The paper presents a statistical test for detecting ancient admixture between three closely related populations, specifically Neandertals and modern humans. The test, called the D statistic, is based on the asymmetry in the frequencies of two nonconcordant gene trees in a three-population tree. The authors derive the analytic expectation of the D statistic under various demographic scenarios, including instantaneous unidirectional admixture and ancestral subdivision. They show that the D statistic is insensitive to some demographic assumptions, such as ancestral population sizes, and can be used to estimate the proportion of archaic ancestry in present-day populations even when no archaic samples are available. The paper also explores the effects of sequencing error and ascertainment bias on the test's performance and applies the test to Neandertal data, finding evidence of admixture between Neandertals and non-African modern humans. The results suggest that Neandertals contributed 1–4% of the ancestry in non-African populations, with a higher contribution in Europe and Asia compared to Africa.The paper presents a statistical test for detecting ancient admixture between three closely related populations, specifically Neandertals and modern humans. The test, called the D statistic, is based on the asymmetry in the frequencies of two nonconcordant gene trees in a three-population tree. The authors derive the analytic expectation of the D statistic under various demographic scenarios, including instantaneous unidirectional admixture and ancestral subdivision. They show that the D statistic is insensitive to some demographic assumptions, such as ancestral population sizes, and can be used to estimate the proportion of archaic ancestry in present-day populations even when no archaic samples are available. The paper also explores the effects of sequencing error and ascertainment bias on the test's performance and applies the test to Neandertal data, finding evidence of admixture between Neandertals and non-African modern humans. The results suggest that Neandertals contributed 1–4% of the ancestry in non-African populations, with a higher contribution in Europe and Asia compared to Africa.