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The ability to recover ancient DNA from skeletal material has completely transformed the field of evolutionary anthropology, making it possible to sequence the genomes of individuals who lived thousands of years ago. In addition to solving the long-standing question of admixture between neanderthals and modern humans and uncovering evidence of dramatic migration events throughout human history, ancient DNA has become an important resource for understanding many facets of natural selection, which is often challenging using today's genetic variation alone. Chapter 1 examines the dynamics of negative selection acting against Neanderthal ancestry in modern humans and establishes its limits over long evolutionary timescales. It shows that the previously reported monotonic decline in Neanderthal ancestry over the last fifty-thousand years, thought to be a result of negative selection, is a statistical artifact caused by incorrect assumptions about modern human demographic history, in particular the gene flow between Africa and West Eurasia. Re-estimation of the Neanderthal ancestry proportions over time using a more robust statistic no longer infers a significant decline in Neanderthal ancestry, which is proven to be consistent with simulations of negative selection across a wide range of selection parameters. Chapter 2 describes the first comprehensive analysis of the Y chromosomes of neanderthals and Denisovans. Although Neanderthals and Denisovans form a sister group to modern humans at the autosomal level, Neanderthal Y chromosomes are more similar to modern humans than Denisovan Y chromosomes. In fact, the Y chromosomes of late neanderthals represent a lineage introgressed from an early modern human population. This introgression, which occurred hundreds of thousands of years, completely replaced the Y chromosomes of early neanderthals, reflecting the observations made from mitochondrial DNA. Population genetic simulations of selection and introgression show that although a complete replacement of both mitochondrial DNA and Y chromosomes is unlikely under neutrality, higher deleterious burden of neanderthals predicts a rapid replacement of both loci by their modern human counterparts. Finally, Chapter 3 presents an R package admixer, designed to facilitate the programming of automated, fully reproducible population genetic analyses using ADMIXTOOLS, a suite of programs widely used in ancient DNA research.