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If I may add a comment here. In head-restrained mice, I have not observed ripples during movement-related theta cycles (defined as having a similar amplitude and frequency as ripples during recent periods of immobility). Gamma cycles are different.
However, if the mouse pauses during a movement period, theta can be transiently disrupted and a small sharp wave and ripple can occur. This is different to ripples occurring during actual theta cycles but could be misinterpreted as occuring within a theta epoch.
I have recorded REM theta less often in mice but do not recall observing ripples during these higher amplitude theta cycles either.
Isolated ripple-like events can take place infrequently during continuous theta in CA1 of urethane-anaesthetised rats with supplemental ketamine and xylazine followed by tail pinch.
Observations based on hundreds of hours of glass electrode recordings mostly in mice