To 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) are studied. These demonstrate scale invariant self-similarity patterns and long-range correlations (LRCs) indicating fractal organization. Phylogenetic hierarchies change when SOD1 orthologs are grouped according to fractal measures, indicating that statistical topographies can be used to study gene evolution. Sliding window k-mer analysis show that majority of k-mers across all SOD1 orthologs are unique, with very few duplications. Orthologs from simpler species contribute minimally (< 1% of k-mers) to more complex species. Both simple and complex random processes fail to produce significant matching k-mer sequences for SOD1 orthologs. Point mutations causing amyotrophic lateral sclerosis do not impact the fractal organization of human SOD1. Hence, SOD1 did not evolve by a patchwork of repetitive sequences modified by point mutations. Moreover, fractal and other methods described here can be used to study the origin and evolution of genomes.

为了了解基因进化的基本过程，例如点突变和片段重复对统计地形的影响，研究了超氧化物歧化酶-1（SOD1）直系同源序列（n  = 50）。这些证明了尺度不变的自我相似性模式和表明分形组织的远距离相关性（LRC）。根据分形度量对SOD1直系同源物进行分组时，系统发生层次会发生变化，这表明统计地形可用于研究基因进化。滑动窗口k-mer分析表明，所有SOD1中大多数k-mer直系同源物是独特的，几乎没有重复。来自较简单物种的直系同源物对较复杂物种的贡献最小（<k-mers的1％）。简单和复杂的随机过程都无法为SOD1直系同源物产生重要的匹配k-mer序列。引起肌萎缩性侧索硬化的点突变不会影响人类SOD1的分形组织。因此，SOD1并不是通过点突变修饰的重复序列拼凑而成的。此外，此处描述的分形方法和其他方法可用于研究基因组的起源和进化。