  The age distributions of stellar cluster populations have long been proposed
to probe the recent formation history of the host galaxy. However, progress is
hampered by the limited understanding of cluster disruption by evaporation and
tidal shocks. We study the age distributions of clusters in smoothed particle
hydrodynamics simulations of isolated disc galaxies, which include a
self-consistent, physical model for the formation and dynamical evolution of
the cluster population and account for the variation of cluster disruption in
time and space. We show that the downward slope of the cluster age distribution
due to disruption cannot be reproduced with a single functional form, because
the disruption rate exhibits systematic trends with cluster age (the `cruel
cradle effect'). This problem is resolved by using the median cluster age to
trace cluster disruption. Across 120 independent galaxy snapshots and simulated
cluster populations, we perform two-dimensional power law fits of the median
cluster age to various macroscopic physical quantities and find that it scales
as $t_{\rm med}\propto \Sigma^{-0.51\pm0.03}\sigma_{\rm
1D}^{-0.85\pm0.10}M_{\rm min}^\gamma$, for the gas surface density $\Sigma$,
gas velocity dispersion $\sigma_{\rm 1D}$, and minimum cluster mass $M_{\rm
min}$. This scaling accurately describes observed cluster populations and
indicates disruption by impulsive tidal shocks from the interstellar medium.
The term $M_{\rm min}^\gamma$ provides a model-independent way to measure the
mass dependence of the cluster disruption time $\gamma$. Finally, the
ensemble-average cluster lifetime depends on the gas density less strongly than
the instantaneous disruption time of single clusters. These results reflect the
variation of cluster disruption in time and space. We provide quantitative ways
of accounting for these physics in cluster population studies.
