Isomorphism of Quasispecies and Percolation Models

Population dynamics of tRNA-like macromolecules and viruses have been interpreted by Eigen (1971,Naturwissenschaften58 , 465–526) on the basis of the “quasispecies” model. The present paper contains a qualitative analysis of the similarities between Eigenʹs quasispecies model and percolation models. In fact, different phenomena characterized by an analogous inner structure can conceivably be described by quite similar mathematical formalisms. The occurrence of a threshold in specific processes predicted by the models is considered first. Secondly, Isingʹs model of ferromagnetism is taken into account in the last section. An interpretation of the above-mentioned biological theory in terms of percolation, implying a zeroth-order approximation to the real situation, might be a point of departure to a deeper insight obtainable with more refined approaches. A better comprehension of biological phenomena might in any case arise from a percolative approach, even if the description of the systems is simplified. An overview of some quasispecies results and some plausible applications are presented.