Ecologists have long desired predictive models that allow inference on population dynamics, where detailed demographic data are unavailable. Integral projection models (IPMs) allow both demographic and phenotypic outcomes at the level of the population to be predicted from the distribution of a functional trait, like body mass. In species where body mass markedly influences demographic rates, as is the rule among mammals, then IPMs provide not only opportunity to assess the population responses to a given environment, but also improve our understanding of the complex interplay between traits and demographic outcomes. Here, we develop a body-mass-based approach to constructing generalized, predictive IPMs for species of ungulates covering a broad range of body size (25-400 kg). Despite our best efforts, we found that a reliable and general, functional, trait-based model for ungulates was unattainable even after accounting for among-species variation in both age at first reproduction and litter size. We attribute this to the diversity of reproductive tactics among similarsized species of ungulates, and to the interplay between density-dependent and environmental factors that shape demographic parameters independent of mass at the local scale. These processes thus drive population dynamics and cannot be ignored. Environmental context generally matters in population ecology, and our study shows this may be the case for functional traits in vertebrate populations.