Polynucleotide Replication and Biological Evolution Peter Schuster Institut fUr Theoretische Chemie und Strahlenchemie der Universitat Wien Wahringerstra6e 17, A-lOgO Wien, Austria Abstract Polynucleotide replication is considered as an example of primitive biological evolution which can be tested experimentally. We distin- guish deterministic selection which is based on differences in the rate constants of replication and degradation and neutral selection, a stochastic phenomenon in finite populations which is a result of the nature of the replication process only. Depending on the structural details of the fitness surface and on the distance from the temporal evolutionary optimum the changes in the population are predominantly due to adaptive or neutral mutations: far from the optimum almost every advantageous mutation will be fixed by adaptive selection whereas fixation of neutral mutation dominates close to the optimum. 1. Mutations and Population Dynamics Biological evolution can be visualized as a succession of transients and metastable states. A state of the population under consideration is characterized by a distribution of frequencies for different types of individuals. We denote these types by I 1 ,I 2 ,······ ,In and the corresponding variables describing the time dependence of their frequencies by x 1 (t), x 2 (t) , .••. ,x n (t) . In addition we assume the variables to be normalized n Lx.(t) = 1. i=1 (1 ) Hence, every state of the population is represented by a point or a vector on the unit simplex (2) 106 E. Frehland (ed.), Synergetics — From Microscopic to Macroscopic Order © Springer-Verlag Berlin Heidelberg 1984