The core of the origin-of-life problem is to explain how a complex dissipative system could emerge spontaneously from a simple environment, perpetuate itself, and complexify over time. This would only be possible, we argue, if prebiotic chemical reaction networks had autocatalytic features organized in a way that permitted the accretion of complexity even in the absence of genetic control. To evaluate this claim, we developed tools to analyze the autocatalytic organization of food-driven reaction networks and applied these tools to both abiotic and biotic networks. Both networks contained seed-dependent autocatalytic systems (SDASs), which are subnetworks that can use a flux of food chemicals to self-propagate if, and only if, they are first seeded by some non-food chemicals. Moreover, SDASs were organized such that the activation of a lower-tier SDAS could render new higher-tier SDASs accessible. The organization of SDASs is, thus, similar to trophic levels (producer, primary consumer, etc.) in a biological ecosystem. Furthermore, similar to ecological succession, we found that higher-tier SDASs may produce chemicals that enhance the ability of the entire chemical ecosystem to utilize food more efficiently. The SDAS concept explains how driven abiotic environments, namely ones receiving an ongoing flux of food chemicals, can incrementally complexify even without genetic polymers. This framework predicts that it ought to be possible to detect the spontaneous emergence of life-like features, such as self-propagation and adaptability, in driven chemical systems in the laboratory. Additionally, SDAS theory may be useful for exploring general properties of other complex systems.