Relation between fixation disparity and the asymmetry between convergent and divergent disparity step responses

The neural network model of Patel et al. [Patel, S. S., Jiang, B. C., & Ogmen, H. (2001). Vergence dynamics predict fixation disparity. Neural Computation, 13(7), 1495-1525] predicts that fixation disparity, the vergence error for a stationary fusion stimulus, is the result of asymmetrical dynamic properties of disparity vergence mechanisms: faster (slower) convergent than divergent responses give rise to an eso (exo) fixation disparity, i.e., over-convergence (under-convergence) in stationary fixation. This hypothesis was tested in the present study with an inter-individual approach: in 16 subjects we estimated the vergence step response to a 1deg disparity stimulus with a subjective nonius procedure. Dichoptic nonius lines were flashed for 100ms with various amounts of delay after the disparity step stimulus (0, 100, 200, 300, 400, and 1000ms). Measured fixation disparity was significantly correlated with the prediction of Patel et al. (2001) based on the asymmetry in convergent and divergent vergence velocity (r=.7, n=14), which explained about 50% (r(2)) of the inter-individual variability in fixation disparity. All subjects with an exo fixation disparity (i.e., static under-convergence) had a weaker dynamic response for convergent than for divergent step stimuli. This confirms a relation between static vergence and asymmetric dynamic vergence, which both are idiosyncratic vergence parameters.