  We investigate the time evolution of dense cores identified in molecular
cloud simulations using dendrograms, which are a common tool to identify
hierarchical structure in simulations and observations of star formation. We
develop an algorithm to link dendrogram structures through time using the
three-dimensional density field from magnetohydrodynamical simulations, thus
creating histories for all dense cores in the domain. We find that the
population-wide distributions of core properties are relatively invariant in
time, and quantities like the core mass function match with observations.
Despite this consistency, an individual core may undergo large (>40%),
stochastic variations due to the redefinition of the dendrogram structure
between timesteps. This variation occurs independent of environment and stellar
content. We identify a population of short-lived (<200 kyr) overdensities
masquerading as dense cores that may comprise ~20% of any time snapshot.
Finally, we note the importance of considering the full history of cores when
interpreting the origin of the initial mass function; we find that, especially
for systems containing multiple stars, the core mass defined by a dendrogram
leaf in a snapshot is typically less than the final system stellar mass. This
work reinforces that there is no time-stable density contour that defines a
star-forming core. The dendrogram itself can induce significant structure
variation between timesteps due to small changes in the density field. Thus,
one must use caution when comparing dendrograms of regions with different ages
or environment properties because differences in dendrogram structure may not
come solely from the physical evolution of dense cores.
