Lack of self-averaging and family trees

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, i.e., there is lack of self-averaging. 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 modem man. In fact, the recovery of mitochondrial DNA 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. (C) 2003 Elsevier B.V. All rights reserved.