Predictions on population responses to perturbations are often derived from trait‐based approaches like integral projection models (IPMs), but are rarely tested. IPMs are constructed from functions that describe survival, growth and reproduction in relation to the traits of individuals and their environment. Although these functions comprise biologically non‐informative statistical coefficients within standard IPMs, model parameters of the recently developed dynamic energy budget IPM (DEB‐IPM) are life‐history traits like “length at maturation” and “maximum reproduction rate”. Testing predictions from mechanistic IPMs against empirical observations can therefore provide functional insights into the links between individual life history, the environment and population dynamics.Here, we compared the population dynamics of the bulb mite (Rhizoglyphus robini) predicted by a DEB‐IPM with those observed in an experiment where populations experienced daily food rations that were either positively correlated over time (red noise), negatively (blue noise) or uncorrelated (white noise). We also selectively harvested large adults in half of these populations. The model failed to generate detailed predictions of population structure as juvenile numbers were overestimated; likely because juvenile–adult interference competition was underestimated. The model performed well at the population level as, for both harvested and unharvested populations, simulations matched the observed, long‐term stochastic growth rate λs.We next generalised the model to investigate how stochastic change affects mite λs, which correlated well with the frequency f of experiencing periods of good environment, but, due to the relationship between f and noise colour ρ, did not correlate well with shifts in ρ. The sensitivity of λs to perturbations in life‐history parameters depended on the type of stochastic change, as well as population growth.Our findings show that responses to differential mortality depend on individual life‐history traits, environmental characteristics and population growth. As long‐term climate change causes ever greater environmental fluctuations, trait‐based approaches will be increasingly important in predicting population responses to change. We therefore conclude by illustrating what questions can be examined with mechanistic trait‐based models like the DEB‐IPM, the answers to which will advance our knowledge of the functional links between individual traits, the environment and population dynamics.