Nonlinear Dynamics Support a Linear Population Code in a Retinal Target-Tracking Circuit

A basic task faced by the visual system of many organisms is to accurately track the position of moving prey. The retina is the first stage in the processing of such stimuli; the nature of the transformation here, from photons to spike trains, constrains not only the ultimate fidelity of the tracking signal but also the ease with which it can be extracted by other brain regions. Here we demonstrate that a population of fast-OFF ganglion cells in the salamander retina, whose dynamics are governed by a nonlinear circuit, serve to compute the future position of the target over hundreds of milliseconds. The extrapolated position of the target is not found by stimulus reconstruction but is instead computed by a weighted sum of ganglion cell outputs, the population vector average (PVA). The magnitude of PVA extrapolation varies systematically with target size, speed, and acceleration, such that large targets are tracked most accurately at high speeds, and small targets at low speeds, just as is seen in the motion of real prey. Tracking precision reaches the resolution of single photoreceptors, and the PVA algorithm performs more robustly than several alternative algorithms. If the salamander brain uses the fast-OFF cell circuit for target extrapolation as we suggest, the circuit dynamics should leave a microstructure on the behavior that may be measured in future experiments. Our analysis highlights the utility of simple computations that, while not globally optimal, are efficiently implemented and have close to optimal performance over a limited but ethologically relevant range of stimuli.