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 twosex integral projection models to investigate the potential ecoevolutionary consequences of selective harvest.T rophy hunting, can result in undesirable phenotypic change (1, 2), sometimes termed "unnatural selection" (3). Hunters may target individuals within a population that possess a trait they seek, such as large body or horn size, or a distinct color morph (4-6). If the trait is heritable, then selection against the character can result in a cross-generational decrease in the character mean (1, 6, 7). Apparent shifts in the distribution of a quantitative character, however, may not occur through genetic mechanisms alone, because hunting can also alter age and sex structure, behavior, and social hierarchies (8-10), which may in turn interact with localized density-dependent and -independent factors to accentuate, or mask, a phenotypic response (6,11,12).To date, there have been some generalizations that hunting management can follow in an attempt to mimic natural mortality and limit selection against desirable traits, such as nose coloration for African lions (13). Where long-term data are available for hunted populations, then a response to unnatural selection can be detected. One relatively new method that provides a broad model framework, within which scenario tests are possible, is integral projection modeling (14, 15). These models are built from the relationships between a continuous quantitative trait such as body mass and demographic functions. Integral projection models (IPMs) are constructed from the statistical relationships between a trait and survival and fecundity, development of the trait over time, and the pattern of inheritance (15). IPMs can be used to calculate quantities useful to population and evolutionary biologists, including population structure and growth rate, net reproductive rate, generation length, and estimates of biometric heritabilities (16). IPMs also avoid the discrete classes of classic matrix models, although they can be approximated as high-dimensional matrices.Recent theoretical development has provided for ...