Most people tend to bisect horizontal lines slightly to the left of their true center (pseudoneglect), and start visual search from left-sided items. This physiological leftward spatial bias may depend on hemispheric asymmetries in the organization of attentional networks, but the precise mechanisms are unknown. Here we modeled relevant aspects of the ventral and dorsal attentional networks (VAN and DAN) of the human brain. First, we demonstrated pseudoneglect in visual search in 101 right-handed psychology students. Participants consistently tended to start the task from a left-sided item, thus showing pseudoneglect. Second, we trained populations of simulated neurorobots to perform a similar task, by using a genetic algorithm. The neurorobots' behavior was controlled by artificial neural networks, which simulated the human VAN and DAN in the two brain hemispheres. Neurorobots differed in the connectional constraints that were applied to the anatomy and function of the attention networks. Results indicated that (1) neurorobots provided with a biologically plausible hemispheric asymmetry of the VAN-DAN connections, as well as with inter-hemispheric inhibition, displayed the best match with human data; however, (2) anatomical asymmetry per se was not sufficient to generate pseudoneglect; in addition, the VAN must have an excitatory influence on the ipsilateral DAN; (3) neurorobots provided with bilateral competence in the VAN but without inter-hemispheric inhibition failed to display pseudoneglect. These findings provide a proof of concept of the causal link between connectional asymmetries and pseudoneglect, and specify important biological constraints that result in physiological asymmetries of human behavior.