Symbolic complexity for nucleotide sequences: a sign of the genome structure
We introduce a method for estimating the complexity function (which counts the number of observable words of a given length) of a finite symbolic sequence, which we use to estimate the complexity function of coding DNA sequences for several species of the Hominidae family. In all cases, the obtained symbolic complexities show the same characteristic behavior: exponential growth for small word lengths, followed by linear growth for larger word lengths. The symbolic complexities of the species we consider exhibit a systematic trend in correspondence with the phylogenetic tree. Using our method, we estimate the complexity function of sequences obtained by some known evolution models, and in some cases we observe the characteristic exponential-linear growth of the Hominidae coding DNA complexity. Analysis of the symbolic complexity of sequences obtained from a specific evolution model points to the following conclusion: linear growth arises from the random duplication of large segments during the evolution of the genome, while the decrease in the overall complexity from one species to another is due to a difference in the speed of accumulation of point mutations.