Saccadic amplitudes during combined saccade-vergence movements result from a weighted average of the target's locations in the two retinas

Recent neurophysiological and behavioral studies have established that the saccadic amplitudes performed during combined saccade-vergence movements are unequal in the two eyes. These studies have not established, however, how the saccadic amplitude of each eye is determined. Our goal here is to fill this lacuna. We use three well-known metric attributes of saccadic movements as constraints and argue that the only quantitative model that obeys these constraints is one where each eye's saccadic amplitude is given by a weighted average of the target's locations in the two retinas. However, this theoretical result does not establish whether the weights in the weighted averaging operation are constant or whether they vary for different targets. To test the simpler of these two possibilities, namely the one of constant weights, we recorded combined saccade-vergence movements performed by human subjects. Our analysis of these movements shows that a constant-weights weighted averaging model provides an excellent description of their saccadic amplitudes. Overall, then, our conclusions are: (1) the two eyes' saccadic amplitudes are determined by weighted averages of the target's locations in the two retinas; (2) for targets within the oculomotor range of natural viewing, which was the range in our experiments, a weighted averaging model that uses constant weights accounts superbly for these saccadic amplitudes. We suggest that the weighted averaging operation that determines saccadic amplitudes is a by-product of a process whose purpose is to yoke the two eyes together. We provide a model explaining how this yoking may be achieved.