Article,
Recent common ancestors of all present-day individuals
Advances in Applied Probability, (1999)
Abstract
Previous study of the time to a common ancestor of all present-day indi-
viduals has focused on models in which each individual has just one parent
in the previous generation. For example, "mitochondrial Eve" is the most
recent common ancestor (MRCA) when ancestry is defined only through
maternal lines. In the standard Wright-Fisher model with population size
n, the expected number of generations to the MRCA is about 2n, and
the standard deviation of this time is also of order n. Here we study a
two-parent analog of the Wright-Fisher model that defines ancestry using
both parents. In this model, if the population size n is large, the number
of generations, Tn , back to a MRCA has a distribution that is concen-
trated around lg n (where lg denotes base-2 logarithm), in the sense that
the ratio Tn /(lg n) converges in probability to 1 as n . Also, con-
tinuing to trace back further into the past, at about 1.77 lg n generations
before the present, all partial ancestry of the current population ends, in
the following sense: with high probability for large n, in each generation
at least 1.77 lg n generations before the present, all individuals who have
any descendants among the present-day individuals are actually ancestors
of all present-day individuals.
