No cause for pause: new analyses of ramping and stepping dynamics in LIP (Rebuttal to Response to Reply to Comment on Latimer et al. 2015)

Abstract

We recently presented a statistical comparison between two models of latent dynamics in macaque lateral intraparietal (LIP) area spike trains--a continuous ramping (diffusion-to-bound) model, and a discrete stepping model--and found that a substantial fraction of neurons (recorded in two different studies) were better supported by the stepping model (Latimer et al., 2015). Here, we respond to a recent challenge to the validity of these findings that focuses primarily on the possibility of a lower bound on LIP firing rates (Zylberberg & Shadlen, 2016). The paper in question proposed alternate formulations of the ramping model, and argued (via indirect analyses) that half the neurons in the population were better explained by the new model; if correct, this would lead to an even split in the number of neurons better explained by each model. These analyses, while interesting, do not alter the conclusions of our original paper. Here, we review the criticisms raised by Zylberberg & Shadlen and report several new analyses using models with lower bounds. First, we show that the stepping model continued to provide a better description of LIP spike trains when fit using only an early period of each trial. Second, we performed a direct model comparison between our stepping model and a ramping-with-baseline model proposed by Zylberberg & Shadlen; we found that (in a pleasing moment of agreement) roughly half the neurons were better explained by each model. Interestingly, inspection of the cells that switched classifications revealed that many did not strictly exhibit the classical ramping PSTHs that motivated these analyses in the first place. We also examined two other issues raised in recent discussions of LIP: (1) We show that a non-integrating model is consistent with some core aspects of behavioral data previously offered as evidence for continuous integration; and (2) We examine analyses based on the response covariance (\"CorCE\"), and show that it does not reliably distinguish ramping and stepping dynamics for our dataset. Taken together, these discussions highlight the value of data-driven characterizations of both neural and behavioral dynamics with appropriate statistical tools.