# The minimal observable clade size of exchangeable coalescents

@article{Freund2019TheMO,
title={The minimal observable clade size of exchangeable coalescents},
author={Fabian Freund and Arno Siri-J'egousse},
journal={arXiv: Probability},
year={2019}
}
• Published 27 June 2019
• Mathematics
• 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…
3 Citations

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