Improving our capacity for predicting range shifts requires improved theory exploring the interplay between ecological and evolutionary processes and the (changing) environment. We introduce an individual-based model incorporating simple stage structure and genetically determined resource allocation rules. Population dynamics are mediated by the resources available and the individual's genetics, and density dependence emerges solely as a consequence of resource levels decreasing as population density increases. Running the model for a set of stylised range-expansion scenarios reveals the extent to which eco-evolutionary processes can matter: spatial assortment of individuals possessing effective range expansion strategies (higher dispersal propensity, semelparity rather than iteroparity) can substantially accelerate range advance, and this is more important than the contribution of novel mutations arising during range expansion. In simulations of range expansion there is a greater risk of extinction when all individuals are given the mean strategy evolved in a stationary range. Additionally, our results demonstrate that the erosion of inter-individual variability during a range-shift can depress population abundance for lengthy periods, even after the climate has stabilised. Our theoretical results highlight the importance of accounting for inter-individual variability in future predictive modelling of species' responses to environmental change.