Evolutionary processes combine many features of complex systems: they are algorithmic; states co-evolve with interactions; they show power law statistics; they are selforganized critical; and they are driven non-equilibrium systems. Evolution is a dynamical process that changes the composition of large sets of interconnected elements, entities, or species over time. The essence of evolutionary processes is that, through the interaction of existing entities with each other and with their environment, they give rise to an open-ended process of creation and destruction of new entities. Evolutionary processes are critical, co-evolutionary, and combinatorial, meaning that thew entities are created from combinations of existing ones. We review the concepts of the replicator equation, fitness landscapes, cascading events, the adjacent possible. We review several classical quantitative approaches to evolutionary dynamics such as the NK model and the Bak–Snappen model. We propose a general and universal framework for evolutionary dynamics that is critical, co-evolutionary, and combinatorial.
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