Our body is colonized by trillions of microbes, forming the human microbiome. The species assemblage in a body part’s microbial community, and their abundances, can differ substantially from one person to the next. Recently, it was shown that the gut microbiomes of different human subjects largely follow the same underlying ecological rules (“universal dynamics”), and thus can be represented by the same population dynamic model, while the inter-personal variability is represented as different steady states. Available data is insufficient for reliable detailed inference of these dynamics, which are highly complex, sparse, and nonlinear. Here, we introduce a new top-down methodology to detect key elements of a complex dynamic ecosystem, based on analyzing its steady states. Specifically, we detect the ecological "keystone species", species whose their existence or absence has a substantial impact on the the entire ecological system. This method is validated on numerical models of GLV dynamics and on synthetic in-vitro microbial communities and applied to analyze real human gut microbial communities. Understanding the key elements of the complex dynamics that governs the microbiome is important for designing effective and ecologically safe interventions.