AbstractTo understand the fundamental processes of gene evolution such as the impact of point mutations and segmental duplications on statistical topography, Superoxide Dismutase-1 (SOD1) orthologous sequences (n=50) were studied. These demonstrated scale invariant self-similarity patterns and long-range correlations (LRC) indicating fractal organization. Phylogenetic hierarchies changed whenSOD1orthologs were grouped according to fractal measures, indicating statistical topographies can be used to study gene evolution. Sliding window k-mer analysis showed that majority of k-mers across allSOD1orthologs were unique, with very few duplications. Orthologs from simpler species contributed minimally (<1% of k-mers) to more complex species. Both simple and complex random processes failed to produce significant matching k-mer sequences forSOD1orthologs. Point mutations causing amyotrophic lateral sclerosis did not impact the fractal organization of humanSOD1. Hence,SOD1did not evolve by a patchwork of repetitive sequences modified by point mutations. Instead, this study proposes thatSOD1gene sequences evolved by regulated interweaving of unique oligomer sequences that led to LRC, signifying convergent evolution.Summary StatementSOD1has long-range correlations which resulted not from point mutations, segmental duplications or patching together sequences from simpler organisms. Instead,SOD1underwent convergent evolution by repeated unique sequence assemblies.