  If one goes backward in time, the number of ancestors of an individual
doubles at each generation. This exponential growth very quickly exceeds the
population size, when this size is finite. As a consequence, the ancestors of a
given individual cannot be all different and most remote ancestors are repeated
many times in any genealogical tree. The statistical properties of these
repetitions in genealogical trees of individuals for a panmictic closed
population of constant size N can be calculated. We show that the distribution
of the repetitions of ancestors reaches a stationary shape after a small number
Gc ~ log N of generations in the past, that only about 80% of the ancestral
population belongs to the tree (due to coalescence of branches), and that two
trees for individuals in the same population become identical after Gc
generations have elapsed. Our analysis is easy to extend to the case of
exponentially growing population.
