I must say I am totally skeptic but just for the record:
Armando G. M. Neves & Mauricio Serva, Extremely Rare Interbreeding Events Can Explain Neanderthal DNA in Living Humans. PLoS ONE. Open Access ··> LINK [doi:10.1371/journal.pone.0047076]
AbstractConsidering the recent experimental discovery of Green et al that present-day non-Africans have 1 to of their nuclear DNA of Neanderthal origin, we propose here a model which is able to quantify the genetic interbreeding between two subpopulations with equal fitness, living in the same geographic region. The model consists of a solvable system of deterministic ordinary differential equations containing as a stochastic ingredient a realization of the neutral Wright-Fisher process. By simulating the stochastic part of the model we are able to apply it to the interbreeding ofthe African ancestors of Eurasians and Middle Eastern 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 living 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 long coexistence time of 130,000 years, a total interbreeding population of order 10⁴ individuals, and with all living humans being descendants of Africans both for mitochondrial DNA and Y chromosome.
Not only the discourse of the authors is strangely ideological (strange insistence in resuscitating the dead horse of multirregionalism and denying the rather unquestionable out-of-Africa model at least in name) but also they come to admit that:
The decision of which model correctly describes the origin of Homo sapiens is obscured by the intricacies of the statistical methods proposed for evaluating the models themselves.
And so they proceed to create their own intricate model and even more intricate interpretation.
Sincerely, their model of continuous admixture would normally cause West Eurasians (at least) to have much more Neanderthal introgression than Papuans, whose ancestors have been far away from West Eurasia (the former Neanderlands) since c. 80 Ka most probably (archaeological evidence of African-related techno-cultures in India, Petraglia 2007), while West Eurasian ancestors would have been in intense contact with Neanderthals all or most of that time until the effective Neanderthal extinction of c. 35,000 years ago.
There's no convoluted model nor mathematical fallacy that can circumvent that: anything but a single admixture episode or process early on in the colonization of Eurasia by Homo sapiens makes no sense.