During the past decade, data generated by high-throughput genotyping technologies have enabled studies probing into two central questions in human evolutionary biology: the characterization of human population genetic structure, and the search for the molecular signature of natural selection. Insights gleaned from these studies have provided important clues for understanding the phenotypic diversity of our species, and variables representing population structure are routinely incorporated as covariates in genome-wide association studies of complex traits and diseases. At a global level, as well as within a continent or even a sub-continental region, geography has been shown to act as the leading driving force in shaping the pattern of genetic variation that we observe today 
. In parallel, analyses based on European, African and East Asian populations have revealed that recent positive selection is a prevalent phenomenon throughout the genome 
. Using data from the Human Genome Diversity-CEPH Panel (HGDP), a recent and comprehensive survey suggests that, while adaptation to local environment is a common theme throughout human evolution, the genetic loci involved in adaptation show little overlap among non-contiguous geographic regions 
While geography poses a significant reproductive barrier, multiple waves of massive trans-continental migration have occurred during the past centuries, giving rise to admixed populations. The ancestry of non-admixed individuals can often be traced to precise regions based solely on genetic data, but characterizing the sub-continental ancestry origins of an admixed individual has not been demonstrated to date. For example, the two largest minority groups in North America, Latinos and African Americans, both arose as a result of mating among populations that had been in historical reproductive isolation. The “Hispanic” or “Latino” populations include the ethnically diverse groups of Latin America; although significant genetic contributions can be traced to Indigenous American, European and West African populations, it has been challenging to determine whether one's Indigenous American ancestors originate from North, Central, or South America. Solving this problem has implications for both a deeper understanding of human evolution and for human disease, since genetic diversity between Latino populations is characterized both by variation in continent-level ancestry – e.g. Mexicans on average have lower African ancestry than Puerto Ricans – and by the population structure among the ancestral Indigenous American populations 
The assessment of the precise ancestral origin and the quantification of genetic structure within an ancestry component are limited, in part, by analytic challenges. Principal Component Analysis (PCA) is a classic technique for multivariate data analysis, which aims to project high-dimensional data to a much lower dimension while capturing the greatest level of variation 
. This approach has gained popularity in genetic analyses due to both computational efficiency and interpretability: when the underlying population structure is driven mainly by reproductive isolation and subsequent genetic differentiation, the principal components (PCs) mirror the geographic origins of individuals 
. By itself, however, PCA is not well suited for studying admixed populations: while leading PCs usually represent the relative contributions of continentally-divided ancestral populations, subsequent PCs may be simultaneously influenced by structures within one or more of the ancestral populations, and are consequently difficult to interpret.
We tackled this problem by employing an analytic strategy that works backwards according to the temporal nature of demographic events that underlie human admixture: genomes are first separated into the major and most recent components that reflect inter-continental migration, then each of those components is further investigated separately. As described below, we apply a probabilistic method for inferring locus-specific ancestry along the chromosome, followed by a variant of PCA to further investigate each of the ancestry-specific genomic components, which we term “virtual genomes”. This hierarchical strategy yields a fine-scale view of genetic structure in admixed populations, and provides insight into the population history of nonextant ancestral populations. As an example, we study a cohort of 492 parent-offspring trios recruited from Mexico City. Our results confirm the a priori expectation that the most significant European contributors to the Mexican gene pool are populations from the Iberian Peninsula, but reveal that the Indigenous American component of the Mexican genomes is more complex.
Studying the genetic structure of admixed genomes also offers the unique opportunity to probe the adaptive landscape of the ancestral populations. This is particularly powerful for studying the Indigenous American populations, for which limited genotype data is available. As proof of principle, we report a novel application of the extended haplotype homozygosity test for recent positive selection to the European and Indigenous American “virtual genomes” evident in the Mexican cohort, and identify numerous loci as potential targets of positive selection.