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Abstract Community assembly is often treated as deterministic, converging on one or at most a few possible stable endpoints. However, in nature, we typically observe continuous change in community composition, which is often ascribed to environmental change. But continuous changes in community composition can also arise in deterministic, time‐invariant community models, especially food web models. Our goal was to determine why some models produce continuous assembly and others do not. We investigated a simple two‐trophic‐level community model to show that continuous assembly is driven by the relative niche width of the trophic levels. If predators have a larger niche width than prey, community assembly converges to a stable equilibrium. Conversely, if predators have a smaller niche width than prey, then community composition never stabilizes. Evidence that food webs need not reach a stable equilibrium has important implications, as many ecological theories of community ecology based on equilibria may be difficult to apply to such food webs.