Evolutionary models for simple biosystems

The concept of evolutionary development of structures constituted a \emph{real} revolution in biology: it was possible to understand how the very complex structures of life can arise in an out-of-equilibrium system. The investigation of such systems has shown that indeed, systems under a flux of energy or matter can self-organize into complex patterns, think for instance to Rayleigh-Bernard convection, Liesegang rings, patterns formed by granular systems under shear. Following this line, one could characterize life as a state of matter, characterized by the slow, continuous process that we call evolution. In this paper we try to identify the organizational level of life, that spans several orders of magnitude from the elementary constituents to whole ecosystems. Although similar structures can be found in other contexts like ideas (memes) in neural systems and self-replicating elements (computer viruses, worms, etc.) in computer systems, we shall concentrate on biological evolutionary structure, and try to put into evidence the role and the emergence of network structure in such systems.