  We consider here an extension of a previous work by Neves and Serva, still
unpublished, which estimates the amount of interbreeding between anatomically
modern Africans and Neandertals necessary for explaining the experimental fact
that 1 to 4% of the DNA in non-African living humans is of Neandertal origin.
In that work we considered that Africans and Neandertals had the same fitness
(neutral hypothesis) and Neandertal extinction was thus an event of fortune. In
this work we consider that Africans had larger fitnesses. We show results for
four values for the fitness difference: 1%, 5%, 10% and 20% and compare them
with the corresponding neutral results. Some technical differences with respect
to the neutral case appear. We conclude that even with 1% fitness difference
Neandertals extinction comes up in too small a time, so the neutral model looks
more suitable for explaining the known data on occupation of some caves in
Israel for a very long time, alternately by Africans and Neandertals.
