Scaling Behavior of Maximal Repeat Distributions in Genomic Sequences: A Randomize Test Follow Up Study

In our previous study (Wang et al., 2008) it is found that the relative frequency distribution of maximal repeat sequencesLog(P(k)) versus the frequency of appearance Log(k) exhibits scaling behavior, i.e. P(k) ~ k-γ. In order to valid the above findings are not due to an artifact, we redone the study by performing the randomize test, and reanalysis the results by plotting the relative frequency of maximal repeat patterns against the rank of the appearance. The rank plots give a better coefficient of determination values than our previous work, i.e. using frequency plot. The rank plot study is motivated by Li et al. (Li et al. 2005). The work gave a rigorous presentation on the theory of scale-free graphs, and it is pointed out that size-rank plot is more reliable than size-frequency plot. In section 2, we give a description of the randomize test procedures. Section 3 is the power-law study results. Section 4 is the summary and discussion. AbstrAct