Mathematical analysis of evolutionary process

Abstract

This paper proposes an analytic framework for the analysis of evolutionary mechanisms at genetic coding level, attempting to provide more detailed description than population genetics. It gives an estimated sequence after T replications in an environment given the initial genetic sequence. We assume that there is a principle obeyed by evolutionary mechanisms at genetic sequence level, such that some law, called action, is suboptimal. We propose such an action for haploid, asexual type living lives with replications involving only point mutations, as a function of fitness and the probability of change in sequence, so the evolutionary process is not a simple hill-climbing. Our method provides an intuitive view on evolution of genetic sequences, and it may be a powerful analysis tool when we need to treat directly the genetic sequence. It is useful for the analysis of real or artificial life such as genetic algorithms. This is a report of a work in progress, and we present the background, development, connection with population genetics, and some possible extensions of our work.