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The representation of priors and decisions in the human parietal cortex [1]

['Tom R. Marshall', 'Centre For Human Brain Health', 'School Of Psychology', 'University Of Birmingham', 'Birmingham', 'United Kingdom', 'Wellcome Centre For Integrative Neuroimaging', 'Department Of Experimental Psychology', 'Oxford University', 'Oxford']

Date: 2024-02

Animals actively sample their environment through orienting actions such as saccadic eye movements. Saccadic targets are selected based both on sensory evidence immediately preceding the saccade, and a “salience map” or prior built-up over multiple saccades. In the primate cortex, the selection of each individual saccade depends on competition between target-selective cells that ramp up their firing rate to saccade release. However, it is less clear how a cross-saccade prior might be implemented, either in neural firing or through an activity-silent mechanism such as modification of synaptic weights on sensory inputs. Here, we present evidence from magnetoencephalography for 2 distinct processes underlying the selection of the current saccade, and the representation of the prior, in human parietal cortex. While the classic ramping decision process for each saccade was reflected in neural firing rates (measured in the event-related field), a prior built-up over multiple saccades was implemented via modulation of the gain on sensory inputs from the preferred target, as evidenced by rapid frequency tagging. A cascade of computations over time (initial representation of the prior, followed by evidence accumulation and then an integration of prior and evidence) provides a mechanism by which a salience map may be built up across saccades in parietal cortex. It also provides insight into the apparent contradiction that inactivation of parietal cortex has been shown not to affect performance on single-trials, despite the presence of clear evidence accumulation signals in this region.

Funding: JOR is supported by a Career Development Fellowship from the Medical Research Council (MR/L019639/1). MR is supported by a PhD studentship from the Wellcome Trust (109064/Z/15/Z). LTH is supported by a Sir Henry Dale Fellowship from the Royal Society and the Wellcome Trust (208789/Z/17/Z). The Wellcome Centre for Integrative Neuroimaging is supported by core funding from the Wellcome Trust (203139/Z/16/Z). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Copyright: © 2024 Marshall et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Although cortical regions concerned with saccade selection exist in both frontal cortex (frontal eye field (FEF)) and parietal cortex (lateral intraparietal area (LIP)), this study focusses on the parietal cortex. The reason for this is mainly practical, as the visual frequency tag signal is attenuated as it propagates forward in cortex and is not detectable in the frontal lobe. However, we note that recent studies using cortical inactivation in rodents and monkeys suggest a key role of parietal saccade regions in construction of the prior. Rats with parietal inactivation showed a reduced influence of previous trials on interval judgements, and parietal neurons were shown to represent information about recent trials [ 23 ]. In contrast, inactivation of frontal eye fields (frontal orienting fields in the rat) affects performance on single trial target selection, but inactivation of parietal cortex does not [ 24 , 25 ]. Therefore, the parietal cortex is a strong candidate for the neural substrate of the prior for saccadic selection.

To probe changes in input gain relating to prior beliefs, we developed a novel approach using human neuroimaging (magnetoencephalography (MEG)), using the method of rapid frequency tagging. We reasoned that a change in input gain, such as one evoked by a change in synaptic weights [ 18 ], should result in a change in gain for even irrelevant sensory stimuli colocated with favoured saccadic targets. In rapid frequency tagging, an irrelevant, invisible perceptual manipulation (high-frequency rhythmic flicker of the targets), known to produce strong increases in oscillatory power in sensory cortices [ 21 , 22 ], is presented. These “tag” oscillations propagate forward through the visual system, thus indirectly probing input gains to higher visual areas such as posterior parietal cortex. Importantly, 2 competing saccadic targets can be tagged with different frequencies so that the representation for the 2 targets can be precisely separated as it propagates forward through the visual system, even if populations of cells tuned to the different targets are partially or completely spatially intermixed. This approach is therefore sensitive to prior beliefs encoded via synaptic plasticity [ 18 ] rather than neural firing rates.

In contrast, the mechanisms by which a prior or model is built up across multiple saccades is less well understood. A prior could be implemented by many possible neural mechanisms. One such mechanism is via modulation of the baseline firing rate of target-selective neurons; this has been observed in monkey LIP. However, such an “active” representation of the prior would be energetically costly over longer timescales [ 7 , 20 ]. A second candidate mechanism has been proposed, in which synaptic weights from neurons in the “input layer” (visual cortex) to the layer representing the prior are adjusted to favour different sensory inputs [ 18 ]. This process, which is largely activity silent in the absence of stimulation but results in a modulation of sensory input gain, would be an energy-efficient way to store priors over longer timeframes.

The mechanism by which candidate saccadic targets “compete” has been elucidated using evidence accumulation paradigms, designed to extend the saccade selection process over hundreds of milliseconds—most commonly random dot kinematograms (RDKs) or “moving dots” tasks [ 14 ]. Spatially selective neurons in frontal and parietal cortical eye fields (FEF and LIP) track the accumulation of evidence in favour of a saccade to their response field [ 10 – 13 ]. Such evidence-tracking activity is consistent with a model in which the neuronal population activity at a given moment represents the log odds that the preferred location will be the target of the next saccade, effectively ramping up to target selection or down to target rejection. The process could arise from ramping at the level of individual neurons [ 10 , 15 ] or from the gradual accrual of “step-changes” in individual neuronal activity [ 16 ] and can be described mathematically as a sequential probability ratio test [ 12 ]. A key element of this decision model is a winner-take-all competition between targets [ 17 ]. An influential biophysically specified form of this model developed by Wang and colleagues describes how 2 pools of neurons compete with each other to determine the choice of saccadic target [ 18 , 19 ]. In the present study, we use the Wang model to identify MEG signatures of the saccade selection process for each individual saccade.

The neural processes underlying the selection of individual saccades are, due to a combination of electrophysiological and modelling work, relatively well understood [ 10 – 13 ], but the representation of the prior is less so; the latter is the focus of the current study.

As an observer views a visual scene, several saccadic eye movements per second are generated in order to direct the eye’s small focal window to points of potential interest. However, each sample does not stand alone—instead, information from multiple fixations is integrated to construct a “model” of the full visual field [ 1 , 2 ], and this model, in turn, acts as a “prior,” influencing the selection of targets for future saccades [ 3 ]. Therefore, the process of active sampling may be viewed as an interplay between 2 concurrent processes with distinct characteristics:

Far from being passive recipients of sensory information, both humans and animals actively sample the environment using their sensory organs. In rodents, active sampling processes include whisking and sniffing; in primates, the most important and best-studied process is the control of saccadic eye movements.

Results

The classic RDK task [26] has previously been used to show the modulatory effects of both probabilistic cueing [27,28] and choice history [29,30] on evidence accumulation. We modified this task in 2 ways (Fig 1A) to generate distinct predictions about the neural signatures of both the competitive process of selecting a single saccade and the integrative process of constructing and representing the prior.

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TIFF original image Download: Fig 1. Adapted dot-motion task. (A) Trial sequences were presented where certain motion directions were more common, with unpredictable “reversals” (top), and stimuli within a trial varied along 2 orthogonal dimensions; number of dots moving left and right, with all other dots moving randomly (bottom). (B) The cross-trial prior probability p(correct direction = right) varied across the experiment, with pseudo-random, unsignalled “blocks” of trials in which the dominant direction was rightwards 20%, 50%, or 80% or the time (grey line). Bayesian learning models were used to estimate direction and strength of beliefs and observer should have about the current trial based on previous trials (purple line). (C) On a given trial, the correct response is given by the dominant motion direction. (D, E) Additionally, 2-d stimulus space can also be parameterized as varying along 2 dimensions: total coherence (middle panel), or the total percentage of coherent motion to the left or right, and competition (right panel), the unsigned difference between proportion of coherent dots moving left and right. (F) Structure of a single trial: A get-ready cue indicated dots were about to appear. All trials began with 1 second of random motion, which temporally separated stimulus onset from evidence onset, meaning we were able to distinguish visual evoked neural responses from evidence accumulation processes. This also provided a temporally extended foreperiod in which neural activity reflecting prior beliefs could be measured. Random motion was followed by a 2.5-second evidence accumulation period, in which coherent motion was present. When the dots disappeared, participants had a 1-second response interval to make a saccade in the direction of perceived dominant motion. Participants were given unambiguous feedback on the correct answer (small centrally presented hemisphere on the correct side), so they could learn the cross-trial prior independently of the quality of evidence on each trial. During the 1-second foreperiod and 2.5-second period of evidence accumulation, the 2 potential saccadic targets were “tagged” with high frequency flicker to selectively entrain neural oscillations. https://doi.org/10.1371/journal.pbio.3002383.g001

In the classic RDK task, participants observe mixtures of randomly and coherently moving dots and accumulate evidence over hundreds of milliseconds to determine the direction of coherent motion, responding with a congruent saccade. We introduced longer-term, cross-trial integration favouring left or right response, to drive the computation of a prior hypothesised to occur in parietal cortex. Additionally, we introduced within-trial competition between left and right options so that the strength of evidence for a target could be dissociated from the direction of evidence (and, therefore, its concordance with the prior).

Cross-trial integration (prior). In classic RDK tasks, the dot direction on each trial is independent. Each option (left, right) is equally likely, and so participants do not have to retain any information about the current trial after the trial ends. In our modified version, we introduced long-term correlations in the dot-motion direction. The probability that the next correct choice would be “right” was not fixed at 50% but took values of 20%, 50%, or 80% for blocks of about 25 trials (changes in prior probability were unsignalled and occurred with a uniform hazard rate of 0.04 (Fig 1B, “true probability” (solid grey line)). Since the dominant direction on previous trials could be useful for determining the direction on the current trial, participants could benefit from integrating information across trials to construct a prior over the dominant motion direction on the next trial (Fig 1B, “prior belief” (purple trace)). We modelled this evidence integration process using a Bayesian ideal observer model (similar to [31,32]), which captured local variations in prior probability, and learning delays. As a summary measure for the strength of the prior belief (i.e., the extent to which the prior favoured leftwards or rightwards motion), we used the expected value from the Bayesian ideal observer (see Methods, Eq 5) of p(rightward = correct), denoted E(q t ). This allowed us to test whether these prior beliefs were reflected in brain activity, either as an influence on the decision process itself or in the 1-second foreperiod prior to evidence presentation on each trial (Fig 1F).

Within-trial competition. In classic RDK stimuli, a single set of coherent dots move to the left or right. In our modified version, all trials included some level of evidence for both choice options (left and right) concurrently, and participants reported the dominant motion direction (Fig 1C). This means that the level of the signal-to-noise or total coherence (total number of left and right dots, compared to random dots, Fig 1D) was manipulated orthogonally to competition (ratio of left to right dots, Fig 1E). Therefore, the strength of evidence on a given trial (the precision of the likelihood function in Bayesian terms) was dissociable from its direction, which could be compatible or incompatible with the prior. This allowed us to test (behaviourally and neurally) for evidence that the prior was used and precision-weighted against current evidence strength. This manipulation also allowed us to localise in time (and space) the single-saccade decision process by testing for the hallmark of a competitive decision process, namely, that activity should depend upon the strength of evidence for the losing option as well as the evidence for the winning option [17]. In particular, we used Wang’s biophysical model of a drift diffusion-like competitive process to model decision-making in parietal and frontal cortex [33]; this model makes precise predictions about the independent effects of competition and coherence on brain activity [34]. These predictions, which were borne out in the MEG data, provide a temporal context in which signals relating to the prior may be interpreted.

Each trial began with a “get ready” cue, followed by 1 second of fully incoherent motion, followed by 2.5 seconds of coherent motion to both left and right that varied over trials (Fig 1F). The purpose of the 1-second incoherent motion period was 2-fold: Firstly, to allow signals pertaining to cross-trial integration to appear prior to evidence accumulation; secondly, to dissociate the onset of evidence accumulation from the onset of visual stimulation, which produces strong evoked activity in posterior brain regions.

Choice behaviour is influenced by the prior in accordance with Bayesian theory Participants (n = 29, final analysis n = 26, for information on participant exclusions, see Methods) performed 600 trials of a modified random-dot motion task with added within-trial competition and cross-trial integration, divided into 4 blocks with short breaks, while MEG was recorded. All participants also completed a practice session of 300 trials, outside the scanner, on a separate day. We first confirmed that participants’ single-trial choice behaviour was influenced by both the total coherence (signal to noise) and the competition between left- and rightward motion, by fitting logistic regressions to participants’ saccade directions (left, right) as a function of percent coherent motion and proportion of coherent dots that moved right. As expected, there was an interaction such that participants were more likely to saccade rightwards when a greater proportion of the coherent dots moved rightwards and this effect increased as the total amount of coherent motion increased (t(25) = 9.74, p < 2 * 10−10, Fig 2A). PPT PowerPoint slide

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TIFF original image Download: Fig 2. Within- and across-trial influences on behaviour. (A) Increasing overall coherence (darker lines) produces a parametric performance improvement (steeper logistic curve). Dots indicate mean observed data; lines indicate logistic fits. (B) Prior belief influences choice behaviour on current trial, leading to a shift in the point of subjective equality (dashed vertical lines). Inset: Raincloud plot showing values of p(Saccade right) for individual participants on trials where 50% of dots moved right. (C) Prior belief shifts point of subjective equality (dashed lines) most strongly when the least information is available on the current trial (coherence is lowest). https://doi.org/10.1371/journal.pbio.3002383.g002 Next, we tested whether participants learned and used the across-trial regularities in the stimulus sequence (the prior). We first confirmed that feedback from previous trials influenced participants’ decision on the current trial using lagged logistic regression (S1 Fig), indicating that participants were indeed retaining information across at least 2 previous trials. To model participants’ prior beliefs, we used a Bayesian ideal observer model [31] (see Methods for full description) to compute, for every trial in a stimulus sequence, the prior belief that an ideal observer should have, based on the feedback observed on previous trials. The “ground truth” or generative probability of rightwards motion was either high (80%), low (20%), or neutral (50%); these probabilities changed unsignalled about every 25 trials (see Fig 1 and Methods). The Bayesian ideal observer model estimated the probability that the dominant motion direction on the upcoming trial would be right or left, based on the feedback from previous trials. The advantage of this approach over using “ground truth” prior probabilities is to capture local fluctuations in probabilities, and learning delays. In all analyses, the “prior belief” is defined as the expected prior probability of rightwards motion from the Bayesian model, which varies smoothly throughout the range 0 to 1. This quantifies the strength of the participant’s expectation for rightwards (versus leftwards) motion, which corresponds to the extent to which a saccade is prepared to the rightwards (versus leftwards) target. For visualisation (Fig 2B), we divided trials using a tertile split according to whether the Bayesian prior strongly favoured rightward or leftward motion, or neither (neutral prior). On “neutral prior” trials, the point of subjective equality (PSE) closely matched the point of objective equality (mean 49.7% right motion). Strong priors in either direction biased the PSE by 10% to 15% (strong left prior; PSE 55% right motion, strong right prior; PSE 42.3% right motion, Fig 2B, inset). A multiple logistic regression confirmed that participants’ choice behaviour was influenced both by the proportion of dots moving right (t test on regression coefficients across the group: t(25) = 14.79, p < 1 * 10−14) and by the prior based on previous trials (t(25) = 2.80, p = 0.0091). These 2 effects did not interact (t(25) = 0.45, p = 0.66). This is evidence that decision-relevant properties of the currently viewed stimulus (the proportion of coherent dots that moved right), and the beliefs participants had developed based on previously viewed stimuli, made independent contributions to their choice behaviour. Because our bidirectional stimulus dissociated strength of evidence (total coherence) from direction of evidence (left versus right), we could test whether participants relied more upon the prior when evidence in the current trial was weak [35] (low total coherence), due to precision weighting, as predicted by Bayesian theory [35]. To visualise this effect, we repeated the Bayesian ideal observer analysis but divided the trials according to the level of total coherent motion on the current trial (Fig 2C, using the same tertile splits as above). As predicted, prior belief biased current choice strongly when there was little decision-relevant motion (at 10% coherence, PSE moved from ≈50% to 10%/90%, Fig 2C, left) but had little effect when a lot of motion was decision relevant (at 90% coherence, PSE moved from ≈50% to 48%/52%, Fig 2C, right). The effect shown in Fig 2C was statistically confirmed using logistic regression. Percent total coherent motion had opposite effects on the influence of current evidence and prior belief on choice; when total coherent motion was high, the current evidence (proportion of coherent dots moving right) influenced behaviour more (Wilcoxon test on logistic regression coefficients for (coherence * prior) interaction across the group: Z = 4.7, p < 3 * 10−6, nonparametric test due to first-level outliers; see Methods) but prior belief influenced behaviour less (Z = −2.52, p = 0.012). This contrasts with the previous analysis where we found no interaction between the prior belief and the degree to which competition influenced choice behaviour. This confirms that participants selectively weighted the 2 sources of evidence available to them; up-weighting the impact of their prior belief—shaped by what they had seen previously—when little sensory evidence was currently available to guide their choice. This precision-weighting resembles the optimal Bayesian strategy for the task [35].

Neural models and neuroimaging Next, we turned to our MEG data for evidence of the neural mechanisms underlying the competitive process of selecting an individual saccade and the integrative process of forming a prior across many saccades.

Biophysical model of the neural mean field We simulated the neural mean field (summed activity of neuronal pools representing the left and right targets) during the saccade selection process using an adaptation of the decision model previously described by Wang and colleagues [33,34]. Because Wang’s model describes the summed activity of all neurons in the decision-making population—the “neural mean field”—it generates useful predictions about the population activity of a brain region measured by MEG. Indeed, this model has been successfully used in a value-based choice task [34] to predict the independent effects of total value (analogous to total coherence in our task) and value difference (analogous to competition in our task) on the event-related field (ERF) as measured in MEG and has previously been fit to brain activity in both parietal [33] and frontal cortex [34,36,37]. We adapted a neural mean-field version of this model to make predictions about how neural responses would vary with competition, coherence, and prior belief in our task. Briefly, the model comprises 2 neuronal pools coding for different choice options, with strong recurrent excitation within a pool and strong inhibition between pools. The between-pool inhibition mediates a winner-take-all competition between options resulting in one pool reaching a high-firing attractor state and the other pool a quiescent attractor state. In the standard version of the model, inputs to the 2 pools are intended to be proportional to the strength of the input stimulus; in our case, number of dots moving left and number of dots moving right. The key feature of this model is that, due to the competition between pools, the decision variable depends on the strength of evidence for the unselected option, as well the selected option [17]. We were able to directly test for the influence of the unchosen option because in our modified random dots task, evidence for the chosen and unchosen dots direction was manipulated independently, allowing us to identify signals driven by competition independently of signal to noise. The model, which uses biologically based parameters, makes specific predictions about the form and timing of neural responses, which could be tested directly in the MEG mean field. The neural mean-field model predicted that, firstly, increasing total coherence (sum of dotsL and dotsR) should produce a parametric increase in neural activity following target onset (Fig 3D) in the time window 100 to 500 ms following onset of coherent motion. Secondly, as competition decreases (i.e., greater absolute difference between dotsL and dotsR), there should be a parametric increase in neural activity following target onset (Fig 3G) in the same time window. PPT PowerPoint slide

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TIFF original image Download: Fig 3. (A) Input to neural mean-field model. Each node received weak variable input corresponding to prior knowledge (purple), weak fixed input corresponding to motion in all directions (brown), and strong variable input corresponding to coherent motion (red). For each input, the baseline level is zero (offset for the visibility of the different traces). (B) Properties of neural mean-field model on a representative trial. Each node contained recurrent excitatory connections and inhibitory connections to the other node and received driving inputs corresponding to the strength of prior belief and to the properties of the dot stimulus. (C) Region of interest used to reconstruct activity in IPS (based on a combination of data and anatomy—see Methods). (D) Neural mean-field model predicts a parametric increase in activity as a function of stimulus coherence. (E) Low frequency in IPS activity displays parametric modulation as a function of coherence. Note: To focus on the evidence-accumulation signal following time point 0, the y-axis has been truncated, obscuring the larger response to incoherent motion onset following time point −1. A zoomed-out version of the same figure can be found in the Supporting information (S3A Fig). (F) Time-averaged mean field from the period indicated by the box in (E). Each dot is an individual participant. An expanded version of the same figure showing individual slopes, and group medians as well as means can be found in the Supporting information (S3C Fig). (G) Neural mean-field model predicts a parametric increase in activity as a function of stimulus competition. (H) Low frequency in IPS activity displays parametric modulation as a function of competition. Note: A zoomed-out version of the same figure can be found in the Supporting information (S3C Fig). (I) Time-averaged mean field from the period indicated by the box in (H). Each dot is an individual participant. An expanded version of the same figure showing individual slopes, and group medians as well as means can be found in the Supporting information (S3D Fig). (J) General linear model reveals effects of both coherence and competition in neural mean-field model in the poststimulus period. (K, L) Significant effects of coherence and competition are observed in IPS in the same poststimulus window. The data underlying this figure can be found in Zenodo (DOI: 10.5281/zenodo.10209832). https://doi.org/10.1371/journal.pbio.3002383.g003

Modelling the prior Prior beliefs about dot direction could be built into this model as a driving input. To model this possibility (for which we ultimately failed to detect evidence in the MEG signal), we adapted the model to include three different input sources in different time windows (Fig 3A and 3B): The first input represented a participant’s prior belief about the upcoming stimulus (purple, Fig 3A and I belief , Fig 3B), the second reflected undifferentiated activity due to random dot motion during the 1-second “incoherent motion” epoch (brown, Fig 3A), and the third reflected properties of the stimulus itself—i.e., the number of dots moving left and right—during the 2.5-second “coherent motion” epoch (cyan, Fig 3A and I dots , Fig 3B). The timing of the driving inputs reflects electrophysiological findings that the initial response of parietal neurons [38,39] to target presentation, prior to evidence accumulation, weakly reflect the influence of prior beliefs on saccade selection [18,40]. Importantly, while the second input “general motion,” input was fixed across trials, the inputs corresponding to prior and to task-relevant motion were variable; Fig 3B illustrates a trial where the visual stimulus contains more rightward than leftward motion (right side; many right-moving dots, strong input to “right” accumulator, few left-moving dots, weak input to “left” accumulator), but the model expects leftward motion (left side; expectation of left-moving dots, strong input to “left” accumulator, weak input to “right” accumulator). The model predicts that weakly increasing input due to prior knowledge in the prestimulus period (Figs 3A and S2A) should (a) slightly alter prestimulus activity (although the change was not significant in our simulations) and (b) bias the initial conditions of the competitive accumulation process such that activity evoked by the much stronger stimulus-driven input parametrically increased with prior strength. This biasing of the accumulation process occurred in our simulations, even though the prior input was no longer active at the time of evidence accumulation, presumably due to the weak prior input biasing the state of the network before the stronger inputs began.

Event-related activity reflects the competitive process of selecting the current saccade We next tested whether the pattern of results predicted by the neural mean-field model were observed in MEG data from the parietal cortex, which is known to track evidence accumulation. We transformed participants’ MEG data to source space using linearly constrained minimum variance (LCMV) beamforming [41] and extracted time series from regions of interest (ROIs) in parietal cortex (Fig 3C, see Methods for ROI definitions). We extracted the time-varying power in the low frequency range (2.8 to 8.4 Hz) as a proxy for the event-related field or ERF, the magnetic field arising from local field potentials in cortex [42]; this was necessary (rather than calculating the ERF directly) because the beamforming (source localisation) procedure introduces arbitrary sign-flips in the ERF, but no such ambiguity in the time-frequency domain. For further details see, Methods/Parietal cortex and frontal eye field low-frequency ROI analysis. This analysis revealed 2 transient responses (Fig 3E, 3F, 3H and 3I); the first shortly after onset of incoherent motion, the second 100 to 500 ms after onset of coherent (i.e., choice-relevant) motion (Fig 3E and 3H, dashed boxes). Concordant with ramping activity observed in electrophysiological studies [10,12], there was a clear parametric modulation of the low-frequency MEG signal 100 to 500 ms after the onset of coherent motion as a function both of total coherence (Fig 3E and 3F) and stimulus competition (Fig 3H and 3I). As predicted, stronger evoked activity was observed with higher levels of total coherence; this is consistent with the observation that ramping evidence-accumulation signals in single-unit studies rise faster for higher coherence levels in standard dot motion tasks [12], whether those signals arise from ramping in individual neurons or from step-changes in neurons leading to a population-level ramp [16]. Stronger evoked activity was observed for lower levels of stimulus competition, indicating that the presence and strength of evidence conflicting with a decision affects the decision process—a hallmark of a competitive system. Statistically, a linear multiple regression with parameters coherence, competition, and prior strength confirmed that the amplitude of the evoked response varied as a function of both coherence and competition; specifically, and as predicted by the neural mean-field model (Fig 3J) activity increased as a function of stimulus coherence (t(25) = 4.67, p = 9 * 10−5), and decreased as a function of competition (t(25) = 2.18, p = 0.039, Fig 3K and 3L). Both effects were tested in a time window 100 to 500 ms after the onset of coherent motion (dashed boxes), defined based on the predictions of the biophysical model. Since ramping activity is also observed in other brain regions such as FEF, we repeated the analysis in this region (S4 Fig). The pattern of results was qualitatively similar. To test whether there was any difference in timing of effects between FEF and parietal cortex, we used permutation testing (permuting the waveforms between ROIs within participants) and found no significant difference in timing between regions (coherence; p = 0.12, competition; p = 0.92). The qualitative correspondence of the MEG activity to a neural mean-field model of a competitive decision process suggests that parietal cortex could be engaged in resolving saccadic choices via competition by mutual inhibition, compatible with previous observations of evidence accumulation signals. However, it is worth noting that evidence from inactivation studies [24,43] suggests that the activity in parietal cortex is not causally necessary for saccade selection—whereas activity in FEF is. Although more recent studies do suggest LIP may play a causal role in evidence accumulation [44], the behavioural effects of targeted inactivation are somewhat transient (despite persistent neural inactivation), which—at a minimum—suggests the existence of parallel or compensatory mechanisms. The signal observed in parietal cortex may, we hypothesised, play a parallel role in integrating this information over a longer timeframe into a cross-saccade prior.

Effects of the prior on the mean field Contrary to our model predictions, prior belief did not significantly modulate the low-frequency MEG signal in parietal cortex (t(25) = 0.80, p = 0.43, S2 Fig). However, the absence of an effect of prior should be interpreted with caution, as for any null result; perhaps the effect was too subtle to be detected in the present paradigm. Furthermore, a relevant theoretical model [18] predicts an interaction between signed evidence on the current trial and signed prior belief based on previous trials. Accordingly, we tested for this interaction; however, no significant effects were observed in the low-frequency MEG signal in parietal cortex (left hemisphere; t(25) = -1.51, p = 0.14, right hemisphere; t(25) = 0.087, p = 0.93).

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