Support is requested to continue a productive collaboration aimed to develop, test, and extend computational models of eye movement control in visual decision making and visual search. Our research program is guided by converging constraints from computational, behavioral, and neurophysiological perspectives that link detailed patterns of behavior in humans and monkeys performing visual saccade tasks with patterns of modulation in neurons recorded in monkeys through the use of computational models that predict behavioral and neural dynamics. We propose new computational modeling of existing monkey behavioral and neurophysiological experiments and new computational modeling of new human experiments that mirror and significantly extend experiments previously conducted with monkeys. Our theoretical foundation is a class of stochastic accumulation of evidence models that mathematical psychologists and systems neuroscientists have converged upon as a general theoretical framework to understand and explain the time course of visual decision making; these include an interactive race model and a gated accumulator model we proposed previously. Unlike most approaches, (1) we quantitatively test alternative model architectures (including race, diffusion, competitive, gated accumulators) on detailed behavioral data in both humans and monkeys, including response probabilities and distributions of correct and error response times for saccades, (2) we constrain model mechanisms and model parameters based on neurophysiological recordings, specifically neurons in frontal eye field (FEF) hypothesized to represent the evolving time-course of task-relevant visual evidence, (3) we quantitatively test model architectures on how well they predict the recorded dynamics of neurons involved in make a visual decision, specifically neurons in FEF that determine when and where the eyes move. Aim 1 will develop and test the gated accumulator model against alternative models of countermanding and control of saccadic eye movements. Aim 2 will develop and test the gated accumulator model against alternative models of speed-accuracy control of saccadic eye movements in visual search. Aim 3 will investigate how to scale the broad class of stochastic accumulator models, including gated accumulator, from a single accumulator associated with each response to ensembles of thousands of accumulator neurons associated with each response. To understand normal behavior as well as illness, disability, and disease, abstract computational models, like stochastic accumulation of evidence models, can be a just right theoretical level in that best-fitting parameters of these models can characterize well individual differences in behavior and provide theoretical markers for understanding brain measures - our models provide that just right theoretical level. Yet to the extent that certain neurological conditions have a biophysical basis at the level of individual neurons and neural circuits, we also need to understand how these abstract computational models map onto neural circuits - making this mapping is also core to our proposed work.