Introduction to the statistical theory of Darwinian evolution

These lectures contain a brief description of evolutionary models inspired by the statistical mechanics of disordered systems. After an introduction describing the Darwinian paradigm of evolving populations, the deterministic quasispecies equation is described, and the simplest fitness landscapes are discussed. The effect of finite population size is then considered, from the opposing points of view leading to stochastic escape and to adaptive walks. A synthesis is attempted. Finally the effects of coevolution are considered, and the promising models of large-scale inspired by the Bak-Sneppen models are described.