  In this paper we consider two populations whose generations are not
overlapping and whose size is large. The number of males and females in both
populations is constant. Any generation is replaced by a new one and any
individual has two parents for what concerns nuclear DNA and a single one (the
mother) for what concerns mtDNA. Moreover, at any generation some individuals
migrate from the first population to the second.
  In a finite random time $T$, the mtDNA of the second population is completely
replaced by the mtDNA of the first. In the same time, the nuclear DNA is not
completely replaced and a fraction $F$ of the ancient nuclear DNA persists. We
compute both $T$ and $F$. Since this study shows that complete replacement of
mtDNA in a population is compatible with the persistence of a large fraction of
nuclear DNA, it may have some relevance for the Out of Africa/Multiregional
debate in Paleoanthropology.
