We then used these covariance matrices to compute the precision with which a population of MSTd neurons in naive or trained animals could discriminate heading, as described below. Importantly, noise correlations did not depend on whether trained monkeys performed a passive fixation task or the heading discrimination task (p = 0.3, t test), as shown in Figure S6 for a subset of neuronal pairs recorded in both tasks. Thus, we are justified in predicting heading discrimination performance from

population activity measured during the Selleck BMS777607 fixation task for both trained and naive animals. We computed population discrimination thresholds from the inverse of Fisher information (If), an upper bound on information capacity that can be extracted by any unbiased

estimator (Abbott and Dayan, 1999 and Seung and Sompolinsky, 1993). Predicted thresholds from If define the performance that an ideal observer could achieve, based on MSTd population activity, in a fine heading discrimination task. For a simulated population of neurons with independent noise, predicted thresholds decreased steadily with population size (Figure 6A, dashed black curve). As expected from previous findings (Bair et al., 2001, Cohen and Maunsell, 2009, Shadlen et al., 1996, Smith and Kohn, 2008 and Zohary et al., 1994b), correlated noise similar to that seen in our naive animals degraded population coding efficiency (Figure 6A, blue curve). For a simulated population of 2000 neurons, the predicted heading discrimination threshold was ∼5-fold larger compared with the case of independent Torin 1 molecular weight noise. Surprisingly, the uniform

reduction in rnoise that we observed in trained animals (Figure 5) had little effect on predicted discrimination PAK6 thresholds, as compared with naive animals (Figure 6A, red curve). Why doesn’t the reduction in mean noise correlation seen in trained animals improve the sensitivity of the population code? We simulated performance of a population of neurons using many covariance matrices that were constructed by systematically varying both the slope and intercept of the relationship between rnoise and rsignal. As shown in Figure 6B, predicted thresholds were very sensitive to changes in the slope of the relationship between rnoise and rsignal. In contrast, changes in the intercept of the rnoise versus rsignal relationship had weak effects on predicted thresholds. Counterintuitively, a uniform increase in rnoise (across all values of rsignal) produced a mild decrease in population thresholds, improving performance slightly (barely visible in Figure 6A, see also Abbott and Dayan, 1999 and Wilke and Eurich, 2002). These simulations suggest that a uniform reduction of noise correlations in trained animals is expected to have little impact on discrimination performance. This conclusion is based on the assumption that all neurons contribute to discrimination performance.