(A) Schematic of the accumulation model of Brunton et al. (2013) used here to compare the contribution of flash- and time-associated noise to behavioral variability. At each moment in time the model represents the accumulated evidence as a decision variable, a(t)(black line). Colored arrows indicate the timing of left (blue) and right (red) flashes. σs2 parameterizes the noise added with each flash, σa2 parameterizes the noise added at each time point, τ (or 1/λ) parameterizes the memory time constant of a(t). λ<0 suggests that the memory decays to a = 0 with time, λ>0 suggests that the magnitude of a(t) increases over time. B parameterizes sticky bounds: if a(t) ever reaches +/-B, integration stops and the animal is committed to that decision (go right/go left, respectively). There are a few other terms in the model that are not represented in the schematic. A bias term represents an offset of a(t) at the beginning of each trial. A lapse rate parameterizes the percent of trials on which the animal behaves randomly. φ and τφ parameterize sensory adaptation dynamics. After a flash, φ is a constant that scales the effect of the flash; it recovers to an unadapted/facilitated magnitude with time constant τφ. φ >1 indicates that successive flashes facilitate; φ <1 indicates that they depress. Fits to those parameters are not shown here, because we found that the inter-flash-intervals presented here were sufficiently long to minimize any adaptation/facilitation effects of subsequent flashes. Light gray lines indicate alternative runs of the model on the same trial. (B) Model fits of flash-associated noise (σs2; blue circles) and noise associated with time (σa2; red circles). To evaluate these parameters in comparable units, σs2 was divided by the average number of flashes per second for each rat. For each subject, noise associated with time (σa2) is close to zero, whereas noise correlated with flashes (σs2) is predominant, consistent with previous studies (Brunton et al., 2013; Hanks et al., 2015). (C) The drift in the accumulator’s memory is parameterized by λ. A leaky integrator would have negative values of λ, an impulsive integrator would have positive values. The time constant of the integrator, τ, is 1/λ. For many, but not all, of the rats, the time constant is close to or greater than 2 s ( λ <= 0.5). (D) The bound value for all except two rats is larger than the maximum number of flashes (on one side) that each rat experienced. This suggests that rats accumulated/used all of the flashes to inform their decision. (E) The bias term for the each rat. (F) The lapse rate term for each rat, represented as the percent of trials in which animals behaved randomly. (G) The number of behavioral trials that were used to fit the model parameters for each rat, represented on a logarithmic scale.