  Although there has been much interest in estimating divergence and admixture
from genomic data, it has proven difficult to distinguish gene flow after
divergence from alternative histories involving structure in the ancestral
population. The lack of a formal test to distinguish these scenarios has
sparked recent controversy about the possibility of interbreeding between
Neandertals and modern humans in Eurasia. We derive the probability of
mutational configurations in non-recombining sequence blocks under alternative
histories of divergence with admixture and ancestral structure. Dividing the
genome into short blocks makes it possible to compute maximum likelihood
estimates of parameters under both models. We apply this method to triplets of
human Neandertal genomes and quantify the relative support for models of
long-term population structure in the ancestral African popuation and admixture
from Neandertals into Eurasian populations after their expansion out of Africa.
Our analysis allows us -- for the first time -- to formally reject a history of
ancestral population structure and instead reveals strong support for admixture
from Neandertals into Eurasian populations at a higher rate (3.4%-7.9%) than
suggested previously.
