The site frequency spectrum in one population, conditioned on the presence of a derived allele in a DNA sequence from one or more closely related populations, is sensitive to recent admixture between populations and to substructure in ancestral populations. The theory of the conditional site frequency spectrum is introduced and extensions to multiple populations is presented. The theory is applied to genomic data from modern humans, Neanderthals and Denisovans in order to determine whether the extra similarity of some modern human populations to Neanderthals and to Denisovans is attributable to recent admixture or ancestral substructure.
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