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 $t_{rm med}propto Sigma^{-0.51pm0.03}sigma_{rm 1D}^{-0.85pm0.10}M_{rm min}^gamma$, 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.
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