Interpretation of the empirical results in terms of the doubly stochastic model. A, Given the same mean firing rate r_mean (≈ 20 sp/s in the schematics), less burstiness explains the observed low FF in empirical data (in correspondence to Fig. 1D). Scenario 1 with r_L = 5 sp/s, r_H = 100 sp/s, τ_L = 350 ms, and τ_H = 65 ms corresponds to the bursting regime with high FF. Low FF can be achieved either by smaller difference between r_H and r_L (Scenario 2 with with r_L = 18 sp/s, r_H = 30 sp/s, τ_L = 350 ms, and τ_H = 65 ms), and/or higher mean dwell time ratio <mml:math display="inline"><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>H</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math>τHτL (Scenario 3 with with r_L = 5 sp/s, r_H = 30 sp/s, τ_L = 350 ms, and τ_H = 525 ms). B, Heatmap of FF as a function of mean firing rate and the scaled difference of firing rates in the two states <mml:math display="inline"><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mi>H</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>r</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>r</mml:mi><mml:mrow><mml:mtext>mean</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math>rH−rLrmean, with τ_L = 350 ms, τ_H = 65 ms, and time bin width Δ = 250 ms. Red line indicates the contour line of FF = 3. Region where FF < 3, which was mostly observed in empirical data, is characterized by smaller difference in r_H and r_L. Scenarios 1 and 2 in A are marked on the heatmap. C, Heatmap of FF as a function of mean firing rate and mean dwell time ratio <mml:math display="inline"><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>H</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math>τHτL, with τ_L = 350 ms, r_L = 5 sp/s, and time bin width Δ = 250 ms. Red line indicates the contour line of FF = 3. Region where FF < 3, which was mostly observed in empirical data, is characterized by high <mml:math display="inline"><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>H</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math>τHτL. Scenarios 1 and 3 in A are marked on the heatmap. D, Heatmap of r_mean as a function of r_L and <mml:math display="inline"><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>H</mml:mi></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>L</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math>τHτL with FF = 1.5 fixed, which was typically observed in empirical data, and with τ_H = 65 ms, Δ = 250 ms. At fixed FF level, stronger mean firing rate under the preferred stimulus is achieved by elevating baseline firing and/or sacrificing spiking sparsity.