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Chaos game representation of mitochondrial genomes : Markov chain model simulation and vertebrate phylogeny

The mitochondrial genomes have provided much information on the evolution of this organelle and have been used for phylogenetic reconstruction by various methods with or without sequence alignment. In this paper, we explore the mitochondrial genomes by means of the chaos game representation (CGR), a tool derived from the chaotic dynamical systems theory. If the DNA sequence is a random collection of bases, the CGR will be a uniformly filled square; on the other hand, any pattern visible in the CGR contains information on the DNA sequence. First we use the Markov chain models to simulate the CGR of mitochondrial genomes. Then we model the noise background in the genome sequences by a Markov chain. A simple correlation-related distance approach without sequence alignment based on the CGR of mitochondrial genomes is proposed to analyze the phylogeny of 64 selected vertebrates.