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A central debate in ecology has been the long‐running discussion on the role of apex predators in affecting the abundance and dynamics of their prey. In terrestrial systems, research has primarily relied on correlational approaches, due to the challenge of implementing robust experiments with replication and appropriate controls. A consequence of this is that we largely suffer from a lack of mechanistic understanding of the population dynamics of interacting species, which can be surprisingly complex. Mechanistic models offer an opportunity to examine the causes and consequences of some of this complexity. We present a bioenergetic mechanistic model of a tritrophic system where the primary vegetation resource follows a seasonal growth function, and the herbivore and carnivore species are modeled using two integral projection models (IPMs) with body mass as the phenotypic trait. Within each IPM, the demographic functions are structured according to bioenergetic principles, describing how animals acquire and transform resources into body mass, energy reserves, and breeding potential. We parameterize this model to reproduce the population dynamics of grass, elk, and wolves in northern Yellowstone National Park (USA) and investigate the impact of wolf reintroduction on the system. Our model generated predictions that closely matched the observed population sizes of elk and wolf in Yellowstone prior to and following wolf reintroduction. The introduction of wolves into our basal grass–elk bioenergetic model resulted in a population of 99 wolves and a reduction in elk numbers by 61% (from 14,948 to 5823) at equilibrium. In turn, vegetation biomass increased by approximately 25% in the growing season and more than threefold in the nongrowing season. The addition of wolves to the model caused the elk population to switch from being food‐limited to being predator‐limited and had a stabilizing effect on elk numbers across different years. Wolf predation also led to a shift in the phenotypic composition of the elk population via a small increase in elk average body mass. Our model represents a novel approach to the study of predator–prey interactions, and demonstrates that explicitly considering and linking bioenergetics, population demography and body mass phenotypes can provide novel insights into the mechanisms behind complex ecosystem processes. [ABSTRACT FROM AUTHOR]