Mean displacement can be more informative than mean square displacement. The pause parameter of the Beauchemin model is not essential for the mean square displacement, but for the mean displacement. Left: Root mean square displacement curves generated for two populations with tfree = 2 min and tpause = 0.5 min, vfree = 18.8 μ m/min (red squares and error bars) or tpause = 9.32 min, vfree = 40 μ m/min (blue circles and error bars). Simulations (N = 10000) with these two parameter yield the same results, as predicted by Proposition 12 (black line). Error bars show the standard error of the mean. Right: Although there is no difference with respect to the mean square displacement, the mean displacement curves of the two simulated populations differ.