Standard deviations and correlations of GC levels in DNA sequences

In a DNA sequence that exhibits long-range correlations, standard deviations among the GC levels of its segments can be up to an order of magnitude higher than in a sequence consisting of independent, identically distributed nucleotides. Conversely, plots of inter-segment standard deviations vs. segment length reveal quantitative information about the correlations present in a sequence. We present and discuss formulae that relate long-range (power-law) correlations between the nucleotides of a sequence to the expected standard deviations of the GC levels of its segments, and to the correlations between them.