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.

Evidence against the facilitation of the vergence command during saccade-vergence interactions.

Combined saccade-vergence movements result when gaze shifts are made to targets that differ both in direction and in depth from the momentary fixation point. Currently, there are two rivaling schemes to explain these eye movements. According to the first, such eye movements are due to a combination of a conjugate saccadic command and a symmetric vergence command; the two commands are not taken to be independent but instead are suggested to interact in a nonlinear manner, which leads to an intra-saccadic facilitation of the vergence command. According to the second scheme, the saccade generator is disconjugate, thus encoding vergence information in the saccadic commands themselves, and the remaining vergence requirement is provided by an asymmetric mechanism. Here, we test the scheme that suggests an intra-saccadic facilitation of the vergence command. We analyze this scheme and show that it has two fundamental properties. The first is that the vergence command is always symmetric, even during the intra-saccadic facilitation. The second is that the facilitated (and symmetric) vergence command sums linearly with the conjugate saccadic command at the final common pathway. Taking these properties together, this scheme predicts that the total magnitude of the saccadic component of combined saccade-vergence movements can be decomposed into a conjugate part and a symmetric part. When we tested this prediction in combined saccade-vergence movements of humans, we found that it was not confirmed. Thus, our results are incompatible with the facilitation of the vergence command hypothesis. Although these results do not directly verify the rivaling hypothesis, which suggests a disconjugate saccade generator, they do provide it with indirect support.