  We consider a large population of asexually reproducing individuals in
absence of selective pressure. The population size is maintained constant by
the environment. We find out that distances between individuals (time from the
last common ancestor) exhibit highly non trivial properties. In particular
their distribution in a single population is random even in the thermodynamical
limit. As a result, not only distances are different for different pairs of
individuals but also the mean distance of the individuals of a given population
is different at different times. All computed quantities are parameters free
and only scale linearly with the population size. Results in this paper may
have some relevance in the 'Out of Africa/ Multi-regional' debate about the
origin of modern man. In fact, the recovery of mitochondrial DNA (mtDNA) from
Neandertal fossils in three different loci: Feldhofer (Germany), Mezmaiskaya
(Northern Caucaso), Vinjia (Croatia), permitted to compare
Neandertal/Neandertal distances with Neandertal/modern and modern/modern ones.
