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Genealogical trees from genetic distances

In a population with haploid reproduction any individual has a single parent in the previous generation. If all genealogical distances among pairs of individuals (generations from the closest common ancestor) are known it is possible to exactly reconstruct their genealogical tree. Unfortunately, in most cases, genealogical distances are unknown and only genetic distances are available. The genetic distance between two individuals is measurable from differences in mtDNA (mitochondrial DNA) in the case of humans or other complex organisms while an analogous distance can be also given for languages where it is measured from lexical differences. Assuming a constant rate of mutation, these genetic distances are random and proportional only on average to genealogical ones. The reconstruction of the genealogical tree from the available genetic distances is forceful imprecise. In this paper we try to quantify the error one may commit in the reconstruction of the tree for different degrees of randomness. The errors may concern both topology of the tree (the branching hierarchy) and, in case of correct topology, the proportions of the tree (length of various branches).