Abstract To understand the dynamics of natural species communities, a major challenge is to quantify the relationship between their assembly, stability, and underlying food web structure. To this end, two complementary aspects of food web structure can be related to community stability: sign structure, which refers to the distributions of trophic links irrespective of interaction strengths, and interaction strength structure, which refers to the distributions of interaction strengths with or without consideration of sign structure. In this paper, using data from a set of relatively well documented community food webs, I show that natural communities generally exhibit a sign structure that renders their stability sensitive to interaction strengths. Using a Lotka–Volterra type population dynamical model, I then show that in such communities, individual consumer species with high values of a measure of their total biomass acquisition rate, which I term “weighted generality”, tend to undermine community stability. Thus consumer species’ trophic modules (a species and all its resource links) should be “selected” through repeated immigrations and extinctions during assembly into configurations that increase the probability of stable coexistence within the constraints of the community's trophic sign structure. The presence of such constraints can be detected by the incidence and strength of certain non-random structural characteristics. These structural signatures of dynamical constraints are readily measurable, and can be used to gauge the importance of interaction-driven dynamical constraints on communities during and after assembly in natural communities.