The aim of my talk is to theoretically investigate the evolution of life history traits in a changing environment with a special focus on aging. More precisely, we want to measure the ability of a population to adapt in a changing environment. I will first present the linear PDE model which describes the mutation/selection processes which drive the evolutionary dynamics and takes into account a changing environment. In order to quantify the effect changing environment on the evolution of life history traits of a population, we investigate the stationary states of our model which describe mutation/selection equilibria. These solutions solve spectral problem. We want to understand the effect for the different parameters on the principal eigenvalues as well as the principal eigenvector.