There have been a number of recent attempts to develop methodologies that do not require sequence alignment for deriving species phylogeny based on overall similarities of the complete genomes. 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 introduce three fast algorithms, namely, dynamical language model with correlation distance, Fourier transform with Kullback-Leibler divergence distance, log-correlation distance, for deriving vertebrate phylogeny based on mitochondrial genomes. The distance-based analyses show that the mitochondrial genomes are separated into three major clusters corresponding to mammals, fish, and Archosauria (including birds and reptiles)respectively. The interrelationships among the mitochondrial genomes are roughly in agreement with the current understanding on the phylogeny of vertebrates revealed by the traditional approaches
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