Selective harvest, such as trophy hunting, can shift the distribution of a quantitative character such as body size. If the targeted character is heritable, then there will be an evolutionary response to selection, and where the trait is not, then any response will be plastic or demographic. Identifying the relative contributions of these different mechanisms is a major challenge in wildlife conservation. New mathematical approaches can provide insight not previously available. Here we develop a size- and age-based two-sex integral projection model based on individual-based data from a long-term study of hunted bighorn sheep (Ovis canadensis) at Ram Mountain, Canada. We simulate the effect of trophy hunting on body size and find that the inheritance of body mass is weak and that any perceived decline in body mass of the bighorn population is largely attributable to demographic change and environmental factors. To our knowledge, this work provides the first use of two-sex integral projection models to investigate the potential eco-evolutionary consequences of selective harvest.