A simple quantitative model of the molecular clock

Abstract

We present the ideas, and their motivation, at the basis of a simple model of nucleic acid evolution: the stationary Markov process, or Markov clock. After a brief review of its relevant mathematical properties, the Markov clock is applied to nucleotide sequences from mitochondrial and nuclear genes of different species. Particular emphasis is given to the necessity of carrying out a correct statistical analysis, which allows us to check quantitatively the applicability of our model. We find evidence that the Markov clock ticks in many different processes, and that its limitations can be understood in terms of a simple idea that we call the "base-drift" hypothesis. This hypothesis correlates the deviations from the stationarity of the Markov process to the evolutionary distance dAB(p) of two species A and B, relative to the process P. We conclude by discussing the implications of our findings for future work.