Decisions about where to move the eyes depend on neurons in frontal eye field (FEF). Movement neurons in FEF accumulate salience evidence derived from FEF visual neurons to select the location of a saccade target among distractors. How visual neurons achieve this salience representation is unknown. We present a neuro-computational model of target selection called salience by competitive and recurrent interactions (SCRI), based on the competitive interaction model of attentional selection and decision-making (Smith & Sewell, 2013). SCRI selects targets by synthesizing localization and identification information to yield a dynamically evolving representation of salience across the visual field. SCRI accounts for neural spiking of individual FEF visual neurons, explaining idiosyncratic differences in neural dynamics with specific parameters. Many visual neurons resolve the competition between search items through feedforward inhibition between signals representing different search items, some also require lateral inhibition, and many act as recurrent gates to modulate the incoming flow of information about stimulus identity. SCRI was tested further by using simulated spiking representations of visual salience as input to the gated accumulator model of FEF movement neurons (Purcell et al., 2010, 2012). Predicted saccade response times fit those observed for search arrays of different set sizes and different target-distractor similarities, and accumulator trajectories replicated movement neuron discharge rates. These findings offer new insights into visual decision-making through converging neuro-computational constraints and provide a novel computational account of the diversity of FEF visual neurons.