[A mathematical model for the dynamics of primitive biological macromolecules and its evolutionary implications]

A mathematical model, adopted from the logistic equations for population growth and interspecific competition in ecology, was proposed for the dynamics of primitive biological macromolecules: [formula: see text] where Nm is the copy number of a kind of biological macromolecule in primitive environment at time t. rm is the intrinsic replicating capacity (rate) of the macromolecule. Km is the carrying capacity (resource limit) of the primitive environment. dNm/dt is the instantaneous rate of increase of copy number of the primitive biological macromolecule beta 12 and beta 21 are competition coefficients concerning the inhibition of macromolecule 2 on macromolecule 1 (beta 12), and macromolecule 1 on macromolecule 2 (beta 21) other lower indexes in the equations refer to macromolecule 1 or 2. By analysing the possible competition outcomes deduced from the model, a conclusion with evolutionary implications could be drawn that the biological diversity would be very low shortly after the origin of life in the primitive biosphere. In other words, the abundant biological macromolecules capable of replicating in the primitive biosphere would be quite unique in kinds, and this uniqueness would therefore be the initial basis of biological evolution which would then go from low biological diversity to high biological diversity. The model is also helpful for the understanding of the origin of repeated sequences which are widely present in the genomes of modern organisms.