In order to investigate the complexity of mutations, a computational approach named Genome Evolution by Matrix Algorithms ("GEMA") has been implemented. GEMA models genomic changes, taking into account hundreds of mutations within each individual in a population. By modeling of entire human chromosomes, GEMA precisely mimics real biological processes that influence genome evolution, and demonstrates that the number of meiotic recombination events per gamete is among the most crucial factors influencing population fitness. GEMA was further modified and employed in a study of genome evolution to re-evaluate Maruyamas phenomenon in modeled populations, which include haplotypes approximating real genomes. It was determined that only under specific conditions, of high recombination rates and abundance of neutral mutations, were deleterious and beneficial mutations younger than the neutral ones as predicted by Maruyama. Under other conditions, the ages of negative, neutral, and beneficial mutations were almost the same. After simulating mutations in a population, actual human genome sequence data from the "1000 Genome Project" Phase I was analyzed. All detected nucleotide sequence differences for 1092 people from 14 populations were computed. The distribution of these differences in individuals were then characterized on basis of their origin (European, Asian or African). By analysis of this genetic information of individuals, the very rare genetic variants were found to largely improve the detection of familial relations. Thus, with affordable whole-genome sequencing techniques, very rare SNPs should become important genetic markers for familial relationships and population stratification. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]