Abstract

The neural dynamics underpinning binary perceptual decisions and their transformation into actions are well studied, but real-world decisions typically offer more than two response alternatives. How does decision-related evidence accumulation dynamically influence multiple action representations in humans? The heightened conservatism required in multiple compared with binary choice scenarios suggests a mechanism that compensates for increased uncertainty when multiple choices are present by suppressing baseline activity. Here, we tracked action representations using corticospinal excitability during four- and two-choice perceptual decisions and modeled them using a sequential sampling framework. We found that the predictions made by leaky competing accumulator models to accommodate multiple choices (i.e., reduced baseline activity to compensate increased uncertainty) were borne out by dynamic changes in human action representations. This suggests a direct and continuous influence of interacting evidence accumulators, each favoring a different decision alternative, on downstream corticospinal excitability during complex choice.

INTRODUCTION

Making the right decision quickly is a fundamental evolutionary objective, because being slow or being wrong can be fatal. Most real-world decisions offer several possible responses. Given the existence of capacity limitations and joint speed and accuracy constraints, how do humans adapt as the complexity of a decision scenario increases? Hick's law (Hick, 1952) illustrates how the number of choice alternatives can profoundly affect the speed of response, but the neurocognitive basis of this effect has only recently begun to be elucidated (Churchland & Ditterich, 2012).

Many researchers now agree that, to make a decision, sensory evidence from the environment is accumulated over time until it becomes sufficient to trigger a response. This process has been formalized in models involving sequential sampling (Forstmann, Ratcliff, & Wagenmakers, 2016; Brown & Heathcote, 2008; Ratcliff & McKoon, 2008; Smith & Ratcliff, 2004; Usher & McClelland, 2001; but see Thura & Cisek, 2016; Thura, Beauregard-Racine, Fradet, & Cisek, 2012). Such models make the putative mechanisms underlying changes in behavior more concrete. For example, the increased RT found when response alternatives proliferate might result from a change in either the quantity of evidence required to reach a decision or the rate at which information accumulates. Behavioral assays help distinguish these accounts, and some models, including the physiologically plausible leaky competing accumulator (LCA) model, (Usher & McClelland, 2001) can account for multi-alternative decision-making in various settings (Tsetsos, Usher, & McClelland, 2011; Ditterich, 2010; Tsetsos, Usher, & Chater, 2010; Brown, Steyvers, & Wagenmakers, 2009; Bogacz, Usher, Zhang, & McClelland, 2007; McMillen & Holmes, 2006). However, only by marrying the quantitative precision of sequential sampling models with appropriate neurodynamic signals can a biologically compelling description of complex choice behavior emerge.

Much of the neural evidence supporting sequential sampling models comes from experiments using binary choices. For example, single-cell recording in monkeys, a method with sufficient temporal resolution to track the decision variable, has shown that firing rates of neurons in the lateral intraparietal area (LIP) but also the FEF and the superior colliculus display accumulation-to-bound characteristics in two-choice saccadic tasks (Hanks & Summerfield, 2017; Gold & Shadlen, 2000, 2003; Roitman & Shadlen, 2002; Paré & Wurtz, 2001; Shadlen & Newsome, 2001). In humans, a number of EEG signals have been suggested to reflect the decision variable, but only in the context of binary decisions (O'Connell, Dockree, & Kelly, 2012; Siegel, Engel, & Donner, 2011; Donner, Siegel, Fries, & Engel, 2009).

Despite the prevalence of the two-choice task in research settings, some studies have also investigated the neural dynamics of multi-alternative decision-making, at least in nonhuman primates. Seminal work by Basso and Wurtz (1997, 1998) showed that activity of monkey superior colliculus neurons decreased with increased possible targets in a saccadic multitarget task. This finding was explored more thoroughly and in the context of sequential sampling models by Churchland, Kiani, and Shadlen (2008), who presented two monkeys with both two- and four-choice random dot motion displays. Both kinds of decision showed the same stereotyped levels of LIP activity at the time of response. However, firing rates differed at the beginning of the decision-making process, as four-choice decisions showed reduced firing rates. In sequential sampling models such as the LCA, lower activity in a given accumulator at the beginning of the decision necessitates larger excursions, that is, more evidence will be required to reach a response boundary. Such heightened conservatism in multiple compared with binary choice scenarios can be interpreted as a mechanism that compensates for increased uncertainty.

Decreased baseline activity has since been supported by a number of single-cell recording studies (Cohen, Heitz, Woodman, & Schall, 2009; Balan, Oristaglio, Schneider, & Gottlieb, 2008; Lee & Keller, 2008). Does this result generalize to humans and/or different sensorimotor pathways? Given that other plausible mechanisms accounting for changes in behavior with the number of choice alternatives can be formulated, via either sequential sampling models (e.g., changes in the rate of evidence accumulation) or alternative perspectives (e.g., Hick's original information–theoretical account), this question holds theoretical importance. However, we are not aware of any studies that have directly investigated dynamic neural correlates of binary versus multiple choice evidence accumulation in the human brain.

Here, we address this longstanding question by assessing the impact of multiple alternatives on the neurodynamic decision variable in humans. Because high temporal resolution data is a prerequisite to tackle this issue and motor-related EEG/MEG signals have limited utility for decisions with more than two response alternatives, we use TMS for this purpose.1 TMS motor-evoked potentials (MEPs) can be used to read out decision-related influences in the primary motor cortex or adjacent premotor areas (Hadar, Rowe, Di Costa, Jones, & Yarrow, 2016; Bestmann & Krakauer, 2015; Hadar, Makris, & Yarrow, 2012; Bestmann et al., 2008; Kiers, Fernando, & Tomkins, 1997). When a decision requires an immediate motor response, motor preparation occurs continuously throughout the decision-making process (Thura & Cisek, 2016; Tsetsos, Pfeffer, Jentgens, & Donner, 2015; de Lange, Rahnev, Donner, & Lau, 2013; Gluth, Rieskamp, & Büchel, 2013; Hadar et al., 2012; Duque, Lew, Mazzocchio, Olivier, & Ivry, 2010; Michelet, Duncan, & Cisek, 2010). Therefore, the corticospinal excitability that MEPs reflect can be used as a correlate of the decision variable and compared directly to the predictions of accumulator models such as the LCA.

By mapping two separate responses, each recruiting a different muscle, to each hand and measuring the activity of both muscles in the hand contralateral to brain stimulation, we were able to record MEPs associated with each response separately. Although single-cell recording studies of decision-making (e.g., Churchland et al., 2008; Basso & Wurtz, 1997, 1998) have typically targeted regions that are anatomically remote from those interrogated using MEPs, their functional roles for the generation of saccades may mirror those of the corticospinal tract for manual actions. We therefore hypothesized that if changes in corticospinal excitability are driven by accumulation-to-bound dynamics as encapsulated in the LCA model, MEP changes associated with each response would display typical characteristics of a decision variable. Specifically, we expected the MEPs' buildup rate to increase with evidence strength and their amplitudes to reach a stereotyped level at the time of response (Spieser, Kohl, Forster, Bestmann, & Yarrow, 2018; Hadar et al., 2016). Importantly, beyond these typical accumulation-to-bound dynamics, we also predicted a reduced amplitude (for potential responses) when participants prepared a four-choice compared with a two-choice decision, as suggested by previously observed lower baseline neural firing rates in nonhuman primates. Note that this was in no sense inevitable, as there are fundamental differences between single-cell recordings of oculomotor neurons in monkeys and the MEP signals reported here. For example, although simultaneous movements of both hands are possible, the oculomotor system is restricted to a movement in a single direction at any given time, which may lead to differences in decision-related neural dynamics. In addressing the possible generalization of this result from the monkey oculomotor system to the human corticospinal tract, we were able, for the first time, to track the decision variable during human multi-alternative decision-making. We thus distinguish theoretical accounts of Hick's law at a neurocognitive level by demonstrating decreased levels of baseline activity with an increased number of alternatives.

METHODS

Participants

We recruited 13 participants (five men) with a mean age of 26.23 (SD = 7.67) years. Because many TMS trials must be discarded for unavoidable reasons (see EMG Processing below; cf. Hadar et al., 2016), each participant completed between two and four sessions (each lasting 1–3 hr) and completed on average 4166 trials. Participants were paid £8 per hour. All procedures were approved by the City, University of London Psychology Department ethics committee.

Stimuli, Design, and Procedure

Participants completed a color discrimination task. In each trial, an array of colored pixels appeared. Arrays consisted of four different colors: green (RGB [0 0.6 0]), red (RGB [0.8 0 0]), yellow (RGB [0.92 0.74 0]), blue (RGB [0.12 0.12 0.61]). Participants were instructed to indicate which color was most prevalent as quickly and as accurately as possible using the corresponding one of four response buttons (see Figure 1).

Figure 1. 

Trial procedure. (A) Color discrimination task. Participants have to indicate which of the precued colors is the most prevalent on the color array. Left: four-choice trial; all possible cues were displayed. Right: two-choice trial; only two of the possible cues were shown. (B) All possible two-choice combinations. In “within” trials, both possible responses were on the same hand, whereas in “between” trials, the two possible responses were on different hands but using the same response (pinch/grasp). (C) Each cue/color was associated with a specific response; The top right cue (here: green) was associated with a right-hand “pinch” response, the top left cue (here: blue) was associated with a left-hand “pinch” response, the bottom right cue (here: yellow) was associated with a right-hand “grasp” response, and the bottom left cue (here: red) was associated with a left-hand “grasp” response. Color–response mappings were randomized across participants, whereas the cue location–response mapping remained the same. (D) Each hand performed pinch and grasp responses, recruiting the FDI and ADM muscles, respectively. Muscles associated with correct responses are shown in green, whereas others are displayed in gray (see C & E). MEPs were only recorded from right-hand muscles (indicated by dark red border). (E) Response categorization. In each trial, right-hand MEPs are associated with two of the response categories. Activation of all categories is probed across trials, as the position of the correct response varied randomly. Top: Four-choice trial in which the stimulus array (not shown) instructs a right grasp response. The incorrect response on the same hand is labeled “Adjacent Error 1,” and the responses on the other hand are labeled “Adjacent Error 2” (homologous to correct response) and “Opposite Error” (nonhomologous to correct response). Middle: Two-choice “within” trial, here involving a choice between left-hand responses. If the left pinch response is correct, the incorrect but cued response (here left grasp) is classed as “Adjacent Error 1,” the response homologous to the correct one on the other hand is labeled “Adjacent Error 2,” and the opposite response is labeled “Opposite Error.” Bottom: Two-choice “between” trial, involving selecting among left or right pinch responses. Here, the right pinch is correct and the left pinch, which is cued but incorrect, is “Adjacent Error 1.” The incorrect response on the same hand as the correct response is labeled “Adjacent Error 2,” and the anatomically opposite response is called “Opposite Error.”

Figure 1. 

Trial procedure. (A) Color discrimination task. Participants have to indicate which of the precued colors is the most prevalent on the color array. Left: four-choice trial; all possible cues were displayed. Right: two-choice trial; only two of the possible cues were shown. (B) All possible two-choice combinations. In “within” trials, both possible responses were on the same hand, whereas in “between” trials, the two possible responses were on different hands but using the same response (pinch/grasp). (C) Each cue/color was associated with a specific response; The top right cue (here: green) was associated with a right-hand “pinch” response, the top left cue (here: blue) was associated with a left-hand “pinch” response, the bottom right cue (here: yellow) was associated with a right-hand “grasp” response, and the bottom left cue (here: red) was associated with a left-hand “grasp” response. Color–response mappings were randomized across participants, whereas the cue location–response mapping remained the same. (D) Each hand performed pinch and grasp responses, recruiting the FDI and ADM muscles, respectively. Muscles associated with correct responses are shown in green, whereas others are displayed in gray (see C & E). MEPs were only recorded from right-hand muscles (indicated by dark red border). (E) Response categorization. In each trial, right-hand MEPs are associated with two of the response categories. Activation of all categories is probed across trials, as the position of the correct response varied randomly. Top: Four-choice trial in which the stimulus array (not shown) instructs a right grasp response. The incorrect response on the same hand is labeled “Adjacent Error 1,” and the responses on the other hand are labeled “Adjacent Error 2” (homologous to correct response) and “Opposite Error” (nonhomologous to correct response). Middle: Two-choice “within” trial, here involving a choice between left-hand responses. If the left pinch response is correct, the incorrect but cued response (here left grasp) is classed as “Adjacent Error 1,” the response homologous to the correct one on the other hand is labeled “Adjacent Error 2,” and the opposite response is labeled “Opposite Error.” Bottom: Two-choice “between” trial, involving selecting among left or right pinch responses. Here, the right pinch is correct and the left pinch, which is cued but incorrect, is “Adjacent Error 1.” The incorrect response on the same hand as the correct response is labeled “Adjacent Error 2,” and the anatomically opposite response is called “Opposite Error.”

Stimuli were generated using MATLAB (The Mathworks) and the Psychtoolbox extension (Kleiner et al., 2007; Brainard, 1997; Pelli, 1997) and presented on a Display++ LCD monitor (Cambridge Research Systems, Ltd.; display size: 41 cm × 30 cm) operating at a refresh rate of 100 Hz and a resolution of 1240 × 786 pixels. Participants sat approximately 100 cm from the screen. The stimulus array subtended 6 × 6 degrees of visual angle. Each colored pixel spanned 2 × 2 screen pixels, resulting in an array of 145 × 145 colored pixels.

Participants held two digital response buttons interfaced via a 16-bit A/D card (National Instruments X-series PCIe-6323, sampling rate 100,000 Hz) in each hand, one between thumb and index finger (pinch) and one against the palm, attached to a plastic cylinder (grasp; Hadar et al., 2012). Pinching contracted the first dorsal interosseous (FDI) muscle while grasping the cylinder activated the abductor digiti minimi (ADM) muscle. Each color was mapped to one of the four response buttons. The color–response mapping was randomized across participants.

Trials consisted of a cue (500 msec), a colored stimulus array (2000 msec or until response), and an ISI (minimum 500 msec). The experiment contained both two- and four-choice trials. In addition, as a positive control, we crossed a manipulation of difficulty with our manipulation of number of choices in a 2 × 2 design. Difficulty negatively affects accumulation rate (Mulder, van Maanen, & Forstmann, 2014; Teodorescu & Usher, 2013; Ratcliff & Rouder, 1998), and this effect has been demonstrated in MEP signals for two-choice tasks (Spieser et al., 2018; Hadar et al., 2016). To manipulate task difficulty, the percentage of pixels of the dominant color varied between 33% (easy) and 30% (hard). The remaining colors each took up 22% and 23% of the array, respectively. The cue at the beginning of each trial informed participants whether a given trial was a two- or a four-choice trial by presenting either two or four colored squares representing the possible choices.

One third of trials were four-choice, one third were two-choice “within” hands, that is, the two possible responses were on one hand (left pinch–left grasp, right pinch–right grasp), and one third of trials were two-choice “between” hands, that is, homologous responses from both hands were possible (left pinch–right pinch, left grasp–right grasp). Trial order was randomized. Note that the difference between two- and four-choice trials lay solely in the instructions conveyed by the cue—the stimulus array and the percentage of the four colors did not change. In the first session, participants completed 150 practice trials to familiarize themselves with the task. Participants then completed between five and six experimental blocks per session, with each block consisting of 168 trials (plus additional trials to regulate TMS frequency; see below).

Stimulation and Recording

Muscle activity was recorded using surface EMG, sampled at 1000 Hz via a 13-bit A/D Biometrics Datalink system (Version 7.5, Biometrics Ltd.) and band-pass filtered (20–450 Hz). Surface Ag/AgCl electrodes (22 mm × 28 mm, Part No. SX230FW, Biometrics Ltd.) were placed above the FDI and ADM of each hand. Reference electrodes were placed approximately 2 cm from each of the four active electrodes. The EMG signals of the right ADM and FDI were also passed to speakers placed on the left and right of the participant, respectively, with noise informing participants that their muscles were not fully relaxed between responses.

Single-pulse TMS was applied using a Magstim Rapid2 biphasic stimulator (The Magstim Co. Ltd.). To induce MEPs in both the ADM and the FDI of the right hand, a 70-mm figure-of-eight coil (external casing diameter approximately 90 mm for each loop) was positioned on the scalp over the left motor cortex. The exact location and stimulation intensity were adjusted for each participant individually and set at approximately 110% of the resting motor threshold. The resting motor threshold was defined as the minimal intensity to elicit an MEP with a peak-to-peak amplitude of approximately 50 μV in 50% of stimulations on both the FDI and ADM of the right hand. TMS position was continuously tracked and maintained using a neuronavigation system (Visor 2, ANT Neuro, The Netherlands).

TMS pulses were planned in 57% of trials from each condition. To ensure a good distribution of TMS pulses during a baseline interval and over the course of the RT, TMS trials were divided into four equally frequent time bins between −200 and 700 msec relative to the stimulus onset (i.e., between 300 and 1200 msec relative to cue onset). Within a given bin, the exact stimulation time was drawn randomly for each trial. Because the experiment followed a single-pulse TMS protocol, pulses were required to occur at a maximal frequency of 0.2 Hz. If, by chance, a planned interpulse interval (IPI) was less than 5000 msec, timing was adjusted. For IPIs of 4–5000 msec, the intertrial interval was increased, decreasing the pulse frequency to 0.2 Hz. For IPIs less than 4000 msec, the planned trial was replaced with the next planned stimulation-free trial. If there were no stimulation-free trials left, random stimulation-free trials were generated to increase the IPI. On average, this method added 434 trials per session, yielding an average of 1354 trials per session. Planned pulses were not delivered if a response had already been detected.

EMG Processing

Preprocessing

All EMG processing was performed in MATLAB (The Mathworks). To remove potential differences in movement time (between right and left hands, or pinch and grasp responses), analyses were conducted based on EMG RTs, that is, the time between stimulus and responding EMG onset. First, the Teager–Kaiser energy operator was applied to detect the onset time of muscle activity associated with each response (Solnik, Rider, Steinweg, Devita, & Hortobágyi, 2010; Li, Zhou, & Aruin, 2007; Li & Aruin, 2005). The discrete Teager–Kaiser energy operator ψ for a given EMG value x of the sample n was defined as
ψxn=x2nxn+1xn1
(1)
A threshold (T) identified the onset of muscle activity,
T=μ+hσ
(2)
with μ and σ representing the baseline mean and standard deviation (−300 to 200 msec relative to cue onset) and h set to 3. In addition, all trials were visually inspected, and the EMG onset time was adjusted manually if necessary. Visual inspection provided no information about the experimental condition of a given trial. Trials with muscular artifacts, no detectable EMG onset, or partial responses on more than one channel were excluded (6.41% of all recorded trials). We further excluded trials with button RTs of ≥2000 or ≤180 msec or EMG RTs of ≥1850 or ≤30 msec (<1% of all recorded trials).

In TMS trials, MEP amplitudes in both channels (FDI and ADM) of the right hand were defined as the maximum minus the minimum EMG value from 10 to 40 msec after stimulation. Trials with muscular preactivation (EMG > 50 μV in the 200 msec period preceding stimulation) were excluded (4.51% of all trials), as were trials with no visible MEP or in which MEP amplitude was uncertain due to amplifier saturation (2.02% of all trials). Trials were also excluded if the participant's response preceded the planned TMS (4.36% of all trials).

In total, 17.53% of all recorded trials (including 35.38% of TMS trials) were discarded, with a similar proportion of trials deleted across conditions. After these preprocessing steps, 44,669 usable trials remained (including 13,588 TMS trials). MEP amplitudes were then z-scored per muscle, session, and participant (but regardless of experimental condition) to normalize their magnitudes. Finally, for all analyses except our baseline comparison (see below), MEP amplitudes associated with incorrect trials were discarded, leading to 11,590 remaining TMS trials.

Recategorization

The FDI and ADM channels were reclassified into one of four categories. MEPs from muscles associated with the correct response were classed as “Correct,” whereas MEPs from the nonresponding muscles formed three different error categories, “Adjacent Error 1,” “Adjacent Error 2,” and “Opposite Error.” Note that for MEP data, these labels generally refer to all potential responses within a given decision, not overt errors (i.e., “Opposite Error” refers to a response that would be incorrect had it been made). Figure 1 illustrates these mappings. The response opposite to the “Correct” response, corresponding to the nonhomologous movement on the incorrect hand, was labeled “Opposite Error.” We used “Adjacent Error 1” for responses that were incorrect but on the correct hand in four-choice trials or responses that were cued but incorrect in two-choice trials. The remaining responses were labeled “Adjacent Error 2.” Note however, that stimulation provided only two (right-hand) MEPs per trial, which were sorted into two of the four categories.

Collation and Smoothing

For each correct/error category and each condition, MEPs recorded in correct trials were pooled across participants and sessions. We therefore normalized stimulation times for each session and participant, expressing them as a percentage of median EMG RT (on stimulation-free trials). Pooled MEP amplitudes were sorted in time and aligned to both the stimulus and the response.

To generate continuous signals, MEP amplitudes were then smoothed via a Gaussian kernel,
Yˆt=i=1Netti22σ2Yii=1Netti22σ2
(3)
where N is the number of MEPs, each being associated with a magnitude Yi and a time ti. The smoothed signal was calculated in time steps of 1% median EMG RT, using a smoothing kernel with a FWHM of 5% median EMG RT.

Statistical Analysis

We report two-tailed p values for all pairwise tests. Differences between conditions for behavioral data (i.e., RTs, EMG RTs, and errors) were inferred using ANOVAs and generalized linear mixed models with logistic link functions, respectively. Generalized linear mixed models were implemented using the MATLAB fitglme command, and all effects of interest (e.g., difficulty, number of response alternatives and their interaction) were clustered within participants and sessions and included as random effects in the model specifications.

For TMS data, based on previous research in nonhuman primates (Cohen et al., 2009; Balan et al., 2008; Churchland et al., 2008), we expected reduced baseline MEP amplitudes when participants chose between four compared with two alternatives. To test this, we took (for each participant) the amplitude of all z-scored MEPs recorded during the cue–stimulus interval and associated with a cued response (i.e., for four-choice trials, all MEPs during the baseline period, whereas for two-choice trials, only MEPs categorized as “Correct” or “Adjacent Error 1”). Following translation and square root transformation of these scores to achieve normality, the difference across conditions was tested using a linear mixed model (with random effects for participant) using the MATLAB fitlme command (which, when compared with a traditional t test performed on averages derived from multiple trials, better utilizes information from all contributing scores). This approach was also applied to an unforeseen prediction emerging from our modeling, regarding differences in late accumulation profiles between opposite errors and other (i.e., adjacent) categories of error.

We also expected the MEP signal to be affected by task difficulty, with steeper accumulation for “easy” than “hard” trials. Under sequential sampling models with multiple accumulators, the difference in their accumulation rates is a key determinant of behavior. Hence, we focused on trials in which two MEPs from a single hand could be used to construct a signal measuring the difference between “Correct” and “Adjacent Error 1” responses, a signal that has been shown to display differences between difficulty conditions (Hadar et al., 2016). For both four-choice and two-choice within-hand trials, we fitted a straight line to the MEP signals derived from this difference. We term the gradient of this line a relativized slope. We did this for both “easy” and “hard” trials and then subtracted the relativized slope for “hard” trials from the slope associated with “easy” trials. These estimates were made for stimulus-locked data, between 50% and 90% median EMG RT, and response-locked data, between −50% and −10% median EMG RT. We used nonparametric permutation tests with 1999 iterations to generate new sets of resampled “easy” and “hard” conditions (without replacement) and calculated the relativized slope difference between them. In each test, the original difference was compared with the resulting null distribution of differences. Note that because these permutation tests were performed on a collated set of trials from all participants, the statistical generalization is to a sampling distribution based on all possible trials from our particular set of participants, rather than one based on all possible participants.

Modeling

We used the LCA model to fit the behavioral data (Usher & McClelland, 2001). The LCA is a race accumulator model and therefore easily extended to more than two alternatives. Accumulation traces are defined by an accumulation rate v plus noise and race toward a decision boundary A. The LCA is designed to explain the accumulation process in a more neurophysiologically plausible way than other models within this framework. To this end, it includes a leakage parameter k as well as a parameter β for mutual inhibition between accumulators. Thus, in a binary decision involving the accumulators m and n, the change in activation in accumulator m is given by
dxmvmkxmβxn+N0σ2
(4)
where v is the input into the accumulator and N(0, σ2) is normally distributed noise with zero mean and a standard deviation σ. In addition, the accumulation process is forced to remain positive,
xmt+1=max0xmt+dxm
(5)
RT is made up of the time required to reach the boundary A and a nondecision time Ter, which accounts for sensory and motor processes before and after the decision process.

Model Fit

We tested three LCA models (see Table 1). In Model 1, we extended the model to include four accumulators. In a four-choice trial, the accumulation rate of the correct accumulator was given by vcorrect, whereas accumulation rate for all other accumulators was given by vincorrect. The starting point zfour-choice was set to 0 and, along with the threshold A and the leakage k, equal across accumulators. Two parameters, βadj and βopp, captured inhibition between accumulators. Inhibition parameters reflected the anatomical adjacency of responses. Specifically, βopp describes the inhibition induced by the evidence associated with the opposite response and opposite hand relative to a given accumulator, whereas inhibition between all other accumulators is given by βadj (see Figure 2). This means that the change in accumulation for each accumulator is given by
dxCorrectvCorrectkxCorrectβadjxAdj.Err1βadjxAdj.Err2βoppxOpp.Err+N0σ2dxAdj.Err1vAdj.Err1kxAdj.Err1βadjxCorrectβadjxOpp.ErrβoppxAdj.Err2+N0σ2dxAdj.Err2vAdj.Err2kxAdj.Err2βadjxCorrectβadjxOpp.ErrβoppxAdj.Err1+N0σ2dxOpp.Err3vOpp.ErrkxOpp.ErrβadjxAdj.Err1βadjxAdj.Err2βoppxCorrect+N0σ2
(6)
Table 1. 
Model Comparison: BIC, AIC, and Likelihood Values for Each Model
ModelNo. of ParametersAICBICLikelihoodParameters
Model 1 10 141,600 141,684 −70,790 veasy-correct, veasy-incorrect, vhard-correct, vhard-incorrect, ztwo-choice-cued, k, βadj, βopp, σ2, Ter 
Model 2 10 142,172 142,256 −71,076 veasy-correct, veasy-incorrect, vhard-correct, vhard-incorrect, ztwo-choice-cued, k, βadj, βopp, σ2, Ter 
Model 3 13 144,859 144,968 −72,410 veasy-four-correct, veasy-four-incorrect, veasy-two-correct, veasy-two-incorrect, vhard-four-correct, vhard-four-incorrect, vhard-two-correct, vhard-two-incorrect, k, βadj, βopp, σ2, Ter 
ModelNo. of ParametersAICBICLikelihoodParameters
Model 1 10 141,600 141,684 −70,790 veasy-correct, veasy-incorrect, vhard-correct, vhard-incorrect, ztwo-choice-cued, k, βadj, βopp, σ2, Ter 
Model 2 10 142,172 142,256 −71,076 veasy-correct, veasy-incorrect, vhard-correct, vhard-incorrect, ztwo-choice-cued, k, βadj, βopp, σ2, Ter 
Model 3 13 144,859 144,968 −72,410 veasy-four-correct, veasy-four-incorrect, veasy-two-correct, veasy-two-incorrect, vhard-four-correct, vhard-four-incorrect, vhard-two-correct, vhard-two-incorrect, k, βadj, βopp, σ2, Ter 

Model 1 has the lowest (best) BIC and AIC values (best BIC and AIC values in bold).

Figure 2. 

LCA model. (A) Four-choice decisions. Four accumulators race toward boundary A (fixed to 1). Each accumulator starts at a starting point zfour-choice (fixed to 0). The accumulator associated with the correct alternative increases at a mean rate vcorrect whereas other accumulators increase at mean rate vincorrect. Accumulators are affected by leakage over time (k, black, dashed). Two inhibition parameters define the inhibition between accumulators. “Opposite” accumulators (i.e., representing nonhomologuous responses on different hands) inhibit each other with a strength of βopp (purple, dashed). All other (i.e., all adjacent) accumulators inhibit each other with a strength of βadj (gray, dashed). (B) Two-choice decisions. Here, the two uncued responses (“Adjacent Error 2” and “Opposite Error”) accumulate only noise (mean rate of 0). The starting points of the accumulators associated with the two cued responses, defined by ztwo-choice-cued, are yoked as a (positively signed) free parameter.

Figure 2. 

LCA model. (A) Four-choice decisions. Four accumulators race toward boundary A (fixed to 1). Each accumulator starts at a starting point zfour-choice (fixed to 0). The accumulator associated with the correct alternative increases at a mean rate vcorrect whereas other accumulators increase at mean rate vincorrect. Accumulators are affected by leakage over time (k, black, dashed). Two inhibition parameters define the inhibition between accumulators. “Opposite” accumulators (i.e., representing nonhomologuous responses on different hands) inhibit each other with a strength of βopp (purple, dashed). All other (i.e., all adjacent) accumulators inhibit each other with a strength of βadj (gray, dashed). (B) Two-choice decisions. Here, the two uncued responses (“Adjacent Error 2” and “Opposite Error”) accumulate only noise (mean rate of 0). The starting points of the accumulators associated with the two cued responses, defined by ztwo-choice-cued, are yoked as a (positively signed) free parameter.

In two-choice decisions, the same four-accumulator structure was used with the following exceptions. Based on previously demonstrated baseline differences (e.g., Churchland et al., 2008), accumulators associated with the cued responses (“Correct” and “Adjacent Error 1”) began at a starting point defined by ztwo-choice-cued, whereas the starting point of the other two accumulators (“Adjacent Error 2” and “Opposite Error”), ztwo-choice-uncued, was set to 0. The accumulation rate of the two accumulators associated with the noncued responses (“Adjacent Error 2” and “Opposite Error”) was also set to 0, so that only noise was accumulated.

Lastly, the drift rates vcorrrect and vincorrect varied across difficulty levels, yielding in total 10 free parameters (veasy-correct, veasy-incorrect, vhard-correct, vhard-incorrect, ztwo-choice-cued, k, βadj, βopp, σ2, Ter). The boundary parameter A was set to 1 as a scaling parameter. Model 1 is schematized in Figure 2.

By setting the accumulation rate of the noncued accumulators to 0 in Model 1, we assumed early attentional selection, gating the signal at a sensory level. Because this is speculative, we also tested a model without this assumption. Model 2 is identical to Model 1, except that accumulation rates of uncued accumulators in two-choice conditions (“Adjacent Error 2” and “Opposite Error”) were not set to 0, but instead to the same vincorrect as “Adjacent Error 1.” Hence, this model had the same 10 free parameters as Model 1.

Finally, we also tested a model with no baseline difference between two-choice and four-choice conditions, but which introduced a difference in accumulation rate instead. Hence, Model 3 is identical to Model 1 with the exception that the starting point is set to 0 for all conditions and that two-choice and four-choice conditions have separate correct and incorrect drift rates (veasy-four-correct, veasy-four-incorrect, veasy-two-correct, veasy-two-incorrect, vhard-four-correct, vhard-four-incorrect, vhard-two-correct, vhard-two-incorrect). Like Model 1, accumulation rates in uncued accumulators were set to 0. This resulted in 13 free parameters for Model 3 (veasy-four-correct, veasy-four-incorrect, veasy-two-correct, veasy-two-incorrect, vhard-four-correct, vhard-four-incorrect, vhard-two-correct, vhard-two-incorrect, k, βadj, βopp, σ2, Ter).

Note that we did not test a model with varying decision boundaries, a variation which is commonly used (e.g., Brown & Heathcote, 2008). In fact, sequential sampling models are unable to distinguish between variations in starting points, variations in boundaries, or a combination of both based on model fits alone (Bogacz, Wagenmakers, Forstmann, & Nieuwenhuis, 2010). Hence, we tested only one of these accounts and, in accordance with suggestions made in the literature (Balan et al., 2008; Churchland et al., 2008; Basso & Wurtz, 1997, 1998), chose a variation in baseline (Model 1/2) to model differences in accumulation excursion between binary and multiple choice alternatives.

To fit each model, normalized EMG RTs from stimulation-free trials were pooled across participants to estimate the model parameters at the group level. A total of 20,000 simulated EMG RTs were compared with the empirical data using Quantile Maximum Probability Estimation (Heathcote, Brown, & Mewhort, 2002), and parameter values were adjusted using a differential evolution algorithm implemented in MATLAB (The Mathworks; Price, Storn, & Jouni, 2005).

The three models were compared by calculating two measures of goodness-of-fit, which consider both likelihood and the number of free parameters, namely the Bayesian information criterion (BIC; Schwarz, 1978) and the Akaike information criterion (AIC; Akaike, 1977). The best fitting model by these measures was then used to generate predicted accumulation profiles.

Predicted Neurodynamics

We simulated 20,000 accumulation paths for each condition, based on best-fitting parameter values obtained for the model showing the best goodness-of-fit to behavioral data. Because we fitted using EMG RTs rather than button RTs (i.e., time to move effectors was not included), we assumed that virtually all of the estimated nondecision time described sensory processes. We therefore started the accumulation profile after a sensory delay given by Ter.

MEPs were simulated as the amplitude of a given accumulator at random MEP latencies. Just as in the experimental data, only simulated MEPs that occurred before the decision boundary was reached were retained. The timing of simulated MEPs associated with correct decisions was then expressed relative to both stimulus and response, and MEPs were smoothed to create simulated continuous MEP signals.

RESULTS

We explored multi-alternative decision-making in humans by utilizing MEP signals as a correlate of the decision variable. Because we were a priori uncertain about how anatomical proximity of responses would affect decision-making, our design initially distinguished two subconditions of two-choice trials, depending on whether cued responses were contained within or spread between hands (Figure 1B). However, because we found no behavioral or neural evidence to suggest that they should be treated separately, we pooled two-choice data for most of our analyses.

Our approach tracked the evolution of preparation for each of up to four response alternatives, which we categorized as “Correct,” “Adjacent Error 1,” “Adjacent Error 2,” and “Opposite Error” (see Methods and Figure 1). We used an LCA model with four accumulators categorized in the same way to model behavioral data and predict the accumulation profile of each accumulator. We were thus able not only to describe neurodynamic decision variables with four or two response alternatives but also to directly compare their profiles to model predictions.

Behavior for Two-choice and Four-choice Decisions Follows Hick's Law and Reflects Choice Difficulty

Because the application of TMS pulses can alter RTs (Day et al., 1989), only stimulation-free trials remaining after preprocessing of EMG were used for behavioral analyses. Figure 3 shows mean behavioral results obtained in each condition. For these analyses, which did not rely on pooling of data across participants (unlike subsequent analyses of the decision variable), we report raw, nonnormalized RTs. The effects of “Number of Alternatives” and “Difficulty” on correct EMG RT were tested with a 2 × 2 repeated-measures ANOVA. EMG RTs were longer for decisions with four alternatives than decisions with two alternatives, F(1, 12) = 207.10, p < .001, ηp2 = .95. Also, harder decisions were slower than easy ones, F(1, 12) = 117.37, p < .001, ηp2 = .91. There was no significant interaction between the two factors (p = .68). The same analysis with button RT as time of response led to qualitatively identical results (main effect of “Number of Alternatives”: p < .001, main effect of “Difficulty”: p < .001, interaction effect: p = .76). These results are consistent with Hick's law.

Figure 3. 

Behavioral results. (A) Mean RTs (left) and accuracy (right) by condition. EMG RTs are shown as filled bars; button RTs are indicated using dashed lines. (B) Proportion of errors per error category for four-choice (left) and two-choice (right) trials. Error bars indicate 95% confidence intervals. *p < .05, **p < .001.

Figure 3. 

Behavioral results. (A) Mean RTs (left) and accuracy (right) by condition. EMG RTs are shown as filled bars; button RTs are indicated using dashed lines. (B) Proportion of errors per error category for four-choice (left) and two-choice (right) trials. Error bars indicate 95% confidence intervals. *p < .05, **p < .001.

Error data are known to violate the assumptions of ANOVA. We therefore instead applied generalized linear mixed-effects models for statistical inference, which revealed significantly lower accuracy in four-choice compared with two-choice trials, t(156) = 5.59, p < .001, and in hard compared with easy trials, t(156) = 9.68, p < .001, with no interaction (p = .052). These results demonstrate that our RT findings do not represent a speed/accuracy tradeoff: Participants were both slower and less accurate in four-choice (and hard) trials. In addition, we compared the proportions of errors arising in the different possible erroneous response categories (Figure 3B). In two-choice trials, the three categories differed significantly from each other, t(117) > 2.58, p < .01, with most errors in the “Adjacent Error 1” category and least “Opposite” errors. In four-choice trials, “Opposite” errors were less frequent, although only “Adjacent Error 1” and “Opposite Error” categories differed significantly, t(117) = 2.27, p = .03. These results indicate that both of the cued responses were prioritized in two-choice trials and that task-irrelevant anatomical constraints affected action selection in our experiment.

Corticospinal Excitability Reflects the Accumulation of Evidence and Is Reduced at Baseline with Four Compared with Two Choices

When analyzing corticospinal excitability, we generally focused on trials in which the correct response was ultimately executed (as we had insufficient overt error trials to yield reliable signals). Smoothed signals were generated using MEPs from muscles associated with each potential response category. The resulting signals are displayed in Figure 4, locked to both the stimulus (top panels) and the response (bottom panels). Following an initial ubiquitous negative drift, in each condition corticospinal excitability associated with the correct response increased as expected over the course of the decision to reach a higher magnitude than all other potential responses, whereas the “Opposite Error” response showed the lowest amplitude.

Figure 4. 

MEP results and model predictions. Smoothed MEP signals (“MEP signal” columns) and LCA predictions (“Model Prediction” columns) for both stimulus-locked (top: A–E) and response-locked (bottom: F–J) signals. Shaded areas and error bars indicate 95% CI; *p < .05, **<.001. (A/F) MEP signals (left) and model predictions (right) associated with four-choice trials. In each panel, signals from easy (solid lines) and hard (dashed lines), as well as each correct/error category (“Correct,” “Adjacent Error 1,” Adjacent “Error 2,” “Opposite Error”) are displayed separately. (B/G) Four-choice MEP signals (left) and model predictions (right) collapsed over easy and hard trials. (C/H) MEP signals (left) and model predictions (right) associated with two-choice trials. Data are divided as per A/F. (D/I) Two-choice MEP signals (left) and model predictions (right) collapsed over easy and hard trials. (E) Top inset panel shows amplitude differences between four-choice (left bar) and cued two-choice (right bar) baseline activity (note that, unlike the rest of the figure, this bar chart contains data from both correct and incorrect trials). (J) Bottom inset panel shows amplitude differences between terminal “Adjacent Error 2” and “Opposite Error” data in both four-choice (left) and two-choice (right) trials.

Figure 4. 

MEP results and model predictions. Smoothed MEP signals (“MEP signal” columns) and LCA predictions (“Model Prediction” columns) for both stimulus-locked (top: A–E) and response-locked (bottom: F–J) signals. Shaded areas and error bars indicate 95% CI; *p < .05, **<.001. (A/F) MEP signals (left) and model predictions (right) associated with four-choice trials. In each panel, signals from easy (solid lines) and hard (dashed lines), as well as each correct/error category (“Correct,” “Adjacent Error 1,” Adjacent “Error 2,” “Opposite Error”) are displayed separately. (B/G) Four-choice MEP signals (left) and model predictions (right) collapsed over easy and hard trials. (C/H) MEP signals (left) and model predictions (right) associated with two-choice trials. Data are divided as per A/F. (D/I) Two-choice MEP signals (left) and model predictions (right) collapsed over easy and hard trials. (E) Top inset panel shows amplitude differences between four-choice (left bar) and cued two-choice (right bar) baseline activity (note that, unlike the rest of the figure, this bar chart contains data from both correct and incorrect trials). (J) Bottom inset panel shows amplitude differences between terminal “Adjacent Error 2” and “Opposite Error” data in both four-choice (left) and two-choice (right) trials.

Contrary to our expectations, there was little difference between “easy” (solid lines) and “hard” (dashed lines) trials in any of the conditions. There were, however, marked differences between four-choice and two-choice decisions. In the four-choice condition, “Adjacent Error 1” (same hand but different action relative to the responding muscle) and “Adjacent Error 2” (other hand but homologous action) traces followed a virtually identical profile of corticospinal excitability. In two-choice trials on the other hand, the two cued responses (“Correct” and “Adjacent Error 1”) are separated from the uncued response traces (“Adjacent Error 2” and “Opposite Error”) throughout the beginning of the trial (note that the cue onset is before the onset of MEP recording). Only toward the end of the decision, presumably when the (time-lagged) process driving selection of the correct response begins to feed continuously into motor cortex, does the “Correct” response increase at a steeper rate relative to the “Adjacent Error 1” response.

To test our hypothesis predicting lower baseline activity in four compared with (cued) two-choice decisions, we compared MEP amplitudes during the cue–stimulus interval (−200 to 0 msec relative to the stimulus onset; equivalent to 300–500 msec relative to cue onset). We applied a linear mixed-effects model, which confirmed our hypothesis, revealing significantly reduced MEP amplitudes in four- compared with two-choice trials, t(5112) = 2.23, p = .026 (see Figure 4).

In addition, we tested the difference in relativized slopes (i.e., correct minus error accumulation rates) between different difficulty levels (for both four-choice and two-choice within-hand trials; solid vs. dashed lines in Figure 4) using a permutation procedure (see Methods). This analysis focused on the final half of the RT period, when differential evidence accumulation between potential responses was observable in corticospinal excitability traces. The empirical slope difference between “easy” and “hard” trials did not exceed the upper/lower 2.5% of their bespoke null distributions, for either stimulus-locked or response-locked MEPs, with either four or two choices. Hence, contrary to our prediction and to previous evidence (e.g., Spieser et al., 2018), there was no easy/hard slope difference (p > .05). To the extent that MEP signals do appear to diverge between easy and hard conditions (e.g., late on during four-choice trials), this divergence is uninterpretable due to high levels of sampling noise.

However, to further explore this unexpected finding, we compared the difference in relativized slopes between fast and slow responses by performing a median split on the data. We then used the same permutation method previously applied to test the difference in slope between “easy” and “hard” trials to instead compare slopes of slow and fast trials. We found that slopes in fast trials were significantly higher than slopes in slow trials (for both four-choice and two-choice within-hand trials), albeit only in the stimulus-locked signal (p < .05), showing that when responses were quicker, corticospinal excitability accumulation was steeper.

Behavioral Modeling Suggests a Competitive Accumulation Process in which Changes in Baseline-to-Boundary Distance Generate Hick's Law

To examine whether accumulation-to-bound models can provide a compelling neurocognitive account of Hick's law, we first fitted a sequential sampling model to the behavioral data. Both the overall parameterization of such a model, selected via model comparison procedures, and the specific changes observed in the resulting parameters across experimental conditions provide insights into the processes that drive behavioral effects. Here, we used the LCA model (Usher & McClelland, 2001), which lends itself easily to multiple-alternative decision-making.

We fitted three LCA model variants to the EMG RT data, all of which included four accumulators and assumed that accumulation rate varied between easy and hard trials. They also assumed the existence of inhibition between accumulators, defined by two inhibition parameters (based on the anatomical adjacency of responses). Our best-fitting model (Model 1 in Table 1, with 10 free parameters) additionally assumed the same accumulation rate in four- and two-choice trials, but a difference in starting point. Hence, this model instantiates an account of Hick's law in which baseline-to-boundary distance drives behavioral changes as the number of alternatives increases. For this model, accumulation rates of uncued accumulators in two-choice trials were set to zero.

As seen in Table 1, varying model assumptions in other a priori plausible ways (by assuming either nongated evidence accumulation in uncued accumulators [Model 2, 10 parameters] or different accumulation rates in four- and two-choice trials [Model 3, 13 parameters]) did not improve the goodness-of-fit, as indexed by BIC and AIC. Because these different model variants capture alternative accounts of Hick's law (in particular, for Model 3, a different rate of evidence accumulation generates differences in RT and errors), this suggests that introducing multiple alternatives into a decision-making process primarily affects the baseline-to-boundary distance of the accumulation process, with a lower starting point in four- compared with two-choice decisions. We therefore proceeded using Model 1 (schematized in Figure 2), for which parameter estimates are displayed in Table 2. Notice how the starting point of accumulation (parameter z) is higher in two-choice cued conditions compared with other conditions. The best-fitting model also suggests greater inhibition (β) between opposite responses than between adjacent ones and higher accumulation rates (v) in easy compared with difficult conditions.

Table 2. 
Estimated Parameter Values for the Chosen Model (Model 1)
Model 1: LCA Parameters 
Leakage (k0.000029 
Boundary (A
Nondecision time (Ter0.2994 
Diffusion constant (σ20.4863 
Inhibition (β) 
 βadj 0.000022 
 βopp 0.0408 
Starting point (z
 Two-choice (cued) 0.2355 
 Four-choice/two-choice (uncued) 
Accumulation rate (v
 Easy 
  Correct 1.3199 
  Incorrect 0.2321 
 Hard 
  Correct 1.1781 
  Incorrect 0.3413 
Model 1: LCA Parameters 
Leakage (k0.000029 
Boundary (A
Nondecision time (Ter0.2994 
Diffusion constant (σ20.4863 
Inhibition (β) 
 βadj 0.000022 
 βopp 0.0408 
Starting point (z
 Two-choice (cued) 0.2355 
 Four-choice/two-choice (uncued) 
Accumulation rate (v
 Easy 
  Correct 1.3199 
  Incorrect 0.2321 
 Hard 
  Correct 1.1781 
  Incorrect 0.3413 

Note that the response boundary A was set to 1 as a scaling parameter and that the starting point z was set to 0 for four-choice trials.

The quality of the fit is shown in Figure 5 (top: four-choice, bottom: two-choice, left: easy, right: hard). The observed (circles) and simulated (lines and crosses) normalized EMG RT distributions are summarized by five quantile estimates (from left to right: 10%, 30%, 50%, 70%, 90%), and the EMG RT (x-axis) and proportion of data (y-axis) associated with each quantile are displayed. Both correct responses (thick lines) and responses in each error category are shown, with the latter on a magnified scale for clarity. The overlap between empirical and simulated quantiles indicates a good overall model fit: The model successfully predicted the complete RT distributions of both correct and erroneous responses. The mean absolute difference between predicted and recorded EMG RT quantiles was approximately 2.5% of median EMG RT for correct responses, confirming that the LCA was able to account for both four- and two-choice decisions.

Figure 5. 

Model fit. Quantiles estimated from behavioral data (circles) and LCA simulations (crosses and lines) for four-choice (top) and two-choice (bottom) decisions. Note that incorrect trials (yellow/orange/red, right-hand ordinate) are shown on a magnified scale compared with correct trials (blue, left-hand ordinate).

Figure 5. 

Model fit. Quantiles estimated from behavioral data (circles) and LCA simulations (crosses and lines) for four-choice (top) and two-choice (bottom) decisions. Note that incorrect trials (yellow/orange/red, right-hand ordinate) are shown on a magnified scale compared with correct trials (blue, left-hand ordinate).

Neurodynamic LCA Model Predictions Capture Both Expected and Unexpected Features of Corticospinal Excitability

To be compelling from a neuroscientific perspective, a model should describe both behavior and its neural substrate and be able to account for observed features of data that cannot easily be predicted otherwise. Hence, we went on to use the estimated parameters derived from our behavioral modeling to simulate average accumulation profiles for each condition. Figure 4 displays the resulting stimulus-locked (top panels) and response-locked (lower panels) predictions for each condition and each accumulator. Note, however, that the predictions have not been fitted to the MEP signal data—they depend instead on fits to the behavioral data, with model selection and parameter estimates based only on those data.

Important qualitative similarities emerged between the MEP signals and the model predictions (Figure 4). Like the MEP signals, LCA “Correct” accumulation profiles increase to dominate all other accumulators over the course of the decision in all conditions, whereas the “Opposite Error” accumulator shows the lowest amplitude throughout. Furthermore, in four-choice conditions, the accumulators associated with “Adjacent Error 1” and “Adjacent Error 2” display a virtually identical profile, whereas in two-choice conditions, the cued accumulators (“Correct” and “Adjacent Error 1”) show a higher activation than the uncued accumulators (“Adjacent Error 2” and “Opposite Error”). Contrary to our initial hypotheses, but in complete agreement with our neural data, there was no clear difference between “easy” and “hard” predicted accumulation profiles.

Given this surprising failure to observe differences between easy and hard conditions, we explored how large a difference between conditions is necessary to result in a visible slope difference. We therefore simulated accumulation profiles based on varying differences between easy and hard accumulation rates. By simultaneously increasing/decreasing the easy/hard accumulation rates respectively by varying percentages while keeping all other parameters the same and visually inspecting the resulting accumulation profiles, we found that slope differences between easy and hard accumulation paths became visible when they were around 2.5 times higher than the empirically observed differences. This increased difference in accumulation rates resulted in simulated RT differences, which were three times as large as those in the original simulation (e.g., in four-choice correct simulations, the original difference between easy and hard trials was 0.06 median EMG RT, whereas the increased difference was 0.20 median EMG RT).

In addition, modeling suggested an amplitude difference between the accumulators associated with “Adjacent Error 2” and “Opposite Error,” which was most pronounced toward the end of the accumulation process. Hence, this modeling step led us to revisit our neural data with an additional prediction. To quantify this effect in the neural data, we compared MEPs from the last quarter of the EMG RT period by applying a linear mixed-effects model (see Statistical Analysis). The results confirmed the amplitude difference between “Adjacent Error 2” and “Opposite Error” in both four-choice, t(462) > 4.59, p < .001, and two-choice, t(881) > 4.089, p < .001, conditions, further illustrating the similarity between predicted accumulation profiles and MEP signals (see Figure 4).

DISCUSSION

Hick's law (Hick, 1952) describes how RT increases with the number of stimulus–response alternatives and was initially believed to reflect the rate of information transmission in choice scenarios. However, sequential sampling models like the LCA model (Usher & McClelland, 2001), which have recently been extended to account for neurodynamic data, provide a useful interpretative lens through which to pinpoint the neurocognitive mechanisms that generate such behavioral adaptations. Slower responses might arise from a decreased rate of information accrual or from a requirement for stronger evidence in the face of greater intrinsic uncertainty. In line with the latter suggestion, previous work has demonstrated that more choice alternatives translate into a lower baseline activity for the decision variable in areas such as macaque LIP (Balan et al., 2008; Churchland et al., 2008). Here we tested the proposal that such decision-related changes in neuronal activity directly influence action representations in the human brain at the level of motor cortex and the spinal cord. To this end, participants completed a color discrimination task with either four or two choices, whereas we tracked the dynamics of corticospinal excitability for all four possible responses. We found that, during perceptual decisions, action representations are continuously updated from a baseline level that varies with task demands, as if dynamically shaped by a competitive accumulation process that trades speed for accuracy as uncertainty increases.

Behaviorally, responses were slower and less accurate with four choices compared with two choices (Brown et al., 2009; Cohen et al., 2009; Hick, 1952). These findings indicate that, although the stimulus did not change and the manipulation was implemented only by the cue, the four- versus two-choice manipulation had a significant impact on participants' decision-making. In addition, categorizing error responses in two-choice trials revealed that the cued but incorrect response occurred more often than any other error, whereas in four-choice trials, errors corresponding to responses sharing some anatomical linkage with the correct response were roughly equal in frequency. Hence, the complexity of the choice scenario affected not only overall RTs and accuracy but also the specifics of response selection on incorrect trials.

Because it is difficult to intuit the predictions of complex multiparameter models, we fitted a sequential sampling model to the behavioral data to simulate evidence accumulation profiles and then compare them to recorded MEP signals, choosing the LCA model for this purpose (Usher & McClelland, 2001). The LCA is an extension of a simple race accumulator model but includes leakage and inhibition parameters to model a more neurophysiologically plausible accumulation. This relatively complex model was chosen because it is easily extended to any number of choice alternatives (Smith & Ratcliff, 2004; Usher & McClelland, 2001) and has been shown to adequately account for multi-alternative decision-making in a number of previous studies (Tsetsos et al., 2010, 2011; Ditterich, 2010; Bogacz et al., 2007; McMillen & Holmes, 2006). In particular, the inhibition between accumulators appears a necessary model characteristic to explain the behaviors associated with the three different error categories utilized here (i.e., the occurrence of fewer opposite than adjacent errors). By incorporating two inhibition parameters, varying the degree of lateral inhibition between responses, the model accounted for behavioral data involving complex anatomical linkages between effectors. Whether the lower value of the inhibition parameter between “adjacent” responses actually reflects less lateral inhibition or a stronger coactivation of responses associated to contiguous stimuli remains to be elucidated. Other models exist with broadly similar architectures (e.g., multi-alternative decision field theory; Roe, Busemeyer, & Townsend, 2001) and are likely to provide similarly plausible accounts of our data.

We tested three different LCA models. Importantly, the best-fitting model utilized a higher starting point in two-choice than four-choice trials. This model outperformed a variant in which Hick's law was instead implemented via changes in the rate of evidence accrual, thereby confirming that RT and accuracy differences between four- and two-choice decisions could arise from reduced baseline activity in multi-alternative choices. Note that we did not test a model that varied in decision boundary rather than starting point. Because these two accounts both affect the excursion of accumulation, they lead to mathematically equivalent RT predictions and could only be distinguished based on neural results. Because previous results (e.g., Churchland et al., 2008) have shown a difference in baseline activity, we focused on testing that account.

Specifically, our modeling implied that action representations should evolve dynamically from differing baseline levels during decision-making. We assessed this by using TMS to induce MEPs in right-hand muscles at random times throughout the trial. By pooling data across participants and smoothing the resulting data points, we constructed an MEP signal for each response category separately (Hadar et al., 2016; Klein-Flügge, Nobbs, Pitcher, & Bestmann, 2013; Klein-Flügge & Bestmann, 2012). Here, the response categories refer to potential responses within a given correct decision, rather than overt errors (i.e., “Opposite Error” refers to a response that would have been incorrect had it been made). In fact, the labor-intensive nature of the MEP signal, as well as high accuracy rates (∼80%), meant we were unable to generate MEP signals associated with overt errors.

The resulting MEP signal reflects corticospinal excitability and has been associated with decision-related evidence accumulation (Spieser et al., 2018; Hadar et al., 2016). Typically, in humans, neural correlates of decision-making produce a single waveform per decision, reflecting either a difference or sum of the hypothetical underlying accumulators (e.g., de Lange et al., 2013; Kelly & O'Connell, 2013; Donner et al., 2009). However, here, tracking each of the four potential responses allowed us to estimate each of the four associated accumulators and thereby provide a richer insight into the decision process than a single summary signal could provide.

To our knowledge, this is the first description of a temporally precise neural correlate of the decision variable for multi-alternative versus binary decision-making in humans. For comparison, estimated model parameters were used to simulate accumulation profiles under the LCA model. Crucially, the resulting profiles were qualitatively similar to those of the measured MEP signals despite the fact that they were predicted from categorically distinct (behavioral) data. In line with our hypotheses, we found a significant baseline difference between four- and (cued) two-choice corticospinal excitability. Subsequently, the “Correct” MEP trace increased throughout the trial and peaked at the response, clearly separated from profiles associated with erroneous responses. Although the clear baseline difference suggests that this is the main mechanism driving changes in RT, it is possible that accumulation excursion is additionally enhanced by a subtle boundary variation, which our method—which inevitably yields less usable MEPs and thus less certainty toward the end of the trial—was less well suited to detect.

We also observed a difference in the trajectories of the potential but erroneous responses between four- and two-choice decisions, just as our behavioral modeling predicted. There was no observable difference between potential errors made with the same hand and those made with the homologous effector but the wrong hand in four-choice trials or, in fact, any of the profiles during the first half of the trial. However, there was a clear separation in two-choice trials, where cued responses showed a higher amplitude than uncued responses throughout the trial. This enhanced activation of the erroneous but cued response affected behavior, specifically the frequencies with which different categories of error were observed. Similarly, in four-choice trials, responses anatomically linked to the correct alternative showed the greatest activation in the second half of the RT period, with a corollary effect on error rates.

The results described so far were broadly as hypothesized (although we did not make a specific a priori hypothesis regarding our different categories of error). However, model predictions also converged with the MEP signal in surprising ways. Contrary to our prediction, both showed little difference between easy and hard accumulation profiles (beyond that attributable to sampling noise). Previous research has shown that manipulations of difficulty typically affect evidence accumulation (Ho, Brown, & Serences, 2009; Ratcliff & McKoon, 2008), as well as associated neural signals (Kelly & O'Connell, 2013; Roitman & Shadlen, 2002), including smoothed MEP signals like the ones used here (Spieser et al., 2018; Hadar et al., 2016). Moreover, modeled accumulation rates were free to vary in each difficulty condition and indeed suggested that RT differences reflected such variation, with higher slopes for easier decisions. However, the difference did not produce distinct predicted accumulation profiles. This surprising result removes a possible objection regarding the putative role of the MEP signal as an accumulation signal, as counterintuitively it showed the very pattern predicted by the model. This convergence is likely explained by a relatively weak manipulation of difficultly. Indeed, even though easy decisions were significantly faster, the effect was small (<50 msec), probably because the dominant color in the easy condition took up just 33% of the display compared with 30% in the hard condition. In fact, similar studies that reported marked slope differences between difficulty conditions also reported much larger RT differences (around 150 msec), translating into larger differences in accumulation value (Spieser et al., 2018), suggesting that larger differences in evidence strength are needed to detect a visible difference in buildup rate. A post hoc analysis confirmed that, although there was no slope difference between easy and hard waveforms, fast decisions were associated with higher slopes than slow decisions, at least in the stimulus-locked signal, supporting the role of the MEP as a correlate of accumulation.

Our modeling constrained noncued alternatives in two-choice trials to have an accumulation rate of zero, implying that attentional mechanisms gate the evidence at a sensory level, before accumulation occurs (Wyart, Myers, & Summerfield, 2015). This model assumption, implemented only because it provided the best behavioral fit, was again supported by our MEP results, which displayed little or no activation of noncued responses in two-choice trials. Note that this was found despite the fact that each stimulus contained all four colors, and the response options were determined by prestimulus cues alone. This finding is in line with previous research demonstrating that a different neural correlate of accumulation, the centroparietal positivity, only displays a buildup if the sensory evidence provided is directly relevant to the decision (O'Connell et al., 2012).

Despite the similarities we have outlined, there were also some marked differences between predicted and recorded accumulation signals. For instance, the slow negative drift visible in all MEP signals (Figure 4) may reflect broad inhibition processes described during action preparation, resulting in MEP suppression in both responding and nonresponding muscles (for a review, see Duque, Greenhouse, Labruna, & Ivry, 2017). Naturally, such nonselective MEP modulation was not reproduced in the model predictions. In addition, the neural data seem to suggest not only a higher baseline for cued responses but also a small simultaneous suppression of uncued responses, which may be an interesting addition to the model. A further slight difference between neural dynamics and model predictions (and indeed characteristics commonly associated with accumulation) relates to the reaching of a stereotyped amplitude at the time of response, which, although not directly tested here, is not clearly visible in the neural data.

At least two reasons might underlie these discrepancies. First, a direct comparison of the model prediction to the data is limited by the quality and nature of the MEP signal. Although a signal based on differences in MEP size between a responding and nonresponding muscle is likely to be a relatively true reflection of decision processes underlying response selection, an MEP signal displaying each response separately, as utilized here, will also contain nonspecific influences, such as motor-level processes. Second, like any model, the LCA can, at best, be an approximation of the true decision-making process. Importantly, sampling models provide a solid theoretical framework to analyze and interpret decision-related neural activity. However, observed dissimilarities at the decision-variable level illustrate how models describe a simplified decision process, which does not always relate in a straightforward manner with the underlying neural dynamics (Purcell & Palmeri, 2017).

In summary, we have demonstrated that multi-alternative decision-making in humans can be accounted for by sequential sampling models and, importantly, that smoothed MEP signals reflecting corticospinal excitability provide a downstream reflection of the accumulation process. Under a sequential sampling modeling framework, higher RTs with increasing numbers of alternatives can be explained by a greater distance between the starting point of accumulation and the response boundary. This affects the signal-to-noise ratio, because larger baseline-to-bound distances require more evidence to be accumulated (Churchland & Ditterich, 2012; Churchland et al., 2008; Usher & McClelland, 2001). In four-choice decisions, which increase uncertainty relative to two-choice decisions, an increase in the baseline-to-bound distance would compensate for this uncertainty at the expense of RT. Here, we have validated this prediction in human decision-making actuated via the corticospinal tract, showing for the first time that the number of choice alternatives in a decision-making task affects the baseline activity of neural accumulation, just as sequential sampling models predict. Furthermore, we have shown that MEP signals can be used to track the evolution of preparation for each of four responses separately, giving insight into each of the four associated accumulators of a sequential sampling model.

Acknowledgments

This work was supported by a Leverhulme Trust Research Project grant (RPG-2014188).

Reprint requests should be sent to Carmen Kohl, City, University of London, Northampton Square, London, EC1V 0HB, United Kingdom, or via e-mail: carmen.kohl@city.ac.uk.

Note

1. 

Other physiological signals may also be appropriate for this purpose, for example EMG (Servant, White, Montagnini, & Burle, 2015, 2016) or the gain of reflex responses (Selen, Shadlen, & Wolpert, 2012). Our choice in part reflects our relative expertise with these techniques, but also the greater likelihood that action-related signals are contaminated by factors unrelated to decision formation as we move further along the sensorimotor pipeline towards the observable action.

REFERENCES

Akaike
,
H.
(
1977
).
On entropy maximization principle
. In
P. R.
Krishnaiah
(Ed.),
Applications of statistics
(pp.
27
41
).
Amsterdam
.
Balan
,
P. F.
,
Oristaglio
,
J.
,
Schneider
,
D. M.
, &
Gottlieb
,
J.
(
2008
).
Neuronal correlates of the set-size effect in monkey lateral intraparietal area
.
PLoS Biology
,
6
,
1443
1458
.
Basso
,
M. A.
, &
Wurtz
,
R. H.
(
1997
).
Modulation of neuronal activity by target uncertainty
.
Nature
,
389
,
66
69
.
Basso
,
M. A.
, &
Wurtz
,
R. H.
(
1998
).
Modulation of neuronal activity in superior colliculus by changes in target probability
.
Journal of Neuroscience
,
18
,
7519
7534
.
Bestmann
,
S.
,
Harrison
,
L. M.
,
Blankenburg
,
F.
,
Mars
,
R. B.
,
Haggard
,
P.
,
Friston
,
K. J.
, et al
(
2008
).
Influence of uncertainty and surprise on human corticospinal excitability during preparation for action
.
Current Biology
,
18
,
775
780
.
Bestmann
,
S.
, &
Krakauer
,
J. W.
(
2015
).
The uses and interpretations of the motor-evoked potential for understanding behaviour
.
Experimental Brain Research
,
233
,
679
689
.
Bogacz
,
R.
,
Usher
,
M.
,
Zhang
,
J.
, &
McClelland
,
J. L.
(
2007
).
Extending a biologically inspired model of choice: Multi-alternatives, nonlinearity and value-based multidimensional choice
.
Philosophical Transactions of the Royal Society, Series B, Biological Sciences
,
362
,
1655
1670
.
Bogacz
,
R.
,
Wagenmakers
,
E. J.
,
Forstmann
,
B. U.
, &
Nieuwenhuis
,
S.
(
2010
).
The neural basis of the speed-accuracy tradeoff
.
Trends in Neurosciences
,
33
,
10
16
.
Brainard
,
D. H.
(
1997
).
The Psychophysics Toolbox
.
Spatial Vision
,
10
,
433
436
.
Brown
,
S.
,
Steyvers
,
M.
, &
Wagenmakers
,
E. J.
(
2009
).
Observing evidence accumulation during multi-alternative decisions
.
Journal of Mathematical Psychology
,
53
,
453
462
.
Brown
,
S. D.
, &
Heathcote
,
A.
(
2008
).
The simplest complete model of choice response time: Linear ballistic accumulation
.
Cognitive Psychology
,
57
,
153
178
.
Churchland
,
A. K.
, &
Ditterich
,
J.
(
2012
).
New advances in understanding decisions among multiple alternatives
.
Current Opinion in Neurobiology
,
22
,
920
926
.
Churchland
,
A. K.
,
Kiani
,
R.
, &
Shadlen
,
M. N.
(
2008
).
Decision-making with multiple alternatives
.
Nature Neuroscience
,
11
,
693
702
.
Cohen
,
J. Y.
,
Heitz
,
R. P.
,
Woodman
,
G. F.
, &
Schall
,
J. D.
(
2009
).
Neural basis of the set-size effect in frontal eye field: Timing of attention during visual search
.
Journal of Neurophysiology
,
101
,
1699
1704
.
Day
,
B. L.
,
Rothwell
,
J. C.
,
Thompson
,
P. D.
,
Maertens de Noordhout
,
A.
,
Nakashima
,
K.
,
Shannon
,
K.
, et al
(
1989
).
Delay in the execution of voluntary movement by electrical or magnetic brain stimulation in intact man. Evidence for the storage of motor programs in the brain
.
Brain
,
112
,
649
663
.
de Lange
,
F. P.
,
Rahnev
,
D. A.
,
Donner
,
T. H.
, &
Lau
,
H.
(
2013
).
Prestimulus oscillatory activity over motor cortex reflects perceptual expectations
.
Journal of Neuroscience
,
33
,
1400
1410
.
Ditterich
,
J.
(
2010
).
A comparison between mechanisms of multi-alternative perceptual decision making: Ability to explain human behavior, predictions for neurophysiology, and relationship with decision theory
.
Frontiers in Neuroscience
,
4
,
1
24
.
Donner
,
T. H.
,
Siegel
,
M.
,
Fries
,
P.
, &
Engel
,
A. K.
(
2009
).
Buildup of choice-predictive activity in human motor cortex during perceptual decision making
.
Current Biology
,
19
,
1581
1585
.
Duque
,
J.
,
Greenhouse
,
I.
,
Labruna
,
L.
, &
Ivry
,
R. B.
(
2017
).
Physiological markers of motor inhibition during human behavior
.
Trends in Neurosciences
,
40
,
219
236
.
Duque
,
J.
,
Lew
,
D.
,
Mazzocchio
,
R.
,
Olivier
,
E.
, &
Ivry
,
R. B.
(
2010
).
Evidence for two concurrent inhibitory mechanisms during response preparation
.
Journal of Neuroscience
,
30
,
3793
3802
.
Forstmann
,
B. U.
,
Ratcliff
,
R.
, &
Wagenmakers
,
E.-J.
(
2016
).
Sequential sampling models in cognitive neuroscience: Advantages, applications, and extensions
.
Annual Review of Psychology
,
67
,
641
666
.
Gluth
,
S.
,
Rieskamp
,
J.
, &
Büchel
,
C.
(
2013
).
Classic EEG motor potentials track the emergence of value-based decisions
.
Neuroimage
,
79
,
394
403
.
Gold
,
J. I.
, &
Shadlen
,
M. N.
(
2000
).
Representation of a perceptual decision in developing oculomotor commands
.
Nature
,
404
,
390
394
.
Gold
,
J. I.
, &
Shadlen
,
M. N.
(
2003
).
The influence of behavioral context on the representation of a perceptual decision in developing oculomotor commands
.
Journal of Neuroscience
,
23
,
632
651
.
Hadar
,
A.
,
Makris
,
S.
, &
Yarrow
,
K.
(
2012
).
The truth-telling motor cortex: Response competition in M1 discloses deceptive behaviour
.
Biological Psychology
,
89
,
495
502
.
Hadar
,
A.
,
Rowe
,
P.
,
Di Costa
,
S.
,
Jones
,
A.
, &
Yarrow
,
K.
(
2016
).
Motor-evoked potentials reveal a motor-cortical readout of evidence accumulation for sensorimotor decisions
.
Psychophysiology
,
53
,
1721
1731
.
Hanks
,
T. D.
, &
Summerfield
,
C.
(
2017
).
Perceptual decision making in rodents, monkeys, and humans
.
Neuron
,
93
,
15
31
.
Heathcote
,
A.
,
Brown
,
S.
, &
Mewhort
,
D. J. K.
(
2002
).
Quantile maximum likelihood estimation of response time distributions
.
Psychonomic Bulletin and Review
,
9
,
1
31
.
Hick
,
W. E.
(
1952
).
On the rate of gain of information
.
Quarterly Journal of Experimental Psychology
,
4
,
11
26
.
Ho
,
T. C.
,
Brown
,
S.
, &
Serences
,
J. T.
(
2009
).
Domain general mechanisms of perceptual decision making in human cortex
.
Journal of Neuroscience
,
29
,
8675
8687
.
Kelly
,
S. P.
, &
O'Connell
,
R. G.
(
2013
).
Internal and external influences on the rate of sensory evidence accumulation in the human brain
.
Journal of Neuroscience
,
33
,
19434
19441
.
Kiers
,
L.
,
Fernando
,
B.
, &
Tomkins
,
D.
(
1997
).
Facilitatory effect of thinking about movement on magnetic motor-evoked potentials
.
Electroencephalography and Clinical Neurophysiology–Electromyography and Motor Control
,
105
,
262
268
.
Klein-Flügge
,
M. C.
, &
Bestmann
,
S.
(
2012
).
Time-dependent changes in human corticospinal excitability reveal value-based competition for action during decision processing
.
Journal of Neuroscience
,
32
,
8373
8382
.
Klein-Flügge
,
M.
,
Nobbs
,
D.
,
Pitcher
,
J.
, &
Bestmann
,
S.
(
2013
).
Variability of human corticospinal excitability tracks the state of action preparation
.
Journal of Neuroscience
,
33
,
5564
5572
.
Kleiner
,
M.
,
Brainard
,
D. H.
,
Pelli
,
D. G.
,
Broussard
,
C.
,
Wolf
,
T.
, &
Niehorster
,
D.
(
2007
).
What's new in Psychtoolbox-3?
Perception
,
36
,
14
.
Lee
,
K.-M.
, &
Keller
,
E. L.
(
2008
).
Neural activity in the frontal eye fields modulated by the number of alternatives in target choice
.
Journal of Neuroscience
,
28
,
2242
2251
.
Li
,
X.
, &
Aruin
,
A.
(
2005
).
Muscle activity onset time detection using Teager–Kaiser energy operator
.
Conference Proceedings: IEEE
,
7
,
7549
7552
.
Li
,
X.
,
Zhou
,
P.
, &
Aruin
,
A. S.
(
2007
).
Teager–Kaiser energy operation of surface EMG improves muscle activity onset detection
.
Annals of Biomedical Engineering
,
35
,
1532
1538
.
McMillen
,
T.
, &
Holmes
,
P.
(
2006
).
The dynamics of choice among multiple alternatives
.
Journal of Mathematical Psychology
,
50
,
30
57
.
Michelet
,
T.
,
Duncan
,
G. H.
, &
Cisek
,
P.
(
2010
).
Response competition in the primary motor cortex: Corticospinal excitability reflects response replacement during simple decisions
.
Journal of Neurophysiology
,
104
,
119
127
.
Mulder
,
M. J.
,
van Maanen
,
L.
, &
Forstmann
,
B. U.
(
2014
).
Perceptual decision neurosciences—A model-based review
.
Neuroscience
,
277
,
872
884
.
O'Connell
,
R. G.
,
Dockree
,
P. M.
, &
Kelly
,
S. P.
(
2012
).
A supramodal accumulation-to-bound signal that determines perceptual decisions in humans
.
Nature Neuroscience
,
15
,
1729
1735
.
Paré
,
M.
, &
Wurtz
,
R. H.
(
2001
).
Progression in neuronal processing for saccadic eye movements from parietal cortex area LIP to superiorcolliculus
.
Journal of Neurophysiology
,
85
,
2545
2562
.
Pelli
,
D. G.
(
1997
).
The VideoToolbox software for visual psychophysics: Transforming numbers into movies
.
Spatial Vision
,
10
,
437
442
.
Price
,
K. V.
,
Storn
,
R. M.
, &
Jouni
,
L. A.
(
2005
).
Differential evolution: A practical approach to global optimization
.
Heidelberg
:
Springer
.
Purcell
,
B. A.
, &
Palmeri
,
T. J.
(
2017
).
Relating accumulator model parameters and neural dynamics
.
Journal of Mathematical Psychology
,
76
,
156
171
.
Ratcliff
,
R.
, &
McKoon
,
G.
(
2008
).
The diffusion decision model: Theory and data for two-choice decision tasks
.
Neural Computation
,
20
,
873
922
.
Ratcliff
,
R.
, &
Rouder
,
J. N.
(
1998
).
Modeling response times for two-choice decisions
.
Psychological Science
,
9
,
347
356
.
Roe
,
R. M.
,
Busemeyer
,
J. R.
, &
Townsend
,
J. T.
(
2001
).
Multi-alternative decision field theory: A dynamic connectionist model of decision making
.
Psychological Review
,
108
,
370
392
.
Roitman
,
J. D.
, &
Shadlen
,
M. N.
(
2002
).
Response of neurons in the lateral intraparietal area during a combined visual discrimination reaction time task
.
Journal of Neuroscience
,
22
,
9475
9489
.
Schwarz
,
G. E.
(
1978
).
Estimating the dimension of a model
.
Annals of Statistics
,
6
,
461
464
.
Selen
,
L. P. J.
,
Shadlen
,
M. N.
, &
Wolpert
,
D. M.
(
2012
).
Deliberation in the motor system: Reflex gains track evolving evidence leading to a decision
.
Journal of Neuroscience
,
32
,
2276
2286
.
Servant
,
M.
,
White
,
C.
,
Montagnini
,
A.
, &
Burle
,
B.
(
2015
).
Using covert response activation to test latent assumptions of formal decision-making models in humans
.
Journal of Neuroscience
,
35
,
10371
10385
.
Servant
,
M.
,
White
,
C.
,
Montagnini
,
A.
, &
Burle
,
B.
(
2016
).
Linking theoretical decision-making mechanisms in the Simon task with electrophysiological data: A model-based neuroscience study in humans
.
Journal of Cognitive Neuroscience
,
28
,
1501
1521
.
Shadlen
,
M. N.
, &
Newsome
,
W. T.
(
2001
).
Neural basis of a perceptual decision in the parietal cortex (area LIP) of the rhesus monkey
.
Journal of Neurophysiology
,
86
,
1916
1936
.
Siegel
,
M.
,
Engel
,
A. K.
, &
Donner
,
T. H.
(
2011
).
Cortical network dynamics of perceptual decision-making in the human brain
.
Frontiers in Human Neuroscience
,
5
,
1
12
.
Smith
,
P. L.
, &
Ratcliff
,
R.
(
2004
).
Psychology and neurobiology of simple decisions
.
Trends in Neurosciences
,
27
,
161
168
.
Solnik
,
S.
,
Rider
,
P.
,
Steinweg
,
K.
,
Devita
,
P.
, &
Hortobágyi
,
T.
(
2010
).
Teager–Kaiser energy operator signal conditioning improves EMG onset detection
.
European Journal of Applied Physiology
,
110
,
489
498
.
Spieser
,
L.
,
Kohl
,
C.
,
Forster
,
B.
,
Bestmann
,
S.
, &
Yarrow
,
K.
(
2018
).
Neurodynamic evidence supports a forced-excursion model of decision-making under speed/accuracy instructions
.
eNeuro
,
5
,
0159-18.2018
.
Teodorescu
,
A. R.
, &
Usher
,
M.
(
2013
).
Disentangling decision models: From independence to competition
.
Psychological Review
,
120
,
1
38
.
Thura
,
D.
,
Beauregard-Racine
,
J.
,
Fradet
,
C.-W.
, &
Cisek
,
P.
(
2012
).
Decision making by urgency gating: Theory and experimental support
.
Journal of Neurophysiology
,
108
,
2912
2930
.
Thura
,
D.
, &
Cisek
,
P.
(
2016
).
Modulation of premotor and primary motor cortical activity during volitional adjustments of speed-accuracy trade-offs
.
Journal of Neuroscience
,
36
,
938
956
.
Tsetsos
,
K.
,
Pfeffer
,
T.
,
Jentgens
,
P.
, &
Donner
,
T. H.
(
2015
).
Action planning and the timescale of evidence accumulation
.
PLoS One
,
10
,
e0129473
.
Tsetsos
,
K.
,
Usher
,
M.
, &
Chater
,
N.
(
2010
).
Preference reversal in multiattribute choice
.
Psychological Review
,
117
,
1275
1291
.
Tsetsos
,
K.
,
Usher
,
M.
, &
McClelland
,
J. L.
(
2011
).
Testing multi-alternative decision models with non-stationary evidence
.
Frontiers in Neuroscience
,
5
,
1
18
.
Usher
,
M.
, &
McClelland
,
J. L.
(
2001
).
The time course of perceptual choice: The leaky, competing accumulator model
.
Psychological Review
,
108
,
550
592
.
Wyart
,
V.
,
Myers
,
N. E.
, &
Summerfield
,
C.
(
2015
).
Neural mechanisms of human perceptual choice under focused and divided attention
.
Journal of Neuroscience
,
35
,
3485
3498
.

Author notes

*

C. Kohl and L. Spieser contributed equally to this study.