Characterizing Fractal Genetic Variation in the Human Genome from the Hapmap Project

Over the last decades, the exuberant development of next-generation sequencing has revolutionized genediscovery. These technologies have boosted the mapping of single nucleotide polymorphisms (SNPs) acrossthe human genome, providing a complex universe of heterogeneity characterizing individuals worldwide.Fractal dimension (FD) measures the degree of geometric irregularity, quantifying how "complex" a selfsimilarnatural phenomenon is. We compared two FD algorithms, box-counting dimension (BCD) andHiguchi's fractal dimension (HFD), to characterize genome-wide patterns of SNPs extracted from theHapMap data set, which includes data from 1184 healthy subjects of eleven populations. In addition, wehave used cluster and classification analysis to relate the genetic distances within chromosomes basedon FD similarities to the geographical distances among the 11 global populations. We found that HFDoutperformed BCD at both grand average clusterization analysis by the cophenetic correlation coefficient,in which the closest value to 1 represents the most accurate clustering solution (0.981 for the HFD and0.956 for the BCD) and classification (79.0% accuracy, 61.7% sensitivity, and 96.4% specificity for theHFD with respect to 69.1% accuracy, 43.2% sensitivity, and 94.9% specificity for the BCD) of the 11 populations present in the HapMap data set. These results support the evidence that HFD is a reliablemeasure helpful in representing individual variations within all chromosomes and categorizing individualsand global populations.