# 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…
2 Citations

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## References

SHOWING 1-10 OF 47 REFERENCES
On the size of the block of 1 for $\varXi$-coalescents with dust
• Mathematics
• 2017
We study the frequency process $f_1$ of the block of 1 for a $\varXi$-coalescent $\varPi$ with dust. If $\varPi$ stays infinite, $f_1$ is a jump-hold process which can be expressed as a sum of broken
Cannings models, population size changes and multiple-merger coalescents
• F. Freund
• Mathematics
Journal of mathematical biology
• 2020
This article gives a more general construction of time-changed Λ - n -coalescents as limits of specific Cannings models with rather arbitrary time changes.
Minimal Clade Size in the Bolthausen-Sznitman Coalescent
• Mathematics
Journal of Applied Probability
• 2014
The asymptotics of distribution and moments of the size $X_n$ of the minimal clade of a randomly chosen individual in a Bolthausen-Sznitman $n-coalescent for$n\to\infty$are shown. Random Discrete Distributions Derived from Self-Similar Random Sets • Mathematics • 1996 A model is proposed for a decreasing sequence of random variables$(V_1, V_2, \cdots)$with$\sum_n V_n = 1\$, which generalizes the Poisson-Dirichlet distribution and the distribution of ranked
Asymptotics of the Minimal Clade Size and Related Functionals of Certain Beta-Coalescents
• Mathematics
• 2013
The Beta(2−α,α) n-coalescent with 1<α<2 is a Markov process taking values in the set of partitions of {1,…,n}. It evolves from the initial value {1},…,{n} by merging (coalescing) blocks together into
Minimal clade size and external branch length under the neutral coalescent
• Mathematics
Advances in Applied Probability
• 2005
Given a sample of genes taken from a large population, we consider the neutral coalescent genealogy and study the theoretical and empirical distributions of the size of the smallest clade containing
Random Recursive Trees and the Bolthausen-Sznitman Coalesent
• Mathematics
• 2005
We describe a representation of the Bolthausen-Sznitman coalescent in terms of the cutting of random recursive trees. Using this representation, we prove results concerning the final collision of the
The Site Frequency Spectrum for General Coalescents
• Computer Science
Genetics
• 2016
This work derives a new formula for the expected SFS for general Λ- and Ξ-coalescents, which leads to an efficient algorithm and obtains general theoretical results for the identifiability of the Λ measure when ζ is a constant function, as well as for the identity of the function ζ under a fixed Ξ measure.