations, consistent with the electrophysiological evidence (31–33). For reasons of convenience, we parameterized this possible difference in the thresholds rather than the baseline. Nevertheless, our preferred interpretation is in terms of variation in baseline.

Critically, these mechanisms cannot be distinguished by examining mean saccade latencies; the entire distribution of latencies needs to be considered (see figure 1 in ref. 9). We (9) have shown that when the LBA model is fit to the data in this fashion, ISR is revealed to be exclusively due to a reduction in accumulation rate for return locations. The question now is: What mechanism(s) in the model mediate the sensitivity of the empirical ISR effect to the statistics of the environment? On the one hand, the finding that the ISR effect is related only to accumulation rate suggests that accumulation rate should also be mediated by the probability of a return saccade being required, because both will ultimately lead to a change in mean RT in Fig. 2; this possibility would represent a simple model of ISR. On the other hand, the sizeable literature relating environmental statistics to changes in baseline activation in models (2) and neurons (31–33) suggests that the baseline tracks the prior probability of a response (e.g., refs. 2 and 34). Because our experimental manipulation is essentially a variation in prior probability, the environmental statistics would be expected to affect the baseline. Finally, it is possible that both baseline and accumulation rate are modulated by environmental probability.

In the model fits we report below, we were interested in how the scaling of the accumulation rate (α) and threshold for the return location (β) varied across the probability conditions. The model was fit to the latency distributions of correct responses and the frequency of errors for each individual observer and session (see Materials and Methods for details). Fig. 4 shows the average fit of the model to the latency and accuracy data, by probability condition (rows) and session (columns). In each graph, the average cumulative distribution function (CDF) for latencies of correct saccades to targets at return (light red) and new (light blue) locations is shown. The defective nature of the CDFs implies that the upper asymptote corresponds to the predicted accuracy in that condition. Also shown are the quantiles averaged from the participants’ data (red and blue crosses correspond to return and new locations, respectively); the rightmost cross in each series is the observed proportion correct, replotted from Fig. 2 for comparison with the model prediction. Below each averaged CDF are the rates of different types of errors in the model (left set of columns) and data (right set of columns); see figure legends for more details. Overall, the model gives a good fit to the data, justifying inference from the estimated maximum likelihood parameters.

Fig. 4.

Fits of the LBA model to saccadic decision-making data. Rows of graphs correspond to the different probability conditions, and columns correspond to experimental session. The main plot in each graph shows the defective cumulative probability density function predicted by the model (solid line) for correct saccades to return (light red) and new (light blue) locations. Also shown are empirical quantiles (crosses) for the return (red) and new (blue) locations; the cross at the extreme right corresponds to observed proportion correct. The embedded plot in each graph shows proportion of responses that were errors in the model (left set of columns) and data (right set of columns). The light red bar shows probability of saccading to a new location when the target was at a return location; the dark and light blue areas in the stacked bar respectively depict the probability of fixating the the return location and the (incorrect) new location when the target was at a new location.

Fig. 5 shows the average values of the proportional factor α scaling the accumulation rate for return saccades (Left) and the threshold for responding for return saccades, β (Right). For both parameters, a value of 1 would correspond to the absence of ISR (dashed horizontal lines). Fig. 5 Left clearly shows that for all three probability conditions α was significantly below the value of 1 [F_{(1, 33)} = 90.36, P = < 0.001]. This result is a replication of our previous finding that ISR is mediated by a reduction in the accumulation rate associated with return locations (9). Importantly, the modulation of ISR by environmental statistics is not reflected in the accumulation rates [F_{(2, 33)} < 1]. Mean α did increase across sessions [F_{(2, 66)} = 9.03, P < 0.001], suggesting that the overall reduction in ISR with practice is mediated by a relatively slow and subtle change in the return accumulation rate.

Fig. 5.

Mean parameter estimates for the linear ballistic accumulator model for the three return probability conditions (separate lines). Left shows the factor α scaling accumulation rates, and Right shows the decision criterion for return saccades (decision criterion for new saccades is fixed at 1). The dashed line shows the expectation of “no difference” between new and return saccades. Error bars represent SEs.

Fig. 5 Right illustrates the critical result. The amount of evidence required to make a saccade to a return location depends strongly and lawfully on the environmental statistics. In the high and low return probability conditions, the mean criterion for return saccades was found to be 0.88 and 1.18, respectively. The mean criterion in the equal probability condition was 1.03 and did not differ significantly from the “no difference” value of 1, the fixed criterion for new saccades [F_{(1, 33)} < 1]. The effect of probability condition on the criterion for return movements was highly reliable [F_{(2, 33)} = 25.07, P < 0.001]. Furthermore, these results are not tied to the specific model we have adopted, or the model analysis we have used. SI Text and Tables S1–S5 show that several variants of the LBA, including a sequential sampling version of the model, all produce the same dissociation between α and β.

The modeling shows a clear dissociation between the mechanism responsible for the basic inhibitory effect (an attenuation in the rate of accumulation) and the mechanism responsible for its tuning to the statistics of the local environment (an adaptive change in the evidence criterion). Importantly, as will be discussed below, the changes in evidence criterion determine whether ISR will manifest itself in behavior.

Discussion

We have shown that ISR is sensitive to the statistical properties of the local context. When return locations are likely to become behaviorally relevant the magnitude of ISR is reduced (indeed, eventually abolished altogether). This effect was manifest in both the accuracy and latency of saccadic responses. We used an evidence accumulation model to address the mechanism underlying ISR and its adaptation to the local environment. Fitting the model to defective latency distributions of saccades to return and new locations showed that ISR is always present in the (mean) accumulation rate: evidence is accumulated at a slower rate when pointing to the return location. Whether “behavioral” ISR in the latency and accuracy was present depended critically on the evidence criterion which, in turn, depended systematically on the statistical context. For instance, in the high return probability condition, behavioral ISR appeared to be abolished by the second session. However, the underlying model parameters show that the accumulation rate for return locations was still suppressed under these conditions. The reduced accumulation rate was offset by a reduction in the amount of evidence required to initiate a return movement. As a result, no ISR was manifest in mean latency and choice accuracy. Conversely, when the return probability was low the criterion was elevated, thereby magnifying behavioral ISR.

These findings integrate well with the known neurophysiological underpinnings of IOR and other intertrial effects in visual-saccadic decision-making (31–33, 35). Previous work (35) suggests that ISR results from a lowered rate of accumulation for SC neurons that selectively code for the return location. This change in accumulation rate was linked to target-related activity and not the prior resting level, because a similar inhibition was not found when the cells were directly microstimulated (35). Although Dorris et al. (35) interpreted this finding as suggesting a lowered rate of extraction of sensory information from the stimulus, in our study the target was visually identical to the nontargets and was distinguished from those locations by an endogenous cue at the currently fixated location (9). Accordingly, we prefer to see ISR as reflecting the lower rate of accumulation for return locations in a general priority map for selection (36, 37). This view is consistent with the suggestion (e.g., refs. 11 and 38) that the SC enacts the effects of IOR but that these are likely to have a source upstream, for example, in FEF (39) and parietal cortex (40).

Behavioral and neurophysiological findings also accord with the finding that the criterion responded to the probability manipulation. Behavioral studies with humans and monkeys have shown that responses are faster and more likely to be directed to targets that have a higher prior probability (2, 31, 33, 41, 42). In the framework of accumulator models, these manipulations of prior probability have been found to modulate the amount of information needed to make that decision (2, 34), exactly as was the case for the return probability manipulation here. This result meshes with neurophysiological studies that show changes in the resting baseline of cells in response to the prior probability of a target appearing in their receptive field (31–33, 41).

One surprising aspect of our results is that the accumulation rate and evidence criterion are independently affected by what are both essentially historical effects. Although such dissociations have been observed (43), the prior probability of an alternative before stimulus onset has been uniquely associated with the criterion of evidence. In the present case, both factors—whether the upcoming saccade is to an old or a new location, and the overall probability of being required to make a return saccade—are factors that are relevant before the presentation of the movement signal, but only one of these affected the evidence criterion. Why these two factors dissociate in this fashion is still something of a puzzle. We suggest that the “standard” ISR reflected in a change in accumulation rate is a fixed heuristic used by the visual-saccadic system and reflects a default, acontextual assumption about the temporal structure of the environment. However, as stated earlier, the temporal statistics of the natural world will vary in a context- and task-specific manner. We propose that that the baseline quickly adapts to track current return probabilities (34). Indeed, the absence of an interaction between session and return probability in our data suggests the effects on criterion emerged rapidly and, therefore, operate on a short timescale. Indeed, it is quite possible that these effects operate on the scale of 2–3 trials (44). Having such a plastic mechanism to track the local probabilistic structure independent of overall, long-run probabilities ensures that human behavior is flexibly adapted to the statistics of the local context.

Materials and Methods

Experiment.

Thirty-six observers (27 female; age range 18–33 yr) participated in the experiment, all of whom had normal or corrected-to-normal vision. Observers in both experiments participated in an endogenously cued saccadic choice task (9). Observers were arbitrarily assigned to one of three return probability conditions. Each observer participated in three, five-block sessions, each session lasting for ≈1 h, and with sessions taking place at least a day apart. They were required to make sequences of two eye movements (72 complete sequences per block). Eye movements were recorded with a spatial resolution of 0.3° and temporal resolution of 500 Hz using an Eyelink II system (SR Research).

A trial began with a circle of radius 1.5° appearing at one of four locations (placed in a square configuration). Observers fixated inside this circle, and a drift correction was performed. Circles then appeared at the other three locations, adjacent circles being separated by 7° visual angle. Simultaneously, a line appeared at fixation indicating the target for the first saccade. Participants were required to perform a single saccade landing on the circle; the actual “region of acceptance” for the target was an unmarked circle of 3° radius centered on the target. If this saccade was successful, after a period of 390 ms, the cue at the previous fixation was removed, and a new cue appeared at the current fixation. If the first saccade was not made successfully, the trial was aborted and a new trial began. Because of this procedure, observers were instructed to perform their saccades accurately. Within this constraint, observers were treating this as a speeded task: Our saccadic latencies are similar to those in other studies in which central cues are used to signal speeded movement initiation (45). All other stimuli, eye movement recording and procedural details are identical to those in previous work (9).

In anticipation of the computational modeling, which assumed a small number of possible discrete responses (the target and the two nontargets), a liberal criterion scoring was applied to saccades. Specifically, for each sequence the second saccade was turned into a discrete response by dividing the display into four quadrants containing the four possible locations (including the point of fixation before the second saccade). The second saccade was then classified according to the quadrant in which it fell: the quadrant of the target; the two quadrants corresponding to the two nontargets; and the quadrant containing the prior fixation (the latter responses being discarded from the analysis). Adopting this liberal criterion made little difference to proportion correct compared to a stricter criterion requiring saccades to fall within the “region of acceptance” of the target.

Modeling.

Description of model.

The basic latency probability density function for accumulator i in the LBA is given by

where Φ is the cumulative normal distribution function. If i is the accumulator for the target, v_i = v_T; otherwise, v_i = v_D. The threshold z_i is also accumulator-specific, to allow for ISR and probability condition effects on the amount of activation needed to trigger that response. The threshold for new locations is fixed at 1 (it is a scaling factor here; see ref. 17 for details), whereas the threshold for the return location is given by the parameter β. The accumulation rate is also allowed to vary between new and return locations, by multiplying the accumulation rate for return accumulators by a scalar α; accordingly, targets at return locations have a mean accumulation rate αv_T, and nontargets at return locations have a mean accumulation rate αv_D. The defective density ψ_i(t) is obtained by multiplying Eq. 1 by the probability that no other accumulator has yet crossed the threshold

where F_j is the (nondefective) cumulative distribution function for accumulator j, given by

φ being the standard normal density function (17), and y being the unshifted latency t – T_er.

Modeling procedure.

Data were partitioned by condition, participant, and session. A set of parameters was estimated for each data partition to reflect the fact that the parameters may vary in an unobservable fashion between observers and across the three testing sessions. Parameters were estimated by maximum likelihood estimation using quantiles. Before fitting, the 0.1, 0.3, 0.5, 0.7, and 0.9 quantiles were estimated for correct saccades to return and new locations, separately for each data partition. The proportion of saccade latencies predicted to fall between these quantiles (or beyond, in the case of the 0.1 and 0.9 quantiles) was calculated by numerically integrating the defective density for the target accumulator and taking the difference between successive quantiles. A likelihood was calculated from the model by using the G² statistic

The 15 cells in Eq. 4 are the 6 proportions demarked by the empirical quantiles × 2 for new vs. return targets, and three cells representing the occurrence of three types of errors (saccades to new locations when the target was a return location; saccades to return location when the target was at a new location; and saccades to the nontarget new location when the target was also at a new location). The quantities p_i and π_i are, respectively, the observed proportions and those predicted by the model. The free parameters v_T, v_D, σ_v, s, T_er, α, and β were estimated by minimizing the G², using the polytope algorithm of (46). For each data partition, 2⁷ different starting values were used to maximize the chance of finding the global minimum.