On mechanisms of neutral evolution of DNA resulting in scale-free behaviour

Abstract

We introduce a family of models incorporating random segmental substitutions and point mutations and demonstrate that such models reproduce algebraic length distributions of exact matches with the slope $-4$ observed earlier in pairwise comparisons of DNA of distantly related species. It is demonstrated that power-law distributions of exact matches emerge when shorter sequences transfer their DNA content to longer sequences, indicating potential mechanisms of the increased genome complexity.