In a general supercritical branching process the distribution is found of the time back to the birth of the n:th father of a random individual. For single-type processes a probability of mutation (at a site of a specified gene) is introduced. With the infinite alleles interpretation that every mutation occurring is unique the class of individuals with the same allele can be viewed as a generalized "macroindividual". Thereby the question of when the first of a series of n mutations occurred is reduced to finding the birth time of the n:th father in the process of macroindividuals. This is done.
%0 Journal Article
%1 jagers1991great
%A Jagers, Peter
%A Nerman, Olle
%A Taib, Ziad
%D 1991
%I Institute of Mathematical Statistics
%J Lecture Notes-Monograph Series
%K branching_processes genealogies
%P pp. 118-126
%T When Did Joe's Great... Grandfather Live? Or: On the Time Scale of Evolution
%U http://www.jstor.org/stable/4355650
%V 18
%X In a general supercritical branching process the distribution is found of the time back to the birth of the n:th father of a random individual. For single-type processes a probability of mutation (at a site of a specified gene) is introduced. With the infinite alleles interpretation that every mutation occurring is unique the class of individuals with the same allele can be viewed as a generalized "macroindividual". Thereby the question of when the first of a series of n mutations occurred is reduced to finding the birth time of the n:th father in the process of macroindividuals. This is done.