Long-period variable stars arise in the final stages of the asymptotic giant branch phase of stellar evolution. They have periods of up to about 1,000 days and amplitudes that can exceed a factor of three in the I-band flux. These stars pulsate predominantly in their fundamental mode, which is a function of mass and radius, and so the pulsation periods are sensitive to the age of the underlying stellar population. The overall number of long-period variables in a population is directly related to their lifetimes, which is difficult to predict from first principles because of uncertainties associated with stellar mass-loss and convective mixing. The time variability of these stars has not previously been taken into account when modelling the spectral energy distributions of galaxies. Here we construct time-dependent stellar population models that include the effects of long-period variable stars, and report the ubiquitous detection of this expected 'pixel shimmer' in the massive metal-rich galaxy M87. The pixel light curves display a variety of behaviours. The observed variation of 0.1 to 1 per cent is very well matched to the predictions of our models. The data provide a strong constraint on the properties of variable stars in an old and metal-rich stellar population, and we infer that the lifetime of long-period variables in M87 is shorter by approximately 30 per cent compared to predictions from the latest stellar evolution models.