Darwinian Evolution, Hypercycles and Game Theory

Adaptation and evolution are quasi synonymous in popular language, it is hence little surprising that the theory of Darwinian evolution is infused with complex systems concepts. We will discuss when a species will manage to successfully mutate while escaping its local fitness optimum, or when it may spiral towards extinction in the wake of an “error catastrophe”. Venturing into the mysteries surrounding the origin of life, we will investigate the possible advent of a quasispecies in terms of mutually supporting hypercycles. The basic theory of evolution is furthermore closely related to game theory, the mathematical theory of socially interacting agents, viz of rationally acting economic persons. The tragedy of the commons occurring in this context describes the over-exploitation of resources. We will learn in this chapter that complex systems come with respective individual characteristics. For Darwinian evolution the core notions are fitness, selection and mutation. On this basis, generic concepts from dynamical systems theory unfold, like the phenomenon of stochastic escape. Furthermore we will show that evolutionary processes affect not only the welfare of an individual species, but the pattern of species abundances of entire ecosystems, which will be discussed in this context the neutral theory of macroecology.