  A few years ago it was showed that some systems that have very similar local
structure, as quantified by the pair correlation function, exhibit vastly
different slowing down upon supercooling [L. Berthier and G. Tarjus, Phys. Rev.
Lett. 103, 170601 (2009); U.R. Pedersen, T.B. Schroder and J.C. Dyre, Phys.
Rev. Lett. 105, 157801 (2010)]. Recently, a more subtle structural quantity,
the so-called "point-to-set" length, was found to reliably correlate with the
average dynamics [G.M. Hocky, T.E. Markland and D.R. Reichman, Phys. Rev. Lett.
108, 225506 (2012)]. Here we use computer simulations to examine the behavior
of fluctuations around the average dynamics, i.e., dynamic heterogeneity. We
study five model glass-forming liquids: three model liquids used in previous
works and two additional model liquids with finite range interactions. Some of
these systems have very similar local structure but vastly different dynamics.
We show that for all these systems the spatial extent and the anisotropy of
dynamic heterogeneity correlate very well with the average dynamics.
