Distilling food web dynamics: top–down and bottom–up drivers of extinction and trophic cascades

Quantifying population dynamics is a fundamental challenge in ecology and evolutionary biology, particularly for species that are cryptic, microscopic, or extinct. Traditional approaches rely on continuous representations of population size, but in many cases, the precise number of individuals is unknowable. Here, a coarse‐grained population model is presented that simplifies population dynamics to binary states – high or low – determined by the balance of bottom–up resource availability and top–down predation pressure. This Boolean framework provides a minimal yet analytically tractable addition to traditional Lotka–Volterra‐based models, enabling direct insights into the role of food web structure in shaping community stability. This approach is used to investigate how trophic interactions influence population persistence, cyclic dynamics, and extinction risk across model food webs. Model predictions reveal that top–down effects are a primary driver of cycling, aligning with theoretical expectations from traditional population models, and that trophic position strongly influences extinction risk, with higher‐trophic species more prone to persistent low‐population states. Additionally, the role of trophic short‐circuits – direct interactions between high‐trophic predators and low‐trophic prey – are explored and found to buffer cascades and alter extinction patterns in ways that are often overlooked in classical models. By simplifying population dynamics to a two‐state system, this framework provides a useful tool for disentangling the structural drivers of community stability. These results highlight the potential of coarse‐grained approaches to complement existing models, offering new insights into trophic interactions, extinction risks, and the susceptibility of species to trophic cascades.