  Considering the recent experimental discovery of Green et al that present day
non-Africans have 1 to 4% of their nuclear DNA of Neanderthal origin, we
propose here a model which is able to quantify the interbreeding events between
Africans and Neanderthals at the time they coexisted in the Middle East. The
model consists of a solvable system of deterministic ordinary differential
equations containing as a stochastic ingredient a realization of the neutral
Wright-Fisher drift process. By simulating the stochastic part of the model we
are able to apply it to the interbreeding of African and Neanderthal
subpopulations and estimate the only parameter of the model, which is the
number of individuals per generation exchanged between subpopulations. Our
results indicate that the amount of Neanderthal DNA in non-Africans can be
explained with maximum probability by the exchange of a single pair of
individuals between the subpopulations at each 77 generations, but larger
exchange frequencies are also allowed with sizeable probability. The results
are compatible with a total interbreeding population of order 10,000
individuals and with all living humans being descendents of Africans both for
mitochondrial DNA and Y chromosome.
