The search over time and space (sSoTS) model attempts to simulate both the spatial and the temporal aspects of human visual search using spiking level neurons, which incorporate some biologically plausible aspects of neuronal firing. The model contains pools of units that (a) code basic features of objects, presumed to reside in the ventral visual stream, and (b) respond in a feature-independent way to stimulation at their location, presumed to operate in the posterior parietal cortex. We examined the effects of selective lesioning neurons responding to one side of the location map. Unilateral damage introduced spatial biases into selection that affected conjunction more than single-feature search. In addition, there was an impaired ability to segment stimuli over time as well as space (e.g., in preview search). These results match previously reported data on patients with posterior parietal lesions. In addition we show that spatial biases in selection increase under conditions in which there is decreased activity from excitatory neurotransmitters, mimicking effects of reduced arousal. Further simulations explored the effects of time and of visual grouping on extinction, generating predictions that were then tested empirically. The model provides a framework for linking behavioural data from patients with neural-level determinants of visual attention.