Following evolutionary theory and an agriculture model, ecosystem research has stressed bottom-up dynamics, implying that top wild predators are epiphenomenal effects of more basic causes. As such, they are assumed expendable. A more modern co-evolutionary and wilderness approach — trophic cascades — instead suggests that top predators, whose effects flow down to fundamental biological processes, are co-equal causes of ecosystem health. Their survival, then, should be supported. This article, based on extensive research including the author's participation in a major field project, provides informational resources for teaching trophic cascades, using wolves as a case study. As charismatic, iconic, thriving but still endangered, well-studied, and terrestrial carnivores, wolves are ideal for enlightening students about what otherwise might be dry abstractions about crucial ecosystem processes. The article ends with student exercises and broader lessons for environmental education.

Many marine ecosystems have the remarkable property that the abundance of organisms of a given body size is approximately proportional to the inverse square of that size. Size-structured models have been developed for which this “invariance-of-biomass” state is an equilibrium solution. These models are built on the coupling of predator growth to prey abundance, where prey suitability is determined by a size-based function referred to as a feeding kernel. In this paper, the local stability of the equilibrium state is investigated in a limiting case where predators only consume prey of a preferred size. In this special case, it is shown analytically that the equilibrium state is always unstable. It is concluded that some degree of diet breadth, in terms of the range of prey sizes consumed by a predator, is an essential prerequisite for the invariance-of-biomass state to be stable, as widely observed in the field.