Animals make behavioural and reproductive decisions that maximise their lifetime reproductive success, and thus their fitness, in light of periodic and stochastic variability of the environment. Modelling the variation of an individual's energy levels formalises this tradeoff and helps to quantify the population‐level consequences of stressors (e.g. disturbance from human activities and environmental change) that can affect behaviour or physiology. In this study, we develop a dynamic state variable model for the spatially explicit behaviour, physiology and reproduction of a female, long‐lived, migratory marine vertebrate. The model can be used to investigate the spatio‐temporal patterns of behaviour and reproduction that allow an individual to maximise its overall reproductive output. We parametrised the model for eastern North Pacific blue whales Balaenoptera musculus, and used it to predict the effects of changing environmental conditions and increasing human disturbance on the population's vital rates. In baseline conditions, the model output had high fidelity to observed energy dynamics, movement patterns and reproductive strategies. Simulated scenarios suggested that environmental changes could have severe consequences on the population's vital rates, but that individuals could tolerate high levels of anthropogenic disturbance. However, this ability depended on where, when and how often disturbance occurred. In scenarios with both environmental change and anthropogenic disturbance, synergistic interactions caused stronger effects than in isolation. In general, larger body size offered a buffer against stochasticity and disturbance, and, consequently, we predicted juveniles to be more susceptible to disturbance. We also predicted that females prioritise their own survival at the expense of the current reproductive attempt, presumably the result of their long lifespan. Our approach provides a general framework to make predictions of the cumulative and synergistic effects of human disturbance and climate change on migratory populations, which can inform effective management and conservation efforts.