The minimal observable clade size of exchangeable coalescents

  title={The minimal observable clade size of exchangeable coalescents},
  author={Fabian Freund and Arno Siri-J'egousse},
  journal={arXiv: Probability},
For $\Lambda$-$n$-coalescents with mutation, we analyse the size $O_n$ of the partition block of $i\in\{1,\ldots,n\}$ at the time where the first mutation appears on the tree that affects $i$ and is shared with any other $j\in\{1,\ldots,n\}$. We provide asymptotics of $O_n$ for $n\to\infty$ and a recursion for all moments of $O_n$ for finite $n$. This variable gives an upper bound for the minimal clade size [2], which is not observable in real data. In applications to genetics, it has been… 

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