Genome evolution is shaped by a multitude of mutational processes, including point mutations, insertions, and deletions of DNA sequences, as well as segmental duplications. These mutational processes can leave distinctive qualitative marks in the statistical features of genomic DNA sequences. One such feature is the match length distribution (MLD) of exactly matching sequence segments within an individual genome or between the genomes of related species. These have been observed to exhibit characteristic power law decays in many species. Here, we show that simple dynamical models consisting solely of duplication and mutation processes can already explain the characteristic features of MLDs observed in genomic sequences. Surprisingly, we find that these features are largely insensitive to details of the underlying mutational processes and do not necessarily rely on the action of natural selection. Our results demonstrate how analyzing statistical features of DNA sequences can help us reveal and quantify the different mutational processes that underlie genome evolution.