Mathematical models of eye movements in reading: a possible role for autonomous saccades

An efficient method for the exact numerical simulation of semi-Markov proce sses is used to study minimal models of the control of eye movements in rea ding. When we read a text, typical sequences of fixations form a rather com plicated trajectory - almost like a random walk. Mathematical models of eye movement control can account for this behavior using stochastic transition rules between few discrete internal states, which represent combinations o f certain stages of lexical access and saccade programs. We show that exper imentally observed fixation durations can be explained by residence-time-de pendent transition probabilities. Stochastic processes with this property a re known as semi-Markov processes. For our numerical simulations we use the minimal process method (Gillespie algorithm), which is an exact and effici ent simulation algorithm for this class of stochastic processes. Within thi s mathematical framework, we study different forms of coupling between eye movements and shifts of covert attention in reading. Our model lends suppor t to the existence of autonomous saccades, i.e., the hypothesis that initia tions of saccades are not completely determined by lexical access processes .