For critical Markov branching processes {Zt} with finite variance and with time to extinction T, we obtain the asymptotic behavior of the two processes {ZuT/T,0<=u<1} and {ZT-u,u>0} as Z0=x--[infinity]. These processes were called by Jagers and co-workers the "path to extinction" and the "verge of extinction"...</=u<1}>

It has been proposed that modern humans evolved from a small ancestral population, which appeared several hundred thousand years ago in Africa. Descendants of the founder group migrated to Europe and then to Asia, not mixing with the pre-existing local populations but replacing them. Two...