BackgroundInferring history from genomic sequences is challenging and problematic because chromosomes are mosaics of thousands of small Identicalby-descent (IBD) fragments, each of them having their own unique story. However, the main events in recent evolution might be deciphered from comparative analysis of numerous loci. A paradox of why humans, whose effective population size is only 104, have nearly three million frequent SNPs is formulated and examined.ResultsWe studied 5398 loci evenly covering all human autosomes. Common haplotypes built from frequent SNPs that are present in people from various populations have been examined. We demonstrated highly non-random arrangement of alleles in common haplotypes. Abundance of mutually exclusive pairs of common haplotypes that have different alleles at every polymorphic position (so-called Yin/Yang haplotypes) was found in 56% of loci. A novel widely spread category of common haplotypes named Mosaic has been described. Mosaic consists of numerous pieces of Yin/Yang haplotypes and represents an ancestral stage of one of them. Scenarios of possible appearance of large number of frequent human SNPs and their habitual arrangement in Yin/Yang common haplotypes have been evaluated with an advanced genomic simulation algorithm.ConclusionsComputer modeling demonstrated that the observed arrangement of 2.9 million frequent SNPs could not originate from a sole stand-alone population. A “Great Admixture” event has been proposed that can explain peculiarities with frequent SNP distributions. This Great Admixture presumably occurred 100–300 thousand years ago between two ancestral populations that had been separated from each other about a million years ago. Our programs and algorithms can be applied to other species to perform evolutionary and comparative genomics.Electronic supplementary materialThe online version of this article (doi:10.1186/s12864-017-3776-5) contains supplementary material, which is available to authorized users.