Evolution of self-replicating macromolecules through natural selection is a dynamically ordered process. Two concepts are introduced to describe the physical regularity of macromolecular evolution: sequence space and quasi-species. Natural selection means localization of a mutant distribution in sequence space. This localized distribution called the quasi-species is centered around a master sequence (or a degenerate set) that the biologist would call the wild-type. The self-ordering of such a system is an essential consequence of its formation through self-reproduction of its macromolecular consti tuents a process that in the dynamical equations expresses itself by positive diagonal coefficients called selective values. The theory describes how population numbers of wild type and mutants are related to the distribution of selective values that is to say how value topography maps into population topography. For selectively (nearly) neutral mutants appearing in the quasi- species distribution population numbers are greatly enhanced as compared to those of disadvantageous mutants even more so in continuous domains of such selectively valuable mutants. As a consequence mutants far distant from the wild type may occur because they are produced with the help of highly populated less distant precursors. Since values are cohesively distributed like mountains on earth and since their positions are multiply connected in the high-dimensional sequence space the overpopulation of (nearly) neural mutants provides guidance for the evolutionary process. Localization in sequence space subject to a threshold in the fidelity of reproduction is steadily challenged until an optimal state is reached. The model has been designed according to experimentally determined properties of self-replicating molecules. The conclusions reached from the theoretical models can be used to construct machines that provide optimal conditions for the evolution of functional macromolecules. Language: English