Graph grammars and applications to specialization and evolution in biology

摘要

In this paper we present a formalization of the specialization process of organisms as given by N. Rashevsky. This is done by means of gluing constructions of graphs and then we formalize the evolution of organisms by successive specialization using the concepts of graph grammars. In fact, this is an extension to higher dimensions of developmental processes as described by L-systems and the development of radial patterns. The gluing construction for graphs and the algebraically formulated theory of graph grammars are developed in detail for the special case of unlabeled graphs in Sections 2 and 4, which can be read separately. In the other three sections the theory is applied to processes of specialization and evolution in biology and several illustrating examples are given.