Abnormal base compositional patterns of genomic DNA sequences are studied in the framework of a hierarchical structure (HS) model originally proposed for the study of fully developed turbulence [She and Lévêque, Phys. Rev. Lett. 72, 336 (1994)]. The HS similarity law is verified over scales between 10(3)bp and 10(5)bp, and the HS parameter beta is proposed to describe the degree of heterogeneity in the base composition patterns. More than one hundred bacteria, archaea, virus, yeast, and human genome sequences have been analyzed and the results show that the HS analysis efficiently captures abnormal base composition patterns, and the parameter beta is a characteristic measure of the genome. Detailed examination of the values of beta reveals an intriguing link to the evolutionary events of genetic material transfer. Finally, a sequence complexity (S) measure is proposed to characterize gradual increase of organizational complexity of the genome during the evolution. The present study raises several interesting issues in the evolutionary history of genomes.
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