a, Running speed of the rat (top, black) and the corresponding LFP (same format as in Fig. 1a) in VR. Both theta and eta amplitudes increase with speed. b, Same tetrode measured in RW on the same day showing speed-dependent increase in theta, but not eta, amplitude. c,d, Individual LFP eta-cycle amplitude and corresponding speed in VR (c) and RW (d) for the entire session in a and b. The broken axis separates two speed ranges – below (outlined) and above 10 cm/s. Each small dot indicates one measurement. The square dots show mean and s.e.m. in each bin in RW (blue) and VR (red). A log speed scale was used for the speed range below 10 cm/s. Linear regression fits are shown separately for both speed ranges (black lines). e, Population averaged theta amplitude, showing strong increase with running speed in RW. Population averaged theta amplitude in VR first decreased at low speeds (0 vs 10 cm/s) and then increased comparable to RW (Supplementary Table 1). f, Same as 3e, but for theta frequency showed significant increase with running speed in RW, but in VR the frequency dropped at very low speeds (0 vs 10 cm/s), and then became speed-independent. g, Same as 3e, but for eta amplitude, showing decrease in eta amplitude with increasing running speed for RW, but sharp drop in eta amplitude at low speeds (0 vs 10 cm/s), and steady increase in amplitude at higher speeds in VR. h, Same as 3e, but for eta frequency, showing no clear dependence of eta frequency on running speed in both RW and VR. i, Individual eta-cycle amplitudes are positively correlated with speed above 10 cm/s across tetrodes in VR (0.09 ± 0.001, p < 10−10), but not in RW (−0.107 ± 0.005, p < 10−10). 7.5% and 43.1% of all tetrode showed significant increase in eta amplitude with running speed in RW and VR, respectively (p < 0.05). j, Individual eta-cycle amplitudes are negatively correlated with speed below 10 cm/s across tetrodes in VR (−0.095 ± 0.003, p < 10−10), but not in RW (0.002 ± 0.003, p = 0.1). Shaded areas and error bars denote s.e.m.