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The self-alignment concentrations, $c(x)$, as functions of the length, $x$,of the identically matching maximal segments in the genomes of a variety ofspecies, typically present power-law tails extending to the largest scales,i.e., $c(x) \propto x^{\alpha}$, with similar or apparently different negative$\alpha$s ($<-2$). The relevant fundamental processes of molecular evolutionare segmental duplication and point mutation, and that recently the stickfragmentation phenomenology has been used to account the neutral evolution.However, disorder is intrinsic to the evolution system and, by freezing it intime (quenching) for the setup of a simple fragmentation model, we obtaindecaying, steady-state and the general full time-dependent solutions, all$\propto x^{\alpha}$ for $x\to \infty$, which is in contrast to the onlypower-law solution, $x^{-3}$ for $x\to 0$ of the pure model (without disorder).%Other algebraic terms may dominate at intermediate scales, which seems to beconfirmed by some species, such as rice. We also present self-alignment resultsshowing more than one scaling regimes, consistent with the theoretical resultsof the existence of more than one algebraic terms which dominate at differentregimes.

Disorder and Power-law Tails of DNA Sequence Self-Alignment Concentrations in Molecular Evolution