First Cycles in Random Directed Graph Processes
It is suggested that explanation of the origin of life is based on the idea of self-organization. A simple model for such a process is a random graph where the vertices represent a vast number of relatively short self-replicating ribonucleotide strands (RNA molecules), and where the directed edges represent catalytic interactions between the different RNA molecules. Given the physico-chemical conditions on how and with what frequency the catalytic formations are made, one can know when the first catalytic feedbacks appear, and how many different RNA molecules they involve. Models are described in the chapter that used to give quantitative estimates of the time of emergence of “real” genes. This is because of the fact that, as a random graph evolves, monotone properties (such as containing cycles) appear rather suddenly. For this one has to assume physico-chemical conditions for the prebiotic environment, then define which random graph model to be chosen. © 1989 Elsevier B.V.
Annals of Discrete Mathematics
Bollobás, B., & Rasmussen, S. (1989). First Cycles in Random Directed Graph Processes. Annals of Discrete Mathematics, 43 (C), 55-68. https://doi.org/10.1016/S0167-5060(08)70566-1