Figure 2. The behavior-dependent sweep integrates aspects of both spatial and temporal sweeps.

Simulated data plotted as in Figure 1A and C. (A) Different phases of theta represent positions reached at different time intervals into the past or future assuming the animal ran at the characteristic speed at that location. (B) Comparison of theta trajectory lengths in areas of low and fast characteristic running speed (rows) at low and fast instantaneous running speeds (columns). When both characteristic and instantaneous running speeds coincide, the behavior-dependent sweep model and the first-order approximation of the temporal sweep model agree (ochre arrow). On the other hand, when changing the instantaneous speed at a given location, the behavior-dependent and spatial sweeps agree (orange arrow). Theta trajectory length is primarily determined by characteristic running speed. Instantaneous running speed has a modest effect caused by the larger change in $x(t)$ during the theta cycle at higher speeds. Place fields (right) are larger in areas of higher characteristic running speed, but do not change size with instantaneous running speed.