ECOME is an interactive, graph-based model for simulating an evolving, closed consumption web. It demonstrates the fundamental behavior of a global ecosystem over evolutionary time using wellestablished ecological/evolutionary principles. Nodes in the graph send biomass along weighted, directed edges. New nodes evolve by speciation and disappear when biomass (i.e. population) shrinks to zero. Consumption rates, predator/prey relationships, and speciation rates are user-defined, following theoretic distributions. The output shows the biomass and biodiversity over time for up to five trophic levels. Using this simple system, we demonstrate that closed ecosystems are inherently unstable in the absence of evolution or in the presence of a single, hyperchanging species, but are dynamically stable and robust to perturbations when the evolution rates for all species follow a normal distribution. Our new application provides provocative lessons for biology students during a time of mass extinction.