The latency between the appearance of a visual target and the start of the saccadic eye movement made to look at it varies from trial to trial to an extent that is inexplicable in terms of ordinary 'physiological' processes such as synaptic delays and conduction velocities. An alternative interpretation is that it represents the time needed to decide whether a target is in fact present: decision processes are necessarily stochastic, because they depend on extracting information from noisy sensory signals. In one such model, the presence of a target causes a signal in a decision unit to rise linearly at a rate r from its initial value s0 until it reaches a fixed threshold theta, when a saccade is initiated. One can regard this decision signal as a neural estimate of the log likelihood of the hypothesis that the target is present, the threshold being the significance criterion or likelihood level at which the target is presumed to be present. Experiments manipulating the prior probability of the target's appearing confirm this notion: the latency distribution then changes in the way expected if s0 simply reflects the prior log likelihood of the stimulus.

A fruitful quantitative approach to understanding how the brain makes decisions has been to look at the time needed to make a decision, and how it is affected by factors such as the supply of information, or an individual's expectations. This approach has led to a model of decision-making, consistent with recent neurophysiological data, that explains the observed variability of reaction times and correctly predicts the effects of altered expectations. Can it also predict what happens when the urgency of making the response changes? We asked subjects to make eye movements to low-visibility targets either as fast or as accurately as possible, and found that the model does indeed predict the timing of their responses: the degree of urgency seems to influence the criterion level at which a decision signal triggers a response.

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The stop-signal or countermanding task probes the ability to control action by requiring subjects to withhold a planned movement in response to an infrequent stop signal which they do with variable success depending on the delay of the stop signal. We investigated whether performance of humans and macaque monkeys in a saccade countermanding task was influenced by stimulus and performance history. In spite of idiosyncrasies across subjects several trends were evident in both humans and monkeys. Response time decreased after successive trials with no stop signal. Response time increased after successive trials with a stop signal. However, post-error slowing was not observed. Increased response time was observed mainly or only after cancelled (signal inhibit) trials and not after noncancelled (signal respond) trials. These global trends were based on rapid adjustments of response time in response to momentary fluctuations in the fraction of stop signal trials. The effects of trial sequence on the probability of responding were weaker and more idiosyncratic across subjects when stop signal fraction was fixed. However, both response time and probability of responding were influenced strongly by variations in the fraction of stop signal trials. These results indicate that the race model of countermanding performance requires extension to account for these sequential dependencies and provide a basis for physiological studies of executive control of countermanding saccade performance.

Reaction times generally follow a simple law economically described by the LATER model, in which a decision signal rises linearly in response to information about a target to a threshold at which a response is initiated, at a rate that varies from trial to trial with a Gaussian distribution. Functionally, LATER may be regarded as an ideal decision mechanism incorporating prior probability, information, and criterion level or urgency; this can be tested quantitatively by seeing whether LATER accurately predicts the effects on latency distributions of manipulating these variables: in this case, information and urgency. We presented subjects with random-dot kinematograms while fixating a central LED. The information content of the display was varied by altering the proportion of the dots moving coherently together either left or right rather than randomly. As soon as subjects detected the direction of coherent movement, they made a saccade in the same direction to one of a pair of LEDs on each side of the fixation target. Subjects responded either carefully, taking time to ensure an accurate judgement, or more hastily and with less regard for accuracy. The distributions of latencies under the different combinations of conditions were found to conform to LATER's predictions. Providing more information or increasing urgency both reduce latency; but they alter the observed distributions in different ways, equivalent to increasing the mean rate of rise on the one hand or reducing the criterion level on the other. Making only simple assumptions about the underlying mechanisms, the observed changes can be accounted for quantitatively.

We used a countermanding paradigm to investigate the relationship between conflicting cues for controlling human saccades. Subjects made a saccade to a target appearing suddenly in the periphery; but on some trials, after a delay, a stop-signal was presented that instructed subjects to inhibit the saccade. As we increased this delay, subjects increasingly failed to inhibit the movement. From measurements of this relationship, and of saccadic latency in control trials, we estimated the average time needed to inhibit the saccade (the stop-signal reaction time or SSRT). SSRTs were similar across subjects, between 125 and 145 ms, and did not vary with target luminance. We then investigated a race model in which the target initiates a response preparation signal rising linearly with a rate varying randomly from trial to trial, and racing against a similarly rising signal initiated by the cue to inhibit the saccade. The first process to cross a trigger threshold determines whether the saccade is initiated or not. In Monte Carlo simulations, this model correctly predicted the probability of successful saccade inhibition as a function of the stop-signal delay, and also the statistical distributions of saccadic latency during trials in which a stop-signal was presented but the subject failed to inhibit the saccade. These findings provide a comparison to results previously described in the monkey, and show that a simple race model with a linear rise to threshold may underlie behavioural performance in tasks of this kind.

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