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We consider a Yule process until the total population reaches size $n\gg 1$,and assume that neutral mutations occur with high probability $1-p$ (in thesense that each child is a new mutant with probability $1-p$, independently ofthe other children), where $p=p_n\ll 1$. We establish a general strategy forobtaining Poisson limit laws for the number of subpopulations exceeding a givensize and apply this to some mutation regimes of particular interest. Finally,we give an application to subcritical Bernoulli bond percolation on randomrecursive trees with percolation parameter $p_n$ tending to zero.

Weak limits for the largest subpopulations in Yule processes with high mutation probabilities