Recent common ancestors of all present-day individuals

Previous study of the time to a common ancestor of all present-day individu als has focused on models in which each individual has just one parent in t he previous generation. For example, 'mitochondrial Eve' is the most recent common ancestor (MRCA) when ancestry is defined only through maternal line s. 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 W right-Fisher model that defines ancestry using both parents. In this model, if the population size n is large, the number of generations, T-n, back to a MRCA has a distribution that is concentrated around Ig n (where Ig denot es base-2 logarithm), in the sense that the ratio T-n/(lg n) converges in p robability to 1 as n --> infinity. Also, continuing to trace back further i nto the past, at about 1.77 Ig n generations before the present, all partia l ancestry of the current population ends, in the following sense: with hig h probability for large n, in each generation at least 1.77 Ig n generation s before the present, all individuals who have anp descendants among the pr esent-day individuals are actually ancestors of all present-day individuals . AMS 1991 Subject Classification: Primary 92D25 Secondary 60J85.