Models of darwinian processes and evolutionary principles.

Evolutionary processes are described as stochastic motions in a genotype space (set of sequences with a Hamming distance) and a phenotype space (vector space of phenotypic properties). Real value functions are introduced which form a landscape over these spaces; smoothness postulates are formulated. Evolution is considered as a kind of hill climbing on these adaptive landscapes. A rather simple diffusion approximation for the phenotypic processes is proposed which leads to similar mathematical problems as the Schrödinger equation for disordered potential distributions.