by Stefan Turner
Abstract: Many evolutionary systems are combinatorial in the sense that the creation of new entities is based on the combination of already existing things. By formalising this kind of dynamics into mathematical models one can realise that evolutionary systems are prototypes of complex systems, where the underlying network structure — that determines the next possible steps in evolution (adjacent possible)— co-evolves with the population of phase space (which things currently exist). We show that these models are self-organised critical and therefore are able to capture several key features of evolutionary systems, such as power laws in creation and extinction statistics, punctuated equilibria, and phases of massive and rapid re-structuring. We show an example where the model can be used to explain innovation dynamics as seen in world trade data.