Abstract
We consider a Yule process until the total population reaches size n 1, and assume that neutral mutations occur with high probability 1 - p (in the sense that each child is a new mutant with probability 1 - p, independently of the other children), where p = p n 1. We establish a general strategy for obtaining Poisson limit laws and a weak law of large numbers for the number of subpopulations exceeding a given size and apply this to some mutation regimes of particular interest. Finally, we give an application to subcritical Bernoulli bond percolation on random recursive trees with percolation parameter p n tending to 0. © Copyright Applied Probability Trust 2017.
Baur, Erich