Power spectrum and mutual information analyses of DNA base (Nucleotide) sequences

On the basis of the power spectrum analyses for the base (nucleotide) sequences of various genes. we have studied long-range correlations in total base sequences which are expressed as 1/f(alpha), behaviour of the exponent alpha for the accumulated base sequences as well as periodicities at short range. In particular from the analysis of content rate distributions of a we have obtained the average value (alpha) over bar = 0.40 +/- 0.01 and (alpha) over bar = 0.20 +/- 0.01 for the human genes and S. cerevisiae genes, respectively. We have also performed the analyses using the mutual information function. We show that there exists a clear difference between the content rate distribution,, of correlation lengths for the sample human genes and the S, cerevisiae genes. We are led to a conjecture that the elongation of the correlation length in the base sequences of genes from the early eukaryote (S. cerevisiae) to the late eukaryote (human) should be the definite reflection of the evolutionary process.