  We use semi-analytic models of structure formation to interpret gravitational
lensing measurements of substructure in galaxy cluster cores (R<=250kpc/h) at
z=0.2. The dynamic range of the lensing-based substructure fraction
measurements is well matched to the theoretical predictions, both spanning
f_sub~0.05-0.65. The structure formation model predicts that f_sub is
correlated with cluster assembly history. We use simple fitting formulae to
parameterize the predicted correlations: Delta_90 = tau_90 + alpha_90 *
log(f_sub) and Delta_50 = tau_50 + alpha_50 * log(f_sub), where Delta_90 and
Delta_50 are the predicted lookback times from z=0.2 to when each theoretical
cluster had acquired 90% and 50% respectively of the mass it had at z=0.2. The
best-fit parameter values are: alpha_90 = (-1.34+/-0.79)Gyr, tau_90 =
(0.31+/-0.56)Gyr and alpha_50 = (-2.77+/-1.66)Gyr, tau_50 = (0.99+/-1.18)Gyr.
Therefore (i) observed clusters with f_sub<~0.1 (e.g. A383, A1835) are
interpreted, on average, to have formed at z>~0.8 and to have suffered <=10%
mass growth since z~0.4, (ii) observed clusters with f_sub>~0.4 (e.g. A68,
A773) are interpreted as, on average, forming since z~0.4 and suffering >10%
mass growth in the ~500Myr preceding z=0.2, i.e. since z=0.25. In summary,
observational measurements of f_sub can be combined with structure formation
models to estimate the age and assembly history of observed clusters. The
ability to ``age-date'' approximately clusters in this way has numerous
applications to the large clusters samples that are becoming available.
